NOISE IN MRI SCANNERS

Transcription

1 UNIVERSITY OF SOUTHAMPTON FACULTY OF ENGINEERING AND APPLIED SCIENCE INSTITUTE OF SOUND AND VIBRATION RESEARCH NOISE IN MRI SCANNERS Thomas Peuvrel A dissertation submitted in partial fulfilment of the requirements for the degree of Master of Science by instructional course.

2 ABSTRACT This work investigates the vibration and acoustic behaviour of different MRI scanners devoted to functional Magnetic Resonance Imaging. There is nowadays a need to control the excessive noise produced by this equipment since one of the current medical research objectives is to monitor the response of the human brain to visual or auditory stimuli. Such equipment usually works in high magnetic field (3 Tesla) and as a consequence of its imaging process (EPI), considerable Lorentz Forces are produced on the gradient coil system which therefore vibrates and radiates sound intensively. With noise levels reaching a range of db(a), the response of the human brain is therefore disturbed and the safety of the patient could not be guaranteed. The project is concerned with the evaluation of this noise annoyance by measuring sound pressure levels inside the bore of three different scanners working with a 3 Tesla magnetic environment and using Echo-Planar Imaging sequences. This assessment is accompanied by a vibration investigation into the gradient coil systems. An experimental protocol has been developed so as to conduct accurately the measurements. It has been aimed at shedding more insight on the vibration and acoustic behaviour by measuring the response at different positions on the structure. Besides the experimental part of the project, a theoretical overview of the system is presented by means of description of an analytical model of vibration and sound radiation mechanisms. An attempt at comparing the results with the theoretical analysis is made. Conclusions have to be drawn with care since large assumptions have been made so as to facilitate the methodology of the investigation. Despite this limitation the investigation has however revealed important information such as a predicted involvement of particular structural modes in the noise generation. Digital processing of the recorded signals emphasises the frequency characteristics of the dynamic and acoustic responses of the structure to the particular excitation that constitutes the EPI sequence. A strong correlation between the imaging sequence and the induced vibration and noise has been found which suggests the feasibility of appropriate noise control and design enhancement of MRI scanners. This work therefore sets the stage for further studies of this complex system which should then be directed to the achievement of exhaustive FE model or to the development of any function that could describe the coupling between Imaging sequences and structural response of the gradient coil system. This should bring considerable progress to MRI scanner design. Other useful information, coming from further analysis of the recorded signals, such as the Loss Factor, Impulse Response Function, is also given.

3 ACKNOWLEDGEMENTS I would like to acknowledge Dr. Matthew Wright for his supervision and guidance during this project and all the people who made this project possible and helped me during the measurements : Mr. John Foster and Prof. Alan Palmer at the Institute of Hearing Research, University of Nottingham ; Dr. Peter Jezzard at the Centre for Functional Magnetic Resonance Imaging of the Brain, University of Oxford ; Dr. Adrian Carpenter at the Wolfson Brain Imaging Center, University of Cambridge. I would also like to thank Dr. Keith Holland, Mr. Rob Stansbridge and Mr. John Fythian at the ISVR for providing with the equipment needed for the investigation. This work is dedicated to my parents who have supported me during all my studies and to my grand parents who have always showed me that life has to be lived simply. A special thanks to Dave and Cedric, my classmates and friends, who have supported me during this year spent in Southampton and who have given a grateful contribution to my project.

4 TABLE OF CONTENTS 1. INTRODUCTION LITERATURE REVIEW Magnetic Resonance Imaging: Overview and System Architecture Magnetic Resonance Imaging - Definition System architecture Characteristics of subsystems involved in the generation of noise Measurement of Noise Levels Results found in the literature Noise generation process Noise measurement procedures Issues: Noise and Vibration Control, Acoustic Modelling and Design of MRI Scanners THEORY STRUCTURAL VIBRATION Free Vibration of Circular Cylindrical Shells Natural Frequency and Mode Shape WAVE PROPAGATION Wave propagation in Thin-Wall Circular Cylindrical Shells Waves in infinite flat surface Flexural Wave Propagation in a Circular Cylindrical Shells SOUND RADIATION Sound Radiation from Circular Cylindrical Shells Acoustic Modes: Cross-Modes in Circular Cross Section Ducts Coupling between Shell Modes and Acoustic Duct Modes...3

5 3. EXPERIMENTAL PROCEDURE FOR VIBRATION AND ACOUSTIC MEASUREMENTS ON MRI SCANNERS PRESENTATION OF THE SCANNERS AND THEIR IMAGING SETTINGS A few words about functional Magnetic Resonance Imaging Scanners The Echo-Planar Imaging sequences...36 a. MRC-IHR Nottingham fmri Scanner EPI sequence...37 b. FMRIB Oxford fmri Scanner EPI sequence...39 c. WBIC Cambridge fmri Scanner Presentation of the Scanners and the design of their relative Gradient coil system...41 a. MRC-IHR Nottingham fmri Scanner system...41 b. FMRIB Oxford fmri Scanner system...43 c.wbic Cambridge fmri Scanner system EXPERIMENTAL PROTOCOLS MRC-IHR Nottingham Acoustic Measurements MRC-IHR Nottingham Vibration Measurements FMRIB Oxford Acoustic and Vibration Measurements WBIC Cambridge Acoustic and Vibration Measurements RESULTS OF THE MEASUREMENTS RESULTS GIVEN BY THE EXPERIMENTAL ARRANGEMENTS Acoustic cap arrangement and Background noise Noise floor arrangement for the vibration measurement ACOUSTIC MEASUREMENTS MRC-IHR Nottingham scanner FMRIB Oxford scanner WBIC Cambridge scanner General comments on the noise measured VIBRATION MEASUREMENTS Accelerations and displacements of the vibration - Relationship Vibration Results...65 a. MRC-IHR Nottingham scanner...66 b. FMRIB Oxford scanner...69 c. WBIC Cambridge scanner...76

6 4.3.3 General comments on the vibration measured FURTHER INVESTIGATION AND ANALYSIS CORRELATION BETWEEN IMAGING SEQUENCE, ACOUSTIC AND VIBRATION RESPONSES MODAL ANALYSIS Computation of the structural and acoustic modes frequencies Discussion on the validity of the model and the results obtained FURTHER INVESTIGATION Damping of the Gradient coil systems Further investigation with Pure Tones and Impulses CONCLUSION NOISE AND VIBRATION CONTROL, OVERVIEW AND PROPOSAL FOR FURTHER INVESTIGATION OF THE PROBLEM CONCLUSION REFERENCES NOTE: The appendixes are presented in the Technical Memorandum of the project. The measurement tables are included in this Memo as well as references of measurements made on the scanners, recorded on DAT tapes and edited in.wav files on CDs.

7 1. INTRODUCTION In medical diagnostics practice, the Magnetic Resonance Imaging scanner plays an increasingly important role. MRI has become a widely used clinical imaging system capable of yielding tomographic images of excellent spatial resolution. The development of MRI hardware and sequence design continues at a fast pace and the last decade has seen the use of MRI to image brain function (functional MRI process). However, one major problem in magnetic resonance imaging equipment is the high level of noise produced during the scanning process (up to db(a)). In the future, it is expected that new, faster scanning techniques, especially those used for functional neuro-imaging (Echo-Planar Imaging, Echo-Volumnar Imaging), will increase the noise problem. Different surveys have shown that the noise seems to be produced by the strong vibration of the so-called gradient coil system. The investigation of the noise in MRI Scanners has therefore focused on two major points ; the strength and nature of vibration of the gradient coil system and the resulting acoustic noise produced inside the bore where the patient s head should be positioned. The three scanners assessed during this project are all used for functional MRI, but nevertheless differ by their geometry, structure and the design of the imaging pulse sequence. It is therefore difficult to relate all the measurements and to draw generalised conclusions about the structural and acoustic behaviour of scanner coil systems. However, it is possible to compare the "correlation" between the electrical excitation pulse applied to the gradient coils and the induced vibration and/or acoustic responses. The investigation of three gradient coil systems revealed some important characteristics by means of digital processing of recorded signals. Nevertheless, it is also important to set the results in theoretical context. Theoretical studies of the Gradient coil behaviour are therefore presented during the dissertation in both structural and acoustic domains. They therefore set the foundation for any further analysis concerning any noise control possibilities. The dynamic complexity of gradient coil systems has required important assumptions. The system can be assumed to be an axisymetric cylindrical shell. Even though, the theoretical analysis is still subject not to match with the measured behaviour of the system. Modelling then appears to be another alternative, usually providing accurate prediction of noise production of MRI Scanners. However, modelling the gradient coil system involves a large amount of important consideration (such as thickness of layers, geometry, physical properties of each constitutive material) which were unknown most of the time, and therefore made modelling works beyond the scope of this investigation. Nevertheless, the description of the theoretical models aims to provide an overview of the physics behind the sound radiation process and aims to introduce the concept of mode shapes, natural frequencies and cut-on frequencies which appear to have a consequent importance in the noise generation mechanism. The following literature review surveys the noise investigations of MRI scanners made during the last fifteen years and underlines the important research currently made in the domain of vibration control of the gradient coil system. Some works will be more deeply examined in this dissertation as they are in the logical progression of the theory

8 already reported and also as they represent realistic improvement in noise control of MRI Scanners. These researches usually involves analytical and/or modelling works. They will then constitute an important background for the critical analysis of the three Scanners behaviours. The literature review also gives an overview of the Magnetic Resonance Imaging process and all the parameters that constitute important references in the investigation. Finally, during the project, a particular investigation was made at the feasibility of the measurements inside this hostile environment for the equipment and transducers that constitutes the 3 Tesla high magnetic field. An experimental protocol has then been developed for each scanner measurement session in order to set up correctly the measurement procedure but also to avoid any artefactual signal induced by the high magnetic strength. These protocols will also be described in the dissertation as they represented a valuable contribution to the project in itself. 1.1 LITERATURE REVIEW. Different surveys have shown that the noise seems to be produced by the strong vibration of the so-called gradient coil system. More precisely, the MRI process involves current flowing through the gradient coils that are rapidly switched in a complex pattern and, since they do so within a large magnetic field, Lorentz forces deform the gradient coils. These movements translate into intense acoustic noise. The literature on noise in MRI scanners, over the last fifteen years, underlines the important issue of assessing and controlling the noise level. The calculation of safe noise dosage was first the main objective of the acoustic surveys as they aimed at estimate the potential hearing loss resulting from the MR Imaging. The problem of the influence of noise levels on medical diagnostic came with the development of functional MRI. In fact, functional imaging aims at investigating accurately the response of the brain to sensory stimuli (for instance, auditive stimuli, lights) and image changes occurring during motor tasks. High noise levels created by the MRI system therefore represent a source of annoyance for medical investigations. This problem could be tackled by designing effective noise cancellation system based on adaptive or active sound cancellation or by controlling noise at source with MRI system design efforts. Important assessment of the acoustics of fmri scanners have been made by the Magnetic Resonance Center (MRC) and the Institute of Hearing Research (IHR) in Nottingham (U.K.). The following literature review will aim to give an introductory review of the previous works on noise problem in MRI scanners in order to set up the background to further acoustic improvements on the fmri scanners studied during this project. This literature review will provide a brief description of the system architecture of MRI scanners which is essential to understand the parameters influencing the noise level inside the bore of the scanner. Measurements of noise levels made on different type of scanners during the last fifteen years will be reviewed so as to give us a quantitative and qualitative appraisal of the problem. Procedures and techniques of measurement will also be discussed. Finally, the current literature provides different solutions to noise issues in gradient-coil system by developing mathematical model for better design or by elaborating noise cancellation systems which have already been designed and installed on both routine and functional MRI scanners. They involve combination of active and passive techniques, adaptive noise cancellation system or active control of sound power radiated from the cylinder shell. Theses techniques described in the literature will be commented and will give an idea of the issues and the developments to consider upon.

