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Improving SAR estimations in MRI using subject-specific models
View the table of contents for this issue, or go to the journal homepage for more
2012 Phys. Med. Biol. 57 8153
(http://iopscience.iop.org/0031-9155/57/24/8153)
Home Search Collections Journals About Contact us My IOPscience
Received 28 August 2012Published 23 November 2012Online at stacks.iop.org/PMB/57/8153
AbstractTo monitor and strategically control energy deposition in magnetic resonanceimaging (MRI), measured as a specific absorption rate (SAR), numericalmethods using generic human models have been employed to estimate worst-case values. Radiofrequency (RF) sequences are therefore often designedconservatively with large safety margins, potentially hindering the full potentialof high-field systems. To more accurately predict the patient SAR values, wepropose the use of image registration techniques, in conjunction with high-resolution image and tissue libraries, to create patient-specific voxel models.To test this, a matching model from the archives was first selected. Its tissueinformation was then warped to the patient’s coordinates by registering thehigh-resolution library image to the pilot scan of the patient. Results fromstudying the models’ 1 g SAR distribution suggest that the developed patientmodel can predict regions of elevated SAR within the patient with remarkableaccuracy. Additionally, this work also proposes a voxel analytical metric thatcan assist in the construction of a patient library and the selection of thematching model from the library for a patient. It is hoped that, by developingvoxel models with high accuracy in patient-specific anatomy and positioning,the proposed method can accurately predict the safety margins for high-fieldhuman applications and, therefore maximize the safe use of RF sequence powerin high-field MRI systems.
(Some figures may appear in colour only in the online journal)
1. Introduction
Higher signal-to-noise ratio (SNR) has driven the development of new technologies forclinical applications of magnetic resonance imaging (MRI) at higher static magnetic fields
1 Authors to whom any correspondence should be addressed.
(B0). Stronger B0 associates with higher operating frequencies and shorter wavelengths ofthe radiofrequency (RF) electromagnetic fields (EMF) within the dielectric tissues. As thewavelengths become comparable to, or shorter than, the dimension of the imaged subjectsand/or that of the RF coils, the wave behaviour of the RF EMF more readily manifests itselfdue to the increasingly complicated field–tissue interactions (Collins and Smith 2001, Liu et al2005a, Ibrahim et al 2009). The RF electric field distributions, in particular, directly affect theRF energy deposition. Measured as a specific absorption rate (SAR), they cause concerns forthe safe use of high-field MRI systems. The whole body or whole head SAR has a tendency toincrease with application frequency (Collins and Smith 2001, van den Bergen et al 2009b). Atspecific anatomical sites, however, local SAR distributions become more concentrated due tothe complex current patterns induced within the heterogeneous media (Collins et al 2004). Theelectric field and SAR distributions can cause further complications as various RF shimmingtechniques are employed to homogenize transmit magnetic fields.
To avoid the risk of local tissue damage due to excessive RF heating, sequence parameters(e.g. flip angle, repetition time and etc) are designed at the regulated SAR limits (Food andDrug Administration 1988, International Electrotechnical Commission 2002). Undoubtedly,the success of SAR control depends heavily on a reliable means of accurately predictingthe distribution of electric fields and the tissue distributions. Since non-invasively measuringelectric fields in vivo is impractical, numerical methods have been an extremely useful andindicative alternative for studying high-field human MRI applications. For example, theyhave been used to develop SAR monitor/prediction methods (Graesslin et al 2012, Homannet al 2011, Zhu et al 2012, Voigt et al 2011a, Eichfelder and Gebhardt 2011), study implantcompatibility/safety (Mattei et al 2012, Powell et al 2011), design parallel transmissionpulses with SAR constraints (Lee et al 2012, Sbrizzi et al 2012), and evaluate the safety ofnew imaging sequences (Metzger et al 2012, Orzada et al 2012) and novel RF systems (Snyderet al 2012, Kobus et al 2012, Zhang et al 2012, Teeuwisse et al 2012, Gilbert et al 2012, Altet al 2012). Simplified body models (Van den Berg et al 2007) and two-dimensional (2D)semi-analytical methods (van den Bergen et al 2009a) are advantageous in terms of simplicityof modelling and speed of convergence. Realistic human models (Dimbylow 1997, Collinsand Smith 2001, Ibrahim et al 2001, Peter 2005, van den Bergen et al 2007) and validatedfull-wave techniques (Yee 1966, Berenger 1994) can, however, improve the accuracy of thesolution (van den Bergen et al 2009b). Previous studies have demonstrated that the maximumSAR magnitudes and overall distributions are sensitive to the position of the patient relativeto the coil (Wolf et al 2012) and to morphological variations (Liu et al 2005b, Homann et al2012). However, it is generally neither feasible to create numerical models for the large rangeof RF coils available, nor practical to create accurate voxel models for individual patients.Therefore, generic coil and patient models are commonly employed to estimate SAR values,which are then used, in conjunction with relatively large safety margins, for clinical planning(Seifert et al 2007). As a result, the efficiency of RF systems and the quality of the imagesproduced can sometimes be non-optimal. Therefore, it is important to use comprehensive full-wave techniques and accurate coil and patient models for reliable SAR predictions, to ensurepatient safety and to allow confident use of the RF power available in high-field system.
