Methods to Evaluate and Increase the RF Safety of Cardiovascular Interventional Devices During MRI. Gregory H. Griffin

Transcription

1 Methods to Evaluate and Increase the RF Safety of Cardiovascular Interventional Devices During MRI by Gregory H. Griffin A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Graduate Department of Medical Biophysics University of Toronto c Copyright 2016 by Gregory H. Griffin

2 Abstract Methods to Evaluate and Increase the RF Safety of Cardiovascular Interventional Devices During MRI Gregory H. Griffin Doctor of Philosophy Graduate Department of Medical Biophysics University of Toronto 2016 Percutaneous revascularization could benefit greatly from MRI guidance and device tracking, but MRI guidance is currently contraindicated due to RF safety concerns. The success rate of such procedures could be improved by devices designed to exploit the unique features of MRI. Unfortunately such devices require long linear conductive structures, which present a significant risk to the patient in the form of RF heating. A priori safety prediction is impractical in vivo and thus, safety is typically investigated in vitro and extrapolated. A method of remotely predicting safety in situ during an exam would be very beneficial for ensuring safety in patients. A method of increasing the safety of revascularization devices would also be necessary to allow their employment in many clinical scenarios. Techniques are developed and presented in this thesis to enable safe, remote quantification of induced RF current and heating in vivo. Also presented is a technique of increasing the safety of revascularization guidewires without altering mechanical properties. The first technique is a method of analyzing phase artifacts introduced into MRI images by RF current flowing on linear conductive structures. The technique fits a theoretical representation of the phase artifact to an acquired image to quantify the current that induced the artifact. The measured current is then used to predict power deposition and heating. The technique is developed theoretically, and demonstrated with an in vitro feasibility study. Extensions to this phase-based technique are also presented. Sources of unwanted phase artifacts in vivo are discussed and it is demonstrated that a custom imaging sequence is capable of eliminating said artifacts. A feasibility study is presented wherein heating is accurately predicted in several pig experiments, using the custom sequence for current characterization. A novel application of floating RF traps, towards suppressing induced current on guidewires, is also presented. Theory of trap function is developed and verified through modelling and in-vitro experimentation. It is demonstrated that traps can feasibly increase the RF safety of guidewires, without altering the guidewire mechanical properties. ii

3 Finally, future studies and extensions of the presented techniques towards robust clinical implementation are proposed and discussed. iii

4 Acknowledgements This work was made possible through advice and support from several people, all of whom I would like to acknowledge and thank. First and foremost, I wish to thank my supervisor Dr. Graham Wright for the countless hours of support and guidance he provided. Dr. Wright s tutelage helped me grow immeasurably in terms of technical ability, research planning, and writing, among other things. Additionally his support through my process of finding (and starting) a job in the final year of my graduate work has put me in an excellent position to have a long and rewarding career in a field directly related to my doctoral studies. Next I would like to thank Dr. Kevan Anderson. His doctoral work was a huge inspiration for mine, and his advice and technical guidance throughout my studies made me a much stronger engineer and physicist. I would also like to thank Howard Chen for great friendship, cheap rent, and much valuable consultation on aspects of MRI and physics in general. Finally from Dr. Wright s group, I am grateful to Dr. Venkat Ramanan for his work and expert knowledge of MRI sequences and programming, and to Jennifer Barry for her help with in-vivo experiments and for keeping things light even when I was pulling my hair out trying to understand why my experiments were not working. Last but not least, I would like to thank my parents for their continuous moral support and belief in me, and my wonderful wife for encouragement and putting up with me while I worked around the clock on my industry job and thesis. iv

5 Contents 1 Introduction, Motivation, & Background Introduction Clinical Motivation Chronic Total Occlusions in Coronary & Peripheral Artery Disease Motivation for Use of Long Conductors Active Implantable Medical Devices RF Heating Induced RF Current Scattered Electric Field and Leakage Current Power Deposition and Heat Transfer Empirical RF Heating Existing Techniques for Characterizing and Investigating RF Safety Electric Field Characterization Current Measurement Temperature Measurement Conclusion Existing Strategies to Mitigate RF Heating Wire Impedance Modification Transmit Field Modulation Summary and Thesis Aims Predicting RF heating During In-Vitro MRI Introduction Theory RF Current Induced Artifact v

6 2.2.2 Predicting RF Heating Methods Induced Current Characterization Algorithm Algorithm for Predicting High-SAR Heating from Low-SAR Current Characterization Simulation Proof of Concept with FEKO Experimental Setup and Scanning Simulations Mimicking Experiment Results Proof of Concept with FEKO Experimental Results Discussion Quadrature Versus Linear Tx/Rx Deriving SAR from Induced RF Current Sources of Unwanted Phase Artifacts Comparison to Similar Techniques and Alternatives Uncertain/Variable Tissue Properties and Perfusion Effect of Complex Electrical Components and Electrode Geometries Conclusions Appendix Artifact from a Curved Wire Arbitrary Wire and Image Orientation Assuming θ 2 + (z) = θ 2 (z) In-Vivo Considerations for Predicting RF Heating Introduction & Motivation Theory RF Induced Current Artifact and In-Vivo Effects Predicting Temperature Rise Methods Experimental Setup & Scanning vi

7 3.3.2 Analytical Workflow Results Phantom Experiment Animal Experiments Discussion In-Vitro Experiments In-Vivo/Situ Experiments Conclusion Miniaturizing floating RF traps for increasing MRI RF safety Introduction & Motivation Theory of Trap Function Coupled Impedance, Z coupled Trap Mechanical Properties Current Suppression Methods Trap Construction Measuring Induced Impedance Modelling Induced Current and Heating Suppression Induced RF Current and Heating Characterization Results Measured Induced Impedance Induced RF Current and Heating Discussion Induced Impedance Current and Heating Suppression Design Considerations and Tradeoffs Effect of Trap Curvature Extensions and Future Work Conclusion Summary & Future Work Quantifying Current In Vivo Practical Clinical Application vii

8 5.1.2 Application to Device Testing Technique Development Further Studies Modelling Patient Safety Towards Integrated Interventional Catheter-Based Floating RF Traps Trap Construction Techniques Further Studies Concluding Remarks 109 References 109 A List of Related Publications 117 A.1 First Author Peer-Reviewed Publications A.2 Collaborative Publication A.3 Conference Presentations A.4 Patents viii

9 List of Figures 2.1 Schematic diagrams of the experiments performed. The wire in each experiment is represented by an orange line and the PAA phantom by a blue rectangle. The position of the phantom relative to the MR bore was constant in all experiments Holder (white) used to fix the FO temperature sensor (beige and dark orange) relative to the wire (red) during heating experiments Induced RF current as calculated by FEKO with unit current applied in the forward and reverse polarization modes. Also shown in black is the quantified current, found by applying the characterization algorithm to the simulated FEKO image Simulated FEKO phase image (a) and the corresponding fit image (b). The absolute value of residuals is shown in (c). Small residuals indicate a good match between the fit and the simulated image Total SAR as calculated by FEKO in the forward mode unit current simulation (a) and scattered SAR as calculated with the presented algorithm applied to the FEKO calculated induced current (b). Absolute value of residuals is shown in (c) Characterized current distributions along the wire length. In all experiments, current was measured in seven locations, as indicated on the plots. The error bars on the plot represent the standard deviation of the current values measured in the six repeats of each experiment. During the process of upsampling and fitting a sinusoidal distribution to the measured current values, the standard deviations were used as inverse residual weighting. 34 ix

10 2.7 Measured and predicted temperature rises as seen near the tips of the wires in all experiments. Shown in blue is the recorded output of the FO temperature sensor. In red is the predicted heating behavior generated using the measured current values. The green line in A represents the temperature rise as calculated by SemcadX. Uncertainty in the predicted temperature rise is visualized by showing the highest and lowest predicted heating curves. This uncertainty is inherent to the holder that was used to fix the temperature sensor, and represents ±0.25 mm in the position of the FO sensor Scattered SAR as calculated using currents along the entire length of conductor (a) and currents only in the distal 2.5 cm of conductor (b). Absolute value of residuals is shown in (c). Small residual values indicate that current in the distal end of the conductor is primarily responsible for heating, thus current in the proximal portion of the conductor can be ignored Acquired phase image and corresponding fit, demonstrating significant gradient artifacts due to nonlinearities. Both images are displayed with a dynamic range of π to π. The full 24-cm field of view is shown Results of fits performed using phase and magnitude information. The top row shows the phase and magnitude images as acquired and reconstructed by the scanner. The middle-left image shows the theoretical phase image that was determined to minimize the magnitude of the RMS difference between the acquired and theoretical phase images. The bottom-right image shows the theoretical magnitude data that was determined to minimize the magnitude of the RMS difference between the acquired and theoretical magnitude images. As can be seen, the theoretical images generated with a phase fit match well with the acquired images while the magnitude fit does not Plot of the normalized peak simulated steady-state temperature rise as a function of wire length at 3T. Maximum temperature rise is expected at approximately λ/2, or 12 cm Plot of the discrete scaled current measurements taken at various locations along the guidewire during the phantom experiment, using a stock GRE sequence and the custom UTE sequence. Also shown are the corresponding sinusoidal fits. All current measurements have an inherent positional uncertainty of ±0.5 cm due to the slice thickness that was used in imaging which has not been shown on the plot for visual clarity Plot of heating measured in the phantom experiment, compared with heating as predicted using current characterization x

11 3.4 Comparison of phase contrast images taken with (a) the stock spoiled gradient echo sequence and (b) the custom UTE sequence. (c) shows the theoretical artifact that was fit to the UTE image. (d) and (e) show the residuals (difference) between the GRE image and fit image, and the UTE and fit image respectively. The red circle in all images delineates the region that was used for fitting to the phase artifact. Significant physiological artifacts can be seen in the image acquired with the stock GRE, whereas the phase distribution in the UTE image is relatively uniform, facilitating isolation of the wire artifact Plot of current values measured in pig 1. Shown on this plot are discrete current measurements taken both in-vivo and in-situ. All current measurements have an inherent positional uncertainty of ±0.5 cm due to the slice thickness that was used in imaging which has not been shown on the plot for visual clarity Plot of heating measured in pig 1 before and after sacrifice, compared with heating as predicted using current characterization with a custom UTE sequence Plot of current values measured in pig 3, with (a) the guidewire partially pulled back from inside the pig and (b) the guidewire fully inserted in the pig. All current measurements have an inherent positional uncertainty of ±0.5 cm due to the slice thickness that was used in imaging which has not been shown on the plot for visual clarity Plot of heating measured in pig 3 with the guidewire at two insertion depths, compared with heating as predicted using current characterization with a custom UTE sequence Image of modelled heating in a perpendicular plane around the tip of the pulled back guidewire in pig 3. The location of the guidewire is indicated by the dot in the center of the image. A significant temperature gradient exists which may account for the offset between measured and modelled heating Image of modelled heating in a longitudinal plane near the proximal end of the pulled back guidewire in pig 3. The location of the guidewire is indicated by the line extending from the left of the image. A significant temperature gradient exists which may account for the offset between measured and modelled heating Schematic representation of the inductive coupling of a series impedance onto the wire and the associated trap geometry xi

12 4.2 Computer drawing of one miniature trap as it was designed. The black portion corresponds to the 3D printed trap body, the rectangular tuning capacitors are denoted by arrows, and the outer and inner cylindrical shells represents conductor. The inner and outer conductors are shorted together with a solder bridge at the end opposite the capacitors A representative trap shown in various phases of construction. The rod denoted by an arrow in (a-c) is a mandrel (green) used to maintain the trap lumen throughout fabrication. The inner conductor with capacitors soldered on is shown in (a). One end of the capacitors is isolated from the inner conductor using an orange polyimide tube. (b) shows the trap body put in place over the inner conductor and capacitors, and (c) shows an image of the full length of the trap, without the outer conductor. The diameter of the mandrel is shown for scale Picture of the setup used to measure induced series impedance, Z. The network analyzer was calibrated with this fixture in place, using custom calibration loads placed between the alligator clips. The impedance of the setup was then measured as pictured as well as with a trap placed on the wire between the alligator clips. The difference of these two measurements provided the induced trap impedance, Z The FO probe (beige) and wire (black) construction used to measure heating at the tip of a wire Measurements of Z coupled made using all traps that were used in experiments. An example of the theoretically ideal impedance is also shown. Z a, Z b and Z c were fabricated with equivalent materials and processes and thus any difference in electrical properties is due to variability in fabrication and assembly Representative FEKO models along with corresponding MATLAB transmission line model calculations. The top line shows FEKO and MATLAB simulations of an unmodified wire setup as in the experiments of this paper. The lower two lines show simulations of wires with one and two traps in place; firstly with one trap in the middle and then with two traps distributed evenly along the length of the wire Induced current results as simulated and measured in the experiments shown in Table 4.1. Simulated current distributions are shown as continuous lines and image-based current values are shown as scatter plot markers. Error bars are defined by the standard deviation between the three current values obtained with three sets of independent images xii

13 4.9 Heating behaviour plots as measured with a FO sensor and as predicted using the simulated current distributions in figure 4.8. Heating evolution lines represent measurements whereas the dot and the x mark represent the expected final temperature value of the two configurations with traps, as calculated using theoretically determined current distributions and heating behaviour. For clarity of results, temperature rise is presented as a relative value. T rel represents the temperature rise produced by each configuration, normalized to the 0 trap experiment Results of simulating various trap densities and wire lengths. The heating has been scaled to the maximum heating present around an unmodified wire Plot of the current induced onto a wire inserted half-way into the standard ASTM phantom as simulated by FEKO, with and without a trap applied to the portion of the wire outside the phantom. The phantom boundary is situated at 50cm; thus the portion of the wire inside the phantom is defined by x > 50 cm Schematic representation of a bent trap coupling a series impedance onto the wire Plot of the flux into a cylindrical trap as a function of trap radius of curvature, scaled to the length of the trap. The curved flux has been scaled relative to the flux that would be coupled into a straight trapout. The beginning point of the line is defined by Eq. 4.7, which describes the smallest radius of curvature that a trap can have without the wire contacting the inner wall of the trap Magnitude and phase of coupled impedance due to two series traps, as a function of the resonant frequency of each trap. It can be seen that trap tuning plays a significant role in determining coupled impedance. The phase is displayed with a dynamic range from π to π xiii

14 Glossary In this thesis several conventions are used that should be noted. Firstly, vector quantities are represented with boldface characters, and scalar quantities with regular type. In certain contexts, the scalar quantity is used to represent the amplitude of the corresponding vector. In cases where this is done, the same symbol is used. For example, the amplitude of the vector field B(x, y, z) is simply the scalar field B(x, y, z). Note that the amplitude of a vector could be complex, in which the case the magnitude of that complex quantity would be denoted with vertical bars, e.g. B(x, y, z). Secondly a horizontal bar over a quantity denotes a unit vector, and a circumflex denotes a quantity due to unit transmit current. For example x is the unit vector in the x direction, and ˆB is the magnetic field produced by a unit current of 1 A in the radio-frequency (RF) transmit coil. List of Abbreviations AIMD FFT GRE MR MRA MRI PAD RF SAR SNR TR TE UTE Active Implantable Medical Device Fast Fourier Transform Gradient Echo Magnetic Resonance Magnetic Resonance Angiography Magnetic Resonance Imaging Peripheral Arterial Disease Radiofrequency Specific Absorption Rate (volumetric power deposition density) [W/kg] Signal to Noise Ratio Repetition Time/interval Echo Time Ultra-short Echo Time xiv

15 xv

16 List of Symbols r r l V A J E B Radial distance Generic position vector Length vector tangent to the wire at all points Voltage Magnetic vector potential Volume current density Electric Field Magnetic Field µ Relative magnetic permeability ɛ σ ω T Relative electrical permittivity Electrical conductivity Angular Frequency Temperature µ Perfusion rate c p ρ κ j τ M γ ξ t I φ θ C L Z R flex R torque Heat capacity Mass density Thermal conductivity Imaginary Unit, j = 1 RF Excitation Pulse Duration Nuclear Magnetization Proton Gyromagnetic Ratio MRI Signal Time Electric Current Angular coordinate in a cylindrical reference frame (phase) Phase of induced RF current (relative to scanner) Capacitance Inductance Electrical impedance Flexural rigidity Torsional rigidity xvi

17 Y G I zz J zz CEM43 Young s modulus Shear modulus Cartesian moment of inertia Polar moment of inertia Thermal dose measured in Cumulative Equivalent Minutes at 43 C xvii

18 Chapter 1 Introduction, Motivation, & Background 1.1 Introduction With the ability to easily image deep within the body and continued development of advanced imaging sequences providing varied forms of anatomical contrast between soft-tissues as well as functional imaging, Magnetic Resonance Imaging (MRI) has come to the forefront in the past decades as the most effective diagnostic imaging tool for a wide range of indications. Furthermore, with the development of real time imaging and non-anatomical techniques such as thermography and interventional tool tracking, Magnetic Resonance (MR) has begun to be thought of as an attractive method of guidance and monitoring for a variety of interventional procedures [1, 2]. The main benefit of MRI over X-ray based imaging techniques, in terms of diagnosis and interventional guidance, is the presence of soft-tissue contrast, which can also be varied in MRI as a function of sequence parameters. Additionally, MRI uses electromagnetic fields to form images and thus applies no ionizing radiation to the patient, providing increased patient safety and perhaps as importantly, increased patient comfort with the knowledge that one will not receive a radiation dose during imaging. The main contraindicating factors for MRI as compared to X-ray imaging are high instrumentation cost as well as long imaging times. However due to the aforementioned clinical benefits, MRI is used widely, representing the preferred diagnostic tool for nervous system, musculoskeletal, gastrointestinal, and some cardiovascular indications, as well as a wide variety of cancers, including prostate and neurological tumours. Several procedures could benefit from catheter-based devices with MRI guidance that for therapeutic, 1

19 Chapter 1. Introduction, Motivation, & Background 2 diagnostic, treatment monitoring or tracking purposes have one or more electrical connections running along the catheter [3 5]. However because MRI uses high power electromagnetic fields to form images, many procedures, both diagnostic and interventional, are contraindicated due to risks to patient safety [6]. While there are several groups of patients typically excluded from MRI examinations, two major cohorts are of particular interest to this work. These patients are categorized as: patients with no permanent metallic objects inside them but who could benefit from interventional procedures involving devices with long thin wires; and patients with an active implantable medical device (AIMD) that is comprised of shielded electronics and long thin wires [6]. This work attempts to address issues associated with interventional MRI procedures and related RF heating. Some potential additional applications regarding scanning of patients with AIMDs are discussed; however interventional MRI is the main motivation for this work. Such interventional devices that are partially comprised of long thin wires pose a significant safety risk in the form of potential heating in vivo. Electric currents induced on conductive devices by coupling to the transmit RF electric field give rise to localized scattered electric fields, which can cause unwanted and significant temperature rises in surrounding tissue, potentially leading to adverse health effects during and after imaging [7 9]. No consensus has been reached on a theoretical modelling approach, or a technique to reduce this form of heating and much active research continues into the physics of heating and induced currents. For this reason, most hospitals follow overly conservative guidelines and refuse to perform MRI-guided procedures, instead continuing to perform these procedures under less effective X-ray fluoroscopy guidance [6]. Therefore, there exists a desire to scan conductive structures in MRI and a need to ensure their safe use through device design and through monitoring and assessment. The major motivation for using linear conductive structures in interventional MRI is guiding percutaneous procedures through the use of MRI tracking enabled by some form of long thin conductor running along the length of the interventional catheter [10]. NOTE: Herein the term wire will be used to generically refer to all long linear monofilament conductors unless otherwise stated. The term cable will be used to generically refer to any poly-filament linear conductive structure unless otherwise stated. In places where only the term wire is used, it can be assumed that the same applies to cables, unless explicitly stated.

20 Chapter 1. Introduction, Motivation, & Background Clinical Motivation Chronic Total Occlusions in Coronary & Peripheral Artery Disease One procedure in particular that would benefit greatly from guidance by MR images is revascularization of chronic total occlusions (CTO) [3, 11]. In this procedure, a plastic catheter is used to guide a stiff wire through the vasculature to the lesion site. This wire is then used to cross the lesion and a balloon is used to dilate the vessel before placing a stent to provide lasting structure and in some cases drug delivery directly to the lesion site. CTOs are common both in coronary and peripheral vessels, motivating revascularization attempts in both locations in the body [11]. In the case of coronary CTOs, the guidewire enters in the iliac or femoral artery and follows a path up through the aorta into one of the coronary arteries. In the case of peripheral CTOs, the guidewire again enters in the iliac or femoral artery, but travels down towards the foot. Due to a large portion of the population being affect and low procedural success rates, both conditions represent a significant burden to the healthcare system. Occlusive peripheral arterial disease (OPAD) affects approximately 20% of those over 59 years of age and results in 160,000 amputations per year in the United States. Revascularization of coronary CTO is attempted in approximately 50, ,000 patients per year in the United States. However, there are many more CTO cases for which revascularization is not attempted. Fewer than two thirds of revascularization attempts are successful; thus 85% of CTOs are treated medically or with bypass surgery, representing the most common reason for referral to bypass [1, 2]. Percutaneous CTO revascularizations are currently guided using X-ray fluoroscopy with a contrast agent injected intra-arterially to depict the vasculature. This method provides only images of the open vessel, no soft-tissue contrast, and purely qualitative tracking of the catheter and guidewire. The absence of soft-tissue contrast and lack of quantitative tracking of interventional devices relative to the blood vessel leads to a high rate of procedural complications and failures, the majority of which are due to inadequate guidance, motivating an improved treatment guidance technique [1, 2]. The main cause of complications is perforation of the vessel wall, due to the high force required to cross a CTO [12]. The two major causes of CTO revascularization failure are lack of soft-tissue contrast in the occlusion and uncertainty of the guidewire position relative to the lumen. Fluoroscopy also delivers significant radiation dose to the patient. Furthermore a toxic contrast agent is required to visualize the vasculature, which imposes an upper limit on the number of images of the vasculature that can be acquired. With appropriate devices, all of these problems can be solved by MRI [3, 10].