9 1.1.1 Magnetic Resonance Imaging Overview and System Architecture Magnetic Resonance Imaging - Definition. [1] MRI stems from the application of nuclear magnetic resonance (NMR) to radiological imaging. The adjective Magnetic refers to the use of an assortment of magnetic fields and resonance refers to the need to match the radio-frequency of an oscillating magnetic field to the precessional frequency of the spin of some nucleus (hence the nuclear ) in a tissue molecule. More precisely, the spin of a hydrogen nucleus (proton) in a magnetic field precesses (circular motion of the axis of rotation of a spinning body about another fixed axis ) about that field at the Lamor frequency which, in turn, depends linearly on the magnitude of the field itself. The idea of imaging is simple ; If a spatially varying magnetic field is introduced across the object, the Lamor frequencies are also spatially varying. Then, the different frequency components of the signal could be separated to give spatial information about the object System architecture.[] Even if MR Imaging is nowadays executed using a large amount of different imaging techniques, we can still sketch a global system architecture ; Firstly, the patient support which brings the patient in the region where the magnetic field is homogeneous. In most case the static field magnet has a cylindrical bore and its center is called isocenter (homogeneous field). The magnet is situated in a RF-screened room (radio-frequency) to avoid spurious signals from the surroundings (from foreign transmitters or even from the driving electronics of the system itself). The system must be told the required scan, including geometrical parameters, the imaging method, and the sequence via the user interface (host computer). For new imaging methods the gradient field strength as a function of time for each direction and the RF waveform must be entered into the system and written in the memory of the host computer. All this information are downloaded to the spectrometer, which consists of the front head controller (controlling the magnet, gradients, RF transmitter and receiver, RF coils switches, etc.) and the data acquisition around the receiver. The Magnetic Resonance Imaging mechanism is described below. There is first an initialisation phase where the RF receiving coils are tuned. After this phase, the sequence can start switching on the selection gradient. All other components (except of course the magnet) are switched off. When the selection gradient reaches its required value, the RF power amplifier is activated. The input signal of the power amplifier is a harmonic signal with frequency ω 0. This signal is modulated in the waveform generator and fed into the power amplifier. The modulated RF signal drives the transmitted coil so that the desired RF magnetic field, B RF, is emitted. When the RF pulse is ready the output line of the power amplifier is switched to the matched load. Also the selection gradient is now switched off. The result of these actions is that the spins in a single slice are excited. Now the dephasing gradient and the phase-encode gradient are

10 switched on to the strength required by the spectrometer. When these gradient pulses have their required surface, they are switched off and the focusing pulse can now be applied. This 180 RF pulse is usually slice selective and applies to the same slice as the excitation pulse. After the focusing pulse, the read-out gradient is switched on. During this gradient pulse the receiver coil is in a tuned state and the receiver is activated. The magnetisation is measured during the time the read-out gradient is switched on and the ADC samples the received signal at a certain point in time t s. The samples are sent to the array processor, the circuit that performs the Fast Fourier Transform, and the image results from this transformation, which is sent to the viewing section. Figure 1 shows a simple schematic front view and cross-section of an MRI scanner. A more precise representation of the system architecture of MRI scanner is given by Figure. Figure 1: MRI Scanner From Kuijpers A.H. Acoustic modeling and design of MRI scanners. [16] Characteristics of subsystems involved in the generation of noise.[3] As the gradient coils system is the source of the acoustic noise, it appears important to described the technical characteristics of the gradient system and the MR Imaging parameters leading the RF excitation pulse which therefore drive the intensity of the Lorentzian forces applied on the coils. The design of the Magnet, RF coils (transmit and receive coils), gradient coil system, magnetic field-gradients (Slice select, Phase-encoding and Read-out gradients), pulse sequence (TR, TE, FOV parameters) determine the image quality and clinical utility but also the levels of the unwanted noise. Magnet design. The magnet is the heart of the MRI system. Magnet manufacturers tend not to publish details of the technical properties in the MRI literature. However, the following trends

11 have been obvious to users from the early 1980s to the present : (1) an increase in the static field strength used, from 0.15 T to 1.0 and 1.5 T in most new European and North American installations ; () a trend away from resistive magnets to high-field superconducting systems, and low-field open imagers using innovative permanent magnets and iron-cored electromagnets ; (3) significant improvements in static field homogeneity and temporal stability ; (4) the introduction of self-shielding superconducting designs to reduce the area affected by stray fields, without the need for massive iron shielding. Note for (1) : the interest in higher fields stems from the fact that the signal to noise ratio (SNR for the Imaging process) increases with the field strength. Magnet design innovations have contributed both to improved image quality and to reduced installation costs. Radio-frequency coils. Good homogeneity is desirable for both transmitting and receiving coils. Good RF receive coils should also give high signal to noise ratio (in imaging), while transmit coils should minimize RF power deposition. The principal innovation since the 1980s was the Circularly Polarised RF magnetic field design. Appropriate coil choice is essential for the right balance between Field-of-View (FOV) and Signal to Noise Ratio. Magnet and Shim X Gradient Amplifier Waveform Generator Y Gradient Amplifier Z Gradient Amplifier Gradient Coils RF Head Coil RF Electronics ADCs RF Amplifier CPU Shim control Image Processor Image Display Console Data Storage Figure : Schematic diagram of a MRI scanner.

12 The Gradient coil system. Description. The gradient coils are magnets used to make deliberate variations in the strength of the main magnetic field. There are three gradient magnets, one in each of the X, Y, and Z planes. The arrangement of the magnets means that each individual point within the MRI scanner is subject to a slightly different, but known, magnetic field. The readout gradient coil is namely the X gradient coil and covers the X-plane which runs left to right through the patient. The Phase encoding gradient coil is namely the Y gradient coil and covers the Y-plane which is the plane at 90-degrees to the ground and running through the patient from the front to the back. The Slice select gradient coil is namely the Z gradient coil and covers the Z-plane which is running through the bore and longitudinally through the patient. The gradient coils are firstly required to produce a linear variation in field along one direction. Linear variation in field along the direction of the field (labelled z- axis) is usually produced by a Maxwell coil. This consists of a pair of coils separated by 1.73 times their radius as shown in Figure 3. Current flows in the opposite sense in the two coils, and produces a very linear gradient. To produce a linear gradient in the other two axes requires wires running along the bore of the magnet. This is best done using a saddle-coil, such as the coils shown in Figure 3. This consists of four saddles running along the bore of the magnet which produces a linear variation in B z along the x or y axis, depending on the axial orientation. This configuration produces a very linear field at the central plane, but this linearity is lost rapidly away from this. In order to improve this, a number of pairs can be used which have different axial separations. B z Maxwell Z gradient Y gradient X gradient coil Figure 3 : Schematic diagram of the Gradient coil system

13 If a gradient is required in an axis which is not along x, y or z, then this is achievable by sending currents in the appropriate proportions to G x, G y and G z coils. If for example a transverse gradient G at an angle θ to the X-axis is required, then a gradient Gcosθ should be applied in the x direction, and Gsinθ in y. The first layer (inner surface) of the Gradient coil system usually includes the X gradient coil (Gx) and the second layer (outer surface), the Y gradient coil (Gy). These two parts of the system are gathered together usually with epoxy resin so as to give cohesion to the system but also to reduce the vibration occuring when the applied currents are driving the gradient coils. Characteristics and Requirements. Good gradient coils should be highly linear over a large Field-of-View, able to switch gradient fields on and off extremely rapidly and induce virtually no eddy currents in the large metal structures which enclose them. Rapid imaging methods such as Echo-Planar Imaging (EPI) and fast spin-echo methods are more efficiently performed in systems with low gradient switching times. The eddy currents is an other source of annoyance but in the field of imaging. They are set up in the superconducting magnet windings by the changing magnetic flux leaking from the gradient coils during switching. They cause temporal distortions of the desired gradient waveforms. They are particularly bothersome when performing EPI and other rapid imaging methods. Even if this eddy currents are not directly source of noise in the gradient system, it is worth to notice this parallel inducedeffect which may or not interfere on Lorentzian force, but nonetheless it made the gradient coils to be actively shielded so that the magnetic flux did not escape from the inner volume of the cylinder former. This resulted in the design of shielded gradient coil reducing therefore the space available in the system and made this hostile environment to leave very little space for extra acoustic shielding. Pulse Sequence design. Pulse Sequence design is a important parameter of noise generation in MRI scanner. Gradient-echo sequence (GRE), Spin-echo sequence (SE), Echo-planar Imaging (EPI) have different settings but they all create very high sound-pressure levels from stray electromechanical radiation. Additionally, in the near future, Echo-volumnar Imaging (EVI) will be pursed to acquire more information per unit time that will exacerbate the noise problem at source. (Note on the meaning of the word echo : in order to form an image, a number of Nuclear Magnetic Resonance signals, or echoes, are required.) Echo-planar imaging (EPI) is an extremely rapid method, gathering all the data to form an image after a single excitation pulse (Ultra-fast single-shot methods). Gradient-echo sequence belongs to the «Short Time-Repetition methods» where sequences collect only one gradient echo per RF excitation but achieved rapid scan times by greatly shortening TR. The Spin-echo sequences are using a number of excitations. Each echo of the echo train is allocated to traversing a particular segment and the pulse sequence is repeated until the echo has collected all the lines in its allocated segment. Spin-echo sequences are often used in shielded magnetic field gradient. GRE an SE sequences are usually found in routine MRI scanners (1.5 T) and EPI method is more devoted to functional RMI scanner (3T). Nevertheless these methods are all characterized by three main parameters which

14 drive the pulse and therefore the induced-noise level: TR = Time Repetition of the pulse; TE = Echo Time of the pulse; FOV = wanted Field-Of-View. These three parameters have to be taken into account during any noise measurement. They describe the pulse sequence and therefore influence the noise level inside the bore of the scanner Measurement of Noise Levels Results found in the literature. Acoustic surveys about noise in MRI scanners have been made during the last ten years. Hurwitz R. et al (1989, [4]) has made in 1989 an acoustic analysis of the gradient-coil noise in MR Imaging system of T. Noise levels were measured at bore isocenter during a variety of imaging sequences in six MR Imaging systems. Measured noise ranged from 8 to 93 db on the A-weighted scale and from 84 to 103 db on the linear scale. McJury M.J. et al (1993 [5], 1995 [6]) made measurements in 1993 of the acoustic noise levels generated on two high field MRI system (1.0 T and 1.5 T) and latter, in 1995, has compared the results between a standard an upgrade gradient sytem. Shellock F.G. et al (1994, [7]) assessed acoustic noise levels occurring in MRI scanners six worst case pulse sequences. The highest noise levels during MR imaging occurred during the use of a gradient-echo (GRE) pulse sequence and was 10 db at the entrance and the exit of the magnet bore and 103 db at the center (A-weighted scale). Shellock F.G. et al.(1998, [8]) has also reported that scanner noise is as high as 115 db(a) during Echo-planar imaging at 1.5 T. Very high-field scanners (3T and 4T) are becoming more commonly used for functional MRI and there is an evidence that the sound level is even greater than at 1.5 T. Foster J.R. et al. (1999, [9]) found that 3 T MR scanner generates EPI acoustic noise in the region of 1 to 131 SPL (13 to 13 db(a)) measured at the position that would be occupied by the patient s head. These results found in the literature have been listed in the following table according to the strength of the static magnetic field and the parameters of the pulse applied to the gradient coil system.

15 Static magnetic field strength ( T ) Pulse sequence TR (msec) TE (msec) 0.35 Gradient-Echo sequence Gradient-Echo sequence Gradient-Echo sequence FLASH D - GRE based Spin-Echo sequence Spin-Echo sequence Gradient-Echo sequence Gradient-Echo sequence FLASH - GRE based GRE steady state GRASS std ( C-Weighted) 1.5 FLASH - GRE based Spin-Echo sequence unknown Spin-Echo sequence SE High resolution ( C-Weighted) 1.5 Echo-planar Imaging unknown unknown unknown unknown 115 unknown FOV ( cm) Slice Thickness (mm) A-weighted Noise level (dba) Linear Noise level (db) These results have also been plotted so as to figure out the probable effect of the static magnetic field on the noise levels measured inside the bore of different MRI scanners. This roughly confirms the tendency of the induced-noise to grow with the strength of the magnetic field.