The accuracy of the SAR predictions largely relies on the coil models and the patientmodels. As proposed in the authors’ recent studies (Jin et al 2010, 2012), the coil models canbe refined by calibration scans using homogeneous phantoms. In this paper, we focus our studyon improving the accuracy of the patient models. Conventionally, the construction of accuratepatient models may require full-body high-resolution scans and accurate tissue labelling.Instead of attempting this time-consuming and labour-intensive task, the current study aimsto create custom/patient-specific three-dimensional (3D) voxel models from existing models.
Improving SAR estimations in MRI using subject-specific models 8155
Image registration techniques will be used, so that a library of high-resolution 3D images withcomplete dielectric tissue parameters can be warped to match low-resolution pilot scans ofthe patient. Hence, numerical SAR calculation can be performed using more accurate voxelmodels that more closely match the anatomy of the patient. In this study, we investigatewhether a registration technique designed to transform and align two intensity images can beapplied to predict patient’s tissue distribution. We go on to investigate whether local SAR canbe estimated more accurately provided the registration of tissue volumes is successful.
2. Materials and methods
This section describes a high-resolution image and tissue library, the construction of patientmodels using non-rigid registration techniques and voxel statistical analysis before and afterthe registration. We then conduct SAR calculations on the constructed patient models, usingthe finite-difference time-domain (FDTD) method (Yee 1966).
2.1. The construction of patient-specific voxel models
2.1.1. A high-resolution MRI library for the development of patient voxel models. Fourvoxel head models (subject 06, 20, 46 and 51) were arbitrarily chosen from the 20 totalavailable models from Brainweb2. These voxel models were constructed from 20 normaladults (Aubert-Broche et al 2006b). The spatial distribution of 11 types of tissues, includinggrey matter (GM), white matter (WM), cerebrospinal fluid (CSF), skull, marrow, dura, fat,tissue around fat, muscles, skin and vessels, were described by 11 probability volumes. Thevoxel intensity of each probability volume represented the fraction of the correspondinganatomical tissue within the voxel. As examples, the spatial distribution of GM, WM, CSFand vessels of the selected models are shown in figure 1(A). The tissue segmentation wasextracted from a series of T1-, T2- and proton density-weighted MR images, MR angiography(MRA) acquisitions and computed tomography (CT) scans (Aubert-Broche et al 2006a). Eachvolume was of 0.5 mm isotropic resolution. The tremendous effort spent to create these voxelmodels with high accuracy should be accredited to the authors. However, it is important tonote that the absolute segmentation accuracy was of little importance in the current study.The inter-subject anatomical variations, as seen from figure 1(A), were important for SARevaluations, whereas the tissue classification were used to define the ground truth for ourinvestigation of the registration method.