21 Chapter 1. Introduction, Motivation, & Background Motivation for Use of Long Conductors A device proposed by Anderson et al. addresses these problems using MRI and tracking/imaging coils installed directly on the catheter [3]. Two orthogonal imaging coils at the tip are capable of imaging the occlusion and quantitatively tracking the catheter position and orientation in real time. A second pick-up coil on the tip of the catheter is capable of detecting the guidewire location and overlaying it on anatomical MR images. Soft tissue contrast in the images shows the physician anatomy within the occlusion and potentially useful crossing channels [13]. Visualization of the guide wire relative to surrounding anatomy enables the physician to ensure the vessel wall is not punctured. While this device has taken useful images in a swine model, there remains the significant problem of heating that must be addressed before this catheter can safely be used in a human [3]. To enable the use of imaging/tracking coils at the tip of a catheter, conductive transmission lines must be used to allow signal from the distal tip to be measured outside the body. These cables represent long thin conductors inside the patient similar to the guidewire that is used for revascularization, which is itself a long thin conductor. Admittedly the guidewire material has been designed for mechanical properties and need not be conductive for effective revascularization; however the industry standard material with the desired mechanical properties is a conductive nickel-titanium alloy known as nitinol [14] Active Implantable Medical Devices Many patients who have permanent medical implants with long thin wires (leads) could also benefit from diagnostic MRI exams for one of the aforementioned conditions. As such, device manufacturers have begun to seek and receive regulatory approval in recent years for AIMDs shown to be safe for MRI scanning under restricted conditions (MR-conditional) [15, 16]. AIMDs with leads present the same safety risk in the form of potential RF heating in addition to the possibility of delivering uncontrolled or unintended therapy and/or causing damage to the implant, resulting in harm to the patient or surgical intervention. A test-standard (ISO/TS 10974) has been published which defines the necessary test flow manufacturers must follow to demonstrate safety under certain conditions to the appropriate regulatory body. Typically, extensive numerical modelling is performed by the manufacturer to relate MR parameters such as SAR, landmark location, or coil selection to the tangential electric field incident on the lead during MRI. Experimental testing by the manufacturer is then used to relate the tangential electric field to patient safety in terms of lead tip heating, unintended therapy, and device damage or malfunction. The relationship between tangential

22 Chapter 1. Introduction, Motivation, & Background 5 electric field and patient safety is described by a transfer function [17]. This approach is theoretically valid; however to identify worst case induced current the manufacturer must model a very large set of patient/coil geometries as well as sequence parameters. This creates a significant time demand which delays device regulatory approval and consequently benefit to patients. Additionally, because the labelling classifications typically employed by manufacturers are so broad, this approach leads to exclusion of many patients from MRI scanning. For example, if a manufacturer performs extensive modelling of all potential lead pathways and determines that 20% of scans performed using body coil transmit would potentially cause harm to the patient, the device would be labelled unsafe for use with the body coil and the safe 80% of scans would be contraindicated. The most direct quantitative measure of AIMD patient safety is induced RF current, since it can be directly related to lead tip heating as well as unintended therapy or device damage. A reliable technique of measuring RF coupling between leads and the scanner (i.e. induced RF current) in situ may allow for application of RF current based scan restrictions rather than restrictions based on more indirect measures such as SAR or coil selection. Were such labelling used, the regulatory approval process could be greatly shortened as the manufacturer would need only to characterize the safety of the device relative to induced current, eliminating the step of finding worst case induced current for certain SAR, landmark, and coil choices. In this approach the current on the device could be characterized in situ in the clinic using a low SAR characterization scan. Scaling this result would provide the current induced by clinically relevant imaging, which could then be compared to labelled current restrictions. This would not greatly impact the clinical workflow, but instead would significantly reduce the test burden on the manufacturer as characterizing device safety versus induced current is much simpler than characterizing versus indirect factors like coil selection or landmark. Furthermore, a large group of scans would be enabled that are excluded under the current approach. Thus a technique of remotely and safely measuring induced RF current on the leads of an AIMD could reduce time between device conception and application of MRconditional labelling, as well as allow for MR scanning of an appreciable patient population who are currently excluded. 1.3 RF Heating Induced RF Current RF heating around a wire or cable inside the MR bore during imaging occurs indirectly due to coupling between the wire or cable and the electric counterpart of the transmit RF magnetic field used for

23 Chapter 1. Introduction, Motivation, & Background 6 imaging [18]. This electric component of the transmit electromagnetic field will be dubbed E 1 in this work. During transmit E 1 induces a voltage along the length of the catheter according to: V ind = L 0 E 1 dl, (1.1) where V ind is the voltage between the tips (ends) of the wire or cable, and l is a length vector tangential to the wire. This induced voltage will give rise to current flow in the wire, governed by the wire characteristic impedance. With conventional circularly polarized excitation by the MR scanner body coil, the transmit electric field points along the axis of the scanner bore and increases linearly in amplitude with radial distance from the transverse centre, potentially reaching root-mean square (RMS) magnitudes on the order of V/m. A length of wire oriented along the static field and close to the bore wall, as is typical in percutaneous procedures, will have a large voltage induced between its ends by E 1. At the tip of a wire, where conductive material meets insulating material, tissue or phantom gel, a significant gradient in electrical impedance exists. Similarly a strong gradient exists at the insertion point where the electrical environment surrounding the catheter changes significantly. Such interfaces can cause strong reflections which give rise to standing wave current distributions along the inserted portion of the catheter. Such distributions are characterized by relatively high current (on the order of ma) in the middle of the immersed section and greatly suppressed current at the insertion point and wire tip. The practical problem of relating the voltage induced between the ends of the wire to the RF current flowing on the wire is an active area of research due to the complex electrical environment around the wire (continuously changing characteristic impedance of the wire along its length) Scattered Electric Field and Leakage Current Assume for the moment that a known induced RF current distribution J ind exists on the wire. As an aside, J ind is used when defining this current in the reference frame of the MR scanner, as the current exists generically in three dimensions and as a distribution across the cross-section of the wire. Later in this work the symbol I ind will be used to describe the same current in the reference frame of the wire. When a thin wire is assumed, J ind can be described as a one dimensional current I ind (the dimension being distance along the wire) rather than a three dimensional current distribution. Given a known harmonic current distribution J (r ) 0 r V, J (r ) = 0 r / V, the magnetic vector potential A

24 Chapter 1. Introduction, Motivation, & Background 7 produced by this current at a position r is given by: A (r) = µ V J (r ) exp ( jk r r ) 4π r r dr, (1.2) where µ is the permeability and k is the complex wave number of the medium surrounding the wire. The electric field radiated by the induced RF current, herein termed the scattered field E s, is given by: E s = jωa j ( A), (1.3) ωɛµ where ɛ is the permittivity and ω is the frequency of the RF field in question Power Deposition and Heat Transfer This scattered electric field deposits RF power, P, in the surrounding tissue, which is the source of heating in the vicinity of the wire. In the MRI community this power deposition is typically given as as power density termed the Specific Absorption Rate (SAR) and reported in units of W/kg. The SAR due to a scattered field E s is given by: SAR = σ E rms 2, (1.4) ρ where σ is the conductivity of the surrounding tissue, ρ is the issue mass density, and E rms is the RMS value of the scattered electric field E s. It can be seen by inspection that near locations of strong current gradients, the scattered electric field will be large. RF-induced current gradients are typically strong and well-localized to regions of altered electrical characteristics (e.g. wire tip and insertion point) and therefore create locations of significant scattered electric field and power deposition. These regions of significant power deposition give rise to potentially dangerous heating, explaining the typical location of dangerous heating at wire tips and/or insertion points. Given a power density SAR, the temperature evolution in the immediate vicinity can be described by Pennes bioheat equation: ρc p T t κ 2 T + µ tiss (T T b ) = SAR, (1.5) where T is the temperature rise and T b is the baseline blood temperature, κ is the thermal conductivity, µ tiss models tissue perfusion, and c p is the tissue heat capacity [19].

25 Chapter 1. Introduction, Motivation, & Background 8 In addition to the scattered electric field, conductors with uninsulated tips can allow for current to flow directly from the conductor into proximate tissue. For example interventional catheters designed for electrophysiological mapping and ablation of the myocardium must have uninsulated electrical contact with patient tissue. Such contact can represent a relatively high RF impedance compared to the impedance seen by current flowing in the bulk of the conductor, thus the majority of current flow in the conductor will form standing waves along the length, and associated scattered fields. However, any heating due to leakage current must be considered in addition to scattered electric fields. Assuming a current I leak flows into the proximate tissue from the wire tip, and assuming a spherical contact at the tip of the wire, the local steady state heating at radial distance r from the center of the spherical contact has been written as [20]: I 2 rms T (r) = 16π 2 σκr tip ( 1 r R ) tip 2r 2, (1.6) where I rms is the RMS value of the leakage current I leak and R tip is the radius of the spherical contact at the tip of the wire. Equation 1.6 does not account for the effect of thermal conduction along the wire, which would serve to dissipate heat in the tissue surrounding the wire tip, and therefore may result in overestimation of the local heating. By simply evaluating equations , it may seem straightforward to predict heating in any situation, however there are a few subtle complications. Firstly, it is far from trivial to predict E 1 due to the complex electrical environment present in biological tissue and determining E 1 experimentally is very time consuming; therefore E 1 is unlikely to be known exactly. Secondly, the changing electrical environment created by various biological tissues along the length of the catheter makes relating the induced voltage to an induced current a complex task. Thirdly, equation 1.5 can only be used to describe the effect of constant well-known perfusion, whereas perfusion in tissues is generally highly variable and not well known. As such, the above description is sufficient for us to understand the physical basis of RF-induced heating but could not practically be used to theoretically evaluate heating potential without experimentation and/or simplifying assumptions Empirical RF Heating Several studies have been carried out demonstrating the complex and largely unpredictable nature of heating [7, 18, 21]. Perhaps the most significant factor affecting RF interaction is catheter position in the bore, as one would expect due to the strong spatial variation of E 1. It can be said in general that E 1 increases with decreasing distance from the transmit coil being used but precise variations are too complex and varied to described generally. It has been shown that modulating E 1 in magnitude and/or

26 Chapter 1. Introduction, Motivation, & Background 9 phase can significantly affect heating and potentially reduce heating in certain situations [9, 22, 23]. Such work helps to reinforce the belief that heating is most significantly affected by incident electric field, indirectly through position in the bore. The effect of inserted length on heating from a wire in the body and the resonant nature of induced current has also been shown to have great effect. A distinct maximum temperature rise induced by a resonant length of coaxial cable was identified early on in the research into RF heating [7]. This is to be expected because only the appropriate length of catheter could support a standing wave current distribution. Another complicating factor related to insulation thickness on a wire has been studied [24]. Through simulation and experiment it was shown that, with a bare tip wire insulated along its length as in an electrophysiology catheter, thicker insulation causes much greater heating at the bare tip. The variation of heating with insulation thickness can be partially explained by altered electrical impedance of the wire due to the changing electrical environment. Additionally, thicker insulation limits heat transfer between surrounding tissue and the wire thus less heat would be dissipated through thermal conduction in the wire. One very interesting and potentially dangerous effect is that of a stenosis in the blood vessel. It was shown in a phantom that heating varies non-linearly and perhaps resonantly with changing distance between the guidewire tip and a nearby stenosis [8]. This effect is likely due to amplifying reflections in the transmit electric field, caused by the interface of the stenosis and the relatively more conductive blood. These studies indicate that RF heating is extremely complicated. In very simple geometries, it is feasible to describe induced RF current analytically; however with arbitrary catheter geometry and a complex environment of various media, such as in vivo, it is nearly impossible to determine the incident field and predict heating a priori. Testing every possible configuration before a procedure is impossible and heating is sufficiently complicated to contraindicate confidently applying a safety measure to all situations without in situ verification and monitoring. Thus, in addition to employing techniques to reduce the level of RF heating that will occur during a procedure, safety must also be monitored during the procedure. 1.4 Existing Techniques for Characterizing and Investigating RF Safety As can be seen by inspection of equations , an RF induced temperature rise, and thus the level of RF safety of a certain device and/or configuration, can be predicted if one has sufficient knowledge of either: the tangential electric field to the wire and the local electrical environment, or the distribution

27 Chapter 1. Introduction, Motivation, & Background 10 of induced RF current on a conductor. Furthermore the RF safety of a device can be characterized by directly measuring any RF heating that is caused by the wire under a certain input power to the MRI. The first two techniques can potentially be executed without causing an unsafe condition for the patient; if sufficiently low input power to the MR scanner is used, one can be certain that characterizing the tangential electric field or induced RF current distribution will be safe. When measuring RF heating directly however, a potentially unsafe condition for the patient must necessarily be created. Thus direct temperature measurement, while representing the most accurate gold-standard for characterizing RF temperature safety, is generally reserved for in vitro investigations Electric Field Characterization The electric field tangent to the wire can be characterized either by analytical approximation, computationally intense modelling or extensive mapping of the transmit magnetic field. In very geometrically and electrically simple configurations, it is possible to use Maxwell s equations to generally describe the electric field present in the MR. For example with a homogenous cylindrical system that is arranged coaxially to the MR bore, it can be shown that the electric field is zero on the axis of the cylinder and increases linearly with decreasing distance from the bore wall. Simplistic configurations such as this can be quite useful for the designer to know and treat as a rule of thumb when considering various preliminary designs; however such treatment has limited practical value. The next step up in complexity involves using computational electromagnetic models to more accurately map the electric field in the scanner. Especially in in vitro RF safety investigations, these models can be quite useful. Using the Method of Moments (MoM) and or Finite Difference Time Domain (FDTD) method, certain interesting phantom configurations can be quickly investigated. The electric field in a rectangular phantom, arbitrarily oriented in the scanner, can be modelled in a matter of seconds with modern computing. This information can be of use when designing phantom experiments, because potential worst-case locations for the wire or lengths of wire that will present maximal heating can be easily identified. Unfortunately simple geometries such as this offer little clinical value when attempting to determine if a patient in a given configuration will be at risk during scanning. The FDTD method can be used to accurately model electric fields in a patient inside the scanner if the entire anatomy and corresponding electrical properties of the patient are known; however even if this information is available the modelling still requires prohibitive computation time when employed using widely available modern computing technology. Furthermore imaging the entire body of every patient who undergoes MRI and segmenting these images to outline anatomical boundaries is not practically

28 Chapter 1. Introduction, Motivation, & Background 11 possible due to time constraints. One Swiss company (IT IS Foundation, Zurich) has created a virtual family of patient anatomical and electrical models for use in modelling. This family has nine members ranging from a small young girl to an obese grown man and most real patients in the scanner could likely be correlated to a member of the virtual family. This would always be an approximation however and no study has been carried out to indicate that only 9 anatomical models can be used to accurately represent the majority of the patient population requiring MRI. Thus clinicians would likely be skeptical of the reliability of this technique for ensuring patient safety. Furthermore even if the virtual family were used in an attempt to closely mimic real patients, the modelling time of several hours on a typical modern desktop computer would prohibit the use of this technique for ensuring patient safety on a case-by-case basis. The most accurate technique to determine in vivo electric fields during MRI would be to map the incident magnetic field B 1 with high resolution using established field mapping techniques [25, 26]. Such field mapping techniques allow only for mapping of the axial magnetic field component, and thus only the longitudinal electric field component could be calculated. This longitudinal field can be useful in simple phantom experiments in which the wire is parallel to the longitudinal axis for the entire length. However it cannot generally be said that an interventional device or implant will be oriented longitudinally and thus this technique cannot be used reliably in vivo Current Measurement To allow for prediction of temperature rises before they occur, it is necessary to have knowledge of induced current, which can be acquired most reliably through measurement. Predicting safety requires measuring current quickly and accurately, at several locations on the catheter. It has proven to be non-trivial to establish a current measurement that is sufficiently rapid and spatially flexible due to a few technical challenges. Any current transducer installed on the catheter is at a fixed location and must transmit signal along the catheter; with several other transmission lines for tracking and imaging, it is difficult to fit all of the wires on a small catheter. An image-based technique using artifacts is spatially flexible, but must accurately and quickly measure and interpret the artifact; it must also be known exactly where on the catheter the measurement is being performed. There have been several techniques and devices proposed for measuring current but most suffer from long experiment times and/or prohibitive size. Existing current measurement techniques can be divided into two major categories: direct sensing which is generally quicker; and image based sensing which is the more flexible technique [19, 27, 28].

29 Chapter 1. Introduction, Motivation, & Background 12 Direct Measurement Direct sensing encompasses any technique that involves placement of a dedicated current transducer on the catheter. Direct techniques are pursued mainly because they are very fast and accurate relative to remote techniques. One technique of directly measuring current through device modification is converting current into an optical signal using a diode bridge, which must be soldered directly into the wire [29]. It has been shown that this current sensor can be used to predict heating around a cardiac pacemaker lead in a phantom experiment. Following a single step to calibrate the current-temperature relationship, a nearly instant measurement of current provides a very fast and reliable temperature prediction. This technique is accurate yet extremely inflexible as it measures current only at the location of the optical coupler. Also, the current-temperature calibration is unique for each catheter position, preventing general application in vivo. Finally the present implementation relies on a fibre optic cable running the length of the catheter; it is not practical to implement this on a clinical catheter due to the prohibitive size of the transducer and fibre optic transmission line. In an attempt to address the problem of a fixed measurement location, a direct current transducer involving no physical connection to the wire was developed based on a toroidal coil acting as a transformer secondary with the wire as the primary [19]. Following a simple calibration, RF currents can be quantitatively measured in real time. This device is quite flexible in that it can be placed anywhere along any wire, the aforementioned calibration need only be performed once for each device, and finally it is very accurate and therefore useful for in vitro investigations. Currently the prohibitive size of the device prevents use in a human. There is potential to monitor currents using the device on the section of wire extending outside of a patient but in many clinically relevant situations the portions of the wire inside and outside the body are essentially isolated due to impedance mismatch at the catheter insertion point, leading to strong electrical reflections. Therefore, measuring current outside the body will not suffice. Remote Measurement Remote, or image-based, techniques attempt to measure and analyze the artifact induced in the MR image by current flowing in the wire(s). The magnetic field created by the induced RF current is at the Larmor frequency and thus couples strongly to B 1, creating local modulation of the RF magnetic field. A qualitative image-based method was proposed which relies on transmitting and/or receiving reverse polarization to isolate signal from the wire [27]. This technique provides reliable detection of induced

30 Chapter 1. Introduction, Motivation, & Background 13 current but has not been used for quantitative measurements. Furthermore, it is possible for RF-induced current to be flowing on the wires and also not induce a dangerous temperature rise. The charge buildup that causes heating is related only to the current gradient and thus this reverse polarization technique could incorrectly classify some safe situations as unsafe. Another method of detecting induced currents is based on quantifying the artifact induced in a standard magnitude MR image by the induced RF current. The extent of the magnitude artifact is proportional to current and has been analyzed to measure the current causing an artifact [28]. This measurement is lengthy, requiring several images to accurately map the B 1 field, as well as two manual steps during post-processing. Present techniques for measuring current represent a strong basis for further investigation. Developing and combining existing methods with new ones could lead to a sufficiently safe, flexible and rapid measurement strategy applicable in vivo Temperature Measurement Direct At present, the safety of a certain modified device is tested using a fluoroptic temperature probe to directly measure temperature rises induced in gel phantoms following long ( 15 min) MR scans according to ASTM standard F [30]. This method does provide an accurate temperature measurement; however there are several limitations to the technique. Firstly, a fluoroptic temperature probe is capable of measuring temperature at only one or a few locations. Measuring temperature at several locations requires very long experiments due to repositioning of the probe; furthermore unexpected hot-spots may be missed. Secondly, only a very specific configuration is tested: the phantom is a homogeneous rectangular prism, the scanner body coil is used for excitation and only one catheter position is considered per scan. It has been demonstrated that RF-current induced heating is quite complicated; testing a single configuration in a homogeneous phantom using only one coil does not adequately ensure safety in all clinically relevant situations. Therefore, motivation exists to develop a safety measurement technique that can be applied during a procedure. In order to minimally affect procedure duration, the measurement technique must be rapid. Furthermore, it must be capable of predicting temperature rises instead of measuring them to allow for safe application in a patient. Finally, to allow for adequate flexibility and application to all devices, the safety prediction measurement must be image-based and involve minimal or no device modification.

31 Chapter 1. Introduction, Motivation, & Background 14 Remote There exist techniques that can be used to directly image a temperature rise during MRI. It has been shown that the precessional frequency of protons in tissue exhibits a linear relationship to temperature [31]. Thus if one acquires an MR image of a sample before and after heating occurs and uses identical imaging parameters, any phase difference between the two images can be said to be caused by changes in precessional frequency due to temperature. With empirical data of the relationship between precessional frequency and temperature, a subtraction of two phase images can be used to accurately quantify any heating that occurred [31 34] Conclusion There are major issues prohibiting the practical reliable implementation of an electric field measurement for determining patient safety. Thus the author believes that a practical, reliable safety characterization method will rely on determining the induced RF current distribution or localized temperature rise. Fundamentally, measuring the local temperature cannot be guaranteed to be safe, because in order to characterize safety one must create a potentially unsafe situation. Therefore a method of safely determining the induced current distribution will be the most reliable and practical solution for ensuring patient safety during MRI. Electric field measurements and direct temperature measurement demonstrate utility in in vitro investigations, but must remain confined to in vitro experiments in which patient health is not at risk. 1.5 Existing Strategies to Mitigate RF Heating Existing strategies to increase the RF safety of a wire during MRI can be divided into two categories. Firstly, the wire can be modified electrically in an attempt to ensure that the resonant frequency of the wire is always far from the scanner bandwidth, or additionally to increase the impedance of the wire at the scanner frequency to reduce the level of current that will be induced by a given incident electric field [35, 36]. Secondly the transmit electric field can be modulated in magnitude and/or phase using a custom transmit coil to reduce coupling between the wire and scanner [9, 37] Wire Impedance Modification In signal transmission cables, balanced differential currents are safe while unbalanced common mode currents cause any unwanted heating [35]. Introducing one or more elements representing high impedances

32 Chapter 1. Introduction, Motivation, & Background 15 to common mode currents and low impedance to differential currents can reduce heating [35, 38, 39]. These elements increase the resonant frequency of the device by effectively breaking the wire into shorter sections. Impedances of this type can be realized using resonant or non-resonant elements; however some resonant elements have the potential to introduce new hot spots in their own vicinity. A tank circuit, a winding of cable in parallel with either a discrete capacitance or the parasitic capacitance of the cable itself, can represent a resonant high impedance structure to common mode currents [24]. It has been shown that a cable winding with a length of cable wound back on top of the initial winding can also suppress common mode currents [24]. These elements while easily fabricated have the potential to themselves heat up if immersed in a lossy dielectric due to the strong electric field that is created inside and near the elements when suppressing currents. Resonant chokes can be implemented around a coaxial transmission line using a triaxial cable with a short section of the outer shield and conductor stripped away; a choke of the correct length will preferentially support common mode currents removing them from the primary shield [38]. This technique is not ideal because the chokes must be several centimetres long and for much of the procedure would not be fully inserted in the patient, reducing efficacy. The device s resonant frequency can also be increased using non-resonant distributed transformers implemented by two rectangular loops in close proximity. Differential currents are transmitted via inductive coupling while common mode currents are almost completely blocked by the physical break in the cable [35]. Transformers do not themselves heat up, and reduce heating at the tip. Unfortunately because transformers are long, rigid and fixed in place on a single wire, they can affect the mechanical properties of the catheter. An attractive and promising method of reducing heating is a contactless cable trap similar to those used on clinical MRI coils [39, 40]. This trap can be tuned to support currents at the Larmor frequency. At the location of the trap, currents will preferentially flow in the trap, removing them from the imaging wire. Unfortunately, there is no implementation of this device small enough to fit inside a human. It has been shown that this trap placed on a wire outside a phantom can suppress local currents but as mentioned, the immersed and free sections of a catheter are typically isolated electrically. It is very unlikely that traps outside the body are sufficient; further development is required toward extending the application of traps to work on wires inside a patient. With miniaturization, floating traps may represent the most promising method of effectively suppressing induced RF currents on wires in a patient. Proposed research will aim to develop a current suppression technique based on traps useful in clinically relevant configurations.