16 Noise Levels measured at the isocenter of MRI scanners Noise Levels dba Series1 Series db (linear) Static Magnetic field strength in the bore, Tesla ( T) Moreover, the cited acoustic studies revealed trends concerning the behavior of the noise generation during the different pulse sequences. It has been found that noise levels at bore isocenter increased during sequences employing thinner section thickness, shorter repetition time (TR) and echo time (TE) and large field of view (FOV). One obvious point was that Gradient-echo sequences produce the largest acoustic noise. Moreover, the current trend toward faster imaging techniques and thinner sections will likely generate even greater noise levels Noise generation process. During imaging, magnetic flux gradients are repeatedly switched on and off at intervals of approximately 5-10 msec. From first principles, current passing through a wire placed in a magnetic field will generate a force orthogonal to the direction of both the field and the current. All the references in the literature have proposed the cause of gradient-coil noise to be pulsating Lorentz forces. The induced noise would be caused by the impact of the gradient coil against their mountings during the pulse sequences. Figure 4 gives a simplified explanation of gradient-coil knocking. The gradient coil is shown as a single winding for illustrative purposes. When the gradient coil is pulsed by current I, a brief force is created in a radial direction.

17 F I B o Figure 4. Gradient coil noise is therefore complex to assess and some of the literature references suggest procedures and techniques for best measurements Noise measurement procedures. The first priority of Hurwitz R.et al. study (1989, [4]) was to verify the reliability of the sound-pressure detection instruments. Neither high magnetic flux nor RF pulses interfered with the measurement of ambient of MR imaging gradient-coil noise. Neither the orientation of the microphone nor the plane of imaging was found to be relevant: the magnetic flux had no lasting effect on the acoustic device. But there are still some precautions to take in the layout when measuring MRI noise. Hurwitz R. et al. (1989, [4]) have mounted the microphone on a small plastic stand positioned so that the microphone diaphragm was at the isocenter of the magnet bore and parallel to the static magnetic field. The microphone was connected to the sound level meter with a 30 meters extension cable (4 meters for Shellock F.G. et al (1994, [7])). Measurements in magnetic fields need the equipment to be tested at first. Referring to Hurwitz R. et al recommendation, after instrument calibration, tests have to be conducted in order to exclude any effects of either the static magnetic field or radio-frequency pulse on the function of the system consisting of the microphone, extension cable, and preamplifier. Usually, the sound meter and recording equipment are placed outside the shielded MR system room and beyond a 3 Gauss (0.3 mt) fringe field of the static magnetic field for Hurwitz R.et al, Gauss (0. mt) for Shellock F.G. et al and 100 Gauss (10mT) for Foster J.R. et al. In the experiment conducted by McJury M.J. et al (1993 [5], 1995 [6]), the meter used was partially sensitive to the main field of the magnet and so was positioned beyond the 0 G (mt) boundary at the front of the magnet bore. But a particular aspect of the procedure was that a section of non-magnetic tubing was connected to the built-in condenser microphone to channel noise from the magnetic isocenter. Measurements were made to calibrate the meter and the tubing combination with respect to the frequency dependence and attenuation of sound. Errors resulting from the frequency dependence of the tube were found to be minimal and a simple single value of correction over the frequency range was used. Equipment: requirements, type and settings. For the accuracy of the acoustic noise measurements, the equipment must be magnetically transparent and reflect air-borne sound pressure rather than artefactually induced signals.

18 In most of cited surveys, the equipment used for sound-level measurement and calibration was manufactured by Bruel & Kjaer (Denmark): Sound level Meter B&K of type 30 [4], 04 [6], 35 [9] ; Condenser Microphone B&K of type 4155 [4], 4165 [9]. Concerning the effect of magnetic field, B&K gives the following guidance: When measurements are to be carried out in strong magnetic field, the influence of the field should be checked using a pistonphone, calibrator or silica gel cap to acoustically shield the microphone. The meter should then drop by 10 or 15 db if the effect of due to the magnetic field is to be assumed negligible. If the damping achieved is considerable less than this and moving the microphone results in a variation in the meter reading, the magnetic field will affect the measurement accuracy. Surveys follow this guidance. Concretely, Foster J.R. et al have noticed that the acoustic cap attenuated the level of the scanner sound by 4 db or more. Thus, interference artefacts made a negligible contribution to the measures. Concerning the sound level meter, it has to be set with special application in mind. The surveys (Hurwitz R.et al.[4]; McJury M.J. et al [5] [6]; Foster J.R. et al.[9]) report measurement made in both Linear (db SPL) and A-weighted (db(a)) scale with the Fast root-mean-square (RMS) time constant (15 ms). Sometimes levels were measured using the peak characteristic (<100µs) which tends to give an higher measured level related to short-term peaks in the signal. Choosing the weighting network can be also an important issue when the aim of the measurement is to quantify the noise level regarding to the human ear sensitivity. Originally, four different weighting curves (A, B, C and D) were made to reflect the fact that the human hearing has a level-dependent frequency dependence. Most of the surveys have reported levels in db(lin) and db(a). Nevertheless, considering the high sound pressure levels reported previously inside the bore of MRI scanner, the use of C weighting network appears to be more appropriate to the investigation. Indeed, the C-curve is designed to follow approximately the equal loudness curve of 100 phons (i.e. the noise is highly perceived), and therefore the C weighting network is used for measuring SPLs of 85 db or more ( A weighting is used in the range of 0 to 55 db). However, the A weighting network is more widespread in the surveys and used for standardisation. db(a) can still be employed independently of the noise levels and its difference with C-weighted levels can actually provide direct information about the spectral properties of the sound measured Issues: Noise and Vibration Control, Acoustic Modelling and Design of MRI Scanners. At first, in MRI scanners, sound attenuation can be achieved by means of energy absorbing materials place on the surface of the radiating structure. For instance, passive noise reduction method have been applied on the fmri scanner studied by Foster J.R. et al.[9] by installing a lining of acoustic foam around the gradient. More precisely, the foam was positioned between the shim coils and the gradient coils with the front-facing foam placed towards to the gradient coils (i.e. towards the noise source). This reduced the scanner sound level at the centre of the bore by 10 db (from 1 to 11 db SPL). No additional attenuation was gained by placing a foam lining between the gradient coil and the RF coil, nor at the head and foot of the scanner bore. The passive technique works quite well for sounds of medium and high frequencies but is very inefficient at low frequencies because the thickness of the absorbing material necessarily increases with decreasing frequency.

19 Active noise control is an alternative to this passive strategy where destructive interference is used to reduce the sound pressure field. Naghshineh K.et al (1998 [10]) proposed a more advanced form of this technique that could be applied on the MRI bore. This technique, named ASAC (Active Structural Acoustic Control) is based on altering the vibrations of a noisy structure such that it radiates very little sound. This alteration is achieved by introducing discrete force actuators at select points on the cylindrical shell. These actuators are driven via digital controller that receives the noise or vibration signal from a sensor array located on the surface of the structure. This technique is successful in controlling the sound power radiated from the cylindrical shell. In a paper made by Qiu Jinhao et al (1995, [11]), the idea of controlling the vibration of the shell excited by the Lorentz force has been developped. Simulation on the vibration control of the shell were carried out by using piezoelectric actuators which produced a bending moment or an in plane force when pulse voltages were applied synchronously with the pulse current of the coils. The simulations showed that the vibration level was successfully reduced in the frequency range of 400Hz-100Hz. In 1995 also, numerical and experimental studies of the vibration and acoustic behaviors of MRI gradient tube were conducted by Ling J.X. et al (1995, [1]) where a 3-dimensional finite element model was developed to study the vibration and acoustic characteristics of the tube using ANSYS (Finite Element Analysis code). Linear transient analysis as well as the coupling dynamic and acoustic analysis has been executed. The linear transient analysis, which deals with the dynamic response of the cylindrical shell under periodic loading, results in the displacement and acceleration times histories of the tube. The coupling analysis predicts the air motion (then the sound wave) on the patient side of the tube. All the numerical results were in good agreement with the experimental data and provided valuable information for evolving the gradient design. Consequently, an optimal design of gradient system has been achieved and provided a 1-15 dba noise level attenuation compared with previous design. Recently, Mechefske C.K. et al. (000, [13]) have shown that the sound pressure distributions along the centerline of a MRI gradient coil cylinder obtained by both simulation and measurement are in close agreement. This suggests that simulation and measurements can correlate well and then FE models can particularly be developed so as to perform accurate acoustic simulation and analysis of the Gradient coil system. FE based simulation method should therefore lead to gradient design improvement. Finite Element Method (FEM) or Boundary Element Method (BEM) in the design process of complex structures are more and more employed and will increase with the computational power of the modern computer and maturation of the software. However this trend to use FEM and BEM in the design process has been discussed by Kuijpers A. et al (1998, [14]) who affirm that this methods have a major drawback : they do not give the insight as they do not relate directly design changes to acoustic response changes. Kuijpers A. et al (1998, [14]) and Kessels P.H.L.(1999, [15]) propose that the problem can be tackled by the development of problem domain specific tools. In these tools the geometry of the acoustic domain is restricted, but this simplification a much better understanding of the acoustical phenomena in that domain is gained. The benefits of that approach is presented in Kuijpers A. PhD thesis (1999, [15]) with the development of a mathematical model for the acoustic radiation of a MRI scanner. The model for the noise production of MRI scanners can be subdivided in parts : a structural part which deals with the generation of structural vibrations due to Lorentz forces excitations and with the structural-acoustic optimization techniques (Kessels P.H.L. companion doctoral thesis 1999, [15]) ; and an acoustical part describing the

20 transformation of the structural vibrations into audible noise (Kuijpers PhD thesis 1999, [16]). Kuijpers affirms that an adequate acoustic model for low-noise design of MRI scanner and its gradient coil must incorporate aspects : the specific geometry of the scanner and its complex boundary conditions. As a first approximation, the geometry of the scanner can be modelled as being axisymetric. In his thesis, Kuijpers proposes the model of a finite duct with opens ends mounted with infinite flanges. This way, it is possible to use duct acoustics theory and achieve increased insight. Moreover, a semianalytical formulation for the acoustic radiation of the model raised by the author (by using a Fourier transformation technique for the Helmotz equation and the velocity boundary condition s at the duct s wall) leads to the development of accurate and efficient numerical tools. Secondly, the boundary conditions can be approximated by assuming that the gradient coil (assimilated as walled duct) can vibrate and thus radiate acoustic energy. The 3-dimensional Boundary Element Method was not feasible because of the huge computational requirements. Nevertheless, this was accomplished by utilising the so-called Fourier-BEM method, which exploits the axisymmetric properties of the geometry without axisymmetric boundary conditions, and hence reduces the dimensionality of the problem by one. The parameter studies, which is another important point of the thesis, revealed that the radiated sound power and the sound pressure level in the MRI bore respond similarly to design changes, in contrast with the velocity level. This means that the radiated power is an appropriate design objective function, because it is directly related to the noise that is experienced. Additionally, it enables the use of the radiation modes reduction technique which is employed by the author for the modal description of the acoustics. Finally, the physical and computational characteristics of the model, determined by parameter study and by comparison with Fourier Boundary Element Method (BEM) models, led the application of the mathematical model in the design process to be viable.