First, the 11 probability volumes of each patient were used to create a 0.5 mm resolutiondiscrete tissue model based on the ‘winner-takes-all’ policy, that is, each voxel was representedby the tissue type that has the largest portion among all types. As shown in figure 1(B), thesehigh-resolution discrete models were then down-sampled to 2 × 2 × 2 mm3 resolutionfor SAR calculations. Bone marrow and ‘around fat’ were combined with bone and fat,respectively, before the conversion. The head models were padded with the neck and shoulderof the NORMAN (Dimbylow 1997) model to create correct loading. NORMAN is ananatomically detailed body model that consists of 41 tissue types and is constructed at2 × 2 × 2 mm3 resolution. Simple morphological operations, such as opening and closing,were then performed to ensure the continuity and smoothness of skin and skull. Each slice ofthe models was checked manually for the correctness of the operations.
To reduce computational complexity and solution time, the stitched models were truncatedto an overall height of 45 cm (from the top of the head). It was found that the inclusion of neck
Figure 1. The tissue volumes and simulated T1 images of the patients. (A) The probability volumesdesignating the spatial distribution of GM, WM, CSF and vessels of the four models. (B) The2 × 2 × 2 mm3 resolution discrete models for SAR calculations. (C) The simulated T1-weightedimages with the following parameters: spoiled FLASH sequence with TR = 22 ms, TE = 9.2 ms,flip angle = 30◦ and 1 mm isotropic voxel size. These images were available from Brainweb.Please refer to the text for more details.
and shoulder model was important for correctly calculating the EMF within the head at 7T(Wolf et al 2012). While significantly reducing the solution time (by ∼50%), the truncation,however, had no discernible effect on the head coil behaviour (no change in S-parameters andcoil impedance was observed). The changes in the magnetic and electric field levels due tomodel truncation were well below 1%. Certain tissue types were no longer present in the voxelmodels. A complete list of the tissues and their properties, as extracted from the literature(Gabriel 1996, McIntosh and Anderson 2010), can be found in table 1. Since the subjectmodels were rigidly aligned, it was relatively easy to place the subjects at the same position(the centre of the brain coincide with the origin of the coordinate system).
3D images of the patients that are aligned with the voxel models are needed to investigatethe efficacy of image registration. The MRI simulator (Kwan et al 1999) was thereforeemployed to simulate 3D MR images from the corresponding probability models, as seenin figure 1(A). Figure 1(C) illustrates the simulated T1-weighted images with the followingparameters: spoiled FLASH sequence with TR = 22 ms, TE = 9.2 ms, flip angle = 30◦
and 1 mm isotropic voxel size. These images were also available from Brainweb. As can beseen from figure 1(C), the inter-subject morphological differences were clearly observable.The tissue distributions of the imaged subjects are typically unknown. These voxel models(figure 1(A)) and their corresponding MR images (figure 1(C)), however, provided knownground truth and realistic complexity of the individual brain structures (Aubert-Brocheet al 2006a, 2006b), making them an ideal candidate for evaluating of the accuracy of theregistration.
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Table 1. Tissues and their physical properties pertinent to SAR calculations. The dielectricproperties (i.e. electrical conductivity and relative permittivity) were extracted for applicationsat 298 MHz.
Electric conductivity Relative DensityMaterial (S m–1) permittivity (kg m−3)
2.1.2. The registration technique for the development of patient-specific model. Byregistering a high-resolution 3D image from a library to the pilot scans of the patient, thetissue distribution and properties available from the library can thus be transferred to fitthe patient. In essence, a registration algorithm finds the spatial correspondence betweenthe source image and the target image by transforming the former to match the latter,so that the two can be studied in the same coordinate system. Registration has foundwide-spread use in medical imaging, including intra-subjection motion correction, distortioncorrection, cross modality image fusion and so on. Registration has been comprehensivelyreviewed by many authors (Hill et al 2001, Holden 2008). Briefly, a typical registrationalgorithm consists of two major components, namely registration metric and deformation.The registration metric measures how closely the two images are aligned, by calculating forexample the distance between corresponding landmarks/features or mutual information. Moresophisticated methods measure image similarity by comparing image attributes (Dinggangand Davatzikos 2002, Ou et al 2011). These similarity metrics are improved by deformingthe source image into alignment with the target image. Geometric deformations are oftenbased on mimicking physical processes, such as fluid flow (Ashburner 2007), or numericalapproximations, such as B-splines (Rueckert et al 1999).
