System and SAR Characterization in Parallel RF Transmission

Transcription

1 System and SAR Characterization in Parallel RF Transmission Magnetic Resonance in Medicine 67: (01) Yudong Zhu, 1 * Leeor Alon, 1, Cem M Deniz, 1, Ryan Brown, 1 and Daniel K Sodickson 1 The markedly increased degrees of freedom introduced by arallel radiofrequency transmission resents both oortunities and challenges for secific absortion rate (SAR) management On one hand they enable E-field tailoring and SAR reduction while facilitating excitation rofile control On other hand they increase the comlexity of SAR behavior and the risk of inadvertently exacerbating SAR by imroer design or layout of radiofrequency ulses The substantial subject-deendency of SAR in high field magnetic resonance can be a comounding factor Building uon a linear system concet and a calibration scheme involving a finite number of in situ measurements, this work establishes a clinically alicable method for characterizing global SAR behavior as well as channel-by-channel ower transmission The method offers a unique caability of redicting, for any excitation, the SAR and ower consequences that are secific to the subject to be scanned and the MRI hardware The method was validated in simulation and exerimental studies, showing romise as the foundation to a rosective aradigm where ower and SAR are not only monitored but, through rediction-guided otimization, roactively managed Magn Reson Med 67: , 01 VC 011 Wiley Periodicals, Inc Key words: RF ower; RF safety; SAR; arallel RF transmission; RF shimming; B1 shimming; RF coil; high field MR; system calibration; linear system During radiofrequency (RF) transmission the RF magnetic field B1 interacts with sins and induces magnetic resonance (MR) signal The concomitant electric field E, necessarily accomanying the B1 field according to the laws of electrodynamics, deosits RF energy in the subject and dictates secific absortion rate (SAR) Conventional RF transmission strives for a uniform B1 in a large volume, which tends to cause, regardless of the location or size of the imaged region, broad-reaching E-field and unnecessarily high RF energy deosition The advent of arallel RF transmission (1,) brought about a new aradigm wherein RF ulses simultaneously drive distributed elements of a multiort transmit coil to effect both satial and temoral variations of the B1 and E fields The markedly increased degrees of freedom (1,3) of arallel RF transmission as 1 Deartment of Radiology, Center for Biomedical Imaging, New York University School of Medicine, New York, New York, USA Sackler Institute of Graduate Biomedical Sciences, New York University School of Medicine, New York, New York, USA Grant sonsor: NIH; Grant numbers: R01-EB011551, R01-EB *Corresondence to: Yudong Zhu, PhD, New York University School of Medicine, 660 First Avenue, New York, NY YudongZhu@nyumcorg Received March 011; revised 4 July 011; acceted 11 July 011 DOI 10100/mrm316 Published online December 011 in Wiley Online Library (wileyonlinelibrary com) VC 011 Wiley Periodicals, Inc 1367 comared with traditional RF transmission were shown to enable tailoring of E field and containing of SAR while imroving fli-angle rofile control For a given coil-subject setu, exloitation of the degrees of freedom in arallel transmission for imroving fli-angle rofile and SAR control is realized through design of RF/gradient ulses Practical control of fli angle rofile in vivo is enabled by subject-secific B1 calibration, which catures the comlex effects of coil-subject geometry, comosition and interaction on the B1 mas and rovides required guidance to the ulse design (based essentially on the Bloch equation) However, due to a lack of subject-secific SAR information, guidance to ulse design for ractical SAR control has not hitherto been ossible in vivo In fact, the extra degrees of freedom of arallel transmission, comounded by a generally oor understanding of SAR in high field MR, often sur concerns that imroer design or layout of RF ulses may exacerbate SAR (eg, by causing excessive constructive interference of electric fields), as oosed to reducing it These safety and erformance considerations underscore the imortance of a racticable SAR rediction method one that, given any set of RF shimming coefficients or RF excitation ulses, redicts the true SAR consequences globally and locally Such a method would enable a aradigm shift from merely SAR monitoring (the current ractice) to roactive SAR management Extensive recent efforts to evaluate and redict SAR have relied uon electromagnetic (EM) field calculations in numerical simulations or exerimental findings in average subjects Yet it remains unclear if it will be feasible to adat the details of the simulated coil-human setu or to extraolate average findings such that the searately obtained SAR characteristics could closely track what haens or will haen to a subject undergoing a scan This work follows the lead of a SAR rediction model (1), which, based on system linearity, relates global or local SAR to arallel RF ulses or RF shimming coefficients with a quadratic function The model has been used in a number of arallel-transmission-related SAR investigations (1,3 9), which demonstrated that design of RF ulses, when guided by the model, enables the extra degrees of freedom inherent in a arallel transmission system to be advantageously exloited, and SAR to be managed The model has also been a foundational element for analyzing and aroaching ultimate RF transmission erformance (8) The SAR model indicates articularly that there is a structure to global and local SAR behavior in arallel transmission and that the uniqueness of a secific coil-subject setu can be encasulated by a comaratively small set of