21 . THEORY. A satisfying theoretical model of the gradient coil system structure is difficult to find. In fact, the complexity of the system, its non-homogeneous layout and its usual dimensions do not permit a total comparison to any analytical model that could seem to be suitable and that could have been developed previously in the literature. It is however obvious that the gradient coil system has a form approximating a circular cylindrical shell. Nevertheless, most of the simple analysis of the dynamic and acoustic behaviour of cylindrical shell were done on shells with thin-wall. It is then a dangerous assumption to compare the gradient coil system to these analytical models, but this gives nevertheless meaningful insight of what could generally occur to the system in terms of vibration or sound propagation. Moreover, this theoretical analysis is mainly justified by the fact that it gives an overview of the problem and describes the parameters on which a possible control development can be based. There is not general agreement in the literature on the linear differential equations which describe the deformation of the shell. A number of theories have arisen and are used. The differences among the theories are due to various assumption made about the form of small terms and the order of terms which are retained in the analysis. The Donnell (1938) and Mushtari (1938) shell theories are the simplest of these theories. The Flügge (1934) and Sanders (1959) shell theories are generally felt to be the most accurate. Nevertheless, over broad ranges of parameters of engineering importance, these theories yield similar results. Each of the shell theories mentioned above describes the motion of the shell in terms of an eighth-order differential equation. Only the Flügge and Donnell theories will be developed in the theoretical part. The Flügge shell theory is indeed much described in the litterature, but is also the foundation of a vibration modes control of cylindrical shell developed by Qiu J. and Tani J. (1995, [11]) which will be commented upon. Donnell shell theory will additionally give simple but nonetheless meaningful prediction of natural frequencies of the studied structures assimilated to cylindrical shells..1 STRUCTURAL VIBRATION..1.1 Free Vibration of Circular Cylindrical Shells. [17] y u r a w v θ z x Figure 5: Cylindrical Co-ordinates System.

22 Let the displacement components of the mid-lane of the shell be u, v, and w in the axial, tangential and radial directions. the motion of the shell is described by the following Flügge's shell equations (Flügge 1960) : ( ) 0 ) ( = ν ρ θ ν + ν + θ + ν + θ + ν + t u E w z R h z R h z R z v R u R h R z s 0 ) (1 4 ) ( = ν ρ θ ν θ + ν + + θ + θ + ν t v E w z R h R v z R h R z u R s 0 ) ( ) (3 4 ) ( = ν ρ + θ + θ + θ θ + θ ν + θ ν + ν + t w E w R h R h z R h z h R h R v R z R h u z R h z R z R h s where r, θ, and z are cylindrical coordinates, t is the time, and the physical characteristics of the shells are defined by the mean radius R, wall thickness h, density ρ s, Young s modulus E, and Poisson s ratio ν. A traveling wave solution is sought for the shell: ] ) / (.exp[.cos ] ) / (.exp[.sin ] ) / (.exp[.cos l z t c i n w w l z t c i n v v l z t c i n u u p p p π θ = π θ = π θ = where u is the deformation parallel to cylinder axis, v is the circumferential deformation and w is the radial deformation. u, v, and w are arbitrary constants to be determined from the equations of motion. Substitution of equations (.) into equations (.1) gives three linear algebraic homogeneous equations for u, v, and w : = w v u a a a a a a a a a, where (.1) (.1) (.) (.1)

23 a a a a a a 1 ν δ = α n 1+ ν = a 1 = i αn, = a = n δ = i να + α 1 1 ν δ α 3 δ (1 4 + Ω Ω, δ = a 3 = n + (3 ν) nα, 4 δ = 1+ [1 + ( α + n ) n 1, ν) αn ] Ω,, (.3) (.3) with α = πr, δ = l h ρ s, Ω = Rω R (1 ν E ) 1/, and ω = πc l p For a nontrivial solution of these simultaneus equations, the determinant of the coefficients of the unknowns should vanish. The resulting characteristic equation is the frequency equation: a ij = 0. (.4) Alternatively, the frequency equation can be written in the functional form: F(Ω, α, n, ν, δ) = 0 (.5) The shell, undergoing free vibration, can be defined in a variety of ways, as shown in Figures 6. The vibration of the shell can consist of a number of waves distributed around the circumference as shown in Figures 6a for n = 0, 1,, 3, and 4. n is the number of circumferential waves in the mode shape. In the axial direction, the deformation of the shell consists of a number of waves distributed along the length of a generator, as shown in Figures 6b for 1/ l, l, 3/ l, where l is the wave length and in other terms, for m = 1, m = and m = 3, where m is the number of axial half-waves in the mode shape. For a given shell, δ and ν are fixed. The natural frequency Ω depends on α and n only. Two special cases are considered : Circumferential modes. Consider those modes of oscillations that are independent of the axial coordinate z ; i.e. those modes having frequencies corresponding to an infinite phase velocity. The equations for these modes are obtained by setting α = 0 in equation (.5) ; i.e.

24 0 1) ( 1 1) ( = δ + Ω δ + + Ω ν δ + = Ω n n n n n Symmetric modes. For n = 0, equation (.5) can be written 0. 1 ) (1 1 1 ) ( = α δ να + + δ Ω α Ω = α ν δ + Ω n and and (.6) n = 0 n = n = 3 n = 1 n = 4 Breathing Beam bending or Translation Ovalling Figure 6a: Circumferential Nodal Pattern Figures 6: Nodal Patterns of Shell with Simply Supported ends without Axial Constraint. From Blevins R.D. Formulas for natural Frequency and mode shape[18]. (.7)

25 m = 1 m = m = 3 (1/) l l (3/) l Figure 6b: Axial Nodal Pattern Circumferential Node Axial Node Figure 6c: Nodal Arrangement for n = 3 and m = 4.1. Natural Frequency and Mode Shape. [18] Recalling the formula for the natural frequency of the cylindrical shell Ω : Ω = 1/ ρ c s (1 ν ) π p R ω, with ω = = πf n, m E l (.8) The natural frequency of the shell therefore depends on the formula of Ω in each structural mode. The general description of the structural modes of the cylindrical shell by Circumferential and Symmetric modes is somewhat not precise. Refering to Donnell shell theory, these two generalised modes (Circumferential and Symmetric) can be precisely decomposed in a series of particular modes which are nevertheless generally coupled during the vibration of the shell. Each of them provides an individual formulation of the parameter Ω given by the Donnell theory. We will confine our attention on the modes which are likely to occur and be responsible for intensive noise radiation. The natural

26 frequencies of the concerned modes will therefore be computed. Chapter 5 will present the results obtained as the analytical solutions for the three Gradient coil systems. The natural frequency can be expressed as : f n, m Ω n, m = πr ρ s E (1 ν ) 1/ (.9) The following modes are analytically supposed to occur in a simply supported Cylindrical Shell without Axial Constraint. These formulas are appropriate for long cylinders where the ratio L/(mR) (effective shell length) is higher than 8. Torsion Modes. (n = 0) (1 ν) 1/ Ω n, m = 1/ mπr L with n = 0 and m = 1,, 3,... (.10) Axial Modes. (n = 0) 1/ R Ω n, m = mπ( 1 ν ) with n = 0 and m = 1,, 3,... L (.11) Radial Modes. (n = 0) Ω 1 with n = 0 and m = 1,, 3,... n,m = (.1) Bending Modes. (n = 1) 1/ m π (1 ν) R Ω n, m = with n = 1 and m = 1,, 3,... 1/ L (.13) Radial-Axial Modes. (n =, 3, 4, 5,...) (Modes dependent on the circumferential angle θ) Ω n, m = (1 ν 4 mπr ) L h + 1R mπr L n + n mπr + L 4 1/ (.14) with n =, 3, 4,... and m = 1,, 3,... Note: For higher circumferential modes, n =, 3, 4,..., the deformation of the shell is dominated by radial motion.

27 . WAVE PROPAGATION...1 Wave propagation in Thin-Wall Circular Cylindrical Shells. [19] Flexural waves and Ring Frequency. If the ratio of cylinder diameter to wall thickness is large, wave propagation involving distortion of the cross section is of practical importance even at relatively low audio frequencies. If the wall thicknesss is uniform, the allowable spatial form of distortion of across section must be periodic in the length of the circumference. The axial, tangential, and radial displacements of the wall must vary with axial position z and azimutal angle θ as : [ U ( z), V ( z), W ( z) ] cos( ), u, v, w = nθ + Φ (.15) where n is known as the circumferential mode order and 0 n. At any frequency, three forms of wave having a given n may propagate along an in vacuo cylindrical shell. Each has different ratios of U, V, W which vary with frequency (Leissa, 1973). It is nearly always necessary to consider the three displacement u,v,w of a cylindrical shell. The principal reason is that a radial displacement of the wall of a cylindrical shell creates tensile or compressive tangential and axial membrane stresses, depending upon whether the displacement is positive or negative, because the length of a circumference is proportional to its radius. For the purposes of studying sound radiation and response behaviour of cylindrical shells that do not contain dense fluids, it is only necessary to consider the vibration waves in which the radial displacement w is dominant, the so-called flexural waves. The speed of propagation of these waves in the direction of the longitudinal axis of the cylinder is very dependent upon the circumferential mode order n because the relative contributions to strain energy of membrane strain and wall flexure depend upon this parameter. In addition, a cylindrical shell exhibits waveguide behaviour in that a mode of propagation having a given n cannot propagate freely below its cutoff frequency, at which the corresponding axial wavenumber and group velocity are zero. A cutoff frequency corresponds to a natural frequency at which the modal pattern consists of a set of n nodal lines lying along equally spaced generators of a uniform shell of infinite length. the cutoff frequency of the n = 0, so-called breathing mode of a shell is termed the ring frequency and is given by : (.16) = c 1 ' / πd, f r where d is the cylinder diameter. At this frequency, radial hooplike resonance occurs. In dynamic shell theory, frequency are usually made non-dimensional by dividing by f r : Ω = f/f r. Then, below Ω = 1, the breathing mode cannot propagate, although axial and tangential n = 0 modes can. One result of the membrane strain on flexural waves propagation speed in cylindrical shells is that the phase velocity of flexural waves in modes of low n can be much greater than the speed of sound in a surrounding fluid at frequencies well below the flat-plate critical frequency, as given the particular combination of shell material, wall thickness and speed of sound in the fluid. The effect is that such modes can radiate rather effectively.

28 .. Waves in infinite flat surface. (.) The vibration of most mechanical systems exhibit complex frequency dependent spatial distributions of amplitude and phase. It is therefore useful to compare actual structures with infinite flat surfaces. In parts.3.1 &.3.3, a comparison of flat-plate and circular cylindrical-shell flexural wavenumber behaviour will be done which will lead to a qualitative discussion of the consequent difference between radiation behaviours. It is therefore helpful to recall the principal characteristics of wave propagation in infinite flat surface and the concept of radiation efficiency, bending or flexural waves and critical frequency. The most important type of vibration of plates is flexural or bending waves. This is governed by a fourth order differential equation, e.g. for one-dimensional waves on a homogeneous plate : Eh ( ν ) 4 w w + ρm h = f, 4 x t ( x t) (.17) where h is the thickness, ρ m is the density, E is the Young s modulus, and ν is the Poisson s ratio. A free wave solution of equation (.17) is of the following form : (.18) w ± t ( x t) Ae jkx e j ω, = This leads to an expression between wavenumber k = π/λ ( spatial frequency ) and ( temporal ) frequency ω : (.19) 3 Eh 4 k ρ ω = 0 m h 1 1 ν ( ) This equation is called Characteristic Equation. The dependence of k = π/λ on ω = π/t is known as the Dispersion Relation : 1 1 k = Eh 4 ( ν ) ρ 1/ 1/ m ω (.0) For acoustic waves in a fluid (e.g. air) k = ω/c o where c o is the speed of sound, independent of frequency. These waves are non-dispersive, and all frequency components travel at the same speed. Bending or fluxural waves are dispersive and therefore the wavespeed depends on the frequency. The corresponding wavespeed c b can be expressed as follows : (.1) c b = ω k b Eh = 1 1 ( ν ) ρ m 1/ 4 ω 1/

29 Dispersion curves, which plots the flexural wavenumber k b as a function of the frequency ω, can then be drawn and present the following characteristics illustrated by Figure 7. Bending Wavenumber k b Sound k Bending Wave k b ω 1/ f c Figure 7: Dispersion Curve for bending waves. Frequency [Hz] The critical frequency f c of a bending wave is defined as the frequency at which the bending wavenumber equals the wavenumber in air. For a homogeneous material, the critical frequency can be expressed as : ( 1 ν ) co 1ρ m f c = πh E The critical frequency is therefore dependent of the material characteristics (E, ν,...) Radiation Efficiency. The sound power radiated from a plate can be expressed as follows: w = ρ c S v σ where S is the total surface area, rad o o v is the surface-averaged mean square normal velocity and σ is called the radiation efficiency. When σ = 1, a structure radiates as efficiently as the infinite flat surface. At low frequencies, σ << 1 and at high frequencies σ tends to 1. Radiation from bending waves. (.3) At low frequencies, i.e. f c << f, σ << 1. For an infinite plate with a free bending wave, the sound radiation is zero. This is because of the Acoustic short-circuiting between the radiation from maxima and minima of the vibration pattern. For a finite plate, the edges and corners results in a net radiation of sound.