A non-rigid registration algorithm, coined DARTEL (short for diffeomorphic anatomicalregistration using exponentiated lie algebra) (Ashburner 2007) was adopted in the current study.DARTEL fits into the category of large deformation models (diffeomorphism). The nonlineardiffeomorphism is achieved assuming a physical model of flow field that has constant Eulerianvelocity (Ashburner 2007). In brief, the source image is deformed as if it were placed ina flow field, where each voxel of the flow fields assumes a constant velocity. By contrast,the varying velocity models assign temporally varying velocity parameters to each voxel ofthe source image. The varying velocity fields are usually approximated by dividing the time
course of deformation into frames and assigning constant velocity to each frame. In contrast,DARTEL adopts a single velocity field. As the deformation propagates over time, each voxelof the source image passes different locations and hence experiences different velocities. Suchmodel provides simplified flow fields compared with variable velocity models and, therefore,reduces the computational complexity and solution time (Ashburner 2007).
In this study, each of the four patient models was regarded as a target in turn. Meanwhile,the rest of the models were used as sources, upon which the geometric deformations wereconducted. Accordingly, we created 12 registration pairs. For each pair of models, the followingoperations were performed.
(1) The 3D MR images of the source and the target were segmented individually using aprobabilistic framework that combines image registration, tissue classification and biascorrection within a single generative model (Ashburner and Friston 2005).
(2) The tissue distribution maps of GM, WM and CSF of the source and target images wererigidly aligned.
(3) The rigidly aligned tissue maps were co-registered to a common template using the methodof DARTEL (Ashburner 2007). DARTEL yielded flow fields (�) that mapped the sourceimage (Is) and the target images (It) to a common template. �s, for example, denotes thetransformation from the common space to the source image space. The initial templatewas created by averaging the source and the target images. It was then iteratively refinedas the source and the target were more accurately warped to this common space.
(4) Since the diffeomorphic framework guarantees consistency under composition, the tissuedistribution of the target can therefore be estimated from that of the source, by thecomposition of the forward and inverse flow fields derived from the previous step:
θ s→t = �t(�−1
s (θ s)) = �t ◦ �−1
s ◦ θ s, (1)
where θs is the tissue distribution of the source s; θ s→t is the tissue distribution of the targett estimated from the source s; �−1 denotes an inverse of the flow field � and symbol ◦indicates composition.
The operations (1) to (4) described above were aided by using a publicly availableMatlab toolbox SPM83. Typically, an energy term is included in the registration cost functionto regularize the amount of image spatial warping. In this study, the linear elasticity energymodel was used to penalize absolute displacements. The initial weighting of this regularizationwas high and then reduced gradually, so that large deformations were restricted initiallyencouraging smoother transitions while better matching of the image details were allowed inthe final iterations. The number of time steps was used to define the number of transformations(i.e. time frames) the source image would experience the flow field. The number of time stepsincreased gradually from 1 to 64 as suggested by the SPM8 manual. This gradual increaseleveraged for less time consumed by the early iterations and smooth final deformations.
We also tested the nonlinear registration method with the target images of variousreduced resolutions. The original 3D target images were down-sampled, retrospectively. Lowerresolution target images require less acquisition and represent faster patient pilot scans. Theoriginal and down-sampled 3D images of subject 20, for example, are shown in figure 2 (Rindicates the ratio by which the resolution was reduced in all directions).
2.1.3. Voxel model statistical analysis. Statistical analysis is typically employed to help studythe tissue agreement between patient models before and after the registration. In the currentstudy, it can also help us gain valuable insight into the correlation between the conformity of
Improving SAR estimations in MRI using subject-specific models 8159
Figure 2. The original and down-sampled 3D images of subject 20 (R indicates the ratio by whichthe resolution was reduced in all directions).
tissues and SAR values. Specifically, the target overlap (TO) was calculated for each pair ofdiscrete patient models as follows:
TOA→B =∑
v
∣∣θA,v ∩ θB,v
∣∣/∑v
∣∣θB,v
∣∣ (2)
where TOA→B calculates the TO agreement between subject A and B, with respect to thelatter’s tissue distribution; θ is used to denote the spatial tissue distributions; v is the index foreach labelled region, such as GM, WM, CSF and so on; ∩ is defined as intersection; and |·|calculates the number of the voxels in the volume. Essentially, TO agreement calculates thepercentage of the tissue voxels that both subject A and B have in common, with respect to thetotal number of tissue voxels of subject B.