2 1368 Zhu et al high RF duty-cycle sequences and for high main magnetic field strength B0, in which cases monitoring and otimization of RF transmission become crucial FIG 1 A system ersective for arallel RF transmission: The transmit channels, the transmit coil and the subject together form a system, with w (n), the arallel RF ulse waveforms, as inuts, and B1 þ field and RF energy deosition as oututs Parallel RF transmission system hardware is normally set u in such a way that the electromagnetic field induced in the subject resonds linearly to the inuts [Color figure can be viewed in the online issue, which is available at wileyonlinelibrarycom] arameters defining that structure This work focuses on devising a clinically alicable method to unveil the structure arameters that are secific to a coil-subject setu, and thereby to rovide accurate SAR guidance for the actual MR examinations of individual subjects with a SAR tracking and rediction caability The method is based on a finite number of in situ measurements, and does not require the use of simlifying assumtions about the subject or the scanner setu Comared to a method relying on simulations or average results, this subject-secific aroach eliminates a major source of error associated with intersubject and inter-rf-aaratus SAR variations In this article, the scoe of the devised method is limited to global SAR and individual channel characterizations THEORY AND METHODS RF Energy Dissiation and Tissue Heating Pennes bio-heat equation describes thermal energy balance for erfused ¼rðkrTÞþh b þ h e where r, C, and k refer to tissue density, secific heat caacity and thermal conductivity, resectively, and h b is the blood-to-tissue heat transfer rate RF energy deosition accomanying RF transmission, which is catured in Eq 1 by the local RF energy deosition rate h e, is a driving force of temerature rise and is roortional to the square of local E field strength: h e ¼ 1 = s E,wheres is electrical conductivity Temoral and volume averaging of h e, when further scaled by aroriate density or mass measurements, give, for examle, head, torso, extremity or whole body average SAR as defined in US food and drug administration (FDA) and IEC guidelines (10) Excessive tissue heating may otentially result from RF energy deosition This risk tends to increase for ½1Š A Linear System Persective An MR scanner commonly modulates both RF and gradient fields when exciting sins Modulation of the RF field is achieved by udating, as secified by a designed RF ulse waveform, the magnitude and hase of a Larmor-frequency sinusoidal ulse that drives a transmit channel and a transmit coil The udating occurs every Dt time increment, which is tyically several microseconds in ractice This modulation is multilied in arallel RF transmission, where a lurality of designed waveforms, sinusoidal ulses and transmit channels, as well as a multiort transmit coil, are emloyed to rovide considerably enhanced suort for the RF field modulation, giving rise to an RF field that varies both in sace and in time Parallel RF transmission includes RF shimming as a secial case A useful ersective to arallel transmission is to treat the transmit channels, the transmit coil and the subject as a single system For any Dt interval, the magnitudehase airs secified by multile RF ulse waveforms, exressed with comlex scalars w ðnþ (n ¼ ort index and ¼ interval index), define the inuts to the system There is one inut configuration er Dt interval The B1 þ field and the RF energy deosition are imortant oututs of the system During RF transmission the B1 þ field interacts with the sins, forming the basis of MR signal induction (or sin excitation) The concomitant E field, necessarily accomanying the B1 field according to the laws of electrodynamics, induces RF energy deosition in the subject To address the goal of creating a target excitation rofile while keeing SAR low, one needs to design RF ulse waveforms, or system inuts, in an otimal way so that the system will resond with both (i) a roerly modulated B1 þ field that works with the gradient field in exciting sins and (ii) a roerly restrained E field that steers clear of excessive RF energy deosition A key rerequisite to the design otimization is accurate rediction of B1 þ distribution and E-induced RF energy deosition given any inut configuration This is ossible in ractice, as described later Parallel RF transmission system hardware is normally set u in such a way that the EM field induced in the subject resonds linearly to the inuts This can be areciated by considering the subject and the RF transmit coil as a multiort network that interacts with a lurality of sources through the orts (Fig 1) The RF ower amlifiers, each resenting to the multiort network equivalently a voltage source in series with an outut imedance, amlify modulated RF ulses and drive the orts Provided that the amlifiers satisfy common linearity secifications, the voltage sources are related linearly to the modulated RF ulses that are fed to the corresonding amlifiers inut terminals In this case, linearity of Maxwell equations dictates that the EM field resonds linearly to the voltage sources and, in turn, to the modulated RF ulses It follows that any EM field

3 System and SAR Characterization in Parallel RF Transmission 1369 comonent at a location within the object, as a function of time, can be exressed as yðtþ ¼L v ð1þ ðtþ; v ðþ ðtþ; ; v ðnþ ðtþ ; ½Š where L reresents a linear maing, y(t) denotes the EM field comonent, v (n) (t) is the modulated RF ulse for ort n, and N is the number of transmit orts Phasor notation is suitable for describing a time harmonic quantity within each Dt interval For examle, at location r inside the object and within the th Dt interval, the E field can be exressed as E(r,t)¼[a x (r)cos(v 0 tþu x (r)) a y (r)cos(v 0 tþu y (r)) a z (r)cos(v 0 tþu z (r))] T The corresonding hasor notation for E is a comlex vector: E (r)¼[a x (r)ex(ju x (r)) a y (r)ex(ju y (r)) a z (r)ex(ju z (r))] T For the same interval, the hasor notation for the modulated RF ulse for the nth ort is the comlex scalar w ðnþ The linear system behavior catured by Eq can thus be exressed in matrix form for the Dt interval: In Eq 3 w ¼ [w ð1þ w ðþ y ¼ Aw; ½3Š w ðnþ ] T is a vector collecting the definitions for the modulated RF ulses the nth entry is the comlex scalar corresonding to the air of magnitude and hase values for the time interval and the nth ort y ¼ [y ð1þ y ðþ y ðlþ ] T is a vector collecting hasor reresentations of the time variables of interest for the same interval (eg, B1 þ field at L satial locations) A is an L-by-N comlex-valued matrix reresenting the linear maing Local and Global SAR Models Linearity allows decomosition of the net E field as a weighted suerosition of E fields corresonding to the N individual sources, with the weights being w ð1þ, w ðnþ In hasor notation E ðrþ ¼ P N n¼1 wðnþ e ðnþ ðrþ where e (n) (r) isthe E field (the resonse) due to a w (the inut) that has its nth entry being one and the rest being zeros This leads to the following exression for local RF energy deosition rate: h e ðrþ ¼ sðrþ je ðrþj ¼ sðrþ E ðrþ E ðrþ ¼ sðrþ X N m¼1 w ðmþ eðmþ ðrþ! X N n¼1 w ðnþ eðnþ ðrþ 3 h i ¼ w ðmþ 6 sðrþ e ðmþ ðrþ e ðnþ 7 4 ðrþ 5 fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} 6 4 w ðnþ 3 def ¼LðrÞ 7 5 ¼ wh LðrÞ w ½4Š where * denotes comlex conjugation, H denotes conjugate transose and underscored indices are row or column indices for vector and matrix entries Equation 4 shows that local! RF ower deosition can be exressed as quadratic functions in w ð1þ, w ðnþ Inmatrixform,h e (r)¼ w H K(r) w It follows that global RF energy deosition rate can also be described by a