33 Chapter 1. Introduction, Motivation, & Background Transmit Field Modulation It has been shown that electric fields can be nulled in the vicinity of wires in simple phantom configurations using existing birdcage transmit coils [37]. This technique can be very effective if the position of the wire is known with great accuracy and if the wire lies completely in a plane perpendicular to the axial plane in the bore of the MR scanner. In such a situation a plane of zero electric field can be created by driving the birdcage coil to apply an appropriate linearly polarized field. Linear polarization is inherently less efficient than the typical quadrature polarization that is applied in most MRI procedures but this decrease in efficiency could be tolerated if it increased patient safety reliably. However due to the necessity of an implant lying fully in a plane this technique will not be generally applicable to patient exams. In general, to null the electric field along a curvilinear path traced out by an interventional device or implant inside a patient, one would need a complex transmit coil array with many small elements allowing the electric field to be customized. This technique is feasible theoretically; however the electronics required to create a dense array of independent transmit coils are prohibitively expensive and complex. Furthermore any attempt to modify and null the incident electric field in the vicinity of the wire will necessarily affect the incident magnetic field, B 1 which is necessary for imaging. Therefore any transmit array solution must be designed for minimal impact on image quality, adding an extra layer of complexity to the problem. In the author s view, at least for the case of interventional devices where geometries of the wire may be changing substantially over the course of the procedure, a more robust solution to increase RF safety will consist at least in part of an electrical modification of the wire. This modification will work to suppress current formation under excitation by an arbitrary incident electric field. Perhaps supplemental safety increases by a simple scheme to reduce the electric field near the wire while maintaining image quality would be useful, but a solution based solely on electric field nulling will likely not be practical for interventional applications. 1.6 Summary and Thesis Aims There exists much motivation to apply MRI techniques to percutaneous revascularization procedures as well as to patients with permanent wire-based medical implants. However at present no consensus exists on a method to generally ensure patient safety when these techniques are applied. Furthermore there exists motivation to facilitate and expedite the in-vitro aspects of interventional and implantable device design, as well as the rigorous process of gaining regulatory approval. To this end, this work attempts to

34 Chapter 1. Introduction, Motivation, & Background 17 develop techniques for rapidly and remotely characterizing the safety of interventional devices in vitro and in vivo. Additionally a method of improving the safety of interventional revascularization guidewires without affecting the required mechanical properties is presented. In order to ensure the safety of an intravascular MRI catheter throughout an entire procedure, it is necessary to monitor RF-induced current as well as attempt to suppress it. Direct current measurement techniques are fast and accurate but the necessity to measure current at different locations and the prohibitive size of direct transducers motivates development of a remote measurement technique. The existing problems with remote techniques can be overcome by using the phase information of the RF magnetic field near the wire. Existing current suppression techniques may suffer from heating of the suppression elements themselves or altered mechanical properties of the catheter. Miniature floating current traps show promise for reducing currents in a wide range of situations while not affecting the catheter flexibility. In the following sections theory and experimentation required to develop the idea of measuring current using phase information are discussed followed by a practical implementation of the measurement. Lastly, development of a new miniature floating trap for current suppression is addressed. This work is presented in separate Chapters as follows: Predicting RF heating during in-vitro MRI (Chapter 2) In this chapter a method of remotely characterizing RF safety using phase image based artifacts is presented. An analytical framework describing the phase artifacts caused by induced RF current is presented, along with a theoretical framework which can be used to relate induced RF current to local heating behaviour. Phantom experiments are presented in which current distribution was measured and compared with simulation results generated by a commercial software package. Furthermore, heating predicted using the measured current distributions is compared to heating as measured by the industry gold standard fibre optic temperature probe. In-vivo Considerations for predicting RF Heating (Chapter 3) In this chapter the remote current characterization method and heating prediction is extended to in vivo application. Pre-clinical studies were carried out in a porcine model using a commercially available guidewire and catheter. With a near resonant length of guidewire extending beyond the distal tip of the catheter, the method developed in Chapter 2 was applied to the guidewire in vivo to characterize induced current distribution and predict local heating. Again a fiber-optic sensor was used as a gold standard to correlate with predicted heating values. The extension to in vivo measurements was complicated for the most part by physiological sources of phase that interfered with the phase artifact due to induced current. To minimize physiological artifacts and allow for

35 Chapter 1. Introduction, Motivation, & Background 18 isolation of the induced current artifact, a custom ultra-short echo time (UTE) sequence was used. Miniaturizing floating traps for increasing RF safety (Chapter 4) In this chapter work towards increasing the safety of commercially available guidewires is presented. Theory was first developed to enable intelligent design and miniaturization of a previously described floating RF trap device. The model for impedance induced by miniature RF traps was confirmed with bench top measurements. Subsequently simulation work was carried out to determine the linear density of traps necessary to reduce heating caused by commercially available guidewires below a clinically acceptable level. Finally in-vitro experiments were carried out to verify the efficacy of miniature traps at reducing heating caused by a thin conductor.

36 Chapter 2 Predicting RF heating During In-Vitro MRI Introduction Conductive medical devices currently contraindicate MRI exams for a large number of patients, due to the risk of dangerous RF heating [41]. The heating characteristics of long conductive structures during MRI scanning have been extensively investigated. Several groups have investigated various methods of improving the safety of catheter-based devices and implanted medical devices, many of which have effectively mitigated heating under specific circumstances [36 38]. However due to the complicated nature of RF heating there lacks a consensus on a generally applicable safety strategy [7 9, 18, 42]. Generally, the safety of a certain device and/or configuration is investigated in vitro before a procedure using a fibre-optic temperature probe. This test method, while accurate, has serious disadvantages. Firstly, testing different configurations requires lengthy repositioning and setup. Secondly, the probe only measures temperature at one or a few isolated points, meaning that dangerous hot spots not predicted before the experiment may not be noticed. These problems can be solved using an imagebased method of investigating heating. Techniques exist to accurately image temperature changes with MRI, however a method of testing safety based on evaluating temperature rise is inherently unsafe in a patient because a dangerous temperature rise must be induced. A method of quickly acquiring images indicative of heating potential would greatly reduce the amount of time required to test a device and 1 This chapter is modified from the article: Safely Assessing Radiofrequency Heating Potential of Conductive Devices Using Image-Based Current Measurements. Gregory H. Griffin, Kevan J.T. Anderson, Haydar Celik and Graham A. Wright. Published 2014 in Magnetic Resonance in Medicine. 19

37 Chapter 2. Predicting RF heating During In-Vitro MRI 20 enable more complete investigation of geometric effects on heating, and would have the added advantage of the ability to determine the safety of a certain configuration in vivo. The ideal method would work in vivo, it would be flexible and could quickly be adapted to many situations. It would be contactless and totally non-invasive and finally it would have the ability to safely characterize induced RF current on a metallic medical device with the intent of predicting unsafe situations. The most-important feature for in vivo implementation is that the characterization method be safe. In this chapter, a phase-based method of analyzing image artifacts to quantitatively characterize induced RF currents on linear conductive devices is presented and demonstrated. The method uses low- SAR, low-flip angle gradient echo phase images to determine induced current. This current distribution can then be used to predict the temperature rise that would be caused in a patient by any other sequence. Experimental measurements are compared with simulations in a phantom mimicking a human torso. It is shown that using a low-sar gradient echo scan, induced current can be safely and accurately determined. Furthermore, it is shown that this induced RF current distribution, safely characterized using a low-sar sequence, can accurately predict heating behaviour under application of other, higher-sar sequences. The proposed method represents a test that can eventually be applied in a patient at the beginning of an interventional or diagnostic scan, enabling a decision on whether or not a certain scan can be performed safely. Additionally, this method could be applied to in vitro investigations performed during device development, enabling more rapid and flexible characterization of the safety of various designs. 2.2 Theory RF Current Induced Artifact The goal of this work is to analytically describe the phase artifact associated with induced RF current on linear conductive structures inside the MR bore. In close proximity to such a structure supporting induced current distribution I ind (z), Ampère s law can be simplified to describe the magnetic field B 2 (z, s) as a function of perpendicular distance s from the conductor and the current flowing at location z. This magnetic field is given by: B 2 (z, s) = µi ind(z) 2πs φ = B 2φ φ (2.1) where µ is magnetic permeability and φ is the angular unit vector in a cylindrical reference frame, the axis of which is collinear with I ind (z), and B 2φ is a complex scalar. The subscript 2 will be used herein to

38 Chapter 2. Predicting RF heating During In-Vitro MRI 21 refer to scattered fields created by current on the conductor. In this cylindrical reference frame, B 2 (z, s) has only a tangential component. Therefore, B 2 (z, s) is linearly polarized and can be described as the sum of two counter-rotating circularly polarized fields of equal magnitude. When a linear conductor creates a field of the form of Eq. 2.1 during imaging, these two counter-rotating fields affect both the transmit and receive sensitivity, leading to a characteristic artifact in the acquired imaged. As is the convention in the MR community, left-handed (LH) fields will be denoted with a superscript plus sign and right-handed (RH) fields with a superscript negative sign. A positive ( e jωt) time harmonic is assumed. The transmit and receive sensitivity of a given coil configuration can be determined using the principle of reciprocity. To illustrate the underlying concepts, theory will be developed for the simple case of single channel linearly polarized Tx/Rx with the scanner body coil, and extensions to quadrature Tx/Rx discussed later in the manuscript. To determine the Tx/Rx sensitivity in the linear polarization case a single conceptual experiment, in which the wire is placed inside the MR bore and in-phase current of equal unit-magnitude is applied to both ports of the body coil, must be considered. The incident field produced by unit, in-phase current applied to both ports of the body coil is termed ˆB 1. This field has an electric counterpart that gives rise to current Îind on the linear conductor, which subsequently creates a scattered field ˆB 2 as in Eq ˆB1 and ˆB 2 are both linearly polarized and one need only look at the sum of their individual LH and RH components to determine the Tx/Rx sensitivity. As is the convention in the MR community, these fields will be represented as complex scalars in the rotating frame, B + 1 and B+ 2. The x-component defines the real part and the y-component the imaginary part. Thus the total LH transverse RF magnetic field defining transmit sensitivity is ˆB + tot = ˆB ˆB + 2, and conversely ˆB tot = ˆB 1 + ˆB 2 defines the receive sensitivity. To determine the forms of ˆB + tot and ˆB tot, fields will be considered in the conventional rotating frame. Generally: ˆB + 2 = 1 (ˆB+ 2 2x + j ˆB 2y) + = 1 2 ˆB + 2φ ( sin φ + cos φ), (2.2) where ˆB + 2x/y represent ˆB + 2 projected onto the x and y axes respectively. More simply: ˆB + 2 = j 2 ˆB + 2φ (cos φ + j sin φ) = j 2 ˆB + 2φ exp (jφ). (2.3) Thus: ˆB + tot = ˆB + 1 exp ( jθ + 1 ) + j 2 ˆB + 2φ exp [ j ( θ φ)], (2.4) where θ + 1 represents the phase of the transmit coil RF field, and θ+ 2 the phase of Îind(z) at the image

39 Chapter 2. Predicting RF heating During In-Vitro MRI 22 location. It can similarly be shown that the total RH component of the RF magnetic field is given by: ˆB tot = ˆB 1 exp ( jθ 1 ) j + 2 ˆB 2φ exp [ j ( φ θ2 )]. (2.5) In this simple case of single channel linearly polarized Tx/Rx with the scanner body coil, one conceptual current, Îind is responsible for both ˆB + 2 and ˆB 2 thus; ˆB + 2 = ˆB 2 = µîind(z), θ 2 + 4πs = θ 2, (2.6) as each field represents exactly half of the linearly polarized field that is created when Îind(z) is induced by a conceptual unit current in the MR RF transmit coil. Furthermore, with perfectly linearly polarized Tx/Rx, ˆB + 1 = ˆB 1 and θ+ 1 = θ 1. With quadrature Tx/Rx, these assumptions regarding ˆB 1 and ˆB 2 are no longer exact; this point is discussed further in section 2.5. With ˆB + tot and ˆB tot determined, the actual acquired signal during imaging can be found by considering the process of applying a non-unit current during transmit. When this non-unit transmit current, I trans 1, is applied for a duration τ and a small flip angle is achieved, the following positively rotating magnetization will be created: M + = jγτm 0 I trans B + tot. (2.7) Here, M 0 is the longitudinal magnetization immediately before excitation, and γ is the gyromagnetic ratio. With the above magnetization, the principle of reciprocity states that the total received signal, ξ, is given by [43]: ) ξ = 2ωM + (ˆB tot = 2jωγτM0 I trans ˆB ) + tot (ˆB tot. (2.8) I trans represents the current required in the transmit coil to create B tot = I trans ˆB tot required for imaging. Combining the leading coefficients in Eq. 2.8 leads to: ξ = A I trans ˆB + tot (ˆB tot ) (2.9) where A is a complex scaling coefficient, ideally uniform across the image. The phase of the signal, ξ, is therefore given by: ξ = A + I trans + ˆB+ tot ˆB tot, (2.10) with ˆB + tot and ˆB tot as in Eqs. 2.4 and 2.5. The term A + I trans ideally provides a uniform offset to the entire phase image; any spatial variation in a phase image containing the described artifact is due

40 Chapter 2. Predicting RF heating During In-Vitro MRI 23 to ˆB+ tot ˆB tot. The above equations give an analytical form for the spatial phase pattern caused by induced RF current, which, of interest, does not depend on transmit current amplitude. The spatial pattern of phase is due only to ˆB+ tot ˆB tot, allowing the investigator to fit this term to an acquired phase image to measure one or more parameters. If it is assumed that ˆB 1 is spatially uniform, any phase variation is due only to ˆB 2 and the parameter of induced RF current can be extracted. In general, the current applied to the body coil during imaging is not a unit current and the applied field B tot = I trans ˆB tot is scaled relative to the unit-current case. However, because the applied field is simply scaled, the phase of the acquired signal does not change and it can be said that B + tot B tot = ˆB+ tot ˆB tot. That is, the RF induced phase artifact depends only on the level of coupling between the body coil and linear conductor in a certain geometry, not on the true power going into the body coil. It is the relative magnitudes of ˆB 1 and ˆB 2 that determine the spatial extent of the induced phase artifact. (If coupling is high and Îind(z) is large, ˆB 2 ˆB 1 and the effect of ˆB 2 will be present throughout the image. If coupling is low and Îind(z) is small, the effect of the wire is negligible and no artifact exists.) Thus if ˆB 1 is known and fixed, a fit of Eq to an acquired artifact will always provide a unique ˆB 2 and Îind(z) value. Furthermore, because the artifact is independent of true transmit power, if B 1 = I trans ˆB 1 is known and used in place of ˆB 1 during the fitting process, the fitting algorithm will simply return a scaled answer I ind = I trans Îind. This independence of the artifact on transmit power is precisely what allows this technique to work with a single image. If it is assumed that the nominal flip angle prescribed during scanning is correct, the true B 1 = I trans ˆB 1 can be easily calculated by dividing the area under the RF pulse into flip angle. If this true B 1 = I trans ˆB 1 is used in place of ˆB 1 when the fitting algorithm matches the theoretical artifact to the acquired artifact, the algorithm will find the commensurate current I ind = I trans Îind that is truly present and responsible for heating Predicting RF Heating The theoretical framework for predicting RF heating due to a volumetric current distribution was described in Section 1.3, and the relevant portion is included again here for completeness. Given a current distribution J(r ) 0 r V, J(r ) = 0 r / V the magnetic vector potential A produced at position r is given by: A(r) = J(r ) exp ( jk r r ) 4πr dr. (2.11) Where µ and k are the magnetic permeability and complex wavenumber of the medium respectively.

41 Chapter 2. Predicting RF heating During In-Vitro MRI 24 The magnetic vector potential can be used to find the scattered electric field produced by J(r ), given by: E s = jωa j ( A). (2.12) ωɛµ Here, ω is the angular frequency; ɛ and µ are the permittivity and permeability of the medium respectively. The SAR can simply be calculated by: SAR = σ E rms 2, (2.13) ρ where σ is the electrical conductivity and E rms is the root mean square (RMS) amplitude of the electric field. Finally, for a generic SAR distribution, the temperature rise T in the volume of power deposition is governed by Pennes bioheat equation [44], given here: ρc p T t κ 2 T + µ tiss (T T b ) = SAR, (2.14) where ρ, c p, κ, and µ tiss represent the density, heat capacity, thermal conductivity and perfusion constant of the surrounding tissue. 2.3 Methods The purpose of this investigation was to characterize the induced RF current distribution on copper magnet wire under various situations, using a low-sar characterization sequence. The current would then be used to predict RF heating near the wire under application of a different higher SAR sequence. Experiments were carried out using quadrature Tx/Rx, therefore, the assumptions that ˆB + 1 = ˆB 1 and θ + 1 = θ 1, are not exact and algorithms were applied accordingly, with these four variables treated as separate parameters. Furthermore, Eq. 2.6 is not exact. As described in the Appendix section 2.7, one can always treat θ + 2 = θ 2, even when not physically true, and the fitting algorithm will return the proper current measurement. The other assumption in Eq. 2.6, that ˆB + 2 = ˆB 2, must be assumed true during the application of the presented technique. The validity of this assumption is discussed further in section 2.5.

42 Chapter 2. Predicting RF heating During In-Vitro MRI Induced Current Characterization Algorithm With a conductive structure in place in the MR bore, this technique requires one low-flip angle gradient echo scan to provide a quantitative measure of induced current in the conductor at the location of the image. All post-processing of images was done in MATLAB (MathWorks, Natick, MA). The first step in processing the acquired, low-sar image involves manually inspecting the magnitude image for the location of highest signal, which was assumed to approximately represent the wire location. Various offsets were then applied to the phase image until again, upon manual inspection, the characteristic line of phase wrap (line dividing largely positive and largely negative phase values) seen in RF induced artifacts had been shifted to the location of highest SNR. Incorrect fitting in the vicinity of this line of phase wrap will produce relatively very large residuals, meaning that the fit will be most accurate in this region. Therefore, it was shifted to the region of the image with highest SNR. A circular mask was then chosen, centered on the wire location, that encapsulated the full RF induced artifact. As discussed above, the shape of the phase image comes from the ˆB+ tot ˆB tot in Eq. 2.10, and the background offset in the image from A + I trans. A two-dimensional quadratic function was fit to the background region outside of the artifact mask, using MATLAB s fminsearch function. The resultant quadratic function was assumed to represent A + I trans and other sources of unwanted background phase artifacts, such as gradient nonlinearities near the bore wall or gradient field mistiming. A function makeartifact was written to calculate the ˆB+ tot ˆB tot using Eqs. 2.4 and 2.5, and 2.6, and built-in MATLAB functions for complex arithmetic, given a set of eight parameters: B 1 +, B 1, I ind, θ 1 +, θ 1, θ 2, x W, y W. (x W, y W ) represents the coordinates of the conductor in the image, relative to the center, and θ 2 is the induced wire current phase term. A discussion is included in the Appendix section 2.7 justifying the combination of θ + 2 and θ 2 into one equal parameter, thereby reducing the number of fit parameters by 1. For magnitude fitting discussed later, makeartifact also output the magnitude of Eq A seven-element vector parameterized the output of makeartifact. Those elements represented all of the parameters mentioned above, except for ˆB + 1, which was calculated using the nominal prescribed flip angle and pulse duration. In the application of this method, it was assumed that ˆB + 1 and ˆB 1 are uniform across the artifact region and to maximize the validity of this assumption the MR body coil was used for Tx/Rx. The quadrature Tx/Rx used in this study invalidates some assumptions mentioned in the Theory section, and ˆB + 1, ˆB 1, θ+ 1 and θ 1 must be treated as distinct. The output of makeartifact was added to the background quadrature function, creating the theoretical image, which was fit to the acquired image using fminsearch to vary the aforementioned seven parameters. The sum

43 Chapter 2. Predicting RF heating During In-Vitro MRI 26 of squared residuals was evaluated over the artifact mask region and normalized to the size of the mask to enable comparison of fits with different resolution. Furthermore, using analyses presented by Conturo and Smith, and Henkelman, the average phase noise was evaluated on a pixel-by-pixel basis across each image using signal magnitude as a surrogate marker for SNR [45 47]. Phase residuals were then weighted inversely to the phase noise to emphasize fit accuracy in high phase-snr regions. The fit-stop criterion was a 1 ma tolerance on the calculated I ind value, the values of the other six parameters were not used Algorithm for Predicting High-SAR Heating from Low-SAR Current Characterization Each set of characterization scans provided seven current values along the conductor for each configuration. It has been shown that in similar experimental configurations, with fully insulated and immersed wires, induced RF current on linear conductors exhibits a half-wavelength sinusoidal distribution [48]. Therefore, a half-wavelength sinusoidal distribution was fit to the measured current values to provide a high resolution induced current distribution for SAR calculation. To account for the uninsulated tips in all experiments and the partial immersion in experiments 3 and 4, the sinusoidal function had a variable wavelength, center point and vertical offset. Therefore, the resulting sinusoidal fits were not necessarily symmetric about the center of the immersed length of conductor and also not constrained to be zero at the conductor tips. If the sinusoidal fit to current produced a non-zero value at the conductor tip, this amount of current was assumed to leak isotropically from the tip and the resultant SAR distribution was calculated using a method described by Venook et al. [20]. This sinusoidal fit was then used as input current to Eqs and 2.12 to calculate the scattered electric field on a 40 x 40 x 40 grid centered on the conductor tip. The resolution of this grid was chosen to be much coarser than the resolution of current samples, and the grid was positioned to ensure that the scattered field would not be calculated at any points in or on the conductor. This scattered field was then plugged into Eq to calculate a scattered SAR distribution. The scattered SAR and the SAR due to current leakage were added, to give the total SAR present during the low-sar characterization scan. Finally, the relative power of the heating and characterization scans was calculated, and used to scale up the low-sar distribution, before using it as the input into Yeung s implementation of Eq. 2.14, described below. To ensure accurate calculations, the sinusoidal distribution was sampled at increasing resolutions, until doubling the number of current samples caused no visible change in the calculated SAR distribution.