Before registration, TO was calculated between every pair of head voxel models in bothdirections. TO was then used to evaluate the effective of registration. For each registrationpair, the TO was measured between the registered model and the target, when the latter wassampled at various reduced resolutions. Taking the registration from subject 51 to subject 20for example, TO was first calculated between θ51 and θ20 in both direction to generate TO51→20
and TO20→51. After the registration, TO was then measured between θ20 and θR51→20 (please
refer to equation (1); R = 1, 2, . . . , 5 indicates the reduction factor of the target image).
2.2. SAR calculations
2.2.1. SAR calculations using the FDTD method. To calculate SAR for the developed voxelmodels, electromagnetic (EM) simulations were carried out. In the current study, a 16-runghigh-pass birdcage coil model was employed as EM source. The coil was of a cylindricalshape with a diameter of 30 cm and a total height of 25 cm. The coil had a cylindrical shield
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with a diameter of 36 cm and a height of 30 cm. A total of 32 gaps were introduced to theend rings for inserting the tuning capacitors. By adjusting the capacitance, the coil was tunediteratively for 7T application (298 MHz). It was then re-tuned carefully whenever the loadingcondition had changed in the subsequent studies. To create circularly polarized excitation, thebirdcage coil was excited at two ports 90◦ apart while they were driven with the equal voltageamplitude and a phase difference of 90◦.
The EM modelling and calculation were performed using commercially available packageSEMCAD X (SPEAG, Zurich, Switzerland). The FDTD method was adopted to provide full-wave numerical solutions to Maxwell’s equations. A 2 × 2 × 2 mm3 grid resolution of thevoxel models was adopted in the FDTD calculation and was maintained throughout the study.It was found that such high resolution was necessary to resolve the thin anatomies, such as theskin and the skull, which were often the dividing membrane of tissues with largely differentconductivities. The RF system was padded with one-tenth and one-eighth wavelength of air inthe x–y-direction and z-direction, respectively. An absorbing boundary condition with uniaxialperfectly matched layers was defined, which uses air volume to truncate the solution into finitespace and to absorb the radiated fields (Berenger 1994). 120 periods were calculated to ensurethat the energy has decay below −45 dB. The voxel SAR results were then extracted fromSEMCAD X and processed using MATLAB (Mathworks Inc., Natick, MA). The voxel SARresults were scaled to a total input power of 1 W, equally distributed to both driving ports.The 1 g SAR was then approximated by averaging the voxel SAR values within a 5 × 5 ×5 window, with a volume of 1 cm3.
2.2.2. Patient positioning. The position of the patient was accessible from the low-resolutionpilot scan, and was maintained in the construction of the corresponding voxel model usingimage registration. In a registration, the target image remains in its original coordinatesystem, while the source image is deformed along with its coordinate system to match thetarget.
A recent study has demonstrated the importance of having accurate knowledge of thepatient positioning. The simulation study for 7T MRI system indicated that the SAR levelschanged up to 22% when a relative shift of 2 cm occurred between the coil and voxel models(Wolf et al 2012). To demonstrate this effect in the current study, we evaluate and compare theSAR values when the NORMAN model (45 cm from the head) was shifted in y-direction of2.5 cm (reducing the distance between the coil and skin of the posterior of the head from 5 to2.5 cm). As illustrated in figure 3(A), this operation could mimic the change in the thicknessof the head padding material. In practice, the birdcage coil was shifted in –y direction for2.5 cm, so that the voxel model and field sensors retained their original positions facilitatingdirect comparison.