quadratic model: Z sðrþ h i j ¼ je ðrþj dv ¼ w ðmþ v 3 6 R sðrþ e ðmþ ðrþ e ðnþ 7 4 ðrþ dv 5 v fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} 6 4 w ðnþ 3 ¼U def 7 5 ¼ wh Uw ½5Š Matrices K and U are named, resectively, local and global ower correlation matrices Both K and U are N- by-n, and can be shown to be Hermitian and ositive semidefinite They cature the effects of field interference and tissue conductivity on RF energy deosition at regional and global scales Total deosited RF energy during RF transmission is a time integral of j, exressed as: j ¼ XP ¼1 Dtj ¼ XP ¼1 ¼ w H full U fullw full ; h w ðmþ i UDt 6 4 w ðnþ UDt 0 B U full ¼ A 0 UDt NPNP where w full is a vector collects all samles of the RF ulse waveforms Similarly, j local ðrþ ¼ XP ¼1 ¼ XP ¼1 Dth e; ðrþ h 0 ¼ w H B full@ w ðmþ i KðrÞDt6 4 KðrÞDt 0 0 KðrÞDt 1 C A w ðnþ NPNP w full quantifies total deosited RF energy at location r over the course of the RF excitation It is to be noted that in characterizing SAR, even in the absence of intercoil couling, RF energy dissiation locally or averaged over an imaging volume cannot be treated by considering the individual sources in isolation This can be attributed to the overlaing of E fields Quantitatively this is reflected in the tyically nonzero off-diagonal entries in K and U these correlation entries quantify the mutually interfering nature of the sources ½6Š ½7Š

4 1370 Zhu et al and encasulate information instrumental for SAR reduction In ractice however, many existing RF shimming or RF ulse calculations attemt to follow RF ower or SAR using a sum of magnitude squares of the waveform samles (11 13), which is equivalent to using an identity matrix in lace of U or K Such an aroach to managing SAR can be subject to significant error For instance, given a set of arallel RF ulses, one can add a 180 hase offset to one of the ulses without affecting the evaluation of w H Iw use of the identity matrix I is incaable of caturing the SAR effect caused by constructive or destructive interference of the E fields driven by the ulses Use of the identity matrix in lace of true ower correlation matrices further assumes no variation in resonse to the multile sources, which is not true in any case where different array elements contribute differently to SAR Results reresented by Eqs 4 and 5 indicate that there is a comact structure to global and local SAR With a roer exerimental calibration scheme it is ossible to unveil this structure and establish ractical subjectsecific SAR tracking and rediction caabilities B1 Calibration as an Examle An RF transmit system with linearity adequately maintained facilitates EM field calibration Measuring EM field resonses in M exeriments of inut configurations w (1) to w (M) results in equations that can be comactly exressed in matrix form: ½y ð1þ y ðþ y ðmþ Š¼A½w ð1þ w ðþ w ðmþ Š Equation 8 ools a total of M Eq 3-tye equations together, with the exeriment index shown as subscrits in arentheses If w (1) to w (M) are linearly indeendent inut configurations and M¼N, then existence of the inverse of matrix [w (1) w () w (M) ] is guaranteed and the EM field resonse to any inut configuration can be redicted This is because matrix A can be fully determined from the measured EM field resonses and the corresonding inuts: A ¼½y ð1þ y ðþ y ðnþ Š½w ð1þ w ðþ w ðnþ Š 1 A simle yet concrete examle is calibration of transmit B1 fields with N exeriments, where the nth exeriment (n ¼ 1,,N) involves driving the nth ort with a unit-amlitude rectangular RF ulse (a sinusoid of unit amlitude and zero initial hase) and the other orts with zero-amlitude RF ulses In this case [w (1) w () w (N) ] is an identity matrix, and [y (1) y () y (N) ] ¼ A stores individual channel field mas For imroved robustness in the resence of noise or erturbations, more or tailored calibration exeriments may be used, which is the subject of active research in the area of transmit B1 field maing (14,15) To illustrate with simler notation, consider one row of Eq 8 It deals with EM field at one satial location and can be rewritten as b ¼ Wx where W is defined as [w (1) w () w (M) ] T, x denotes the transose of the lth row of A, and for B1 maing, b is a ½8Š ½9Š vector collecting B1 þ at the lth location measured in calibration exeriment 1 through M (M N) If the noise covariance matrix of measured b is V, the classic solution to x is given by the best linear unbiased estimate (16): x ¼ðW H V 1 WÞ 1 W H V 1 b ½10Š Clearly, for multiort arallel RF transmission, calibrating A satisfies one rerequisite of the RF ulse design rocess The calibration allows the satiotemoral variation of the B1 þ field, and further, the sin excitation rofile, to be redicted for any set of RF ulses, which in turn enables excitation rofile control via aroriatelydesigned arallel ulse waveforms This illustrated framework for establishing a model (and determining A) oints to a few imortant considerations, including hysical basis of the rediction model, measurement noise handling, tailoring of calibration (secifically, design of the calibration configurations that W catures), and sensing or measurement scheme These are examined in deth below in the context of ower and global SAR characterization, which are the focus of this work Subject-Secific Global SAR Calibration and Prediction An MR system with linearity well maintained has RF ower dissiation characterized by Eqs 4 and 5, which facilitates SAR calibration and minimization By the law of conservation of energy the net RF ower injected into the N-ort network should be equal to combined RF loss in the subject, in the transmission hardware (including the coil) and through radiation The latter two are normally related to w in the form of quadratic functions as well, giving rise to the following exression for total RF loss: net injected RF ower ¼ total RF ower dissiation ¼ w H U w ½11Š In Eq 11 U¼UþU other,whereu other, a ositive semidefinite matrix, characterizes RF losses in hardware and through radiation (17) Reduction of these losses that are outside the subject is an imortant goal of coil/shielding/ comonent design and imlementation In cases where RF loss in the subject dominates the total RF loss, U becomes a good aroximation of U In any case total RF ower dissiation/u reresents an uer bound, or conservative estimate, of RF ower deosition/u in the subject With ower sensors at the orts caable of measuring forward and reflected ower (Fig 1), the difference between sum of forward ower and sum of reflected ower, P n ðnþ fwd P n ðnþ, gives net injected RF ower, allowing U to be estimated through exeriments Secifically, given w q, an inut configuration for the qth exeriment, measured forward and reflected ower values are related to w q by X n ðnþ fwd;q X n ðnþ ;q ¼ wh q U w q ¼ X i;j ðw ðiþ q Þ w ðjþ q F ij ½1Š Equation 1 is a linear equation with F ij, the entries of U, as the unknowns, and roduct terms, (w ðiþ q )* w ðjþ q,as