44 Chapter 2. Predicting RF heating During In-Vitro MRI 27 To calculate the temperature evolution given a certain power density, the Green s function of the bioheat equation was applied similarly to its application in [49]. However, instead of calculating the one dimensional radial temperature distribution as in Yeung s study, a three-dimensional convolution was performed in this study, providing a result in Cartesian coordinates. The convolution was performed in the Fourier domain, by multiplying the transformed power density and Green s function before applying the inverse Fourier transform to the product. The field of view of the power density was set to double that of the Green s function to allow for stability. To produce the time evolution shown in this study, it was necessary to perform one convolution for each time-point, but in practice the steady-state temperature distribution can be calculated almost instantly with a single convolution Simulation Electrical properties of the PAA gel measured using a technique first proposed by El-Sharkawy et al were used in numerical simulations of the experiment [50]. Simulations were carried out using the method of moments (MoM) implemented in FEKO (Altair, MI, USA) [51] as well as the finite-difference timedomain (FDTD) method implemented in SemcadX (SPEAG, Switzerland) [52]. For both simulations, the scanner body coil was modeled as a 16-rung birdcage coil, of length 105 cm and 35 cm radius. A cylindrical shield of radius cm and length 120 cm outside the rungs was also modeled. Appropriate capacitors were placed on the end ring between the rungs to tune the coil to 64 MHz. Two voltage sources were placed 90 apart, and driven in quadrature. The magnitude of voltage in each source was equal, and determined by normalizing the simulated LH magnetic field to the nominal flip angle. The wire was modeled as copper (σ = 51.83) MS/m with a 12.7 µm polyurethane coating along the curved surface of the wire and bare contact with the PAA gel at the tips. The dielectric constant was set to 3.6 for polyurethane and 92 for PAA gel, which had a conductivity of 0.52 S/m. In the MoM simulations, the geometry was meshed using triangles and tetrahedra with sides at most λ PAA /10 in length. This led to wire segments and 1860 triangles used to model the surface of the PAA phantom, requiring between 1 and 3.5 GB of total memory and requiring 5 minutes to run. The commercial MoM package FEKO does not provide a thermal solver thus FEKO results are compared with experimental results using induced RF current distribution in lieu of predicted temperature rise. The resolution of the SemcadX (v ) EM field simulation was 83, 82, and 34 voxel/mm in x, y, and z coordinates, respectively. The electromagnetic field calculated in this simulation was used as the input for the thermal simulation, also implemented in SemcadX. A total of 242 W input power was applied to obtain the desired transmit magnetic field and a discrete vasculature thermal model

45 Chapter 2. Predicting RF heating During In-Vitro MRI 28 with no-perfusion was used to obtain thermal plots for comparison with the measured and predicted temperature rises [53]. The SemcadX simulation took more than 72 hours to run on a desktop computer with quad-core CPU and 8GB RAM and no GPU acceleration, and thus was only performed for one configuration Proof of Concept with FEKO The validity of the technique presented in this manuscript relies on two major cornerstones: First, that under certain assumptions a phase image acquired with low flip-angle can accurately quantify the induced RF current during transmit, which can then be extrapolated to other sequences simply by scaling. And, second, that given an induced RF current distribution, heating behaviour in the vicinity of the conductor can be accurately predicted. This study was carried out using quadrature Tx/Rx, therefore, assumptions mentioned in the Theory section 2.2, which hold true for linear Tx/Rx, require some modification. The assumption that ˆB + 2 ˆB 2, i.e., Î+ ind Î ind, however, is necessary and must be justified for quadrature Tx/Rx. To validate this assumption, two FEKO simulations were carried out, simulating the conceptual experiments of applying unit current in the forward and reverse polarization modes. The two ports on the body coil were both driven with unit current, and the phase of the quadrature port was set to +90 degrees in the forward polarization case and -90 degrees in the reverse case. The induced RF current in both forward and reverse polarization modes was then compared. Furthermore, a simulated phase image was formed using the FEKO calculated transmit and receive sensitivities, taken as the LH and RH components of the magnetic field in the forward and reverse modes, respectively. The image was simulated using a previously written MATLAB function, written to mimic the process of encoding and signal reception, calculating simulated raw data given a certain transmit and receive sensitivity. The current characterization algorithm was then applied to the simulated FEKO image, to ensure that with quadrature Tx/Rx induced RF current can still accurately be quantified. Finally, using the extracted Î+ ind from the forward mode proof of concept simulation, the scattered SAR distribution was calculated in the vicinity of the conductor tip using the algorithm described above. This scattered SAR calculated using Eqs was then compared with the total (incident plus scattered) SAR distribution, calculated in FEKO, on the same grid in the vicinity of the wire tip.

46 Chapter 2. Predicting RF heating During In-Vitro MRI Experimental Setup and Scanning In all experiments, a rectangular phantom filled with Poly-Acrylic Acid (PAA) gel was used to mimic an adult torso (figure 2.1). The wire was placed in the blood-mimicking PAA according to ASTM standard F a [30]. An adult torso was approximated by a plastic 65 x 42 x 9 cm rectangular prism filled with PAA gel prepared to match the average properties of the human body at 64 MHz, as defined by the ASTM standard. The standard calls for σ = 0.47 S/m±10% and = 80 ± 20, following preparation of the gel, the measured gel properties, σ = 0.52 S/m and = 92 were deemed acceptable according to the standard. This phantom was placed in the left-right center of the table of a 1.5T GE Optima 450 W system (GE Healthcare, Milwaukee, WI) with the bottom surface 12 cm below the isocenter and the landmark in the longitudinal middle of the phantom. Experiments were performed using two different wire types; one AWG24 ( = mm) and one AWG26 ( = mm) copper magnet wire (Belden, USA). All wires had insulation along the entire length, and were clipped and uninsulated on the surface of each end. In all experiments, temperature was measured and recorded throughout all characterization and heating scans using a fiber-optic (FO) probe (±0.1 C) (OpSens, Quebec, Canada). A custom holder seen in figure 2.2 was used to fix the FO sensor approximately 1.8 mm adjacent to the tip of the wire. For all studies, the body coil was used for transmission and reception of the MR signal. Figure 2.1: Schematic diagrams of the experiments performed. The wire in each experiment is represented by an orange line and the PAA phantom by a blue rectangle. The position of the phantom relative to the MR bore was constant in all experiments. Schematic diagrams of all experiments are shown in figure 2.1. In the first experiment, AWG26 copper magnet wire of length 25 cm ( λ/2) was fully immersed and placed 11 cm to the left and 7.5 cm below the isocenter, while centered lengthwise in the phantom. The wire used had an insulating coating

47 Chapter 2. Predicting RF heating During In-Vitro MRI 30 Figure 2.2: Holder (white) used to fix the FO temperature sensor (beige and dark orange) relative to the wire (red) during heating experiments. at least 12.7 µm thick along the entire length and was uninsulated at the tips where the wire had been cut. The second experiment differed from the first only in that AWG24 was used. The third and fourth experiments involved partially immersed lengths of wire, mimicking a percutaneous intervention. In these experiments, 1.2 m of AWG24 and AWG26 wire were used, respectively. The wires were positioned such that the immersed length of wire was in the same position as the length of wire investigated in the first two experiments, with the rest of the wire lying in air along the table. The fifth experiment involved a 25 cm length of AWG24 wire, positioned only 2 cm from the phantom wall simulating a worst-case situation, i.e., the most significant artifacts due to gradient imperfections. The wire was at the same height of 7.5 cm below the isocenter, and centered lengthwise in the phantom as before. The sixth and final experiment investigated a 25 cm length of AWG24 wire held at a fixed angle to the static field. The wire was fully in the plane 7.5 cm below the isocenter and the tips of the wire in this experiment were located at (x, y, z) = ( 14, 7.5, 12) and ( 8.25, 7.5, 12) with all numbers in centimeters and the isocenter at the origin. A low-sar, RF-spoiled gradient echo sequence (echo time/repetition time [TE/TR]=10/100) with a flip angle of 10 was used to image phase artifacts and characterize induced RF currents on the wire in all experiments. Images acquired had a resolution of 0.94 x 0.94 x 1.5 mm with a scan time of 55 seconds. In all experiments, seven images were acquired, each providing one RF current value; five images within the distal 5 cm of each wire, one at the center of each wire and one image 1 cm from the proximal tip.

48 Chapter 2. Predicting RF heating During In-Vitro MRI 31 Following each fit it was confirmed that the mean phase residual was no more than twice the inherent phase uncertainty caused by noise. The current characterization process was performed six times for each configuration to allow for repeatability and variability investigation. Using the six current values at each location on the wire, a standard deviation was calculated and used as inverse residual weighting during the upsampling fitting process, described below. Furthermore, it is this standard deviation that is shown as error bars on all current plots. Following acquisition of the low-sar, current characterization images, the transmit gain was adjusted to 80 and a fast-spin echo sequence (TR/TE=425/14 ms) with an echo train of 4, was applied for 16 minutes as suggested in the ASTM standard, to induce heating in each experiment Simulations Mimicking Experiment For comparison with experimental results, the transmit case was simulated in FEKO for each experiment, and the resultant I + ind extracted. The transmit power of each FEKO simulation was scaled such that the background transmit field in the absence of the wire matched the calculated nominal transmit field magnitude at the isocenter. FEKO was used to calculate the induced RF current in all six configurations; however due to the long time required for simulation, only the first experiment was simulated using SemcadX. 2.4 Results Proof of Concept with FEKO The induced RF current calculated by FEKO with unit currents in both forward ( Î+ ind ) and reverse ( Î ind ) modes is shown in figure 2.3. Good agreement between the two induced current profiles is evident. The simulated image using the Tx/Rx sensitivities calculated by FEKO is shown in figure 2.4(a), alongside the theoretical match as found by the characterization algorithm (b) and the absolute value of the corresponding residuals (c). The small residual values indicate that the theoretically matched artifact closely resembles the simulated image. The current value found by the characterization algorithm applied to the simulated FEKO image is shown as a black dot in figure 2.3. Most importantly, the measured current value accurately represents the induced RF current, indicating that reliable measurements can be made with quadrature Tx/Rx. The FEKO calculated total SAR is shown in figure 2.5(a) alongside the scattered SAR (b) calculated using Î+ ind and Eqs and the absolute value of the residuals (c). Again, small residuals indicate

49 Chapter 2. Predicting RF heating During In-Vitro MRI Induced RF Current (ma) FEKO forward case FEKO reverse case Calculated from simulated image Position (cm) Figure 2.3: Induced RF current as calculated by FEKO with unit current applied in the forward and reverse polarization modes. Also shown in black is the quantified current, found by applying the characterization algorithm to the simulated FEKO image. (a) (b) (c) Figure 2.4: Simulated FEKO phase image (a) and the corresponding fit image (b). The absolute value of residuals is shown in (c). Small residuals indicate a good match between the fit and the simulated image. that scattered SAR closely resembles total SAR when fields are not calculated on or in the conductive structure.

50 Chapter 2. Predicting RF heating During In-Vitro MRI 33 (a) (b) (c) Figure 2.5: Total SAR as calculated by FEKO in the forward mode unit current simulation (a) and scattered SAR as calculated with the presented algorithm applied to the FEKO calculated induced current (b). Absolute value of residuals is shown in (c) Experimental Results The purpose of the experimental method is two-fold; to characterize the distribution of induced RF current flowing in a conductor, and to use that current distribution to predict heating around that conductor. The intermediate results of low-sar current characterization as well as FEKO simulation are shown in figure 2.6. Good agreement is seen between the experimentally characterized and simulated current distributions. The predicted and measured temperature rises for all experiments are shown in figure 2.7. The results of experiment 1, as simulated with SemcadX, are shown as a green line in figure 2.7(a). Simulation results, remotely predicted RF heating, and measured RF heating agreed well in all experiments. 2.5 Discussion It can be seen in all plots that the predicted temperature rise, calculated using data from prior, low-sar, current characterization scans combined with theory described earlier, agrees well with the measured temperature rise. No measurable temperature rise was seen during any current characterization scans. Furthermore, current distributions calculated using FEKO and temperature rises calculated with SEM- CAD agreed well with measured values. The fast spin echo scan used for heating had a SAR approximately 560 times that of the spoiled gradient echo scan used for characterizing current. Temperature rise is proportional to local SAR, therefore, one would not expect measurable temperature rises during application of the low-sar characterization sequence, unless rises on the order of hundreds of degrees were detected during the heating scan. Thus, it has been demonstrated that safe current characterization is possible in a configuration that produces a dangerous temperature rise under application of a higher-sar sequence.

51 Chapter 2. Predicting RF heating During In-Vitro MRI Upsampled characterization FEKO results Measured values Upsampled characterization FEKO results Measured values current (ma) current (ma) position (m) position (m) (a) experiment 1 (b) experiment Upsampled characterization FEKO results Measured values Upsampled characterization FEKO results Measured values current (ma) current (ma) position (m) position (m) (c) experiment 3 (d) experiment Upsampled characterization FEKO results Measured values Upsampled characterization FEKO results Measured values current (ma) current (ma) position (m) position (m) (e) experiment 5 (f) experiment 6 Figure 2.6: Characterized current distributions along the wire length. In all experiments, current was measured in seven locations, as indicated on the plots. The error bars on the plot represent the standard deviation of the current values measured in the six repeats of each experiment. During the process of upsampling and fitting a sinusoidal distribution to the measured current values, the standard deviations were used as inverse residual weighting.

52 Chapter 2. Predicting RF heating During In-Vitro MRI ΔT ( C) Δ T ( C) 4 4 ΔT ( C) AWG26 Predicted AWG26 Measured AWG24 Predicted AWG24 Measured 1 1 SemcadX Measured 0.2 Predicted Time (min) Time (min) Time (min) (a) experiment 1 (b) experiment ΔT ( C) 0.5 ΔT ( C) Predicted 0.1 Measured Measured Time (min) Predicted Time (min) 4 (c) experiment 3 (d) experiment ΔT ( C) 2 ΔT ( C) Measured Predicted 0.2 Predicted Measured Time (min) (e) experiment Time (min) (f) experiment 6 Figure 2.7: Measured and predicted temperature rises as seen near the tips of the wires in all experiments. Shown in blue is the recorded output of the FO temperature sensor. In red is the predicted heating behavior generated using the measured current values. The green line in A represents the temperature rise as calculated by SemcadX. Uncertainty in the predicted temperature rise is visualized by showing the highest and lowest predicted heating curves. This uncertainty is inherent to the holder that was used to fix the temperature sensor, and represents ±0.25 mm in the position of the FO sensor Quadrature Versus Linear Tx/Rx One assumption, namely that ˆB + 2 = ˆB2, is true in the case of linear Tx/Rx but not necessarily true with quadrature Tx/Rx. The proof of concept simulation in FEKO showed that the induced currents in forward and reverse modes were approximately similar, thus the above assumption held true in the specific configuration used in this study. The validity of this assumption with quadrature Tx/Rx in

53 Chapter 2. Predicting RF heating During In-Vitro MRI 36 general, however, has been previously investigated [27]. This study derived an expression for the ratio between the longitudinal forward mode electric field and the longitudinal reverse mode electric field. It is these longitudinal electric fields that induce RF currents on conductive structures. It was shown that in general, highly symmetric loads can be assumed to produce approximately equal longitudinal electric fields, and thus induced RF currents, in forward and reverse mode. For some highly symmetric or off-center loads, linear Tx/ Rx may be required in the application of this technique, to ensure the above assumption holds Deriving SAR from Induced RF Current Eqs and 2.12 describe the scattered electric field created by the induced RF current alone, which was used along with leakage current to predict heating in this study. In practice, however, the total electric field surrounding the conductor is the result of 2.12 added to the incident electric field that would be present if the conductor were not in the bore. In general, if the introduction of a conductor into an otherwise safe configuration induces significant heating, it can be said that the magnitude of the scattered field is much larger than the incident field and the scattered field will approximate the total field well. Significant differences between scattered and total fields could occur on the surface of the conductor, where the total tangential electric field is ideally nulled. Scattered field calculations were only carried out in bulk tissue surrounding the conductor to avoid this complication, and the incident electric field was ignored in all calculations. Figure 2.5 shows good agreement between the scattered SAR as calculated using Eq and the total SAR as calculated by FEKO in the forward mode proof of concept simulation, justifying the use of scattered field in place of total field when calculating SAR. The sinusoidal distribution used to model induced RF current was derived by Acikel et al for fully insulated, fully immersed conductors. The model was adapted for uninsulated tips and partially immersed conductors by allowing for fitting a sinusoid with a vertical offset and arbitrary center point. Accurate results were obtained with this adjusted model; however its validity has otherwise not been theoretically justified. Figure 2.8(a) shows the same SAR distribution as figure 2.5(b), calculated using the full induced RF current distribution. Figure 2.8(b), shows the SAR distribution on the same grid, calculated using only induced currents in the distal 2.5 cm of the conductor, current was assumed to be zero elsewhere in the conductor. It can be seen that the two SAR distributions match almost exactly, indicating that current near the tip is solely responsible for heating. Thus, accurate characterization of the distribution along the entire length of the conductor is not necessary. The modified sinusoidal distribution was used in this study but given figure 2.8, a less complicated linear fit of the tip region

54 Chapter 2. Predicting RF heating During In-Vitro MRI 37 would have sufficed and may be used in the future. (a) (b) (c) x Figure 2.8: Scattered SAR as calculated using currents along the entire length of conductor (a) and currents only in the distal 2.5 cm of conductor (b). Absolute value of residuals is shown in (c). Small residual values indicate that current in the distal end of the conductor is primarily responsible for heating, thus current in the proximal portion of the conductor can be ignored Sources of Unwanted Phase Artifacts Several sources of unwanted phase artifacts exist which could reduce the accuracy of current characterization performed with this technique. Namely; gradient nonlinearities and mistiming, local magnetic susceptibility variations and chemical shift, and blood flow can all give rise to unwanted artifacts in phase-contrast images. In experiment 5, significant gradient nonlinearities were present in the region of the wire. These were accounted for using the background phase fit described earlier in this manuscript. An example of a measured image and the corresponding fit acquired during experiment 5 is shown in figure The other three aforementioned sources of phase error can be minimized through intelligent design of the low-sar pulse sequence used to characterize current [54]. With an SNR of 8, as used in all low-sar current characterization scans in this study, the mean phase error is approximately 0.14 radians. With a center-out, radial, or spiral acquisition and a realistic TE of 100 µs, typical artifacts induced by chemical shift and susceptibility can be reduced below the noise level in the phase-contrast images, allowing for accurate fits of RF induced phase artifacts Comparison to Similar Techniques and Alternatives The present gold-standard technique for assessing RF safety is a direct temperature measurement performed with a FO temperature sensor. This measurement is very accurate and precise but typically very difficult to reproduce. Furthermore, the measurements are inflexible as temperature can be measured at only one or a few locations. Most importantly, a dangerous situation can only be detected in this way

55 Chapter 2. Predicting RF heating During In-Vitro MRI 38 Figure 2.9: Acquired phase image and corresponding fit, demonstrating significant gradient artifacts due to nonlinearities. Both images are displayed with a dynamic range of π to π. The full 24-cm field of view is shown. by inducing a temperature rise. As shown here, knowledge of the induced current distribution can be used to predict dangerous situations using safely acquired data. Thus the presented technique could be used to safely assess the heating potential of a given device with the patient inside the MR bore, which cannot be done with a direct temperature measurement. Two previous works have addressed quantifying induced RF current using image artifacts, both of which analyzed magnitude artifacts [20, 28]. It is the belief of the author that the presented phasebased approach can be more robust, and applied more quickly. As with previous works, the presented technique assumes that ˆB + 1 and ˆB 1 are uniform across the artifact region. To maximize the validity of this assumption, it is important to use the MR body coil for Tx/Rx. First, as demonstrated by Conturo and Smith in 1990, phase images inherently have 2π times the dynamic range of magnitude images reconstructed from the same data, suggesting that phase images inherently have a higher quality and should allow more accurate interpretation of artifacts [45]. Furthermore, the information content stored in phase data is richer due to the typically more homogeneous distribution of phase data within the available dynamic range. Also demonstrated in this work is the fact that correlated noise degrades magnitude information while leaving phase information unaffected. Thus phase images can have higher SNR than the corresponding magnitude image. Second, a characteristic feature of all RF current induced phase artifacts is a line of phase wrap. Phase unwrapping was considered but in fact this sharp edge in the phase image promotes accurate fitting, as the residuals from this region will be very high compared with smoothly varying regions of the image. Furthermore, it was observed that the location of this line of phase wrap can be varied among infinite paths, simply by applying a constant phase offset to the entire image. As described, this fact was exploited during all fitting steps to shift the line of wrap to highest SNR location. Note this offset does not affect the current characterization, as it is absorbed in the background fitting process. In

56 Chapter 2. Predicting RF heating During In-Vitro MRI 39 practical applications, this line of wrap could also be shifted according to radiologist interpretation of image quality. No analogous technique can be applied to relocate the magnitude artifact in the image. Third, in low-snr situations, it is believed that phase fitting can provide more accurate current characterization than magnitude fitting. To demonstrate this, the current characterization algorithm was performed on both magnitude and phase images and acquired current values and fit images were compared. In all fitting attempts, the same initial guess was used for all parameters when fitting to both phase and magnitude images. Figure 2.10 shows one example of acquired and fitted phase and magnitude images; evidently the magnitude fit did not provide an accurate current value. Finally, unwanted in-vivo phase artifacts would be dealt with using some of the fastest possible scans, promoting rapid application of this technique. To eliminate unwanted in-vivo magnitude variations long scans would be used to allow for full relaxation of all spins, and even then, proton density weighting cannot be removed from an image Uncertain/Variable Tissue Properties and Perfusion As with any attempt to model heating in the body, accurate heating predictions using this technique rely on accurate knowledge of the surrounding tissue thermal and electrical properties. Reasonable estimates of the properties can be obtained, but uncertainty will always exists in in-vivo situations. If a practical situation arises in which tissue properties are in question, a theoretical sensitivity analysis would be required. In other words, two analyses could be carried out, one assuming the maximum possible value for the property and the other assuming the minimum. The results of these analyses would indicate the potential uncertainty in final calculated temperature as a result of uncertain tissue properties, which could be judged for safety by the physician. Furthermore, no perfusion was included in this study. In practical in vivo situations, however, perfusion will always serve to reduce heating. Therefore, ignoring perfusion will always produce liberal heating prediction, and potentially overly safe scanning. If required, perfusion can be estimated with various imaging methods and accounted for during heating prediction [55] Effect of Complex Electrical Components and Electrode Geometries When applying this technique to realistic conductive devices in patients, the electrical properties of a conductor may not be uniform along its length. In this case care must be taken to ensure accurate characterization of the induced current distribution. In the vicinity of any electrical components, more closely spaced images would be necessary to capture all important features in the current distribution.