30 At high frequencies, i.e. f > f c, σ tends to 1. Sound is radiated at an angle θ to the plate as illustrated in Figure 8. The relationship between acoustic and bending waves can be expressed with the following relations : λ k air b = λ = k air b sin θ, sin θ Radiated Sound θ Figure 8: Sound Radiation of Plate At the critical frequency sin θ = 1, i.e. sound is radiated parallel to the plate...3 Flexural Wave Propagation in a Circular Cylindrical Shell. [19] Flexural-type waves propagating in a uniform cylindrical shell may be characterised by axial and circumferential wavenumbers k z and k s, as shown in Figure 9. r y Φ k s k z θ k cs z a x Figure 9: Cylindrical Coordinates System The wavefronts of free propagating waves of wavenumber k cs form a helical pattern like a barber s pole, the angle between the wavevector and a generator of the cylinder being given by θ = tan -1 (k s /k z ). Characteristic waveguide modes can be formed by the superposition of helically propagating waves having the same axial wavenumber components k z and oppositely directed circumferential wavenumber components ± k s. The closure of the shell in the circumferential coordinate direction requires that the wave variables be continuous around the circumference and that the characteristic

31 circumferential patterns take the form sin(k s s) or cos(k s s), where s = aφ and k s = n/a (n = 0, 1,, 3,..., ), so that an integer number of complete circumferential wavelengths, λ s = π/k s = πa/n, fit around the circumference. The wavenumber relationship is : k ( n ) k k k / a z = cs s = cs (.4) where k cs is the wavenumber of the two propagating helical wave components. The two most important cylindrical-shell parameters are the non-dimensional frequency Ω = ωa/c l = ω/ω r and the non-dimensional thickness parameter β = h / 1a, where h is the wall thickness and a the mean radius of the shell, c l the longitudinal wavespeed in a plate of the shell material, and ω r = c l /a (rad.s -1 ) the ring frequency (.16). The physical significance of these parameters is as follows: The ring frequency ω r is the lowest frequency at which an n = 0 axisymmetric-mode resonance can occur. The longitudinal wavelength in the shell wall equals the shell circumference when Ω = 1, and an n = 0 breathing, or hoop, resonance occurs at this frequency. Note that ω r is depedent upon the cylinder radius, but not on the wall thickness. An important property is that the ring frequency separates frequency regions in which wall curvature effects are more, and less, important. This property will be commented in more details in the next part..3 SOUND RADIATION..3.1 Sound Radiation from Circular Cylindrical Shells. [19] The influence of shell curvature on sound radiation derives primarily from its effect on the flexural wave dispersion characteristics, particularly at low wavenumbers. Curvature generally increases flexural wave phase velocities through the mechanism of mid-plane strain, with a consequent increase of radiation efficiency. Associated with the increase in wave speed is a reduction in the density of natural frequencies. The surface radial velocity of a wave propagating axially in a cylindrical shell of infinite length may be represented as v ( z, Φ, t) = v cos nφ exp[ j( ωt k z)], n n z (.5) n = 0, 1,, 3,... for the cylindrical coordinate system shown in Figure 8. Sound energy can be radiated as long as the surface axial wavenumber k z is less than the acoustic wavenumber k. The cosinusoidal variation with Φ in equation (.5) results from the interference between circumferential wavenumber components travelling in opposite directions around the cylinder; that is to say that equation (.5) represents the interference field of two helical waves of equal and opposite circumferential wavenumber and equal axial wavenumber. Under the conditions: k z < k, k s = n/a > k, and k z + k s > k, (.6)

32 which are not relevant to the n = 0 mode, adjacent zones of positive and negative volume velocity distributed around the circumference, seen in Figures 6, do not completly cancel. However, their close proximity, in terms of acoustic wavelength, makes their radiation very inefficient. The n = 0 breathing mode radiates as a line monopole; the n = 1 bending mode radiates as a line dipole; the n = ovalling mode radiates as a line quadrupole, and so on, the efficiency of radiation at any frequency decreasing with increase in the order of the equivalent source. The corresponding expressions for power radiated per unit length, for ka << 1 and k z << k, are 1 Pn = 0 = π ρoca( ka) vo, 1 3 Pn 1 = π ρ ca( ka) v1, (.7) = o Pn = = π ρoca( ka) v. 3 The value of the circumferential wavenumber k s = n/a (n is the circumferential number and a is the cylindrical radius) for a given n decreases with the increase of cylinder radius. Hence large radius cylinder modes of order n can satisfy the condition k z + k s < k (.8) at frequencies for which the equivalent modes of smaller cylinders, having the same radial wavenumber, give k z + k s > k. In this case, inter-zone cancellation does not occur and the cylinder radiates with a radiation resistance close to ρ o c per unit area. This shows that it is not sufficient that the frequency at which a cylinder vibrates in the bending modes (n = 1) should exceed the critical frequency based upon the bending waves phase velocity in order to radiate efficiently; it is also necessary that: (k - k z ) 1/ a > 1. (.9) For thin-wall cylinders in which the wall thickness is much smaller than the radius, the n = 1 bending-mode axial wavenumber is: k z = (ρω / a E) 1/4 (.30) The transition from inefficient to efficient radiation occurs rather rapidly, as Figure 10 indicates, so that for most practical purposes sound radiation from transversely vibrating slender bodies can be considered to be negligible if equation (.9) is not satisfied. Similarly, only when equation (.8) is satisfied will radiation from the cross-sectional distortion be significant. Note: The theory, which have been described so far, only intends to give an overview of the sound radiation mechanism and its characteristics that could maybe tally with the experimental investigation. Assimilating the MRI gradient coil system as a thin cylindrical

33 shell somewhat simplifies the vibration and the sound radiation of the studied systems. The assumption of thin walls cannot usually be justified. Nevertheless, the information of a radiation efficiency dependent on the structural mode, the properties of the dispersion relationship, the characteristics of the wavenumber diagram constitute a meaningful knowledge which enables to elaborate correctly the procedure of investigation. The following theoretical parts will see the development of the dispersion relationship for thin cylindrical shell, cut-off frequencies of both structural and acoustic modes. They aim to introduce the coupling between shell modes and acoustic modes which will inevitably occur, but they also set the context in which decoupling or any other control can be worked out. Figure 10: Radiation Efficiencies of Uniformly Vibrating Cylinders. From Fahy F. Sound and Structural Vibration Dispersion Relationship and Cutoff Frequencies of Flexural modes. There are many thin-shell equation of varying degree of complexity, the differences arising largely from differences in the assumed strain-displacement relationships (Leissa, 1973). In this part, Frequency and Dispersion relationships derived in relatively simple form will be used to emphasise the features of cylindrical shell behaviour that cause the sound transmission characteristics to differ markedly from those of a flat plate. One approximate form of thin shell equation (Helck, 196) yields the following flexural-wave dispersion relationship between the non-dimensional axial wavenumber k z a and the nondimensional frequency Ω, for given non-dimensional circumference wavenumber k s a = n : Ω = ( k za) ( k a) n ( 1 ν ) ( + n ) z + β [ ] ( ) ) ( 4 ν) ν k za + n ( 1 ν) (.31)

34 in which ν is Poisson s ratio. This expression is accurate for thin cylindrical shells (β << 10-1 ) and for values of n. The first term on the right-hand side of the equation is associated with membrane strain energy and the second, which contains β, is associated with the strain energy of wall flexure. The cross sectional resonance frequencies, or cutoff frequencies of an infinitely long cylinder, are given by equation (.31) with k z = 0, which corresponds to an infinite axial wavelength. It is most important to observe that these frequencies are determined by strain energy of wall flexure: they correspond to Rayleigh s inextensional mode frequencies, which were derived by assuming that the median surface of the shell wall did not strain. The resulting equation for Ω can be expressed as follows: ν + ν Ω n = β n ν n n (.3) Except for the lowest-order modes, the cutoff frequencies are reasonably well approximated by the formula : Ω βn (.33) n Equation (.33) also indicates that the number of cutoff or cross-sectional resonance frequencies below the ring frequency is given approximately by: n r 1/ β (.34) Wavenumber Diagram. Wavenumber diagram can be very useful in helping to identify those forms of vibration most effective in radiating sound. In order to illustrate the form of the shell wavenumber diagram, equation (.3) is simplified by the omission of the less-important flexure term. The approximate form of dispersion equation is [Heckl, 196] : ( k aβ 1/ z [( k aβ ) ( ) ] 1/ + nβ 1/ z ) 4 + [( k ) ( ) ] 1/ 1/ zaβ + nβ Ω (.35) where β = h /1a, Ω = f/f r, and h is the wall thickness. This produces a wavenumber diagram of the form shown in Figure 11.

35 Figure 11: Universal constant-frequency loci for flexural waves in thin-walled circular cylindrical shells (n > 1). Fahy F. Sound and Structural Vibration The curvature of a cylindrical shell produces coupling between radial, axial, and circumferential motions, and there are consequently three coupled equations of motion and three classes of propagating waves (Leissa, 1973). Although only the radial motion of the shell determines the sound radiation, the form of the radial motion, and the associated dispersion characteristics, are significantly affected by mid-plane strains, especially at frequencies well below the ring frequency fr = c1' / πa. These so-called membrane effects considerably raise the phase velocities of waves whose displacement is predominantly radial, so much so in some cases, that these waves have supersonic phase velocities at frequency well below the critical frequency based upon the shell wall considered as a flat plate. Above the ring frequency, curvature effects disappear and the shell vibrates like an equivalent flat plate. The membrane effect on wave speed is seen in the bending of frequency loci toward the origin. A strange consequence of this behaviour is that at one frequency two helical waves of the same axial wavenumber, but different circumferential wavenumber can propagate. Waves of low circumferential wavenumber involve greater membrane strain energy than waves of higher circumferential wavenumber. This leads to a rather unexpected variation of natural frequency with axial and circumferential wavelength..3. Acoustic Modes: Cross-Modes in Circular Cross Section Ducts. [0] In the Cross-modes of Circular Cross Section Ducts, the Velocity Potential Φ has to satisfy the following propagation equation: (, 1 Φ ) ( r, θ, z, t) Φ r θ, z, t = 0 (.36) c t o where the operator. can be expressed in the cylindrical coordinates system