5 System and SAR Characterization in Parallel RF Transmission 1371 the coefficients Carrying out calibration exeriments with N or more roerly selected inut configurations layed out one at a time can robe the RF loss characteristic of the multiort network In articular, the coefficient and ower values from the exeriments allow assembly of Eq 1-tye equations and subsequent determination of all the entries of the N-by-N Hermitian matrix U This rocess does not involve MR imaging and may be comleted in a fraction of a second with an automated measuring system Once the calibration is comlete, the global SAR model w H U w redicts, for the secific subject, the SAR consequence of any inut configuration or arallel RF transmit ulses The Aendix shows an algorithm that was develoed for rescribing inut configurations alicable to the calibration The algorithm maintains the robustness of the solution against erturbation or noise by constructing a comlete set of Eq 1-tye equations with a condition number of N The above scheme can be extended to model and redict individual channel forward or reflected ower In this case Eq 1 is modified to assume the form: ðnþ fwd;q ¼ wh q UðnÞ fwd w q ¼ X i;j ðnþ ;q ¼ wh q UðnÞ w q ¼ X i;j ðw ðiþ q Þ w ðjþ q FðnÞ fwd;ij ðw ðiþ q Þ w ðjþ q FðnÞ ;ij ½13Š ½14Š As is clear from examining Eqs 1 14, the same coefficient and ower values for determining U are sufficient for further determining U (n) fwd s and U (n) s, and thereby characterizing the individual RF transmit channel s forward and reflected ower The redicted values for the nth channel s forward and reflected ower given an arbitrary inut configuration w are w H U (n) fwd w and w H (n) U w, resectively Subject-Secific Planning and Monitoring of Power Transmission When alying arallel RF transmission in ractice, couling and interaction taking lace in the multiort coil structure as well as in the subject can significantly affect individual channel RF ower transmission towards and away from the subject Tracking and redicting the effects and roactively managing ower transmission is imortant for ensuring a smooth scan The resent method s caacity for redicting the forward and reflected ower for any RF excitation are most relevant: (i) Given the eak ower rating of the ower amlifiers assigned to drive the arallel transmission channels, knowing in advance the eak ower requirements for the individual channels allows the user to roactively adat the excitation ulse design (eg, by alying VERSE (18)) and/or reconfigure the transmit hardware (eg, by udating the ower combination scheme alied to the comonent amlifier units) (ii) Given the reflected ower handling caacity of the amlifiers/circulators on the arallel transmission channels, knowing in advance large eak reflected ower for the individual channels similarly allows the user to imlement software- and/or hardware-based mitigation strategies (iii) As a sulement to ower transmission measurements, checking the individual channel ower redictions against actual measurements, or comaring the U matrices determined at baseline and that udated eriodically afterwards, rovides diagnostics that can detect in real-time system changes caused by, for examle, hardware failure, system instability or atient osition change, and can be used as triggers to susend scanning as needed In other words, using the ower rediction models both in lanning and in monitoring may avert amlifier eak ower or voltage standing wave ratio faults, rotection hardware breakdown, and excessive SAR due to system failure With these functionalities as well as global SAR rediction for guiding ulse design, the resent method is henceforth referred to as a Power Prediction and Monitoring (PPM) method Simulation Studies Parallel RF transmission cases were studied with finite difference time domain (FDTD) simulations (xfdtd, Remcom, State College, PA) For each case FDTD calculations quantified EM field and net RF ower dissiation corresonding to various inut configurations, allowing assessment of global SAR calibration and rediction Exclusion of coil loss and measurement noise is relatively straightforward in simulations, which facilitates an examination of the exact effects of field interferences and array coil loading on global SAR as well as an illustration of global SAR rediction accuracy A first study examined feasibility of global SAR calibration and rediction in 7T body imaging The setu involved a human model with heterogeneous electrical roerties and tissue density, and an RF coil comosed of four loo elements laced cm from the back of the human model (Fig a) The FDTD calculations used a cell size of 5 5 5mm 3 A total of 39 simulations were conducted emloying the same coil-subject setu but different inut configurations For each inut configuration the net ower dissiation reading, as generated by the FDTD calculation erformed for the inut configuration, was recorded To emulate a use scenario of calibration followed by actual scanning, the first 0 of 39 exeriments were conducted with inut configurations rescribed for SAR model calibration as described earlier These 0 inut configuration secifications and their resulting net ower dissiation values were used to assemble a set of 0 Eq 11-tye equations, which was solved with a least squares fit to give an estimate of U Given the estimate of U and the secification of any one inut configuration, denoted as w, w H U w rovides a rediction of net RF ower dissiation In the remaining 19 exeriments the inut configurations were randomly rescribed Plugging each of these 19 inut configuration secifications into w H U w gave a redicted net RF ower dissiation, which was comared to the corresonding one that was directly quantified by the FDTD calculation The comarison allowed an assessment of the accuracy of the model-based global SAR redictions and the validity of the rediction model