57 Chapter 2. Predicting RF heating During In-Vitro MRI 40 Figure 2.10: Results of fits performed using phase and magnitude information. The top row shows the phase and magnitude images as acquired and reconstructed by the scanner. The middle-left image shows the theoretical phase image that was determined to minimize the magnitude of the RMS difference between the acquired and theoretical phase images. The bottom-right image shows the theoretical magnitude data that was determined to minimize the magnitude of the RMS difference between the acquired and theoretical magnitude images. As can be seen, the theoretical images generated with a phase fit match well with the acquired images while the magnitude fit does not. In general, with closely spaced and intelligently located characterization slices it will be possible to accurately characterize a current distribution on a conductor with electrical components. For extremely complex devices, however, before use in a patient, one or more phantom experiments with FO sensors may be necessary to ensure accurate heating prediction can be achieved. If this method were unable to predict the heating behavior, the cause of the error could likely be investigated and the current characterization method calibrated to account for the electrical complexity.

58 Chapter 2. Predicting RF heating During In-Vitro MRI 41 Direct current measurements have not been performed to confirm the remotely acquired current characterization obtained using low-sar phase images. It is the view of the author, however, that sufficient experimental validation of this technique has been presented in the form of validation with simulation and a comparison of measured temperature rise to temperature rise predicted using only current values obtained from the low-sar image-based characterization. 2.6 Conclusions A novel method for remotely characterizing induced RF current on conductive structures in MRI, using low-sar characterization images, has been presented. No temperature rise was induced during any current characterization scan. However, these scans accurately predicted a dangerous temperature rise induced by a high-sar sequence subsequently applied. This indicates that RF heating can safely be assessed in phantom experiments by the low-sar, remote current characterization technique described in this manuscript. 2.7 Appendix Artifact from a Curved Wire The magnetic field generated by an infinitely long line of current is given in Eq In the case of a current line of finite extent, equation is modified to give the following expression: B 2 (z, s) = µi ind(z) 4πs (cos α 1 + cos α 2 ) φ. (2.15) α 1,2 are the angles formed between the line of current and a line connecting the ends of the current to the calculation point. To justify use of the simplified Eq. 2.1, one can define a tolerance to be treated as an acceptable discrepancy between Eqs. 2.1 and For example, assume that a maximum of 5% deviation between the two equations is acceptable for a calculation being performed adjacent to the center of the current line (α 1 = α 2 ). In this case, the following condition must hold: cos α 1, (2.16) Taking the inverse tangent of α 1,2 gives twice the ratio between the maximum allowable perpendicular distance to the line of current and the length of the line. With a 5% tolerance, this ratio is approximately

59 Chapter 2. Predicting RF heating During In-Vitro MRI Thus to produce an accurate current measurement, a region with diameter no more than one third of the straight segment length can be used for fitting Arbitrary Wire and Image Orientation In general, the conductive structure being used in a procedure will not be parallel to the static magnetic field and/or perpendicular to the image plane. Both situations are easily treatable with some simple algebraic substitution. At the point of the image plane, let ϑ be the angle formed between the wire and static field and ζ the angle between the image plane and wire. To account for this, one must multiply sin ζ onto the s term in Eq. 2.1 and cos ϑ onto each ˆB 2φ term in Eq Assuming θ 2 + (z) = θ2 (z) In general, θ 2 + (z) = θ 2 (z) + δ(z). For a given current measurement, longitudinal position is fixed, thus z = z image and θ 2 + (z image) = θ2 (z image) + δ(z image ). Due to the additive nature of Eq. 2.10, a constant phase offset can be used to facilitate fitting as described in the manuscript. Adding an offset to the entire image results in an erroneous measure of A + I trans but will not affect the validity of the induced current measurement. Again due to the additive nature of Eq adding a phase offset in postprocessing is equivalent to applying the same offset to either the positively or negatively rotating frame. For example in the positively rotating frame: ξ + δ(z image ) = A + I trans + ˆB+ tot ˆB tot δ(z image ) ( ) ξ + δ(z image ) = A + I trans + ˆB+ tot δ(z image ) ˆB tot (2.17) ( ξ + δ(z image ) = A I trans (ˆB+ tot e jδ(zimage)) ) ) (ˆB tot. With the transform ˆB + tot ˆB + tote jδ(zimage) applied, it becomes clear that the investigator can choose to treat θ + 2 and θ 1 as equal without sacrificing induced current measurement accuracy as this is equivalent to adding an offset to the acquired image. ˆB + tote jδ(zimage) = ˆB + 1 exp [ j ( θ + 1 δ(z image) )] + j 2 ˆB + 2φ exp [ j ( θ φ δ(z image) )] (2.18) ˆB + tote jδ(zimage) = ˆB + 1 exp [ j ( θ + 1 δ(z image) )] + j 2 ˆB + 2φ exp [ j ( θ 2 + φ)]. (2.19) When this is done, two fit parameters; θ + 2 and θ 2 are combined. Two other fit parameters; A + I trans and θ + 1 are simply redefined A I trans δ(z image ), θ + 1 δ(z image). This results in one less fit

60 Chapter 2. Predicting RF heating During In-Vitro MRI 43 parameter required to accurately measure the induced current Îind.

61 Chapter 3 In-Vivo Considerations for Predicting RF Heating Introduction & Motivation During percutaneous cardiovascular interventions and some diagnostic imaging of patients with active implanted medical devices, there are situations in which patients with a long conductive structure inside them would benefit from MR scans. To ensure patient safety in such scenarios, it is necessary to characterize the RF heating potential of the conductive device before executing the exam. Using direct temperature measurements is not practical for in-vivo applications, as a potentially dangerous temperature rise must be induced in the process. Dangerous RF interactions leading to heating are a direct result of current flowing in the wire, due to coupling between the wire and the incident electric field produced by the scanner. Thus one potential strategy for safely characterizing RF heating potential in vivo is to use a relatively low-sar sequence to quantify the induced current distribution on a wire and relate this to radiated power and subsequently heat from the wire. Recently, several efforts to use the RF current induced magnitude artifact for characterization of current levels have been reported [20, 28]. This approach can yield accurate quantification of induced RF current; however, its robustness depends on multiple images with relatively high SNR, as well as the absence of magnitude artifacts that cannot be eliminated through sequence customization. The only 1 This chapter is modified from the article: Towards in-vivo quantification of induced RF currents on long thin conductors. Gregory H. Griffin, Venkat Ramanan and Graham A. Wright. Submitted for review to Magnetic Resonance in Medicine. 44

62 Chapter 3. In-Vivo Considerations for Predicting RF Heating 45 sufficiently robust approach necessitates a dedicated receive/transmit toroid coil, essentially allowing for the field from the guidewire to be isolated [56]. This dedicated coil approach requires running the exposed portion of the guidewire through the coil lumen, and therefore cannot be applied to fully immersed conductors, such as leads of an active implantable medical device. A potentially more robust approach was demonstrated in vitro in Chapter 2. Fits to the phase artifact in images acquired perpendicular to the wire can provide sufficiently accurate current values for RF safety characterization. This phase-based technique does not depend on the magnitude sensitivity of the transmit and/or receive coil. It does however require that phase variation around the wire in the image occurs primarily due to induced RF current. It was shown in Chapter 2 that phase variation due to non-linearities in the gradient fields could be accounted for through fitting a smoothly varying second order function to the background phase distribution. However, several other sources of unwanted phase contrast exist in vivo. Effects such as chemical shift, susceptibility artifacts, and blood flow can induce phase errors that could degrade the accuracy of a phase-based remote current characterization technique. The significant sources of unwanted phase in vivo are associated with phase accrual after excitation, due to off-resonance effects. Thus phase error can be minimized by employing a short echo time and fast readout acquisition [54]. The phase artifact due to induced RF current is effectively encoded in the transmit and receive sensitivities and as such does not depend on acquisition timing. The purpose of this study is to present results of applying the previously described phase-based current characterization algorithm in vivo, using a custom UTE spiral trajectory sequence. The minimized echo time, and associated fast readout of the sequence allows for minimization of phase artifacts and accurate fitting of theoretical phase distributions to images acquired in vivo. As there is no gold-standard for measuring induced RF current in vivo, fibre-optic temperature measurements near the tip of a guidewire are used for validation of the current results. Results of current and temperature measurements in a phantom experiment are presented to demonstrate equivalence between current characterization with a stock GRE sequence and the custom UTE sequence. Results of current characterization and temperature measurements performed in three animal experiments are also reported. To eliminate the effect of perfusion and blood flow on RF heating, temperature measurements post sacrifice are compared to heating predicted using current characterization performed in vivo and in situ.

63 Chapter 3. In-Vivo Considerations for Predicting RF Heating Theory RF Induced Current It was shown in Chapter 2 that, to adequately model induced RF heating around the tip of the wire, it is only necessary to account for the induced current distribution within approximately 2.5 cm of the wire tip. The electrical environment (characteristic impedance) and the incident electric field responsible for the RF current on the wire do not change significantly over this distance; therefore the induced current will follow a smoothly varying distribution. Furthermore, since the induced RF current will tend to zero at an insulated wire tip, the induced RF current can be adequately modelled by a sinusoidal distribution [48, 57]. The following equation can be used to model current distribution in the distal 5 cm of a wire, with x representing the position of the sample relative to the tip of the wire and a, b, c, and d representing fit parameters. ( I fine = a sin π x b ) + d (3.1) c Artifact and In-Vivo Effects Assuming a small flip angle is applied, the principle of reciprocity states that the received MR signal from a point in space (x, y) due to an initial homogeneous longitudinal magnetization M 0 is given by [43]: ξ(x, y) = 2jωγτM 0 I trans ˆB + tot(x, y) ( ˆB tot (x, y)), (3.2) where ω, γ, and τ represent the frequency of the signal, the gyromagnetic ratio of the medium, and the duration of application of the RF excitation respectively. I trans represents the complex RF current applied to the transmit coil, and ˆB tot + and ˆB tot are the transmit and receive sensitivity respectively. Eq. 3.2 defines the spatial distribution of received MR signal, and the spatial distribution of the phase of that signal can be written as: ξ(x, y) = A + I trans + ˆB+ tot (x, y) + ˆB tot (x, y). (3.3) The term A represents the phase of a complex scaling coefficient that is related to the initial longitudinal magnetization and duration of the excitation pulse. The above Eqs. 3.2 and 3.3 represent the spatial distribution of phase at time t = 0 after the application of RF excitation. In general, the

64 Chapter 3. In-Vivo Considerations for Predicting RF Heating 47 received signal s r acquired at a time t 0 is given by [58]: s r (t) = ξ(x, y)e iφ(x,y,t) dxdy, (3.4) x y where φ is the signal phase at a given spatial location and time, and φ(x, y, 0) = 0. Ideally, this phase can be written as: φ ideal (x, y, t) = t ω(x, y, τ)dτ = ω 0 t + γ t o 0 G(τ) rdτ (3.5) where ω 0 represents the resonant (Larmor) frequency. G(τ) is the applied gradient field and r is a vector representing spatial position. During acquisition, the received signal s r (t) is demodulated at the resonant frequency and when applied to data in the form of Eqs. 3.4 and 3.5, the commonly used Fourier reconstruction reproduces ξ(x, y) exactly, ignoring relaxation which affects only signal magnitude and not phase. In general, there are several sources of discrepancy between the aforementioned ideal phase distribution and the true phase of the signal measured during imaging. The two majour in-vivo specific effects leading to phase errors can be categorized as: sources of off-resonant signal, and blood flow or motion in general. Off-Resonance Sources Three main sources of off-resonant signal exist in general during in vivo imaging. Chemical shift is characterized as a slight shift in the static field experienced by the nucleus being imaged (typically protons), arising from magnetic shielding caused by electrons immediately surrounding the nucleus (proton). The amount of shielding and thus the shift in the magnetic field experienced by the proton is dependent on the associated molecule. The equation typically used to describe chemical shift is: B sh = B 0 (1 σ) where σ is a dimensionless constant unique to each molecule. This effective static field B sh gives rise to a lower resonant frequency ω cs = γb sh = ω 0 γb 0 σ. Independent of chemical shift, the static field is practically not perfectly uniform due to the finite extent of the coil used to generate B 0, and other factors. Static field coils are typically shimmed during installation to produce a static field with homogeneity on the order of one to several parts per million [59]. In a 3T field this corresponds to a static field error of approximately 3 µt or a frequency offset of ±127.7 Hz, potentially leading to a phase error of 180 just 7.8 ms after the end of the excitation pulse. Furthermore, bulk magnetic susceptibility (χ) differences throughout the imaging sample can lead to static field variations. χ variations on the order of are not uncommon in-vivo. Depending on the geometry of the interface between two tissues of differing susceptibility, the resulting static field

65 Chapter 3. In-Vivo Considerations for Predicting RF Heating 48 variation can be on the order of a few ppm, similar to the aforementioned inherent inhomogeneity discussed earlier. Each of the above sources of off-resonant signal has an undesired and uncontrolled effect on signal phase. No matter the source of off-resonant signal, the effect of off-resonant signal on phase can be described as: φ(x, y, t) = φ ideal (x, y, t) + ω E (x, y)t, (3.6) where ω E represents the overall frequency error. Acquisition, or signal readout, typically occurs over a period of time centred on the signal echo and thus the spatial phase distribution during the time of signal acquisition is given by φ acq = φ(x, y, T E ± t readout /2) with t readout representing the duration of each readout period. By minimizing TE then, the undesired effects of off-resonance sources are reduced. Blood Flow The presence of blood flow in an image means that certain components of the MR signal appear at different positions in space throughout the image acquisition. There are several undesired results of blood flow on an MR image, some of which can have significant effects on phase. In general, phase effects due to moving blood can be understood by including a time dependent position in Eq. 3.5, i.e: φ blood = γ t 0 G(τ) r(τ)dτ, r(t) = r 0 + vt at (3.7) The Fourier reconstruction method assumes that the gradient-induced phase corresponds to only the first, time invariant term in Eq In the presence of blood flow, the higher order terms in Eq. 3.7 are in general non-zero and thus cause unexpected phase which can lead to reconstruction errors such as signal loss or blur and spatial offsets, which affect magnitude images, and produce phase variations, which could have a significant effect on the algorithm applied in this work. It is evident from Eq. 3.7 that in general as acquisition time increases, the effects of blood flow on phase also typically increase (depending of course on the specific gradient fields applied). By minimizing the acquisition time, i.e. using a UTE sequence, the undesired effects of blood flow are reduced Predicting Temperature Rise In order to use current measurements obtained with a specific sequence to model heating produced during application of another sequence, either the current values or the local power deposition must be scaled. Specifically, the local power deposition calculated using equations 2.12 and 2.13 can be linearly

66 Chapter 3. In-Vivo Considerations for Predicting RF Heating 49 scaled according to the relative SAR of the two sequences. The relative SAR of a given sequence can be found either by recording SAR values reported from the scanner, or alternatively by integrating the applied RF waveform. If the applied RF waveform ρ(t) is downloaded from the scanner, the scaled power deposition of the sequence can be calculated as: P avg = 1 T R T R 0 ρ 2 (τ)dτ. (3.8) P avg as calculated above is proportional to the SAR of the sequence, and TR is the repetition interval of the sequence. The ratio of P avg for the two sequences can be used as a scaling factor to use current characterization acquired with one sequence to predict heating produced by another sequence. 3.3 Methods The purpose of this investigation was to show that a previously described method of quantifying induced current using a safe low-sar imaging technique [60] could be extended to in vivo situations, specifically by using a spiral UTE sequence rather than a cartesian GRE sequence. As a first step, accuracy with the UTE method was checked. To this end images were acquired with both sequences in a phantom experiment and current characterization, as well as temperature prediction and measurement results were compared between sequences. As described above the main motivation for using a UTE sequence rather than a GRE was to reduce in vivo phase artifacts and accurately quantify induced currents in vivo. As in-vivo GRE images contain phase artifacts that preclude accurately fitting the RF current phase artifact, only UTE images were acquired in vivo and compared against temperature measurements. To eliminate the effect of blood flow and perfusion on temperature measurements, UTE images were acquired in vivo in a porcine model and following sacrifice of the animal, when the exact same set of images were acquired in situ and heating was measured. Results of predicted heating as calculated with in vivo and in situ images were compared with heating measured in situ Experimental Setup & Scanning Sequences All imaging was performed on a 3T MRI scanner (Discovery MR750, GE Healthcare, UK). A stock balanced GRE sequence was used as the gold-standard for acquisition of phase artifacts in vitro. All GRE images were acquired with the following parameters: TE/TR = 2.244/100 ms, FOV = 20 cm,

67 Chapter 3. In-Vivo Considerations for Predicting RF Heating x256 matrix size, slice thickness = 1 cm and number of averages (NEX) = 10. Additionally a custom UTE sequence was used to acquire phase artifacts for current characterization. The UTE sequence employed a spiral acquisition and resampling onto a Cartesian grid allowing for Fast Fourier Transform (FFT) reconstruction. All UTE images were acquired with the following parameters: TE/TR = 0.202/6.9 ms, FOV = 20 cm, slice thickness = 0.5 cm and NEX = 1. The NEX = 1 was necessary due to a programming limitation in the custom sequence; however four sets of identical UTE images were acquired for each configuration and the complex data was averaged in post-processing using MATLAB to simulate an increased NEX and produce elevated SNR. The FFT reconstruction resulted in a matrix size of 256x256 but since the k-space data was resampled from the spiral trajectory to Cartesian coordinates the true resolution cannot be taken as the quotient of the FOV and the matrix size. In this study, the true resolution of the UTE images was 2.16 mm. From these studies, expected currents and associated temperature increases were calculated based on relative RF power deposited. In order to maximize temperature rise and thus temperature SNR, a high-sar fast spin echo sequence was used as described in the ASTM standard on RF heating [30]. Specifically, the sequence used had the following parameters: TE/TR = 14/425 ms, echo train length = 4, FOV = 40 cm, matrix size = 256x256 and slice thickness = 1 cm. Resonant Length Determination Numerical modelling was performed using MATLAB to estimate the immersed length of wire that could be expected to produce the greatest temperature rise. A uniform incident electric field was used, and a modified transmission line model was used to calculate the expected induced current for various length of immersed guidewire, ranging from approximately 1-75 cm (0 3λ) [48]. The induced current was then used to calculate local power deposition and steady-state temperature as described in Chapter 2. The results of this modelling provided an estimate of the resonant length of guidewire, which was used as a starting point in choosing the lengths of wire that would be tested experimentally. Phantom Study In order to compare current characterization results obtained using the UTE sequence with results obtained using the previously described gradient-echo sequence, a phantom experiment was performed. The phantom used was constructed according to the ASTM standard [30]. The phantom was a rectangle constructed to have a 65x42x9 cm space, that was filled with PAA gel prepared according to the ASTM standard. A guidewire 150 cm in length and 0.89 mm in diameter, with a 3 cm flexible tip (Radifocus Glidewire, Terumo, Tokyo, Japan) was partially inserted into the phantom in the scanner, oriented

68 Chapter 3. In-Vivo Considerations for Predicting RF Heating 51 longitudinally to the scanner bore, such that approximately 15 cm of guidewire was immersed in PAA and the rest of the guidewire lay along the MR table extending out of the bore. The axial position of the guidewire was approximately (x, y) = (15, 2) cm relative to the isocenter and the landmark was set at the midpoint of the inserted portion of the guidewire. To enable measurement of the guidewire induced heating, a fibre-optic temperature sensor (OpSens, QC, Canada) was affixed to the tip of the guidewire using a UV curable epoxy (Dymax, CT, USA). The sensor was positioned parallel to the guidewire and the tips of the guidewire and temperature sensor were aligned longitudinally. Imaging was performed to characterize induced RF current using the UTE sequence described in this study as well as the stock GRE sequence. Axial images (perpendicular to the guidewire) were acquired along the entire inserted portion of the guidewire. No spacing was used between images, leading to current samples every 0.5 cm with the UTE images and every 1 cm with the GRE images. In-vivo Swine Experiments The results of three in-vivo swine experiments are reported in this chapter. The pigs were prepared using intramuscular ketamine injections for sedation, then they were intubated and isoflurane was administered to maintain anesthesia. In each in-vivo experiment, a shortened ( 4cm) sheath catheter was inserted into the left carotid artery of the pig, and the revascularization guidewire was advanced approximately cm beyond the distal end of the sheath catheter until the tip of the guidewire was located in the ascending aorta. X-ray fluoroscopy was used for guidance during placement of the guidewire, before relocating the animal from the X-ray suite to the MR table with the guidewire inside. All animals were positioned in a supine, feet first orientation in the scanner. Pads were used to position the pig as close to the wall of MR bore as possible to maximize the electric field at the guidewire and thus the associated induced RF current. The landmark for all imaging was set at the position of entry of the guidewire. The magnitude artifact (flip angle enhancement) present in GRE images was used to locate the wire in the MR bore, and enable approximate centring of the UTE images on the wire position. UTE images were acquired along the entire length of the inserted portion of the guidewire, providing quantitative current values every 0.5 cm along the length of the wire; however as described above only a subset of the acquired values were used in predicting heating. Following acquisition of UTE images along the catheter length, the animal was sacrificed using an intravenous injection of 240 mg ml pentobarbitol sodium (Dorminal, Rafter 8 Products, Calgary, Canada). To demonstrate equivalency between current values obtained with in-vivo and in-situ images, the UTE acquisition that was applied in vivo was repeated in situ. Following the in-situ UTE acquisition heating was measured using the fast spin echo sequence described above.