36 (See Figure 5, p13) as follows: 1 r = + + r r r r θ z (.37) The relation between the Particle Velocity and the Velocity Potential is given by: ( r, θ, z, t) = Φ( r, θ, z t) u, (.38) where the operator. can be expressed in the following cylindrical coordinates:.. = r r θ z (.39) The equation that relates acoustic pressure and velocity potential is: p ( r, θ, z, t) = ρ o Φ ( r, θ, z, t) t (.40) When harmonic motion is assumed, equation (.36) reduces to the Helmotz equation in cylindrical coordinates. ψ ( r, θ, z, t) + k ψ( r, θ, z, t) = 0 (.41) where Φ(r, θ, z, t) = ψ (r, θ, z) e jωt and k = ω/c o. Writing ψ (r, θ, z) in the form: ( r, θ z) = F( r) G( θ) H ( z) ψ, (.4) Substituing this expression into the equation (.41) and separating the variables yields to three ordinary differential equations of the forms: 1 r r r F r d H dz d G dθ ( z) ( θ) + k z H z + m G ( ) = 0 ( θ) = 0 ( r) m + ( k k ) F() r = 0 z r (.43) (.44) (.45) Since no Boundary Conditions are assumed for the z direction, the general solution to (.43) is used: jkz z jkz z H ( z) = A e + B e (.46) z No definite Boundary Conditions are specified for the θ direction. However, there is a periodicity requirement such that: z

37 G ( θ = 0) = G( θ = π) (.47) This results in a solution for equation (.44) of the form: G ( θ) = A. cos( mθ) + B.sin( mθ) θ θ (.48) Rearranging equation (.45) yields: r d F ( r) df( r) + r + ( r η m ) F() r dr dr where η = k - k z. This equation is Bessel s equation of order m. Its solution is given by: F ( r) = A J ( rη) + B Y ( rη) r m r m (.49) (.50) J m (rη) is Bessel function of the first order m. Y m (rη) is Bessel function of the second order m, or so-called Neumann function. One of the restrictions on the solution to equation (.49) for the problem at hand is the function F(r) must be bounded at r = 0. Since, Y m (rη) is unbounded at r = 0, this term is deleted and the solution of equation (.49) becomes ( r) = A J ( rη) F r m (.51) A rigid duct wall is located at r = a. Thus the Particle Velocity in the r direction at r = a must be equal zero. jωt Φ( r, θ, z, t) ( F( r) G( θ) H ( z) e ) ur r= a = 0 or ur = = r r df dr This Boundary Condition is satisfied when: ( a) d[ ( A J ( aη) )] = a m dr = 0 (.5) dj dr Where β mn = aη mn m ( β ) mn = 0 The following table gives values of β mn for which the equation dj m ( β ) dr mn = 0 (.53) is satisfied. β mn n = 0 n = 1 n = n = 3 n = 4 n = 5 n = 6 m = m = m = m = m = m =

38 m = It is noted that η mn = β mn / a. F(r) for the m,n mode can be written: r F() r mn = Amn J m β mn a (.54) The total solution for the Cross-Modes in a Circular Duct that are travelling in the positive z direction is: ( ) ( ) ( ) cos mθ r ω β j t kz z Φ r, θ, z, t = Amn J m mn e (.55) m= 0 n= 0 sin( mθ) a Velocity Potential The Mode Function for the m,n Cross-Modes is given by: ψ ( r, θ) mn cos = sin ( mθ) ( mθ) J m β mn r a (.56) The above equation implies that either the sine or cosine term can be used for the mode function. Cutoff Frequency. The Cutoff Frequency for a m,n Cross-Mode is obtained from the expression: η = k - k z = (β mn / a) or k z = k β a mn (.57) β mn ω πf k z must be a real value number. Thus k and k = = a co c o The Cutoff Frequency can therefore be expressed as follows:. ( f ) mn c βmnc = πa o (.58) This frequency only depends on the radius a and therefore on the considered m,n mode. Recalling equation (.40) and equation (.55) : p Φ ( ) ( r, θ, z, t) r, θ, z, t = ρ and Φ( r, θ, z, t) o t = m= cos Amn 0 0 sin n= ( mθ) ( mθ) J m β mn r a e ( ωt k z ) j z

39 It is possible to express the cross-mode proper to a rigid-walled cylindrical shell in terms of its acoustic pressure: p mn ( r, θ, z, t) = P mn cos sin ( mθ) ( mθ) J m β mn r a e ( ωt k z ) j z (.59) The term (β mn r/a) of the above equation (.59) is equal to η mn r with η mn = k - k z. We can therefore rearrange equation (.59): p mn ( r, θ, z, t) = P mn cos sin ( mθ) ( mθ) J m j( ωt kz z ) ( η r) e mn (.60) where η mn is defined as the radial wavenumber and determined by the zero normalparticle wall boundary condition as solution of the equation (.53) when r = a. The characteristic solutions are multi-valued for a given m. m indicates the number of diametral pressure nodes and n the number of concentric circular pressure nodes. The patterns are illustrated in Figure 1. n = 1, m = 0 n =, m = 0 n = 3, m = 0 n = 1, m =1 n =, m=1 n = 3, m = 1 n = 1, m = n =, m = n = 3, m = Figure 1: Fourier-Bessel mode shapes for the pressure inside the duct..3.3 Coupling between Shell Modes and Acoustic Duct Modes. The acoustic coupling between the fluid contained in a cylinder and the shell is very much dependent upon the relative axial phase speeds of the waveguide modes in the two media. The radial and axial wavenumbers satisfy the acoustic wave equation: k = k z + η mn (.61) The cutoff frequencies below which a particular mode cannot propagate freely and carry energy in a infinitely long duct are given by: k z = k ηmn = 0, or ka = ηmna = βmn (.6)

40 Values of β mn were given in the above table (p9). In terms of the ring frequency of the shell (ω r = c l /a (rad.s -1 )), the equation (.6) can be written in the term of the nondimensional frequency : ω ωa πc ia kaci ci ci Ω = = = = = η = β mn ' ' ' mna (.63) ω λ ' mn ' r cl cl cl cl cl where c i is the speed of sound in the contained fluid and c l the longitudinal wavespeed in a plate of the shell material. For instance, equation (.63) and the value of β mn for the m = 1, n = 0 give the lowest cutoff frequency : c Ω = 1, c i ' l (.64) The dispersion relationship (.61) can be represented graphically by the non-dimensional axial wavenumber k z against the non-dimensional frequency Ω mn, i.e.: k z a = Ω mn (c l / c l ) - β mn but the appropriate values of β mn and c l /c l must be employed. There is unfortunately no universal form of combined structural and acoustic wavenumber diagram. Nevertheless, the acoustic duct modes and the shell wall modes do not exist independently in a fluid-filled duct. The dispersion diagrams for the shell waves and the fluid waves may be superposed as shown in Figure 13. Only waves of equal circumferential order m may couple. Figure 13 shows that equality of fluid and shell axial wavenumbers can occur : This is a coincidence condition.

41 β = h / 1.a shell and fluid share same m value of n irrelevant Figure 13: Illustration of coincidence between shell and fluid modes. Fahy F. Sound and Structural Vibration In most practical cases, coincidence between the lower-order shell modes and the acoustic modes of low radial order n occurs at frequencies close to the acoustic mode cutoff frequencies because menbrane effects keep the slope of the structural wavenumber curve low, whereas the acoustic wavenumber curves rise rapidely with Ω. The lowest possible coincidence frequency, corresponding to coincidence between the beam-bending mode and the (1,0) acoustic mode, corresponds closely to the cutoff frequency of this mode, which is given by equation (.64). Between this frequency and the ring frequency, a number of further such coincidences can occur; any one shell mode can be coincident with all the acoustic modes of equal circumferential order m and increasing radial order n. The relationship between the internal acoustic and shell wavenumbers is of cruicial importance in determining the coupling of the media.

42 3. EXPERIMENTAL PROCEDURE FOR VIBRATION AND ACOUSTIC MEASUREMENTS ON MRI SCANNERS. Noise and Vibration measurements inside any MRI scanners require particular attention to the working environment. The bore and surroundings of the scanner are hostile to any measurements made with metallic component devices such as transducers, microphones, cables, recorders. The 3 Tesla high magnetic field is a source of interference when the aim of the investigation is to obtain reliable measurements. Therefore a specific protocol has been developed so as to ensure enough accuracy for these measurements. It is however important, while establishing the experimental procedure, to be aware of the expected signals to record. This procedure should contribute to a correct choice of transducers or other equipment to use for a successful measurement session. A strong correlation between the acoustic or vibration signals and the impulse sequence of the imaging process was already expected before making the measurements. The imaging process and its characteristics have therefore been primarly studied. The following part will present an overview of each scanner design, the gradient coil system in particular, and Echo-Planar Imaging sequences used in the functional Magnetic Resonance Imaging process. This will be helpful to qualitatively understand the results presented in Chapter 4 and should also give insights of what could be achieved in the design of the imaging sequence so as to control the Lorentz forces and therefore the induced vibration and noise. 3.1 PRESENTATION OF THE SCANNERS AND THEIR IMAGING SETTINGS A few words about functional Magnetic Resonance Imaging Scanners. All the assessed scanners were devoted to functional Magnetic Resonance Imaging. FMRI is a technique for determining which parts of the brain are activated by different types of physical sensation or activity, such as sight, sound or the movement of a subject's fingers. The brain mapping is achieved by setting up an advanced MRI Scanner in a special way so that the increased blood flow to the activated areas of the brain shows up on functional MRI scans. The subject in a typical experiment will lie in the magnet and a particular form of stimulation will be set up. For example, the subject may wear headphones so that sounds can be played during the experiment. Then, MRI images of the subject's brain are taken. Firstly, a high resolution single scan is taken. This is used later as a background for highlighting the brain areas which were activated by the stimulus. Next, a series of low resolution scans are taken over time, for example, 150 scans, one every 5 seconds. For some of these scans, the stimulus will be performed, and for some of the scans, the stimulus will be absent. The low resolution brain images in the two cases can be compared, to see which parts of the brain were activated by the stimulus. After the experiment has finished, the set of images is analysed. Firstly, the raw input images from the MRI scanner require mathematical transformation (Fourier transformation, a kind of spatial "inversion") to reconstruct the images into "real space", so that the images look like brains. The rest of the analysis is done using a series of tools which correct for distortions in the images, remove the effect of the subject moving their head during the experiment, and compare the low resolution images taken when the stimulus was off with those taken when it was on. The final statistical image shows up bright in those parts of the brain which were activated by this experiment. The functional imaging procedure therefore involves special settings of the sequence and therefore characteristically drives the gradient coil system responsible of the high noise generation.

43 3.1. The Echo-Planar Imaging sequences. Echo-planar imaging (EPI) is an extremely rapid method, gathering all the data to form an image from a single excitation pulse (Ultra-fast single-shot methods). EPI is fundamentally just a method of spatial encoding. Tomographic image formation requires spatial encoding in three dimensions. In most cases, one dimension is determined by slice selective excitation (refer to Figure 14 for axis labels). Briefly, a radio frequency excitation pulse with a narrow frequency range is transmitted to the subject in the presence of a spatial magnetic field gradient. Because the magnetic resonance phenomenon depends on an exact match between the radio frequency excitation pulse frequency and the proton spin frequency, which depends in turn, on the local magnetic field, this pulse will excite the Magnetic Resonance signal over a correspondingly narrow range of locations: an imaging slice. The differences between EPI and conventional imaging occur in the remaining in-plane spatial encoding. Phase Matrix Slice Selection Readout Figure 14: The three axes used for spatial encoding of MR images. One dimension of spatial encoding is achieved by slice selective excitation (the Slice Selection axis). The other two are encoded by phase and frequency. The Slice Selection axis is also referred as the Z axis. The Readout axis is variously labeled the Frequency or X axis; the Phase Encoding axis is sometimes labeled the Y axis. When a magnetic field gradient is applied across this excited slice, it will cause the spin frequency to be a function of position. The spatial resolution (pixel size) of an MR image depends on the product (actually the integral) of the imaging gradient amplitudes and their on duration (for example, a gradient of 0.5 gauss/cm, left on for 10 msec yields a spatial resolution of 0.47 mm). This reflects spatial encoding along one in-plane dimension only: the Readout direction. In Fourier transform imaging, the encoding for the second in-plane dimension is created by applying a brief gradient pulse (along a second gradient axis) before each readout line. For 18 lines of resolution in this axis, 18 separate lines must be acquired, each for 10 msec. The total readout duration is therefore 18 x 10 msec, or 1.8 seconds. In EPI, much larger gradient amplitudes are used. A gradient of about.5 gauss/cm is typical. With five times the gradient amplitude, the encoding duration can be reduced by five and fold to 10/5 = msec/line, so that the total spatial encoding time for our reference image is reduced from 1.8 seconds to 56 msec. In practice, however, this is not a practical configuration. Most significantly, the gradients cannot instantly reach such large magnitudes, and the rise time therefore becomes a significant fraction of the readout duration. Secondly, the decay of the MR signal during

44 readout introduces blurring into the images. Because of these tradeoffs, most EPI studies are performed at somewhat lower resolution. In-plane voxel (elementary volume of the matrix or thicknesss of the slice, i.e. spatial resolution) sizes between 1.5 and 3 mm are typical. Characteristics of the Echo-Planar Imaging Sequence used during the acoustic and vibration investigation of the Scanners. a. MRC-IHR Nottingham fmri Scanner EPI sequence. The EPI pulse sequence used was a Modulus Blipped Echo-planar Single-pulse Technique (MBEST) sequence. It enables a rapid switching of a strong gradient to form a series of gradient echoes (GE), each with a different degree of phase encoding, which can be reconstructed to form an image. Its characteristics in terms of waveform components and duration are described as follows. The Slice select is a single square wave immediately before the Broadening and Switch. The Broadening or Phase encode to refer as above, is a small triangular waveform at each zero-crossing of the Switch. The Switch or Readout to refer as above, is a 1.9 khz sinusoid for 65 whole waves plus some buildup waves (67 waves, approximately 35 ms).