6 137 Zhu et al FIG Global SAR calibration and rediction in a simulation study involving a heterogeneous human model and an RF coil comosed of four loo elements a: Geometry of the human model and the array coil b: Power as a function of inut configuration Based on the net ower values quantified by the FDTD calculations for the 0 inut-configuration cases rescribed for calibration, the ower correlation matrix U was determined In each of the additional 19 inut-configuration cases the net ower redicted with the calibrated global SAR rediction model w H U w aeared to be in excellent agreement with the net ower quantified directly by FDTD, demonstrating the validity of the model To investigate imact of coil-subject setu on the global SAR model, in a second study two different setus were modeled each involving four identical loo elements of size 7 7cm laced about 1 cm above a uniform water hantom (Fig 3) Overlaing of elements was accommodated by dislacing the elements slightly relative to one another in the anterior osterior direction The water hantom had dimensions of cm 3, with conductivity 06 SI/m and relative ermittivity 80, aroximating electrical roerties of human tissues at 98 MHz With either setu the set of inut configurations included 16 rogramed ones for model calibration and 8 randomly generated ones for model validation Global SAR characteristics exhibited by the two setus were comared Phantom and In Vivo Studies On a whole body 7 T scanner (Siemens Medical Solutions, Erlangen, Germany) with eight channel arallel RF transmission caability, exeriments were erformed to evaluate the global SAR calibration and rediction method under actual MR imaging conditions Forward and reflected ower on the eight transmit channels were measured using a ower sensor (NRP-Z11, Rhode & Schwarz, Munich, Germany) connected to directional coulers located at the outut orts of the RF ower amlifiers An RF switch (National Instrument Dual 16x1 MUX) and customized alication software for instrument control and data logging were additionally used to automate sequential collection of all ower measurements using the single ower sensor FIG 3 Investigation of the imact of coil-subject setu on the global SAR model a,d: Two different simulated setus, each involving four identical loo elements of size 7 7cm laced 1 cm above a uniform water hantom b,e: Absolute magnitude of estimated global ower correlation matrix U for each setu Off-diagonal entries indicate ower correlations between distinct transmit elements, whereas variations in diagonal entries correlate with loading differences caused by the elements varying roximity to the lossy object The structure of U for Setu 1 (b), for examle, indicates significant ower correlations between transmit elements 1 and 3 and and 4, consistent with exected interference atterns given the geometrical arrangement of the elements and the object c,f: Power as a function of inut configuration With either setu the set of inut configurations included 16 rogramed ones for model calibration and 8 randomly generated ones for model validation

7 System and SAR Characterization in Parallel RF Transmission 1373 FIG 4 Exerimental global SAR model calibration and validation a: Photograh of a coil with four striline elements used for fourchannel arallel transmit MR of a cylindrical hantom b: Photograh of a general coil-object setu with four loo elements arbitrarily laced on a head-shaed hantom c: Four redesigned 18 ms-long staircase-shaed arallel RF ulses were used to introduce 36 inut configurations, including 16 for model calibration (definitions shown in the table) and 0 randomly generated inuts for validating the model-based global SAR redictions The inset shows the definitions of the calibration inuts d: For the four-loo array coil setu, a comarison of model-based SAR redictions with actual measurements [Color figure can be viewed in the online issue, which is available at wileyonlinelibrarycom] One set of ower measurements was erformed in a setu for arallel transmit MRI of a cylindrical hantom (s ¼ 07S/m, e r ¼ 80) The four-ort Tx-Rx array coil used in these exeriments was comrised of four strilines on an enclosing former (Fig 4a) (Additional strilines and a searate sodium birdcage colocated on the same former as art of a multinuclear coil designed for other uroses were not used in these studies) Four resecified 18 mslong staircase-shaed arallel RF ulses (Fig 4c) were used to introduce 36 inut configurations, including 16 rogramed ones for model calibration, followed by 0 randomly generated ones for model validation The ulses were layed out several times to allow the automation software adequate time to communicate with the RF switch and the ower sensor for sequential collection of all ower measurements The study was reeated in a more general coil-object setu, where four loo elements that formed a Tx-Rx array coil were arbitrarily laced on a head shaed hantom (Fig 4b) In vivo evaluations were conducted in human volunteers In one study an eight-channel striline array was used for arallel transmit MRI of a volunteer s left knee on the 7T scanner Eight 40 ms-long staircase-shaed arallel RF ulses were used to introduce 100 inut configurations, including 64 (designed with the algorithm shown in Aendix) for model calibration and an additional 36 randomly generated configurations for model validation The automation rogram for instrument control and data logging was integrated with a data analysis scrit written in Matlab (MathWorks, Natick, MA) and Cþþ It is aroriate to integrate into a scanner s existing PRESCAN the staircase ulsing scheme in which the SAR model is calibrated and validated before the MR scan The established SAR rediction model can then be used to guide the calculation of SAR-minimized excitation ulses before the MR scan Such roactive SAR management was imlemented in an actual imaging study where large-ti-angle arallel excitation ulses were used for hantom imaging on the 7T scanner The ulses were designed with the rediction model incororated (19) The corresonding net ower, quantified as sum of forward ower measurements in all channels minus sum of reflected ower measurements in all channels Pn ðnþ fwd P n ðnþ was recorded as a function of time during layout The exerimental result was comared to the rediction given by the model to check the accuracy of the guidance the model had rovided to the calculation of the SAR-minimized ulses (ie, the agreement between what the design algorithm thinks is the SAR consequence of a design and the actual SAR consequence) Evaluations of Suort for Planning and Monitoring Exeriments were further conducted to examine otential use of the ower rediction models in lanning and monitoring of arallel RF transmission on an MR scanner Some modifications were alied to the hantom exeriment setu described earlier For this study, instead of using the stock directional coulers that are located at the outut orts of the ower amlifiers, three MR comatible directional coulers were laced near the inut orts of three loo elements The latter formed a three-ort Tx-Rx array coil, and were again laced around the head-shaed hantom in an arbitrary fashion The modified directional couler (ower sensing) locations allowed tighter tracking of ower dissiation in the subject as significant RF losses in the long cables linking the amlifiers and the coil are excluded from the ower measurements and rediction models (For instance, RF loss in cables account for over 50% of total RF ower delivered by the RF ower amlifiers on our 7T system) Calibration and validation were erformed as before Continued investigations examined diagnostic and monitoring otential of the resent method by artificially introducing fault conditions After calibration and