69 Chapter 3. In-Vivo Considerations for Predicting RF Heating 52 In experiment 1, UTE images were acquired in vivo and in situ for a single guidewire insertion depth ( 20cm) and heating was measured. In experiment 2, images were acquired in vivo and in situ with a single insertion of approximately 20 cm again, however due to equipment failure during the experiment, temperature data was not acquired. Finally in experiment 3, current and temperature data was acquired with the guidewire at two unique insertion depths of approximately 15 and 20 cm (insertion depth 1 and 2 respectively) Analytical Workflow For each unique image that was acquired with either sequence, a fit to the phase artifact in the region of the wire was performed to quantify the induced RF current flowing in the wire at the location of the image. The details of the algorithm that was applied to produce a quantitative current value are described in Chapter 2. One additional step was included in the algorithm during this investigation. Before executing the fit to the phase artifact the image was masked to exclude any regions of low signal. This was done by calculating the mean and standard deviation of the signal magnitude in an area of the image outside the animal (i.e. the mean and standard deviation of the background noise). Any pixel that had a signal magnitude within one standard deviation of the noise mean was excluded from fitting. This step was added to ensure that areas inside the animal that produced no signal such as the lungs or intubation tube were not included in the fit. Images were acquired either every 0.5 or 1 cm along the length of the guidewire and thus the fitting process produced a coarsely sampled current distribution for each experimental configuration. The following analysis was then applied to each coarsely sample distribution to produce a predicted temperature evolution in the vicinity of the wire tip. Resampling the Current Distribution The first step given a coarsely sampled current distribution was to resample the current distribution at a higher density. This is necessary for the subsequent step of calculating the local power deposition with high resolution. To perform the resampling, a half-wavelength sinusoidal distribution as described in Eq. 3.1 was fit to the coarsely sampled values. In the phantom experiments the location of the wire tip was known with high accuracy and thus the tip position of the wire was fixed during the fitting process (i.e. b in Eq. 3.1 was set to 0 and not allowed to vary during fitting). The following initial guesses were used during fitting to the in-vitro current distributions: the maximum current value produced from phase artifact fitting for a, the length

70 Chapter 3. In-Vivo Considerations for Predicting RF Heating 53 of inserted wire was used for c, and 0 was used for d. With the in-vivo and in-situ data sets, the guidewire position inside the bore was not known with the same level of precision and thus the location of the wire tip in the fit was allowed to vary during fitting. Because any error in the expected location of the wire tip would offset the relative location of all current measurements equally, one parameter b was sufficient to address this error. The same initial guesses for a, c, and d were used during fitting to the in-vivo and in-situ distributions, and an initial guess of 0 was used for b. The sinusoidal fitting was performed iteratively, with any anomalous current values omitted from the coarse distribution after each iteration. Anomalous current values were identified visually by plotting all measured values on the same axes as the sinusoidal fit. Since different sequences were used independently to quantify the same current distribution, it was necessary to scale the resultant current distributions by the applied RF field, B 1. To determine the applied field, the applied RF waveform was downloaded from the scanner and integrated. The magnitude of the incident magnetic field was then calculated as the ratio of the prescribed flip angle to the product of the integral and gyromagnetic ratio. In addition to the graphical comparisons of current values determined with UTE and GRE images and the corresponding sinusoidal fits, standard error metrics were evaluated for various pairs of data and are reported in Tables 3.1 and 3.2. The standard error metric used in this evaluation is defined as: S(Y, Y Σ (Y Y ) = ) 2, (3.9) N where N is the number of points included in the sum. Firstly, standard error was evaluated to compare a set of measurements to the fit distribution that was determined for those measurements (S(X M, X F )). Secondly standard error was evaluated to compare two sets of measurements that should ideally be equal (S(X M, Y M )) and finally standard error was evaluated to compare two fit distributions that were found for measurements that should ideally be equal (S(X F, Y F )). Calculation of Local Power Deposition As mentioned, in order to accurately predict heating near the tip of the wire knowledge of the current distribution on the wire is required only within 2.5 cm of the wire tip. For greater accuracy in this study, the distal 5 cm of the wire were considered. Thus, after fitting the distribution described above to the coarsely sampled current measurements, 200 samples spaced evenly within 5 cm of the distal wire tip were generated for use in calculating the local power density (SAR). The distal 5cm was treated as a

71 Chapter 3. In-Vivo Considerations for Predicting RF Heating 54 linear current source in three dimensions, and the resultant scattered electric field was calculated using the magnetic vector potential. For each set of measurements, the scattered field was calculated in a 2x2x2 cm cube centred on the tip of the wire, with a 1 mm isotropic resolution. This scattered electric field was converted to SAR using Eq Note that since the in-vivo/in-situ current characterization measurements produced an estimate of the tip location (b in Eq. 3.1), the power density calculations were each referenced to the tip position as determined by the sinusoidal fit results from the previous step. Furthermore, because the guidewire is fully insulated electrically, the leakage current from the tip of the guidewire was assumed to be zero and the SAR due to direct leakage current was not included in power deposition calculations. For the in vitro phantom study, the complex electrical permittivity of the PAA gel was measured using a previously described technique based on measurement of the impedance of a coaxial transmission line partially filled with the gel and the mass density of the PAA gel was determined by simply weighing 1 L of the gel and converting the measurement to kg/m 3 [61]. For analysis of the in-vivo/in-situ results, it was assumed that the power deposition was calculated in a volume of blood, and thus the complex permittivity and mass density of blood was used in calculation of the SAR [62 65]. Prediction of Local Induced Temperature Rise The local heating behaviour was modelled using a Green s function solution to solving Pennes bioheat equation (PBHE) in the vicinity of the wire tip similarly to [49]. First the relative power of the current characterization scans and the heating scan was calculated, and used to scale up the SAR distribution calculated as described above. This scaled SAR distribution was used as an input to a solution of Eq The temperature distribution solution to Eq was found using a three-dimensional convolution of the Green s function and the SAR distribution, implemented in the Fourier domain for computational efficiency. In implementing Eq for the in vitro heating prediction, the heat capacity c p and thermal conductivity κ of the PAA gel were taken as the nominal values described in the ASTM RF heating standard, i.e. c p = 4150 J kgk and κ = α c p ρ = W mk where α = m2 s is the nominal thermal diffusivity as given by the ASTM standard [30]. For the in-situ heating prediction, the thermal properties of blood were used in solving the PBHE, specifically c p = 3594 J kgk and κ = W mk [66, 67]. Upon initial inspection of the heating prediction curves, it was noticed that the shape of the predicted temperature evolution did not adequately match the shape of the temperature measurements. It was hypothesized that this was due to the significantly different thermal properties of the UV curable epoxy, and compensation for the thermal properties of the UV curable epoxy through informed variation of the

72 Chapter 3. In-Vivo Considerations for Predicting RF Heating 55 heat capacity and thermal diffusivity used in solution of the PBHE was included [68]. A more detailed explanation and interpretation of this compensation is included in the Discussion section. Temperature was then sampled from the three dimensional distribution at the location (x, y, z) = (0.75, 0, 0) mm relative to the wire tip for comparison with the measured temperature results. This was the expected position of the centre of the face of the FO temperature probe; however there is a significant uncertainty in this estimate, which is depicted in part by error bars in heating plots. 3.4 Results Phantom Experiment Trel Length (cm) Figure 3.1: Plot of the normalized peak simulated steady-state temperature rise as a function of wire length at 3T. Maximum temperature rise is expected at approximately λ/2, or 12 cm. The results of modelling expected heating for various lengths of immersed wire are shown in figure 3.1. The predicted temperature rise was scaled to the maximum heating for any length. The peak heating occurs with approximately 12 cm of immersed wire, which is almost exactly λ/2.

73 Chapter 3. In-Vivo Considerations for Predicting RF Heating 56 Heating The induced RF current on a guidewire in the ASTM phantom as quantified using artifacts in GRE and UTE images is shown in figure 3.2. Good agreement between current values determined using UTE images and the values determined using GRE images is evident. Perhaps more importantly, good agreement also exists between the finely sampled sinusoidal fits to UTE and GRE current values. This indicates that the UTE sequence can be used in place of the GRE sequence to quantitatively characterize RF current distributions for the purpose of assessing RF safety. The heating measured in this guidewire configuration is shown in figure 3.3, along with the heating as calculated using the UTE- and GREcharacterized current distributions as inputs. Heating predicted with both GRE and UTE current distributions accurately matched heating as measured. Scaled current measurement (A/µT) Discrete UTE current UTE Current Fit Discrete GRE current GRE Current Fit Location relative to wire tip (cm) Figure 3.2: Plot of the discrete scaled current measurements taken at various locations along the guidewire during the phantom experiment, using a stock GRE sequence and the custom UTE sequence. Also shown are the corresponding sinusoidal fits. All current measurements have an inherent positional uncertainty of ±0.5 cm due to the slice thickness that was used in imaging which has not been shown on the plot for visual clarity.

74 Chapter 3. In-Vivo Considerations for Predicting RF Heating T ( C) 2 1 UTE heating prediction Measured heating GRE heating prediction Time (minutes) Figure 3.3: Plot of heating measured in the phantom experiment, compared with heating as predicted using current characterization Animal Experiments Figure 3.4 shows examples of phase images acquired with the GRE and UTE sequences with a wire in place in an animal, as well as the corresponding phase artifact fit that was found to most closely match the UTE phase image. Also shown are the residual images depicting the differences between the experimental phase images and the fit image. The current values measured using the UTE sequence in vivo and in situ, post-sacrifice of pig 1, are shown in figure 3.5 and the associated heating measurement and calculated heating is shown in figure 3.6. The discrepancy between heating measured in vivo and heating predicted by imaging is due to the fact that the cooling effect of blood flow was not considered during heating prediction. For current plots generated using in-vivo and in-situ data, the tip location has been taken as the expected tip location based on knowledge of the length of guidewire inserted, X-ray fluoroscopy imaging and MRI localization scanning. This location has been termed the estimated tip location because the true location of the wire tip was known only within several millimetres. Due to the thickness of the slices used to characterize current (1 cm) the tip location calculated through current fitting also has an uncertainty on the order

75 Chapter 3. In-Vivo Considerations for Predicting RF Heating 58 (a) (b) (c) (d) (e) Figure 3.4: Comparison of phase contrast images taken with (a) the stock spoiled gradient echo sequence and (b) the custom UTE sequence. (c) shows the theoretical artifact that was fit to the UTE image. (d) and (e) show the residuals (difference) between the GRE image and fit image, and the UTE and fit image respectively. The red circle in all images delineates the region that was used for fitting to the phase artifact. Significant physiological artifacts can be seen in the image acquired with the stock GRE, whereas the phase distribution in the UTE image is relatively uniform, facilitating isolation of the wire artifact. of several millimetres. The location of the zero-crossing of each sinusoidal fit can be interpreted as the tip location determined by each set of current values. Evidently current distributions based on in-vivo and in-situ data agree closely both in slope and magnitude. Current values and sinusoidal fits for both insertion depths in pig 3 are shown in figure 3.7. Again, in-situ and in-vivo current results agree closely, producing similar sinusoidal fits in the distal region of the guidewire. The corresponding heating as measured and as calculated using the in-vivo current distributions is shown in figure 3.8. Heating was also calculated using the in-situ distribution but is not included in this plot for visual clarity, as it was very similar to that calculated using in-vivo data.

76 Chapter 3. In-Vivo Considerations for Predicting RF Heating 59 Scaled current measurement (A/µT) Discrete In Situ Measurements In Situ Current Fit Discrete In Vivo Measurements In Vivo Current Fit Location relative to estimated wire tip (cm) Figure 3.5: Plot of current values measured in pig 1. Shown on this plot are discrete current measurements taken both in-vivo and in-situ. All current measurements have an inherent positional uncertainty of ±0.5 cm due to the slice thickness that was used in imaging which has not been shown on the plot for visual clarity. 3.5 Discussion In-Vitro Experiments Current Characterization The discrete current measurements taken in vitro using the GRE and UTE sequences agree well in magnitude as a function of position. Since the discrete current values used to produce the current distribution fits for both sets of images were not at the same positions on the wire, no standard error between the GRE and UTE discrete current measurements is reported; however, one can observe visually on the plot that the two sets of discrete measurements follow a similar trend. This claim is demonstrated quantitatively in the standard error of A µt between current fits with both sequences. The current values characterized in this study range from A µt, thus the standard error between fits is more than one order of magnitude smaller than the current values acquired, indicating that the upsampled current fits agree well. The major application of this technique would be in using current characteri-

77 Chapter 3. In-Vivo Considerations for Predicting RF Heating T ( C) 2 1 Heating in situ Heating predicted by in situ measurements Heating predicted by in vivo measurements Time (minutes) Figure 3.6: Plot of heating measured in pig 1 before and after sacrifice, compared with heating as predicted using current characterization with a custom UTE sequence. zation to quantify RF safety; thus the current distribution fits are the more important output of the measurements. Irrespective of the agreement between individual current values obtained at discrete locations, if the current fit produced by the UTE sequence matches the fit produced by the GRE sequence, as is the case in this study, the UTE sequence is equally suitable for predicting RF heating. Experiment S(GRE M, GRE F ) S(UT E M, UT E F ) S(UT E F, GRE F ) In Vitro Table 3.1: Standard error metrics relating to the in vitro experiment. Reported are the standard error of the fit to GRE data and the fit to UTE data. Also included are the standard errors between the two sets of measured data and the two fits. All standard error values have the units of the reported current distributions, A µt. Heating Heating predicted by both the GRE the UTE current fits agreed adequately (within 1 C at all times) with the measured heating in the phantom. However, some difference between the shape of the predicted and measured heating curves is evident in the early stage (first minute) of heating. This is due to

78 Chapter 3. In-Vivo Considerations for Predicting RF Heating Scaled current measurement (A/µT) Location relative to estimated tip (cm) (a) Scaled current measurement (A/µT) Discrete In Situ Measurements In Situ Current Fit Discrete In Vivo Measurements In Vivo Current Fit Location relative to estimated tip (cm) (b) Figure 3.7: Plot of current values measured in pig 3, with (a) the guidewire partially pulled back from inside the pig and (b) the guidewire fully inserted in the pig. All current measurements have an inherent positional uncertainty of ±0.5 cm due to the slice thickness that was used in imaging which has not been shown on the plot for visual clarity. uncertainty in the exact geometry and thermal properties of the UV epoxy between the tip of the guidewire and FO sensor. The UV epoxy was necessary to create a sufficiently robust bond to withstand insertion into the animal and navigation through the vasculature; however, it increased the uncertainty inherent in the model of local RF heating. Local heating was modelled as discussed earlier assuming a region of homogenous thermal properties, consistent with the nominal properties of the PAA gel in

79 Chapter 3. In-Vivo Considerations for Predicting RF Heating T ( C) Time (minutes) 15 cm measurement 15 cm prediction 20 cm measurement 20 cm prediction Figure 3.8: Plot of heating measured in pig 3 with the guidewire at two insertion depths, compared with heating as predicted using current characterization with a custom UTE sequence. which the in-vitro experiment was carried out. Since there was some UV epoxy between the guidewire and FO sensor, the authors decreased the thermal conductivity used in the calculation slightly from the nominal value for the PAA, to account for lower thermal conductivity of the UV epoxy and to improve the agreement in shape between modelled and measured heating curves. This induced greater uncertainty in the modelled heating curves, but was necessary with the setup used In-Vivo/Situ Experiments UTE vs. GRE Phase Artifacts The images in figure 3.4 serve to demonstrate the main advantage of/motivation for using a UTE sequence to remotely characterize RF current in lieu of a GRE sequence; phase artifacts due to sources other than the induced RF current are minimized in the UTE image relative to the GRE image. Significant phase artifacts exist in the GRE image due to gradient non-linearity (left region of the image, green arrow) which have been greatly reduced in the UTE phase image. As discussed in previous work, a smoothly varying background phase distribution can be used to account for low-frequency phase variations such as

80 Chapter 3. In-Vivo Considerations for Predicting RF Heating 63 those due to gradient non-linearity. Usage of the UTE sequence may provide for accurate quantification of current values in regions of greater gradient distortions than if a GRE sequence were used because the UTE sequence serves to reduce the phase contribution from distorted gradient fields. Additionally phase artifacts due to fat surrounding the epaxial muscles in the lower region of the image (dark ovular shapes in the GRE image, white arrow) have been greatly reduced. While these artifacts did not occur within the fit region in this example, a background phase fit applied to the UTE image would produce a more accurate result than if applied to the GRE image. Additionally, in the upper left portion of the fit region phase artifacts due to subcutaneous fat (black arrow) are noticeable in the GRE image and have been all but eliminated in the UTE image, enabling a more accurate fit to the induced RF current phase artifact. Perhaps most importantly, the phase due to blood flow in the carotid artery (centre of the fit region, blue arrow) in which the guidewire was located, has been minimized in the UTE image. This region has the greatest influence on the fit results given the line of phase wrap in the image. It is paramount that phase immediately surrounding the wire accurately represents phase due only to the induced RF current, and the UTE sequence enables this. With manual input from an operator, a GRE image acquired in vivo could perhaps be used to generate an accurate characterization of induced RF current (within 10-20% of that achieved with the UTE image). Specifically, if the radius of the fit mask indicated by the red circle in figure 3.4 were reduced by an operator to exclude the phase artifacts due to subcutaneous fat, an accurate fit to the induced current phase artifact could likely be achieved, resulting in a temperature prediction that is good enough to ensure patient safety. However; it cannot generally be said whether this approach would result in a higher or lower current value than that achieved with the UTE image. Furthermore, this would require manual intervention to fine tune the fit mask and input from a radiologist on the location and physical origin of unwanted phase artifacts. Finally this approach would only be feasible if no significant physiological phase artifacts overlap spatially with the induced current artifact. Therefore a UTE sequence that inherently minimizes off-resonance sources of phase and works to isolate the phase artifact from induced current would represent the optimal strategy for in-vivo application of this technique. UTE sequences are not necessarily implemented as stock sequence options on clinical scanners, which may present a hurdle to immediate clinical application of this technique. However; when a UTE sequence is implemented the presented technique is faster and more robust.

81 Chapter 3. In-Vivo Considerations for Predicting RF Heating 64 Current Characterization Since blood flow reduced in-vivo RF heating to an immeasurably low level, it was necessary to sacrifice the animal to allow for measurement of RF heating in the absence of such flow-induced cooling. The purpose of measuring temperature in this study was not to validate a method of modelling heating in vivo, but rather to compare heating measurements to heating predicted by image-based current characterization, with the intent of verifying the accuracy of said current characterization. Thus in-situ (post-sacrifice) heating measurements were used to eliminate the effect of blood flow and perfusion. Because in-situ heating data would be used to verify in-vivo current characterization, it was necessary to demonstrate equality between current fits in vivo and current fits in situ. From the current plots presented in Figures 3.5 and 3.7, as well as the statistical metrics summarized in Table 3.2, it is evident that in-situ and in-vivo current characterization produced statistically equivalent fits. The largest standard error value between in-vivo and in-situ discrete datasets was 21 ma µt, which is significantly below the majority of current values that were measured. Furthermore, the more imporant metric is the agreement between current fits as it is these fits that ultimately quantify RF safety. The standard error between current fits determined from in-situ and in-vivo data ranged from 1-17 ma ma µt, with the majority being below 10 µt. The typical current values measured were on the order or tens to hundreds of ma µt, indicating that in-situ and in-vivo measurements provided equivalent current fits from the respective discrete sample sets. Experiment S(IV M, IV F ) S(IS M, IS F ) S(IV M, IS M ) S(IV F, IS F ) Pig Pig 2 Full Insertion Pig 2 Pulled Back Pig 3 Full Insertion Pig 3 Pulled Back Table 3.2: Summary of the standard errors of the current fits for in-vivo and in-situ images acquired in all pigs, as well as the standard error between the two sets of measurements and the two fits. IV refers to current values acquired in-vivo, and IS to current values acquired in-situ. Subscript M denotes measurements and subscript F denotes fit values. All standard error values have the units of the reported current distributions, A µt. Heating Heating predictions and measurements agreed adequately for all in-vivo and in-situ experiments. Agreement between the heating measured in vivo and predicted heating cannot be expected because blood flow cooling was not considered in the thermal modelling. Additionally, measured heating was lower with 20 cm of guidewire inserted than with 15 cm, as expected based on figure 3.1. There was a small offset present between the heating measurements and predicted curves, which was likely due to a small

82 Chapter 3. In-Vivo Considerations for Predicting RF Heating 65 error in the estimated location of the fibre-optic sensor relative to the guidewire tip. The guidewire represents a physically small current source and thus large temperature gradients exist in the local RF heating caused by the guidewire. Therefore a small discrepancy between the believed fibre-optic sensor position and the position used in the calculation to sample the heating behaviour could lead to the observed offset. An example calculated temperature distribution around the wire tip for pig 3 is shown in axial and longitudinal planes in figures 3.9 and 3.10 to help illustrate this point. 2 T ( C) Position (cm) Position (cm) Figure 3.9: Image of modelled heating in a perpendicular plane around the tip of the pulled back guidewire in pig 3. The location of the guidewire is indicated by the dot in the center of the image. A significant temperature gradient exists which may account for the offset between measured and modelled heating. The thermal modelling used in this study did not account for blood flow and thus represents a conservative estimate of the expected in-vivo RF heating. Such modelling provides for extra margin of safety if being used to evaluate potential danger to the patient. This has the benefit of increased confidence that a patient will not be harmed, especially since potential situations exist in which an interventional device could block blood flow and eliminate this source of cooling. However, it also creates the potential for contraindication of certain imaging exams that may in fact be safe in terms of

83 Chapter 3. In-Vivo Considerations for Predicting RF Heating 66 2 T ( C) Position (cm) Position (cm) Figure 3.10: Image of modelled heating in a longitudinal plane near the proximal end of the pulled back guidewire in pig 3. The location of the guidewire is indicated by the line extending from the left of the image. A significant temperature gradient exists which may account for the offset between measured and modelled heating. RF heating. Additionally, the guidewire itself may serve to conduct heat away from the tip and reduce the temperature rise. Due to the relatively small volume of the guidewire and the low surface area of the contact interface between the guidewire and tissue it is likely that this effect would account for only a minor contribution to cooling compared to blood flow and perfusion. Further investigation into the effect of blood flow, perfusion and potential guidewire cooling, towards more accurate modelling of induced RF heating in-vivo rather than in-situ would be beneficial, allowing for presentation of heating estimates with and without various cooling mechanisms accounted for to the clinician. The results of the heating experiments and the statistical analysis of the discrete current values and fits indicate that a low level of heating, on the order of a few degrees, can be accurately predicted using current characterized with the UTE sequence. It was shown that induced RF current could be characterized at discrete locations in vivo with an accuracy on the order of 10 ma µt and that a small set of these discrete measurements could be used to fit a smooth distribution and accurately predict

84 Chapter 3. In-Vivo Considerations for Predicting RF Heating 67 heating on the order of a few degrees. Temperature rises of this magnitude over time periods of minutes represent the lowest heating that could be cause for concern for patient safety, as the thermal dose due to lower temperatures over this time scale would not be harmful. Therefore, this technique represents a feasible method to evaluate RF safety, as it has the ability to accurately identify the least dangerous of potentially dangerous situations. Any configuration leading to higher RF heating and thus increased safety risk would also involve higher induced RF current and could therefore be identified with this technique. The SAR of the UTE sequence used in this study was approximately half that of the fast spinecho sequence used to produce measurable heating. Thus the UTE sequence as currently implemented could in certain cases cause heating during current characterization. Fortunately, since less than 10 UTE slices are typically required to produce an adequate current distribution fit, and each slice requires approximately one second to acquire, it is highly unlikely that the UTE sequence would deliver a harmful thermal dose to the patient. Additionally, if a reduction in SAR of the UTE sequence were needed, the TR could be increased without affecting the results of current characterization. In such a case, the SNR implications of the change in TR would need to be considered. 3.6 Conclusion Extensions to a previously discussed approach to remotely characterize induced RF current on conductive structures in MRI were presented. A custom UTE sequence was used to minimize phase artifacts in vivo, in an attempt to allow for image-based characterization of RF currents induced on long conductors in vivo. A phantom experiment was presented to demonstrate that the custom UTE sequence produced equivalent current characterization results to those achieved with a stock sequence, when a previously published characterization algorithm was applied to both images. Heating data acquired during a phantom study and several in-situ porcine experiments was used to verify that accurate currents values were obtained using the custom UTE sequence, demonstrating feasibility of the proposed UTE sequence to evaluate and quantify RF heating risk non-invasively. Overall, it was successfully demonstrated that current can be accurately quantified in vivo using the custom UTE sequence. However, there were some underlying assumptions that may in general not be true in in-vivo situations. The major assumptions include: local homogeneity of the transmit and receive sensitivities and homogeneity of the tissue electrical and thermal properties in the immediate vicinity of the wire. Prior to using current distributions acquired with the presented technique to evaluate patient safety, further investigation into the validity of these assumptions, as well as their effect on