45 1 Figure 15 : EPI Signal Components Arbitrary units "Switch" Electrical Signal Time [seconds] 1 Arbitrary units "Slice" Select Signal Time [seconds] 0. Arbitrary units "Broadening" Electrical Signal Time [seconds] The total duration of the sequence is determined as we have seen by the spatial resolution and the size of the matrix. The dimension of the matrix is 18x18x16 slices/volume, giving a spatial resolution of 4x4x4 mm (voxel size). These 16 slices constitute a total signal of approximately 1.1s length of time which can be decomposed in 16 slices of 35 ms each plus 16x3 ms of gap between slices. The Echo time (TE) and Repetition time (TR) have to be mentioned as they constitute an important reference but also as they influence the noise perceived by the patient during the scans. The Echo time is determined by the 1.93 Hz Switch frequency and is 36 ms. The Repetition time which is the total start-to-start time for volumes is 5 s. The three main waveforms of the Nottingham EPI sequence have been recorded during the measurements as they are driving the noise production and moreover constitute a useful reference for the analysis of other signals. Figure 15 shows the recorded waveforms constituting the EPI sequence in the time domain. Additionally their spectrum in the frequency domain are presented in Figure 16. The EPI sequence is referred as the Continuous signal in the Measurement Tables given in Appendix.

46 10 - Figure 16 : PSD of EPI Signal Components Switch signal Slice select signal Broadening signal Magnitude [Arbitrary Units] Frequency Resolution: 16 Hz Frequency [Hertz] b. FMRIB Oxford fmri Scanner EPI sequence. The EPI sequence used for MR imaging with the Oxford scanner provides a resolution of 64x64 ( Dimensions of the Matrix) and enables 3 mm of thickness for each slice (Voxel). The Echo time (TE) was 50 ms and the Repetition time (TR) was 500 ms. Another information was the bandwidth of the sequence which was 100 khz for the EPI sequence referred as EPI 1 in the measurements table in Appendix???, and 00 khz for the EPI. The Field-of-View parameter (FOV) was 19x19 mm. These two sequences are the most employed and also noisiest sequences used by the FMRIB. The Readout signal, previously called Switch signal is a 3 square-wave signal of Hz which lasts approximately 50 ms. The Broadening signal is named Phase encode here. Figure 17 and 18 illustrate the signals composing the EPI and their relative spectrum in the frequency domain.

47 1 Figure 17 : EPI1 Signal Components Arbitrary units "Readout" Electrical Signal Time [seconds] 0.5 Arbitrary units "Slice" Select Signal Time [seconds] Arbitrary units "Phase encode" Signal Time [seconds]

48 10 0 Figure 18: PSD of EPI1 Signal Components Readout signal Slice select signal Phase encode signal 10-5 Magnitude [Arbitrary Units] Frequency Resolution : 1 Hz Frequency [Hertz] c. WBIC Cambridge fmri Scanner. Two EPI sequences were used in Cambridge. The EPI1 provides a resolution of 18x18 ( Dimensions) and enables 5 mm of thickness for each slice. 3 Slices were executed during the Imaging Process. The Repetition Time is 160 ms and the Field-Of-View was set to be 5 cm. The bandwidth of the sequence was 00 khz. The other sequence used is referred as EPI in the Appendixes and is characterised by a Matrix of 18x64 dimension with a thickness of 5 mm, a repetition time TR of 4s and an echo time TE of 30 ms. The Field-Of-View was 5 cm with a spectral bandwidth of Hz. 1 Slices were executed during each imaging sequence. Unfortunately, the components of these EPI sequences were not recorded on the DAT for technical reason.

49 3.1.3 Presentation of the Scanners and the design of their relative Gradient coil system. The assessed scanners were all designed specifically for ultra-fast imaging for brain functional magnetic resonance imaging studies. The point of interest, while investigating the vibration and acoustical behaviour of MRI scanner, is the Gradient coil system. a. MRC-IHR Nottingham fmri Scanner system. The scanner is a 3 T Whole body imaging and spectroscopy system. The 3 Tesla magnet is a superconducting magnet cooled by liquid helium and nitrogene and provides a strong highly homogeneous magnetic field. Gradient coil System. Figure 19 describes the Head Gradient coil. Its length, radius and thickness are important parameters for the analytical investigation of its vibration and acoustical behaviours. The RF coil, which broadcasts the RF signal to the patient and/or receives the return signal, is inserted inside the bore of Gradient coil system, where the patient s head is positioned during the imaging process. The wires made of copper, the epoxy resin and the cooling system confer its anisotropic constitution.

50 395 mm 5 mm 5 mm Wires Wires Outer Core 700 mm 350 mm 0 mm Isocenter 175 mm Wires Wires 155 mm Inner 445 mm Figure 19 : Dimensions of the Gradient Head coil system During the experiments, the settings of the EPI sequence lead the gradient coils to be driven differently in terms of nature and amplitude of currents. Indeed, the imaging process decides the excitation of the gradient coils. Three major class of images are usually obtained in MR Imaging. They are named Coronal, Transverse and Sagittal. Figure 0 illustrates these three different type of brain images.

51 Figure 0: Illustration of the different type of Brain images obtained by MRI. From AOS Magazine, Review of Medical Imaging Techniques. Each of these type of images involves the gradient coils to be particularly driven by the 3 main components of the EPI sequence. Table 1 indicates the relative settings of the Nottingham Gradient coil system for each type of images. X-gradient coil (Gx) Y-gradient coil (Gy) Z-gradient coil (Gz) Transverse Readout signal Phase encode signal Slice select signal (Switch) (Broadening) Coronal Slice select signal Phase encode signal Readout signal Sagittal Phase encode signal Slice select signal Readout signal Table 1 : Nottingham Scanner Imaging settings for EPI sequence. The Coronal Image settings has only been used during the measurements. These settings differs from scanners. The vibration and acoustical responses are then expected to be different depending of the wanted multiplanar reconstruction of the brain. b. FMRIB Oxford fmri Scanner system. The FMRIB scanner is an advanced 3T Varian/Siemens MR imaging system. It is equipped with both a body gradient coil and a fast head gradient coil insert.

52 Gradient coil System. The FMRIB Gradient coil system is different from the MRC-IHR system by its nonuniform layout. This system does not have a symmetrical disposition of the gradient coils as Figure 1 shows. The wires are settled differently inside the Gradient coil system compared to the other head coils. It reinforced the dissymmetric loading of the Lorentz forces on the system. One specificity of this system is that the Imaging isocenter (and therefore the zone of perceived sound) is 180 mm away from the foot end and therefore let a wide unoccupied space behind the head in the Gradient system bore. Wiring 595 mm 540 mm 379 mm Isocenter 80 mm 180 mm 350 mm 1030 mm

53 Figure 1: Dimensions of the Gradient Head coil system. The EPI sequences and the Imaging settings interfere as well on the vibration and noise production. Three different EPI settings (i.e: three different type of images) has been used during the measurements in Oxford. Another EPI sequence (ref: EPI, only on RF coil) and others type of signals (such as an impulse and few pure tones) have also been used. The following Table gives a description of the characteristic electrical loading on each gradient coil referring to its corresponding class of images. The acoustical and vibration behaviour of the scanner to these three set of gradient settings have been investigated during the measurements in Oxford. The results and details of the measurements are displayed in the Tables in Appendixes. X-gradient coil (Gx) Y-gradient coil (Gy) Z-gradient coil (Gz) Transverse Phase encode signal Readout signal Slice select signal Coronal Readout signal Phase encode signal Slice select signal Sagittal Slice select signal Phase encode signal Readout signal Table : FMRIB Oxford Scanner Imaging settings for EPI sequence. c. WBIC Cambridge fmri Scanner system. The WBIC scanner is a BRUCKER 3 Tesla MRI System. The imaging settings and their requirement on the driving of the gradient coils are presented in the following Table.

54 X-gradient coil (Gx) Y-gradient coil (Gy) Z-gradient coil (Gz) Axial Phase encode signal Readout signal Slice select signal Coronal Readout signal Slice select signal Phase encode signal Sagittal Slice select signal Phase encode signal Readout signal 3.. EXPERIMENTAL PROTOCOLS. The experimental protocol was developed for the first set of measurements which took place in the University of Nottingham at the Magnetic Resonance Centre. The protocol describes the experimental procedure which was used to investigate the scanner in terms of its vibration and acoustical behaviour. The other sets of measurements made on Oxford FMRIB scanner and Cambridge WBIC scanner followed the same procedure. However, some of the equipment were changed so as to qualitatively and quantitatively improve the measurements. The changing executed for each other set of measurements will also be described.

55 3..1 MRC-IHR Nottingham Acoustic Measurements. Equipment and Procedure. The equipment has been selected in order to avoid any artefactual signals that could have been induced by the high magnetic environment (See Table 3). Moreover, the procedure made sure that the electrical equipment which contained ferro-magnetic components was progressively brought into the scanner room so as to control their potential attraction by the 3T static field or the damage of the high-field strength. Half-inch Microphone - Free-field response Bruel and Kjaer Type 4155 Long Screened connecting cables Bruel and Kjaer 0 db Attenuator Bruel and Kjaer Type ZF 003 Sound Level Meter with digital display, Weighting network and time constants set for Type 1 measurements Bruel and Kjaer Type 30 S/N # Sound Level Calibrator SPL 94 db at 1000 Hz Bruel and Kjaer Type 430 Microphone Support: Wood Rod (9x9 mm square section) + Strings + Blocks of wood Channel Digital Audio Tape Recorder (DAT) AIWA HHB 1 PRO Stereo Headphones Pro-Luxe PX 91 Acoustic Cap : constructed with a calibrator insert and a plastic dehumidifier cap. (or silica-gel cap) Bruel and Kjaer Type DB 0311 Table 3 : Equipment used for the acoustical investigation of Nottingham Scanner. To make valid measurements in that hostile environment, the procedure takes into account the factors that depend upon the accurate representation of the acoustic situation. The calibration of the entire arrangement (Microphone, Cables and Sound Level Meter) was executed in the control room away from the high magnetic field. The Sound Level Meter and the DAT recorder were positioned approximately 5 meters away from the scanner and linked to the microphone by screened cables. Only the microphone and a certain length of cable were in the bore of the scanner. To verify and avoid any contamination of the recorded signal, two careful operations were conducted. First, the influence of the field has been checked by using a calibrator or silica-gel cap to acoustically shield the microphone. The meter reading has then to drop by 10 to 15 db if the effect due to the magnetic field is assumed negligible. Secondly, the cable and microphone were attached to a wooden rod suspended by strings (fixed at the top-ends of the scanner), which was adjusted to position the microphone and cable along the axis of the RF coil. The cable was fixed straight onto the rod so as to avoid the scanner field-induced voltage. This wooden rod was also used for microphone placement inside the RF & gradient coils system and constituted a useful position ruler. The layout of the scanner room is shown in the following Figure.