8 1374 Zhu et al FIG 5 Automated SAR model construction for in vivo arallel Tx MR resulted in an 18 s calibration and validation rocess Results from an in vivo study indicated that the redictions given by the calibrated global SAR model were in excellent agreement with direct measurements (a), with a worst case rediction error of less than 10% (b) Results from a further study on the use of a calibrated SAR rediction model in RF ulse otimization indicated that the model offered reliable guidance to the ulse design algorithm the redicted net RF ower as a function of time was in excellent agreement with that actually measured during the layout of the designed arallel excitation (c) [Color figure can be viewed in the online issue, which is available at wileyonlinelibrarycom] validation under a baseline condition, the system hardware was altered to emulate two system fault scenarios In Case 1 one caacitor in the loo structure of Element 3 was desoldered, causing an oen condition In Case an extra segment of coaxial cable was added to the cable linking Element and its corresonding ower amlifier, adding a hase offset of about 45 degrees The actual measurements taken after the alterations were comared to the baseline measurements and the baseline model redictions, and differences in rediction models were further noted RESULTS Results from the FDTD simulation using the human model are summarized in Fig Based on the net ower values quantified by the FDTD calculations for the 0 inut-configuration cases rescribed for SAR model calibration, U was determined In each of the additional 19 inut-configuration cases, Fig b shows that net ower redicted with w H Uw, the calibrated global SAR model, was in excellent agreement with net ower quantified directly by FDTD The average ercentage difference between redicted and directly quantified net ower was % In Fig 3c,f, results from the second FDTD simulation study again indicate high accuracy achieved by the calibrated global SAR models In addition, as shown in Fig 3b, the magnitude of estimated U for Setu 1 shows significant off-diagonal ower correlations between Elements 1 and 3 and and 4, consistent with the interference atterns exected of the geometrical arrangement of the elements and the object (deicted in Fig 3a) Similar observations may be made for Setu (geometrical arrangement shown in Fig 3d, magnitude of estimated U shown in Fig 3e) For each setu, variation in the diagonal entries of U correlates with loading difference due to the elements varying roximity to the lossy object In Setu for examle, Element 4 was the furthest from the object, while Elements 1 and were the closest Furthermore, notice that for the two setus the ratios of the largest to the smallest eigenvalues were 31 and 63, resectively These indicate that with either setu, different RF ulses with the same sum of magnitude squared could have significantly different SAR consequences (u to a factor of 31 and 63, resectively) An identity matrix-based SAR model would not be able to distinguish between such ulses For each of the two arallel Tx hantom studies, results demonstrated feasibility of the global SAR calibration and rediction method under actual MR imaging conditions (Fig 4) The measurement hardware was suortive of global SAR modeling and rediction The method handled both a conventional encircling Tx array coil and a more generally configured Tx array coil well, roducing robust U estimates and giving model-based SAR redictions that closely matched actual measurements Results for the fourloo array coil setu are shown in Fig 4d The measurement automation in the in vivo study streamlined the calibration and validation rocess The entire rocess of RF ulse layout on the scanner, U determination, and measurement-versus-rediction dislay that allows the user to validate the calibration, was comleted in less than 18 s Figure 5a shows that the redictions given by the calibrated global SAR model were in excellent agreement with direct measurements Also notice that model calibration was erformed at a low ower levels, yet the validity of the rediction model held over a considerably wide test range, suggesting robust modeling as well as good system linearity Similar results were achieved in an additional in vivo study The mean 6 standard deviation of the difference between the redicted and measured ower were 368% 6 439% and 51% 6 383% for the two studies, resectively In both studies and in all validation cases the maximum rediction error was less than 11% For the hantom exeriment emloying designed largeti-angle arallel excitation, Fig 5c shows excellent agreement between redicted and measured global RF ower deosition The measured net ower was nevertheless somewhat lower than that redicted at shar eak locations This was attributed, in art, to the timing offset between ower measurement and RF ulse udate (every 10 ms) Measurement imerfection was estimated to account for rediction error of u to 10% (0) Figure 6 shows one set of results from the study that evaluated the lanning and monitoring otential of the resent method These results demonstrate that the resent method was able to accurately redict not only the net ower transmission but also the individual channel

9 System and SAR Characterization in Parallel RF Transmission 1375 remained linear, which allowed ower recharacterization by reeating the calibration and validation stes leading to udated U ðnþ fwd, UðnÞ and U For the baseline, Case 1 and Case, the significant eigenvalues of U were {4, 43}, {5, 9}, and {19, 41}, resectively In further screening of the sectra of U ðnþ fwd and UðnÞ, shar contrast was resent between Case 1 U ð3þ and baseline U ð3þ, and between Case U ðþ fwd and baseline UðÞ fwd, esecially in terms of the largest eigenvalue (Fig 8c,f) Similarly, differences in atterns of eigenvectors were noticed between the baseline and fault cases These along with the attern changes of eigenvalues were certainly reflected in U ðnþ U ðnþ and U (magnitude shown in Fig 8a,d) fwd, FIG 6 Three channel arallel Tx study with a coil-object setu that had three loo elements arbitrarily laced on a head shaed hantom and formed a Tx array coil Global SAR model calibration and validation was erformed, which led to model redictions that accurately matched net ower measurements (bottom lot) The ower measurement data were further rocessed to calibrate redictive models