85 Chapter 3. In-Vivo Considerations for Predicting RF Heating 68 safety evaluation, would be suitable.

86 Chapter 4 Miniaturizing floating RF traps for increasing RF safety Introduction & Motivation The field of interventional MRI has been a very active area of research over recent decades [69 71]. Revascularizations of occlusive arterial disease require at least one conductive device, the guidewire, not for electrical transmission but rather for the mechanical properties achievable only with specific alloys. In revascularization procedures, the guidewire essentially acts as a needle used to cross an occlusive lesion. To achieve a successful crossing, guidewires with specifically tuned mechanical properties are required; sufficient flexibility is necessary to allow the guidewire to snake through blood vessels and turn sharp corners, while the guidewire must be sufficiently stiff firstly not to kink around these tight corners but more importantly to poke through an occlusive lesion that could very well be hardened by calcified plaque. Guidewire materials and diameters have been extensively researched and developed to provide specific mechanical properties that maximize the success rate of revascularization procedures using current guidance techniques, i.e. X-ray fluoroscopy [14, 72, 73]. Furthermore clinicians performing percutaneous catheter procedures have become accustomed to existing guidewires and their properties. The point is, guidewires have certain mechanical properties that must be maintained. It has been shown that percutaneous interventions and revascularization procedures in particular could benefit from MRI guidance to facilitate advancement of the catheter down the patent vessel to 1 This chapter is modified from the article: Miniaturizing Floating Traps to Increase RF Safety of Magnetic Resonance Guided Percutaneous Procedures. Gregory H. Griffin, Kevan J.T. Anderson, and Graham A. Wright. Published 2016 in IEEE Transactions on Biomedical Engineering. 69

87 Chapter 4. Miniaturizing floating RF traps for increasing MRI RF safety 70 the occlusion, enabling crossing of the lesion with the guidewire, as well as increasing patient safety by reducing the risk of the guidewire perforating the blood vessel. The reduced perforation risk is achieved because MRI guidance can provide the clinician with more accurate knowledge of the guidewire location relative to the vessel wall than can be provided by X-ray fluoroscopy [71]. With certain MRI devices clinicians can actually see soft-tissue structure within an occlusion [3], allowing extremely precise guidance of a guidewire through the softest or most easily crossed channel in the occlusions. The heating characteristics of long linear conductive devices have been extensively investigated, and it has been shown that in general a method of mitigating this heating risk is necessary to ensure safe scanning [8, 9, 18, 74]. Several groups have investigated various methods of improving the safety of catheter based devices, many of which have been somewhat effective in certain configurations [35, 38, 40, 75]. However, all such effective mitigating techniques have required direct physical modification of the risk-posing conductor or modification/customization of the MRI scanner [37, 76 78]. The work in this chapter presents a technique that could be implemented without modification of the guidewire or the stock MR scanner, allowing for the maintenance of important mechanical properties and avoiding site-by-site modification or customization of MR systems. As mentioned above, guidewires are conductive, thus posing a safety risk, and have specific required mechanical properties; it is important to leave a guidewire unmodified while mitigating heating risks. A device potentially capable of achieving this is a floating RF trap, previously demonstrated by Seeber et al. [39]. This trap device acts by inductively coupling to any conductor passing through the trap lumen, thus adding a series impedance without making physical contact or mechanically modifying the conductor in any way. The trap initially presented by Seeber et al. however was built on a macroscopic scale, for suppression of induced shield currents on transmission lines coming from surface coils. It can be shown that for a conductor such as a guidewire, partially inserted into a patient, electrical modification of the portion outside the patient can have little effect on the current induced on the portion inside the patient. A demonstration of this phenomenon in simulation has been included in Appendix A of this chapter. Due to this effect, a method of altering the impedance of a guidewire inside the body is preferable. Miniaturizing Seeber s floating trap devices can allow for this without altering the mechanical properties of guidewires. Catheters, which are typically used in addition to guidewires, already have similar linear geometry to floating traps and a relatively large volume for accommodating traps. Additionally catheters have less demanding mechanical requirements than guidewires, therefore catheters represent a potentially useful platform for inserting miniature floating RF traps into the body, by embedding such traps into the catheter walls. This chapter presents several miniaturized, catheter-sized (9F outer diameter) floating traps designed

88 Chapter 4. Miniaturizing floating RF traps for increasing MRI RF safety 71 for application inside the human body and discusses the design challenges involved in miniaturizing such devices. A catheter device with distributed traps built into the catheter wall is proposed; increasing RF safety of any conductor passing through the catheter (and thus trap) lumen. It is shown that the electrical properties and effects of catheter-sized traps can be accurately modelled. Furthermore it is shown through simulation that a certain minimum density of traps along the length of the catheter may significantly suppress induced RF currents and thus reduce RF heating to an acceptable level in a broad range of clinically relevant situations. Phantom experiments were carried out to show that distributed miniature traps suppress current and reduce RF heating as predicted by theoretical modelling. 4.2 Theory of Trap Function As mentioned above, the principal benefit of a floating trap for the purpose of current suppression to increase safety of interventional procedures is the ability to electrically modify a conductive wire passing through the trap lumen, without requiring any mechanical alterations to the wire. This is achieved through the inductive coupling of a resonant series impedance to the wire. The trap geometry used to achieve this inductive coupling is shown schematically in figure Coupled Impedance, Z coupled The trap can be conceptualized as an elongated toroid, consisting of two coaxial cylinders of conductive material. Figure 4.1 shows the longitudinal cross section of the top, or upper half of such an elongated toroid. A long linear wire passing through the centre of the trap lumen (inner conductive cylinder), carrying current I, and extending far beyond the longitudinal extents of the trap will couple a flux Φ into the trap body given by: Φ = b a µ 0 I 2πr dr l = µ ( ) 0I b 2π ln l; (4.1) a where a and b are the inner and outer radii of the trap respectively, and l is the length of the trap. Referring to figure 4.1 the flux described in Eq. 4.1 is the integral of the magnetic field (perpendicular to page) due to the wire over the area of the rectangle enclosed by the circuit. Note that it has been assumed in this equation that I is constant along the wire over the length of the trap, a valid assumption for short traps less than a few centimetres long. Thinking of the wire/trap system as an inductively coupled transformer, with the wire as the primary coil and the trap as the secondary, it can be inferred from Eq. 4.1 that the mutual inductance of the system is M = µ0 2π ln ( b a) l. Incidentally, the trap as a

89 Chapter 4. Miniaturizing floating RF traps for increasing MRI RF safety 72 pair of coaxial conductors has self-inductance, L t, given by the same expression, therefore: L t = M = µ ( ) 0 b 2π ln l. (4.2) a Thus the impedance coupled from the trap (secondary) into the wire (primary) is given by: Z coupled = ω2 M 2 Z t = w 2 L 2 t ( ), (4.3) R t + j ωl t 1 ωc t where Z t is the impedance of the trap circuit, governed by the resistance R t, inductance L t and capacitance C t inside the trap circuit. This coupled impedance can be conceptualized as the change in impedance of a wire with and without a trap in place, and thus Z will be used to refer to coupled impedance herein. Note that the equivalence between self- and mutual inductance is a fortunate consequence of this geometry however these two quantities will not in general be equal. The trap consists of two parallel curved plates of conductor, and thus has self-capacitance, as well as resistance due to the imperfect conductor used. The self-capacitance and resistance of the trap, C t and R t are given by C t = 2πɛ ln ( l ωµ ) l, R b t = π (a + b) 8σ, (4.4) a where σ and µ are the conductivity and permeability of the conductor used in the trap respectively. The self-capacitance of the trap is equal to the well known capacitance per unit length of coaxial conductors. The details of the derivation of this trap resistance have been included in Appendix D of this chapter. For practical geometries the capacitance of the coaxial cylinders is insufficient to resonate the self-inductance at 64 or 128 MHz (Larmor frequencies of 1.5 T and 3 T MRI scanners respectively) and thus discrete capacitors were used to tune floating traps. In fact, the capacitance of the trap body itself is negligible ( 0.25%) compared to the discrete components used in this study. These discrete components help to tune floating traps to the desired frequency. Unfortunately due to the size constraints placed on catheter based devices, the associated resistance of the discrete capacitors has a significant effect on trap function and must be included as part of R t. This is discussed in more detail in later sections Trap Mechanical Properties The proposed design involves floating traps built into a catheter wall. While not as vital as guidewire mechanical properties, it is important to consider catheter mechanical properties as well, thus trap mechanics must also be modelled. Torsional and flexural rigidity of the trap depend on the inner and

90 Chapter 4. Miniaturizing floating RF traps for increasing MRI RF safety 73 l L t R t R C C t b wire a I ind wire Figure 4.1: Schematic representation of the inductive coupling of a series impedance onto the wire and the associated trap geometry. outer trap radii as well as the material properties of the trap body; the Young s and shear modulus Y and G. The flexural rigidity of the trap is proportional to the Young s modulus and the quartic difference of the inner and outer radii (b 4 a 4 ). Torsional rigidity is proportional to the shear modulus and the quartic difference [79]. While mechanical properties are not characterized or designed for in this work, mechanical properties of traps built in to catheters must be considered and thus this discussion of mechanical properties has been included Current Suppression Induced RF currents are suppressed through the inductive coupling of an impedance from the floating trap to the wire. Starting from a modified transmission line model (MoTL) proposed by Acikel and Atalar for modelling RF induced currents, the exact effect of a given coupled impedance on induced RF currents can be determined [48]. The aforementioned model uses per unit length impedance properties, defined piecewise along a wire to model induced current. To model the added current suppression caused by a floating trap, the coupled impedance calculated using Eq. 4.3 is simply divided by the length of the trap, giving a per unit length coupled impedance, Z coupled = Z coupled l. Following this, Z coupled is added

91 Chapter 4. Miniaturizing floating RF traps for increasing MRI RF safety 74 to the per unit length impedance of the wire itself, over the spatial extent of each trap. This produces an effective wire with Z that varies along the length of the wire, with regions affected by traps having a higher Z and thus lower current flow for an equivalent applied electric field or voltage. 4.3 Methods Trap Construction The bodies of the traps were fabricated using an in-house stereolithography system, or 3D printer. A hollow cylindrical body, with two longitudinal slits at one end for securing capacitors in place, was used. Due to material availability, Accura Clearvue (3D Systems, SC, USA) was used as the substrate. This did result in a stiffer trap than desired; however, in the initial iteration of the design higher priority was placed on electrical properties in order to prove the concept. In the future a more flexible material may be found to allow for appreciable curvature of the traps. Specific trap dimensions and corresponding rationales will be discussed later but first it is important to describe the construction of the traps. A representative computer drawing of the trap design is shown in figure 4.2. An actual trap in various stages of fabrication can be seen in figure 4.3. The placement of the capacitors can be seen as well as the polyimide tube that was used to wrap around the inner conductor, holding the inner conductor in place as well as electrically isolating the inner conductor from one end of the tuning capacitors. A description of the trap assembly process follows. Firstly two rectangles of flex circuit (DuPont Pyralux R, 12µm copper layer on 45µm polyimide substrate) are cut to form the inner and outer conductors respectively. The inner conductor is wrapped around a mandrel, with the conductive side out. A polyimide tube approximately 80% the length of the conductive tube is placed over the conductive tube, to hold the inner conductor during fabrication as well as to electrically isolate the inner conductor from one end of the tuning capacitors. The trap body is then slid onto the assembly over the inner conductor/polyimide tube and the capacitors are soldered at the end opposite the trap body as in figure 4.3b. Finally the outer conductor rectangle is placed over the trap body with the conductive side facing in and solder paste is used to attach the capacitors at the body end as well as to short the inner and outer conductors at the end of the trap opposite the capacitors. In order to function effectively in a 1.5T MRI scanner, the traps used in this study were tuned to resonate at approximately 64 MHz. To achieve this, trap dimensions were chosen as follows: a = 0.55 mm, b = 1.5 mm, l = 14.1 mm. Two 1000 pf, high Q ( 1 MHz), non-magnetic capacitors in a 0603 package (1.6x0.8x0.8 mm) (Vishay Electronics, PA, USA) were used to resonate the trap body

92 Chapter 4. Miniaturizing floating RF traps for increasing MRI RF safety 75 Capacitors Figure 4.2: Computer drawing of one miniature trap as it was designed. The black portion corresponds to the 3D printed trap body, the rectangular tuning capacitors are denoted by arrows, and the outer and inner cylindrical shells represents conductor. The inner and outer conductors are shorted together with a solder bridge at the end opposite the capacitors. mandrel mandrel mandrel 0.8mm (a) (b) (c) Figure 4.3: A representative trap shown in various phases of construction. The rod denoted by an arrow in (a-c) is a mandrel (green) used to maintain the trap lumen throughout fabrication. The inner conductor with capacitors soldered on is shown in (a). One end of the capacitors is isolated from the inner conductor using an orange polyimide tube. (b) shows the trap body put in place over the inner conductor and capacitors, and (c) shows an image of the full length of the trap, without the outer conductor. The diameter of the mandrel is shown for scale. at a frequency slightly above 64 MHz. Three traps were built with the aforementioned geometry and components, in the manner described above, and used for experimentation in this study. The traps were intended to be equivalent but were labelled A,B, and C to distinguish them during measurements. Using Eq. 4.3 the theoretical induced impedance was calculated using the aforementioned parameters and compared to the following measurements for confirmation of the trap model.

93 Chapter 4. Miniaturizing floating RF traps for increasing MRI RF safety Measuring Induced Impedance Induced impedance was measured as the difference between the impedance of a loop of wire, and the impedance of that same loop of wire with the trap in place at the middle. The fixture shown in figure 4.4 was used to calibrate a network analyzer (Agilent (now Keysight), E5061B) with a short, open and 50 Ω load between the alligator clips. Following this calibration, the induced impedance of each trap was calculated as the difference of impedance measurements taken with and without the trap installed over the wire between the alligator clips. Figure 4.4: Picture of the setup used to measure induced series impedance, Z. The network analyzer was calibrated with this fixture in place, using custom calibration loads placed between the alligator clips. The impedance of the setup was then measured as pictured as well as with a trap placed on the wire between the alligator clips. The difference of these two measurements provided the induced trap impedance, Z Modelling Induced Current and Heating Suppression A Method of Moments (MoM) simulation was run with a commercial software package (FEKO, Altair, MI, USA) to evaluate the incident electric field on a wire parallel to the axis of the MR bore, and inside the homogeneous ASTM F a phantom at an axial location of (x, y) = (11, 8) cm from the bore isocentre [30]. This field was then used as the incident excitation to model current suppression due to traps using the MoTL implemented in MATLAB [48]. For this modelling, the theoretical maximum achievable trap impedance (with Q capacitors = 1000), according to Eq. 4.3, was converted to a per unit length impedance and added to the characteristic impedance of the wire. This trap/wire combination was then treated as a single transmission line with non-uniform characteristic impedance in the model for investigation of induced RF currents under application of the simulated electric field. To validate this

94 Chapter 4. Miniaturizing floating RF traps for increasing MRI RF safety 77 model for the trap/wire combination, representative FEKO simulations were carried out to compare the suppressed current calculated with FEKO, an established commercial product, and with the MATLAB implementation of the MoTL. For this comparison, a theoretical trap impedance of 40Ω due to traps tuned to 65 MHz was used for each trap, corresponding to theoretical traps that behave perfectly according to Eq. 4.3 with Q capacitors = Following this, an extensive set of MATLAB simulations was run to determine if a certain density of traps along the length of a wire could sufficiently suppress current in a broad, clinically relevant range of configurations. The modelling attempted to simulate a guidewire being advanced through a catheter that had a certain density of traps installed along the length. A MATLAB script was written to automate the process of advancing the guidewire and simulate various lengths of inserted guidewire (0.1λ 3λ) being fed through catheters with various trap densities ( 0 λ ) λ. A theoretical induced impedance of 40Ω due to a trap tuned to 65 MHz per Eq. 4.3 was used in this simulation as above. The wavelength used in this modelling was calculated using the complex permittivity of the phantom gel as measured using a method described by El-Sharkawy et al. [61]. Given a complex permittivity, the wavelength in the medium is given by λ = 2π R (k) = 2π R ( ω ), (4.5) µ ɛ c where ɛ c is the complex permittivity of the lossy dielectric in question. For each configuration in this simulation set, the induced current was used to predict the heating level in a homogeneous phantom with the method described in chapter 2 of calculating the radiated electric field (and thus power density distribution, or specific absorption rate (SAR)) in the vicinity of the wire using a Green s function approach and subsequently applying the bioheat equation to calculate expected temperature rise near the tip of the wire [60] Induced RF Current and Heating Characterization To verify the suppression of current and heating expected with a given trap density and wire length, several trap configurations were implemented and scanned in a 1.5 T MRI scanner (GE, Milwaukee, WI). The torso phantom specified in ASTM F a was used, along with a fiber optic (FO) temperature probe (OpSENS, QC, Canada) to measure heating at the tip of the wire. The FO probe was held parallel and directly adjacent to the tip of the wire, as shown in figure 4.5. Thread was used to tie the wire and sensor together. The phantom was placed directly on the scanner table, and the wire was suspended 4.5 cm above the bottom of the phantom, using plastic holders. The wire was oriented parallel to the

95 Chapter 4. Miniaturizing floating RF traps for increasing MRI RF safety 78 bore of the scanner and centred longitudinally in the bore. All wires were held at approximate axial coordinates (x, y) = (11, 8) cm. Table 4.1 shows the various set-ups that were tested experimentally. The wavelength is fixed by the scanner frequency and phantom permittivity; both trap spacing and density are shown for clarity (although one can be derived from the other). FO sensor tip wire tip 1mm Figure 4.5: The FO probe (beige) and wire (black) construction used to measure heating at the tip of a wire. For each trap experimental configuration, axial RF-spoiled gradient echo images were acquired and the method described in chapter 2 of quantifying induced RF current using phase artifacts was applied [60]. Images were acquired with a spacing of 2.7 cm; three sets of images were acquired to provide a measure of uncertainty in the current values. Independently the MoTL model was used to simulate the expected current distribution with trap(s) in place, using the same approach describe in section This simulated current distribution was then compared to the acquired current measurements and used to predict heating behaviour in the wire tip. Table 4.1: Experimental Configurations Configuration # Wire Length (cm) Trap Density Trap Spacing (cm) # Traps /λ /λ /λ

96 Chapter 4. Miniaturizing floating RF traps for increasing MRI RF safety Results Measured Induced Impedance The induced trap impedance, Z coupled, was measured for each trap using the setup depicted in figure 4.4. The results of these measurements are shown in figure 4.6. Furthermore, the theoretically ideal trap impedance as calculated using the aforementioned trap geometry and discrete capacitor characteristics was calculated using Eq In calculating the theoretical trap impedance, resistance in the solder bridge was assumed to be negligible and the equivalent series resistance due to each capacitor was calculated assuming Q =1000 for each capacitor. The equivalent series resistance in the capacitors was added to the trap resistance in the denominator of Eq This theoretical impedance is included in figure 4.6 for comparison Induced RF Current and Heating The results of the comparison of the MATLAB MoTL implementation and FEKO simulations are shown in figure 4.7. FEKO and MATLAB models line up very well, indicating that MATLAB will be sufficient going forward to model various trap densities and the effect of these trap distributions on RF currents induced during MRI. The complex permittivity of the gel was measured at 64 MHz, and found to be ɛ ɛ 0 = ɛ r σ ωɛ 0 i = i. This complex permittivity corresponds to a dielectric constant of ɛ r = 84.4 and a conductivity of σ = 0.53 S/m. The dielectric constant was within the range of ɛ r = 80±20 defined in the ASTM standard. The conductivity was slightly higher than the expected conductivity of 0.47 S/m ±10%. For the purposes of this study however the conductivity of the gel is not paramount, as long as it is accurately measured and used in wavelength calculations. Calculating the wavelength of a 64 MHz wave in this gel yielded λ = 0.41 m (this value was used to scale the trap spacings and wire lengths used in this study). Figure 4.8 shows the current distributions of experimental configurations 1-3 as simulated using the modified transmission line model, and image-based current measurements for experiments 1 and 2. Continuous lines represent simulated current distributions while points are used to illustrate the discrete image-based current measurements. The current measurements broadly agree with the simulation results, both in terms of the shape of the current distribution as a function of position and also in the relative reduction in current due to the traps. Results of heating predictions using the simulated current distributions of figure 4.8, as well as the measured heating behaviour using a FO sensor are shown in figure 4.9. Results have been reported as

97 Chapter 4. Miniaturizing floating RF traps for increasing MRI RF safety Z ideal Z a Z b Z c Z(Ω) Frequency (MHz) Figure 4.6: Measurements of Z coupled made using all traps that were used in experiments. An example of the theoretically ideal impedance is also shown. Z a, Z b and Z c were fabricated with equivalent materials and processes and thus any difference in electrical properties is due to variability in fabrication and assembly. relative temperature increases, normalized to the heating seen with no traps in place. Since there is a significant temperature gradient around the tip, error bars are included on predicted heating behaviour to reflect the uncertainty in position of the FO sensor; the upper margin representing the closest expected FO sensor position (i.e. highest heating) and the lower margin the farthest expected position (i.e. lowest heating). These error bars correspond to an estimated uncertainty in the sensor position of ± 0.25 mm. The error bars have been staggered horizontally for visual clarity, but all error bars and scatter points correspond to a time value of 30 seconds. Measured heating was reduced by application of one and two traps, and the ratio between heating with one and two traps agrees with predictions. However an underestimation of the predicted heating as compared to the measured heating can be seen, further

98 Chapter 4. Miniaturizing floating RF traps for increasing MRI RF safety FEKO Results MATLAB MoTL Results Iind(a.u.) Position on wire (cm) Figure 4.7: Representative FEKO models along with corresponding MATLAB transmission line model calculations. The top line shows FEKO and MATLAB simulations of an unmodified wire setup as in the experiments of this paper. The lower two lines show simulations of wires with one and two traps in place; firstly with one trap in the middle and then with two traps distributed evenly along the length of the wire. discussion of this result and a potential explanation is given in section The results of modelling various trap densities applied to various lengths of inserted guidewire are shown in figure It is shown in the left portion of the figure that certain trap densities as modelled can significantly reduce heating on all lengths of inserted guidewire. 4.5 Discussion Induced Impedance The measured induced impedance plot in figure 4.6 serves to answer two questions. Firstly, are the electrical properties of miniaturized traps correctly modelled by Eq. 4.3 and secondly can the miniaturized