56 1.5 m m 1 m Moving trolley bed Gradient coils (Head position) Screened Cables Scanner bore > 5 m Wooden Ruler SLM & DAT Wall Control Room Figure : Disposition in the Scanning room [MRC Nottingham]. The background noise was recorded inside the bore in Fast RMS time constant mode in order to ensure that it was sufficiently below the measurements that were taken. Then, the measurements of noise at three positions were conducted. The long axis of the microphone was aligned with the axis of the coil and pointed towards approximately the point where the top of the patient s head should be. Sound pressure levels and equipment settings (DAT recording level, weighting and times constants) were noted on the Acoustic Measurement Table given in Appendixes. It was intended to take the sound pressure levels using both linear and A-weighted scales, and with Fast root-mean-square (RMS) time constant (effective averaging time 15ms), Peak (<100 µs) and Impulse time constant modes. The latter is designed to represent human perception and response to impulsive noise. For further temporal and frequency spectrum analysis, the left channel of the DAT tape recorded the microphone acoustic signal while the right channel recorded the electrical signals driving the 3 gradients coils picked off at current monitoring points. Figure 3 indicates and assigns the position points of the microphone along the axis of the RF & gradient coils system.

57 Gradient coils RF coil 3 T scanner bore Wooden ruler String 3 1 Patient support side Patients head side 0.40 m 0.45 m Microphone Position Figure 3: Microphone positions along the axis. 3.. MRC-IHR Nottingham Vibration Measurements. Equipment and Procedure. As well as the acoustics measurements, the equipment has been chosen in order to minimise the artefactual signals and damages that could have occurred during the measurements. The following Table 4 gives the reference of equipment chosen with particular application in mind to perform thorough and meaningful vibration measurements: Piezoelectric Accelerometer Bruel and Kjaer Type 4375 SN # Charges Amplifier Bruel and Kjaer Type 635 SN # Accelerometer Leads Green 318 pf Melted Wax for accelerometer attachment Channels Digital Audio Tape recorder (DAT) AIWA HHB1 PRO Channels Oscilloscope HAMEG 0 MHz HM 03/5 SN # 994 Table 4 : Equipment used for the vibration investigation of Nottingham Scanner. The important magnetically-transparent requirement for the vibration transducer is difficult to meet. Most of the accelerometers usually used for vibration measurements are piezoelectric devices made of metallic components. Nevertheless, according to the

58 manufacturer, B&K accelerometers are very insensitive to magnetic fields. The sensitivity lies between 0.5 and 30 ms - per Tesla (0.005 and 0.3 g per Kgauss). However, there will be some induced motion of the seismic masses because it will have some magnetic permeability. Moreover, it is expected that currents will be induced in the accelerometer cable. It is therefore a good policy to check the background noise level of the vibration measurement system. This is done by mounting the accelerometer on a non-vibrating object and measuring the apparent vibration level of this arrangement. By using this procedure, the influence of the magnetic field on the accelerometer and cables can also be investigated. The idea was then to put an accelerometer isolated from vibration by a layer of plastic foam inside the RF & Gradient coils bore. Figure 4 describes this arrangement. 3 Tesla Static Magnetic field + Switching fields Environment Accelerometer Accelerometer RF Coil inner surface or Figure Gradient 4: Noise coil Floor system Arrangement. inner surface Foam m Patient s head support Figure 5: Position of accelerometer on the inner surface of the RF coil. If during the switching pulse sequence, the apparent vibration level of the installation is less than one third of the measured vibration (i.e. its noise floor is at least 10 db below

59 the vibration levels to measure), the actual vibrations measurements can be obtained with reasonably good accuracy. The installation has to be rigidly attached inside the bore in order to avoid its attraction on the inner surface of the coils (due to electromagnetic induced motion). Following this stage, the accelerometer was mounted on different places on the inner surface of the coils. The mounting of the accelerometer on the surface was done with melted wax which allowed quick test vibration measurements and provided good dynamic response. The location of the mounting should provide a short and rigid vibration transmission path to the vibrating source avoiding any compliance and damping elements present in the structure. Figures 5 & 6 define the positions which have been chosen for the accelerometer mountings on the inner surface of the RF coil and the gradient coils system and also on the inner surface of the main bore, where vibrating behaviour appeared to engender important consequences in the noise generation. Main Bore 0.9 m (inner ) 4 RF+ Grd coils Accelerometer Square section Al. runners Main scanner bore Gradient Coils RF Head Coil Air cavities 0.7 m (inner ) Support Figure 6: Position of accelerometer on the inner surface of the main bore. The inner surface of the RF coil is made of Perspex, and the inner surface of the Gradient coils system is made of Epoxy, both flat and robust. The inner surface of the main bore is made of aluminium sticky-backed tape. Therefore, the nature of the test surfaces are all suitable for wax mountings and should provide accurate vibration measurements. The temperature of surfaces should not cause any decrease in the coupling stiffness or detachment of the transducer. The random important vibrations should occur in the frequency range 0-5 khz. Therefore the accelerometer B&K Type 4375 has been chosen for its matched frequency response and its sensitivity to record the expected acceleration. The charge amplifier B&K Type 635 enables the integration of the acceleration signal measured by the accelerometer using its integration network and will convert the measurements into acceleration, velocity or displacement. The acceleration data, relevant for further analysis, was then recorded on the left channel of the DAT tape; the right channel recorded the electrical signal. The positions of the accelerometers on the inner surface of the RF coil and on the inner surface of the gradient coils system have been chosen in accordance with the expected main excitation of vibration modes. At one end of the coil, measurements of the vibration were taken at four different positions separated by a angle of 45 [Positions : 1.1, 1., 1.3, 1.4]. The Charge Amplifier, set in acceleration, and an oscilloscope connected to its output monitored the vibrations at these

60 positions and revealed the position of the most important acceleration. The corresponding accelerations were recorded on the DAT tape. On the middle of the RF and Gradient coils surfaces, acceleration at the longitudinally equivalent positions [.1,.,.3,.4] was also recorded. Finally, the acceleration at the other end was measured and referred as position [3.1]. The settings of the charge amplifier (Measurement mode, Low and High frequency limits, Amplifier Sensitivity) of each positions were written on the Vibration Measurements Table given in Appendixes FMRIB Oxford Acoustic and Vibration Measurements. The FMRIB scanner was driven by many other signals than the typical EPI sequences. Impulse signal and pure tones were used so as to give more insight of the structural vibration behaviour of the gradient coil system. A 8 channel DAT recorder was then used in order to gain some time and to make the measurements easier. The microphone, via the Sound Level Meter, was delivering the acoustic signal in Channel 1; four accelerometers, via four respective charge amplifiers, enabled us to record the acceleration of the vibration at 4 positions simultaneously [Ch., Ch3., Ch4., Ch5.]. Finally, the EPI sequence electrical components or other signals were recorded on Channel 6. Details are provided in the Measurements tables given in Appendix. Figure 7 illustrates the disposition of the equipment in the scanner and control rooms. In fact, the equipment was far away from the scanner bore (more than 10 meters) as it was possible for the cables and leads connecting the accelerometers and Microphone to go through a duct in the wall separating the control room from the scanner room. The SLM, charge amplifiers, DAT recorder, Oscilloscope were then positioned inside the control room which is shielded against the high magnetic field. Figure 8 described the positions of the accelerometers an microphone in accordance to the references written in the measurements tables. Tables 5 & 6 give the technical references of the equipment used when assessing Oxford FMRIB scanner. Wooden Ruler Scanner bore Gradient coils (Head position) Moving trolley bed 10 m Screened Cables & Acc. Leads

61 180 mm 180 mm 180mm 1.1 Position Position. 3.1 Position Patient s head support Microphone RF Coil inner surface or Gradient coil system Accelerometer Figure 8: Position of accelerometers and the microphone inside FMRIB Oxford. Half-inch Microphone - Free-field response Bruel and Kjaer Type Long Screened connecting cables (3x4m) Bruel and Kjaer Type AO 018 Sound Level Meter with digital display, Bruel and Kjaer Type 30 Weighting network and time constants S/N # set for Type 1 measurements Sound Level Calibrator SPL 94 db at 1000 Hz Bruel and Kjaer Type 430 Microphone Support: Wood Rod (9x9 mm square section) + Blocks of wood 8 Channel DAT DATA recorder TEAC RD-135T ISVR S/N # 0091 Stereo Headphones Pro-Luxe PX 91 Acoustic Cap : constructed with a calibrator Bruel and Kjaer Type DB 0311 insert and a plastic dehumidifier cap. (or silica-gel cap) Table 5 : Equipment used for the acoustical investigation of FMRIB Oxford scanner. 4 Piezoelectric Accelerometers 1: B&K Type 4375 SN # : B&K Type 4375 SN # : B&K Type 4375 SN # 97930

62 4: B&K Type 4375 SN # unknown 4 Charges Amplifiers Bruel and Kjaer Type 635 Accelerometer Leads. B&K Melted Wax for Accelerometer Attachment 8 Channel DAT DATA Recorder TEAC RD-135T ISVR S/N # 0091 Digital Storage Oscilloscope Tektronix 1 60 Mhz ISVR SN # 0096 Table 6 : Equipment used for the vibration investigation of FMRIB Oxford scanner. Disposition of the Equipment in the FMRIB Control Room WBIC Cambridge Acoustic and Vibration Measurements. The measurements at Cambridge WBIC followed the same experimental procedure as in Oxford and used the same equipment. Naturally, the layout of the scanning room was different and the gradient coil system as well. Figure 9 illustrates the disposition in the scanning room. The gradient coil system has its isocenter 16 mm away from the "foot" end of the scanner. Therefore, the position [1.1], [.1], [3.1], [4.1] are 16 mm distant from each others. Unfortunately, the exact dimensions of the gradient coil system are unknown. The last picture shows a close look at the disposition of the Acoustic an Vibration equipment inside the bore of the scanner.

63 Examination Room 1.5 m Wooden Ruler Scanner bore Gradient coils (Head position) 5m Moving trolley bed Console SLM DAT Ch. Amps Operating Room Screened Cables & Acc. Leads Figure 9 : Disposition in the Scanning room (WBIC Cambridge).

64 Disposition of the equipment inside the scanner bore for the investigation of its vibration and acoustic behaviours (WBIC Cambridge Scanner). 4. RESULTS OF THE MEASUREMENTS. The result of the measurements made on the different scanners will be given in this chapter. The first session of measurements took place at the Magnetic Resonance Centre, University of Nottingham, the 1st July 000. A second session was organised at the Oxford Centre for Functional Magnetic Resonance Imaging of the Brain, University of Oxford, the 0th September 000. Finally, the last measurements of the project were made at the Wolfson Brain Imaging Centre, University of Cambridge, the 16th October 000. Sound pressure levels inside the bore and acceleration of the vibration on the inner surface of the gradient coil system and/or the RF coil were measured and recorded following the guidance elaborated in the experimental protocol. Working in this high magnetic environment requires special awareness of the possible inaccuracy of the signals delivered by the transducers. First, the results of the arrangements, which have been used in order to avoid the errors, will be presented and will confirm the accuracy of the experimental procedure. Acoustic and Vibration results will then be given and commented upon in the context of their relative MR imaging settings, their relative position in the system and of course their strength. 4.1 RESULTS GIVEN BY THE EXPERIMENTAL ARRANGEMENTS.