of individual channel forward and reflected ower, which gave w H U ðnþ fwd w and wh U ðnþ w, nth channel forward and reflected ower redictions resectively, for any inut configuration w For the randomly rescribed inut configurations (Stes 10 18), redictions from these models were in excellent agreement with actual measurements (lots labeled Ch n fwd and Ch n ) ower transmission in both forward and reflected directions Three additional sets of results were obtained in the study, with setus that included a baseline and two that had artificially introduced faults For the baseline case, calibration and validation stes were erformed Figure 7a shows U ðnþ fwd, UðnÞ and U that were estimated from the nine calibrating stes For the subsequent nine validating stes (each with an inut configuration that was randomly generated) Fig 7b shows a comarison between the model based redictions and the actual measurements Again, high rediction accuracy was achieved by the resent method Similar calibration and validation stes were also erformed for fault cases 1 and Figure 8b shows that the oening of Element 3 in Case 1 caused significant changes in Channel 3 reflected ower measurements from baseline, esecially for exeriment stes whose inut configuration significantly engaged Channel 3 (eg, Stes 14, 16, and 17) Figure 8e shows that the extra hase shift along Channel caused significant changes in Channel ower measurements from baseline, esecially for exeriment stes where the inut configuration significantly engaged Channel (eg, Stes 11, 13, and 18) As exected, the ease of detecting a fault based on a comarison of rediction and measurement was inut configuration-deendent However, a systematic detection was ossible by evaluating the eigenvalues or eigenvectors of U In Cases 1 and, the altered system DISCUSSION AND CONCLUSION From the ersective of advancing high field MR, it aears inevitable that one needs to erform in vivo SAR model calibration for managing SAR, just as one needs to erform B1 ma calibration for managing excitation rofile Given the task of scanning a secific subject, to maximize erformance one uses B1 and SAR calibration results acquired in the resence of the subject as key inuts to guide otimization of ulse or shimming calculations Performance aside, to ensure a smooth scan it is highly desirable to accurately characterize RF ower transmission and deosition, and thereby comly with safety and hardware limits These considerations on erformance and safety oint to a sensible in vivo MR aradigm: a PRESCAN rocess calibrates SAR rediction models secific to the subject and erforms model-guided excitation ulse calculations to manage SAR for the intended scans; actual scans then roceed with the oerator knowing in advance the SAR consequence, knowing that RF transmit has been FIG 7 Baseline model calibration and validation for system fault monitoring a: Magnitude dislays of U ðnþ fwd, UðnÞ and U, which were calibrated using ower measurements obtained under Inut configurations 1 9 b: Comarison of model redictions with ower measurements for randomly generated Inut configurations indicated accurate rediction These models/data serve as a reference for detecting system changes from baseline at a later time

10 1376 Zhu et al FIG 8 Cases 1 and in a system monitoring study The baseline was altered to emulate two system fault scenarios In Case 1 the baseline setu underwent a system change in which Element 3 was forced to oen Recharacterization was erformed a: shows udated U ðnþ fwd, UðnÞ and U b: shows redictions, measurements, as well as redictions from baseline models (circles) c: shows maximum eigenvalues of Case 1 U ðnþ fwd and UðnÞ (solid bars) vs that of baseline U ðnþ fwd and UðnÞ (nonfilled bars) In Case the baseline setu underwent a system change in which Channel had an extra hase offset of about 45 degrees Results are similarly dislayed in (d) (f) Note the attern change of a ower correlation matrix s eigenvalues: For the baseline, Case 1 and Case, the significant eigenvalues of U were, {4, 43}, {5, 9}, and {19, 41}, resectively In terms the largest eigenvalues, further note the shar contrast between Case 1 U ð3þ and baseline U ð3þ, and between Case U ðþ fwd and baseline UðÞ fwd (c,f) erformance-otimized for this secific subject and won t exceed safety limits or hardware caability, and knowing in real-time should any of the transmit chains malfunction Given the linearity of a common arallel RF transmission setting, an aroach is resented that emloys the concets of a multiort network and an overall linear system to directly link any RF ulses (system inuts) to RF fields and SAR in the scanned subject (system oututs) The accordingly established PPM method enables, for examle, accurate characterization and roactive management of global SAR in vivo without forcing one to deal with subject, coil or hardware details This is in contrast with other ossible sensing and rocessing aroaches that rely on voltage, current or field resonses measured on or around the transmission hardware (1,) with nontrivial sensor setu and hase-sensitive detection While allowing one to infer some characteristics of RF transmission and SAR, these intermediate measurements may not lead to definite guidance to RF ulse design without additional calibrations that comlete the determination of the link between the RF ulses and global SAR In a nutshell the PPM method, using judiciously defined inut configurations, erforms a finite number of calibration exeriments and records the oututs of the overall system The results of these calibration exeriments are then used to build quadratic rediction models caable of relating any redetermined RF ulses to RF transmission and global SAR, and assisting in system error detection The effects of field interferences and array coil loading on RF transmission and global SAR are catured by the models These effects are nonexistent or less comlex in a conventional RF transmission setting, and cannot be correctly catured with seudo RF ower models (eg, the common sum of magnitude squares of ulse waveform samles) that were originally introduced for regularization (11) In characterizing subject-secific global SAR with the PPM method, ower measurements taken at a set of discrete sensor locations together with the law of conservation of energy are used to monitor and redict an integral of non-negative local RF ower deosition RF ulse or shimming calculations that minimize the integral under the guidance of PPM tend to curb the occurrence of excessive local SAR Structurally this tendency may be areciated by noticing that minimizing w H U w is equivalent to minimizing sum of w H K(r) w over voxels (Eq 5) where U and K(r) s are ositive semidefinite a w with excessive w H K(r) w at a location tends (but does not guarantee) to elevate w H U w, which would steer the calculations to favor other designs Due to the integral nature overestimation of global SAR in the subject could result if the ower