99 Chapter 4. Miniaturizing floating RF traps for increasing MRI RF safety Current (ma) Position on wire(cm) MoTL w/o trap MoTL w/ Z b in middle MoTL w/ Z b, c distributed Measured w/o trap Measured w/ Z b in middle Figure 4.8: Induced current results as simulated and measured in the experiments shown in Table 4.1. Simulated current distributions are shown as continuous lines and image-based current values are shown as scatter plot markers. Error bars are defined by the standard deviation between the three current values obtained with three sets of independent images. traps be assembled and fabricated as designed. As can be seen in the plot the shape and height of the magnitude of induced impedance approximately agree with the modelled ideal impedance. The height of the peak of induced impedance is determined by the factor ω 2 L 2 /R t, indicating that the trap inductance and resistance are accurately described. The peaks of measured Z curves are consistently lower than

100 Chapter 4. Miniaturizing floating RF traps for increasing MRI RF safety Trel traps Z b in middle Z b,c distributed Z b expected final Z b,c expected final Time (seconds) Figure 4.9: Heating behaviour plots as measured with a FO sensor and as predicted using the simulated current distributions in figure 4.8. Heating evolution lines represent measurements whereas the dot and the x mark represent the expected final temperature value of the two configurations with traps, as calculated using theoretically determined current distributions and heating behaviour. For clarity of results, temperature rise is presented as a relative value. T rel represents the temperature rise produced by each configuration, normalized to the 0 trap experiment. the peak of the ideal Z curve, and furthermore there is variation in the width of the peaks, i.e. the Q value of the resonance in the traps as built varied and was consistently lower than the Q predicted by modelling. The Q of this RLC circuit is given by ω 2 L 2 /R. These observations can be explained by the omission of the resistance of the solder bridge in calculating Z ideal. The resistance in the solder bridge serves to increase the overall trap resistance and therefore reduce the height and quality, or Q, of the Z curve. Furthermore the variability in Q between traps can be understood by considering the variability in the geometry and size of the solder bridge in each trap. Due to human error during trap fabrication, the length and radial symmetry of each solder bridge varied significantly between traps. In

101 Chapter 4. Miniaturizing floating RF traps for increasing MRI RF safety 84 Figure 4.10: Results of simulating various trap densities and wire lengths. The heating has been scaled to the maximum heating present around an unmodified wire. order to improve the efficacy of miniature traps in the future, traps should be designed with a copper disc at the end opposite the capacitors, instead of with a solder bridge. The solder bridge was used for fabrication ease in this study but a copper disc could improve induced impedance significantly. The shape of the Z peaks is also approximately as predicted by the ideal Z curve, indicating accurate modelling. Because the impedance coupled into the wire is not purely resistive, but rather a complex impedance consisting of resistance and reactance, the traps were designed to ensure that the reactance of each trap had the same sign; that is, the traps were all designed to resonate at slightly higher frequencies than 64 MHz, producing a positive reactance. This was done to avoid a series resonance between adjacent traps, which would produce a low total coupled impedance onto the wire. If all traps were designed to resonate perfectly at 64 MHz the random tolerances in trap fabrication and components would lead to a batch of traps with approximately half having positive and half having negative reactance. If these opposite reactance traps were placed in series on a catheter, they would resonate to a low impedance

102 Chapter 4. Miniaturizing floating RF traps for increasing MRI RF safety 85 and reduce the effect of current suppression, perhaps drastically to the point that dangerous heating could occur. A quantitative demonstration of the effect of mis-tuned traps on induced impedance has been included in Appendix C of this chapter. Designing all traps to resonate on one specific side of 64 MHz allows for confidence that even with trap tolerances leading to uncertainty in trap impedance, all resonant frequencies will remain on the chosen side of 64 MHz and coupled impedance will remain high. Due to fabrication tolerances, miniature floating traps are not always tuned exactly as intended. As built for this study, traps could be reproducibly tuned within 10% of the desired operating frequency, however improved fabrication is still needed to reliably produce more effective traps. Regardless of the reproducibility of traps with the desired properties however, each trap must be tested after fabrication to ensure functionality and any potential distribution of traps must be modelled with the specific properties of the component traps to ensure accurate assessment of safety. While traps are accurately modelled by Eq. 4.3, the coupled impedance due to traps on the catheter scale is not very large. In order to maximize the coupled series impedance, high Q capacitors must be used exclusively to ensure that the equivalent series resistance of the capacitor is small compared to the parasitic resistance of the trap conductive components Current and Heating Suppression As expected the MATLAB MoTL implementation and FEKO experiments agree quite well. For the distributed trap comparison, there is a slight discrepancy, the MoTL model predicted marginally better current suppression than FEKO. This can be explained by the fact that FEKO models traps as impedances induced at single points on the wire, while the MoTL model accounts for induced trap impedances being spread over the length of the trap. This leads to a smoother current distribution calculated with MoTL and overall lower current values. However figure 4.7 does serve to validate the MATLAB MoTL implementation. A validated MATLAB model is beneficial due to the relatively rapid calculation of induced RF current performed by MATLAB compared to FEKO simulations, and the relative ease with which various distributions of traps can be simulated in MATLAB, avoiding the need for computer drawings in FEKO. While most of the measured current values agree well with simulated current distributions, it seems that near the distal tip, on the right edge of the current plot, the two measured values are significantly different than the simulated distribution. These two measured values near the distal tip (x 11 cm from the centre of the wire) are higher than predicted. This can be explained by the infinite wire assumption present in the application of the current measuring technique used in this study [60]. The technique as

103 Chapter 4. Miniaturizing floating RF traps for increasing MRI RF safety 86 applied assumes that the wire extends far beyond the imaging slice in both directions, if in fact the wire is truncated, the measurement will return a current value greater than what is actually flowing in the wire at that point. Due to the good agreement between measured current values and predicted distributions, it is believed that the discrepancy between measured and predicted heating as seen in figure 4.9 is due to errors in the calculation of the termination impedance of the wire and/or position of the FO sensor relative to the wire tip rather than errors in the effect of traps on induced current. The measured heating is due in part to radiated electric fields associated with strong current gradients near the wire tip, however the other significant portion of measured heating is due to leakage current flowing out of the uninsulated tips of the wire and directly into the surrounding phantom gel. If the impedance of the contact between the tip and surrounding gel were miscalculated, it could result in an incorrect portion of predicted heating coming from leakage currents and thus an improper assessment of the effect of trap current suppression on heating. Traps reduce current along the wire and lower the current gradient at the tip; however a lesser effect is observed on the leakage current flowing out of the tip. This phenomenon can be understood by considering the factors that determine the levels of bulk current and leakage current. Bulk current is induced by the electric field tangent to the wire along its length, and the magnitude of bulk current depends heavily on the ratio of the incident tangential electric field (i.e. the applied voltage) and the impedance in the wire. By inducing series impedance in localized regions on the wire, traps can have a significant effect on bulk current levels. On the other hand, the leakage current is determined mainly by the mismatch between impedance at the tip of the wire and impedance in the surrounding tissue. The electrical matching between the wire tip and the surrounding lossy dielectric medium does not depend on the impedance of the wire at the trap sites. If a large impedance mismatch exists at the tips, then current will be mostly reflected and vice versa. Furthermore, the predicted heating values were found by calculating the temperature distribution around the wire tip and sampling heating at the expected location of the FO sensor, a small error in this location could contribute to the observed offset. Error bars were included in figure 4.9 to represent an uncertainty in the relative positions of the sensor and wire due to the thickness of the wire and FO sensor; however if the wire and FO sensor tip were not perfectly aligned axially, this could give rise to an offset between measured and predicted heating as seen. Aside from this offset, the ratio of heating with one and two traps in place was consistent between prediction and measurement, indicating that the local SAR reduction due to one and two traps was accurately modelled even if the position of the FO sensor was not precisely known.

104 Chapter 4. Miniaturizing floating RF traps for increasing MRI RF safety Design Considerations and Tradeoffs There are several tradeoffs involved in the design of a miniature trap. The desired resonant frequency is essentially fixed by the static field strength at which the trap is meant to operate, but all trap properties can be varied in achieving this goal. The trap electrical and mechanical properties are all affected by the geometry in different ways: inductance goes up with inner/outer radii ratio but is independent of absolute thickness; inductance also goes up with increasing length. Resistance goes down with increasing inner or outer radii but goes up with increasing length. Capacitance is affected mainly by discrete components, the maximum size of which is determined by the trap wall thickness. Torsional and flexural stiffness both go up with increasing wall thickness. Technical trade-offs are determined to maximize electrical performance within the mechanical constraints associated with the clinical goal of the catheter-guidewire system. A workflow to design effective miniature traps follows; these steps were used in choosing the trap parameters used in this study. First and foremost, the desired resonant frequency will determine the product of capacitance and inductance, according to the well known equation describing a resonant LC circuit: ω = 1 LC. Then, the outer trap radius will be chosen based on the smallest blood vessel which the catheter should be able to access, the outer radius was set to b = 1.5 mm ( 9 F) corresponding to a typical catheter for peripheral revascularization. The minimum inner radius can then be chosen based on the diameter of the guidewire and any other instruments that must travel down the lumen of this catheter; again, targeting a peripheral revascularization procedure, we set a = 0.55 mm ( 3 F). The wall thickness corresponds to the smallest capacitor dimension, and thus the largest allowable capacitor package. Using capacitor packages that are no bigger than the determined wall thickness, the capacitance values are determined based on part availability. The largest available capacitance for a given package should in general be used to minimize total trap length. Note that high-q non-magnetic capacitors must be used to minimize trap resistance and thus maximize coupled impedance. Given the capacitor package, one can calculate the length of a trap required to produce the inductance needed to resonate the capacitor. This calculation produces several geometry choices, each of which can be evaluated for the tradeoff between stiffness due to wall thickness and long length. These designs must be evaluated on a case-by-case basis to allow for practically functioning catheters; i.e. if a trap will be quite stiff due to thick walls, it must be sufficiently short not to adversely affect the catheter mechanical properties overall.

105 Chapter 4. Miniaturizing floating RF traps for increasing MRI RF safety Effect of Trap Curvature If traps were implemented into an intravascular catheter, one would expect that traps would bend to some extent during the procedure, indeed in many procedures they must bend to allow advancement of the catheter to the lesion site. In order to investigate the effect of trap curvature on electrical properties, a treatment and calculation of the effect of trap curvature on induced impedance has been performed, the details and results of which can be found in Appendix B. In this analysis it was shown that if a trap bends and the wire moves closer to one side of the trap than the other, the mutual inductance (flux coupled) between the trap and wire increases. This can be understood through the nature of magnetic fields. As the wire moves closer to one side of the trap, the flux through that side increases while the flux through the other decreases. However the magnetic field from the wire is more intense in close proximity to the wire and thus the increase in flux through the near side of the trap would outweigh the decrease of flux through the far side. Consequently, the induced series impedance due to a trap will increase as a trap is bent and highly flexible traps are therefore beneficial. Note that whereas the change in mutual inductance will serve to increase the magnitude of coupled impedance, the resonant frequency of the system will not change. The resonant frequency of the coupled impedance is determined solely by the self-inductance of the trap and the capacitance present in the trap with which the self-inductance resonates, as can be seen by inspection of the denominator of Eq Thus it is advantageous both electrically and mechanically to design traps for maximum flexibility Extensions and Future Work This study is intended to serve as a proof of concept for the effects of miniature traps on induced RF current and heating, as well as the associated modelling of such effects. However significant further investigation is needed towards implementation of such miniature traps into an interventional catheter; the stated motivation of the work. Primarily, a method for robustly splicing traps into the wall of an interventional catheter would need to be investigated. The author envisions a technique involving a tube longer than the trap that passes through the inner trap lumen and into the catheter on either side of the trap. This approach coupled with a catheter braid over the outer surface of the entire trap/catheter assembly could potentially provide for robust flexural and torsional performance, however further investigation of mechanical properties would be needed. Additionally, investigation into techniques for more reliably producing traps with the desired electrical properties is also needed. Significant variation of electrical properties among traps was seen in this study. This was due to geometrical and assembly variations caused by human imprecision during trap

106 Chapter 4. Miniaturizing floating RF traps for increasing MRI RF safety 89 fabrication. For example, the effective length of the traps was quite variable in this study due to the solder bridge used to short the inner and outer conductors at one end. This bridge was not well-controlled and affects both the resistance and inductance of the trap; a specialized conductive disc or a geometric net comprising the inner and outer cylinders and end disc would be more suitable. Machine cutting the flex circuit for the inner and outer conductors could drastically improve reproducibility as well. Finally, a substrate material capable of withstanding high temperatures could be used to allow for assembly of the trap before baking to form solder connections, reducing any human imprecision affecting placement and soldering. Per figure 4.10, a trap density of approximately 4/λ (i.e. a catheter with 4 traps per wavelength) may serve to reduce RF heating around a wire by a significant amount ( 90% reduction) no matter how far the catheter and wire have been inserted into a patient, as long as the wire is never extended more than λ/4 past the end of the catheter, i.e. past the last trap. However, this calculation was performed assuming perfectly fabricated traps, tuned to 65 MHz with a coupled impedance of 40 Ω and serves only as a good starting place for future investigation. This simulation indicates that the proper distribution of traps could perhaps serve to reduce the heating risk of an unmodified guidewire in a range of clinically relevant situations; however significant further investigation is needed to verify this claim. Furthermore, in practice manufacturing imperfections may cause increased or decreased resonant frequency and coupled impedance, and each specific distribution of traps would need to be modelled to determine whether it will adequately suppress currents given the imperfections in the fabrication of the specific individual traps. In general it can be said that traps with lower coupled impedance would need to be spaced closer together to reduce heating to the same level however the specific spacing change needs to be calculated in each individual case. The work presented in this study was carried out in a 1.5 T scanner and thus traps were designed for use at 64 MHz. With the improved SNR of 3 T imaging it is likely that future investigators may implement traps designed to operate at 128 MHz, or even higher frequencies. Thus the tradeoffs associated with higher frequency traps are identified here. The optimal trap spacing discussed above would be altered. Since the wavelength decreases at higher frequencies, the required λ/4 spacing is reduced and the mechanical properties of a catheter with traps may be more significantly affected. One benefit of operation at higher frequencies, though, is that a lower inductance is required in the trap; therefore each trap itself can be shorter. Additionally, since the coupled trap impedance is proportional to the square of resonant frequency, the ability of traps to suppress current at higher frequencies would be enhanced. One potential issue with this is that the Q factor of the traps increases proportionally with the maximum coupled impedance. Due to the fabrication inconsistencies this could cause even greater difficulty when

107 Chapter 4. Miniaturizing floating RF traps for increasing MRI RF safety 90 tuning. With proper development of fabrication and assembly processes for greater reproducibility, this issue could be mitigated. Overall there are several considerations related to trap efficacy and practical implementation that must be considered when the resonant frequency is altered. Finally, the effect of two series traps tuned to opposite sides of the scanner operating frequency, as mentioned in the discussion section and Appendix C of this chapter could be further investigated. This is a potential concern that was modelled for this study, but further experimentation to demonstrate this effect is needed. 4.6 Conclusion A novel application of floating RF traps, specifically the miniaturization of floating traps for implementation into intravascular catheters, was demonstrated. It was shown with fabricated traps and bench-top measurements that coupled trap impedance can be accurately modelled as a function of trap geometry and component values. Furthermore it was shown through comparison of custom simulation with an established commercial software package that the effects of coupled trap impedance on induced RF current can be accurately and quickly modelled with a modified transmission line model. Custom simulation was then used to illustrate that certain distributions of traps along the length of an intravascular catheter can potentially suppress RF heating to safe levels in a wide range of clinically relevant situations. Phantom experiments were then used to confirm that modelled RF current suppression due to coupled trap impedance is close to measured current suppression, through measurements of induced current and RF heating in the vicinity of wires fully immersed in a torso-mimicking phantom. In short, it has been shown that miniaturized traps, if implemented into an intravascular catheter, can potentially effectively mitigate RF heating risks associated with long linear conductors, without altering the important mechanical properties of said conductors. Appendix A Effect of trap outside body A trap applied to the portion of a guidewire outside the patient body can have little effect on induced current on the portion of a guidewire inside the patient body. To illustrate this effect, a simulation was carried out using FEKO, wherein induced current on a 100 cm guidewire inserted half-way into an ASTM phantom was calculated. The induced current along the entire 100 cm length of wire was calculated with and without a trap in place on the un-inserted length of the guidewire. The trap used in this simulation induced 40Ω of impedance on to the guidewire and was applied 25 cm from the proximal

108 Chapter 4. Miniaturizing floating RF traps for increasing MRI RF safety 91 tip of the wire, i.e. at the middle of the un-inserted section. Results of this simulation are shown in figure Whereas the trap has significant impact on the induced current outside the phantom, very little change in current is observed at the distal tip of the wire, i.e. the location of most significant heating Unmodified current Trap applied outside phantom Phantom boundary Trap location Iind(a.u.) Position on wire (cm) Figure 4.11: Plot of the current induced onto a wire inserted half-way into the standard ASTM phantom as simulated by FEKO, with and without a trap applied to the portion of the wire outside the phantom. The phantom boundary is situated at 50cm; thus the portion of the wire inside the phantom is defined by x > 50 cm. Appendix B Efficacy of Bent Trap A curved trap will still have approximately concentric cylindrical inner and outer conductors and the distance between these conductors will not change significantly, except for a small amount due to com-

109 Chapter 4. Miniaturizing floating RF traps for increasing MRI RF safety 92 pression in the trap body itself. Therefore the self inductance of the trap will not change significantly, and the resonant frequency of the trap will stay approximately constant with curvature. The mutual inductance between the trap and the wire, i.e. the flux coupled from a current on the wire into the trap body, could change significantly however due to the changing proximity of the wire and the inner trap wall. What follows is an approximate analysis of the effect of trap curvature on mutual inductance and therefore induced impedance. This allows for interpretation of the effect of catheter curvature on trap efficacy. l L t R t R C C t b wire a I ind Figure 4.12: Schematic representation of a bent trap coupling a series impedance onto the wire. Imagine a curved trap with inner and outer conductors equally curved, as in figure 4.12, this is an appropriate approximation given the above assumption of negligible compression in the trap body. The guidewire would bend as well if the catheter bent, however not with the exact same curvature as the catheter, and thus a theoretically straight guidewire allows one to consider the worst case scenario in which the coupled impedance would be affected the most relative to the straight catheter and guidewire case. One considers a top portion of the trap as shown in the schematic, and a bottom portion which would essentially be a copy of the top portion but located below the wire in the schematic. The overall flux coupled from the wire into the trap will be related to the average of the flux through these two portions, as other out-of-plane sections of the trap will be less curved and the top and bottom portions will have similar but lesser effects on coupled flux. The flux coupled from a straight wire into the top and bottom portions of the trap in this setup is given by the following expression: Φ = µ 0I 2π l/2 l/2 [ ( ρ2 x ln 2 )] ρ 2 l 2 /4 ± b ρ2 x 2 dx (4.6) ρ 2 l 2 /4 ± a

110 Chapter 4. Miniaturizing floating RF traps for increasing MRI RF safety 93 where r is the radial distance from the wire, ρ is the radius of curvature and x is the horizontal dimension, i.e. position along the wire. The positive and negative signs are applied to calculate the flux coupled into the top and bottom sections respectively. These equations are valid only if one assumes that the trap does not curve sufficiently for the inner cylinder to contact the wire and cause bending in the wire itself. The radius of curvature that would lead to a bent wire depends on the trap geometry and is given by the following expression: ρ bend = a 2 + l2 8a. (4.7) The induced impedance on the wire will be proportional to the square of the flux coupled into the trap (mutual inductance) and thus figure 4.13 shows a plot of the square of the average of the two expressions in Eq. 4.6, as a function of radius of curvature, normalized to the flux into a straight trap with a wire in the centre. The starting point of the plot is defined by Eq. 4.7 evaluated for the trap geometry discussed in this paper. Appendix C Series Resonance As mentioned earlier, if two traps in series were tuned to opposite sides of the scanner operating frequency, a potential series resonance could occur, creating a low impedance circuit for induced RF currents. Figure 4.14 shows plots of the magnitude and phase of the series impedance of two traps (simply an addition of two instances of Eq. 4.3 as functions of frequency), as functions of traps resonant frequency. If the resonant frequency of both traps is within 1 MHz of the desired frequency, the trap combination will behave almost as if perfect. It is clear though that if one or both traps are significantly detuned for any reason, current suppression could be significantly reduced. The most dangerous situation would occur if one trap was tuned above the scanner frequency and the other below. This can be seen in the bottom-left and top-right of figure 4.14 as the magnitude of coupled impedance is reduced to almost zero. Appendix D Resistance of the trap In general, the resistance of a cylindrical structure can be calculated using the well established formula R = l σa where σ is the conductivity of the medium, l is the length of the structure and A is the crosssectional area. In the case of AC resistance, the skin effect plays a role in determining the cross-sectional

111 Chapter 4. Miniaturizing floating RF traps for increasing MRI RF safety (φ/φstraight) ρ/l Figure 4.13: Plot of the flux into a cylindrical trap as a function of trap radius of curvature, scaled to the length of the trap. The curved flux has been scaled relative to the flux that would be coupled into a straight trapout. The beginning point of the line is defined by Eq. 4.7, which describes the smallest radius of curvature that a trap can have without the wire contacting the inner wall of the trap. area. At RF frequencies, current flow will not be uniform across the cross-section of a conductor, but rather the flow will be concentrated near the conductor surface. The skin-depth defines the distance below the surface in which current will be confined. Therefore the cross-sectional area in which AC current flows in a cylinder is given by: A 2π a δ, as long as δ << a, where a is the radius of the cylinder and δ is the skin-depth. In the case of copper, at frequencies much below f = Hz as is the case in this study, the skin-depth is given by: δ = 2 σωµ medium. where µ is the magnetic permeability of the Combining the above equations, the resistance of the trap can be derived. Note that the trap resistance is comprised of the resistance of two cylinders, the inner and the outer, of radius a and b respectively, not including the resistance of the connection between the inner and outer cylinders. Such resistance represents a series contribution and would be added to the value of R t.

112 ! b [MHz]! b [MHz] Chapter 4. Miniaturizing floating RF traps for increasing MRI RF safety Z coupled ! a [MHz] (a) ! a [MHz] (b) Figure 4.14: Magnitude and phase of coupled impedance due to two series traps, as a function of the resonant frequency of each trap. It can be seen that trap tuning plays a significant role in determining coupled impedance. The phase is displayed with a dynamic range from π to π. R t = l σa l = σ 2π(a + b)δ l σωµ = σ 2π(a + b) 2 l ωµ = π (a + b) 8σ (4.8)