11 System and SAR Characterization in Parallel RF Transmission 1377 measurements include hardware RF loss in addition to RF loss in the subject However this effect does not imact the validity of treating the quantified global SAR as the uer-bound of the true global SAR Mitigation of the effect is ossible through imrovements in hardware/measurement scheme (discussed later) Subject-secific local SAR characterization is a considerable challenge, a ractical solution of which is a rerequisite for addressing with confidence the ossibly more limiting (3) local SAR limits The PPM method, working with satially resolved ower or temerature measurements, has otentials, as exlored in a reliminary investigation (4) In comarison a numerical simulation aroach romises to rovide an abundance of information that are difficult to obtain noninvasively These include satially resolved field, SAR or even temerature information that may enable the use of a multironged strategy for mitigating local SAR (5) Possible SAR quantification errors resulting from a mismatch between the simulated and the real settings are difficult to analyze or manage however, which imacts validity of simulation-based SAR estimates and sells the need for an in vivo alicable scheme for assessing the match or for bounding the errors Imlementation of PPM does not require secial hardware MR scanners equied with arallel RF transmission channels already check in real-time, with RF ower monitors (10,6), forward ower transmission in the individual cables linking the RF ower amlifiers and the multiort transmit coil, and are rogramed to sto the scan uon detection of an excessive level of total forward ower The new imlementation entails an ugrade of the RF ower monitors caacity to include individual channel reflected ower, and a rogram that rocesses the forward and reflected ower readings according to the descritions described in the THEORY AND METHOD sections As the transmit and receive eriods of an MR exeriment tyically do not overla, the arallel receive channels on the scanner could be utilized to demodulate directional couler oututs and convert the results to ower readings during RF transmission The resulting arallel ower sensing/monitoring caacity could facilitate the imlementation of the PPM method While the built-in RF ower monitors and arallel receive channels were not readily accessible on our system to allow further demonstrations, the resent investigation did rovide indications of the caability of a full fledged imlementation: (i) Calibration comleted within a second The total amount of time required for laying out the calibration configurations scales with N It can be fit into 1 s with the staircase-tye ulses and arallel RF ower sensing, if N is not substantially greater than 3 This makes the time cost of erforming a calibration in vivo negligible (ii) Tighter characterization of global SAR, which can be exected in a sensing setu that has directional coulers located close to the coil and better controlled ower sensors This imroves the guidance rovided to ulse design otimization and hels refine the SAR limit setting on the scanner (iii) Real-time monitoring and automatic rotection The individual channel ower characterization and rediction caability, when leveraged to check channel integrity during the scan, hels ensure real-time detection of hardware failure Such events as breakdown of comonents in the transmit hardware, alteration of coil geometry/lacement, and subject osture change could all lead to changes in system characteristics, manifesting as a discreancy between redictions and measurements, or, between characterizations done before and after the change A system state change is a cause for intervention, including susension of scanning for subject and scanner rotection There is a link between the global SAR model resented here and the scattering matrix S of an N-ort network (7) Given an S matrix that is determined from incident and reflected wave measurements (amlitudes and hases) taken at the N directional coulers during a calibration, one can subsequently exress total RF ower dissiation in the network as a H (I-S H S) a for any a, where a is an N-by-1 vector collecting the instantaneous incident wave measurements taken at the N orts This leads to U ¼ L H (I-S H S) L, where matrix L catures the linear maing from w to a as well as other scaling in the system L is fixed for a given hardware-subject setu An additional link between the global ower correlation matrix and arallel receive noise covariance matrix W was suggested in the ast, based on the rincile of recirocity (8) In addition to offering alternative ways to calibrating a global SAR model, these links also suggest that the global ower correlation matrix rovides imortant information about S and W, and vise versa For examle, knowledge of U and L allows determination of all of the scattering matrix S s eigenvalues This examle offers insights on the sensitivity of a U-based scheme in detecting system state changes The system ersective described earlier reinforces the rationale for a arallel transmission oeration mode involving calibration þ ulse design þ transmission It also hels inoint the limitations of some concetions As a simle examle, in the early days of arallel transmission develoment some thought that B1 þ of any element in a transmit array coil should be maed while all other elements are detuned or deactivated One issue here is that detuning or deactivation alters the system, making it different than what is encountered during the actual arallel RF transmission Similarly, for schemes that attemt arallel transmission ower calibration through S or C measurement, it is imortant to make the measurement condition the same as what is in lace during actual arallel RF transmission In an examle where C is measured using the receiver chains, due to changes in imedance seen by the orts (from the low inut imedance of the reamlifiers to the 50 V outut imedance of RF ower amlifiers), likely alteration of RF current and field atterns within the network (including the coil structure and the subject body) can result in changes in RF loss characteristics, rendering the derived SAR model less accurate redicting the RF loss characteristics for the actual arallel transmit MRI In both examles above, system alteration can invalidate the alication of (a linear system s) suerosition rincile and can cause errors in using calibration data for rediction or for guiding actual MR Along the same line, the benefits of in