3. Results
3.1. Patient-specific voxel models
3.1.2. Mutual total overlap (MTO) for the selection of matching models. In this work,a library of MRI images and tissue volumes was used for the construction of the patient-specific voxel models. It is essential to develop a metric, which can used to compare themodels and guide the selection of the matching model for a patient. The insight into such apossible metric can be gained from studying voxel statistics. The TO measure between eachpair of models can be found in table 2 (‘TOS→T ’ column). As indicated, subject 06 and 46
Improving SAR estimations in MRI using subject-specific models 8161
(A)
(B)
(C)
Figure 3. The modelling and SAR results before (left) and after (right) shifting the NORMANmodel in y-direction by 2.5 cm. (A) The numerical models of a birdcage coil and NORMAN. (B)The coronal (top) and sagittal (bottom) slices that pass the maximum 1 g SAR location beforeshifting. (C) The coronal (top) and sagittal (bottom) slices that pass the maximum 1 g SAR locationafter shifting. Yellow texts in the graph are used to indicate maximum 1 g SAR of the correspondingmodel, whereas the white texts are used to denote the maximum 1 g SAR of the slice shown.
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Table 2. TO measures between voxel models before and after image registration. TOS→T denotesthe TO agreement between the source S and the target T, with respect to the latter’s tissuedistribution. θ is the spatial tissue distributions. θS→T indicates the tissue distribution of thetarget T estimated from the source S. R is the factor, by which the target image resolution isreduced.
had low TO agreements as targets (e.g. TO20→06 = 64.03% and TO51→06 = 66.77%) andhigh TO agreements as sources (e.g. TO06→20 = 74.55% and TO06→51 = 75.70%). SinceTO agreement was calculated as the number of tissue voxels that the pair of models had incommon divided by the number of tissue voxels of the target. A large deviation of TO measuresbetween a pair of subjects in different directions indicates large difference in subjects’ totalvoxel count and, therefore, in size and weight. In fact, subject 06 and 46 had lossy tissuemass of 9.18 and 9.60 kg respectively, comparing to 9.03 and 9.04 kg for subject 20 and 51respectively.
High MTO measures between subject 20 and 51 were also recorded in table 2 (i.e.TO51→20 = 75.28% and TO20→51 = 73.30%). Mutually high TO measures not onlysuggest high tissue conformity in the voxel scale, but also indicate that the two modelshave similar numbers of total voxel counts and, therefore, similar overall sizes and weightsas evidenced by the subjects’ weight calculations (9.03 and 9.04 kg for subject 20 and 51,respectively).
3.1.3. Patient-specific voxel models via registration. As DARTEL was employed to warpthe tissue volumes of the source to the target in each registration pair, the TO measures(equation (2)) were calculated and organized in table 2 (‘TOS→T ′’ columns, where T ′ = θR
S→Tdenotes estimated target models using registration; and R = 1, 2, . . . ,5 indicates the reductionfactor of the target image resolution). The data in table 2 was extracted into a box plot, as showin figure 4. In general, higher resolution target images (lower R) contributed to higher averageTO with more consistency. The median (red bar across the box) and deviation (approximated bythe height of the box) of the TO measures degraded gradually and steadily as lower resolutiontarget images were adopted in the registration. However, when the reduction factor R was ashigh as 5, the registration was still able to improve the TO agreement considerably. When thesubject pair 20–51 was studied carefully, the registration improved the TO measures of themfrom approximately 74% to 80% and 78% when the target image resolution was not reduced(R = 1) and was reduced five-fold (R = 5), respectively.
Improving SAR estimations in MRI using subject-specific models 8163
Figure 4. The box plot of TO measures for registration pairs before and after image registration.The raw data used in this plot can be found in table 2.
3.2. SAR calculations
3.2.1. SAR variations between patient models. Including the absorbing boundaries,approximately 13.6 million cells were used to resolve the calculation space of the coil-patientmodels. When different subjects were loaded, the birdcage coil experienced little observablechanges in resonating conditions. Small adjustments were made whenever necessary to re-tunethe coil to 298 MHz. The magnitude and phase of B+
1 of different subjects remained largelyunchanged, as illustrated in figure 5. However, the SAR levels and distributions changeddramatically. The coronal and sagittal slices of the maximum 1 g SAR for all the subjectsare illustrated in figure 6. In contrast with the rest of the subjects, whose maximum 1 gSAR occurred in the centre of the brain, subject 46 had the maximum 1 g SAR located atthe frontal lobe. It is also clearly seen from figure 6 that subject 06 had significantly highermaximum 1 g SAR of 0.2928 W kg−1 comparing with the rest of the subjects. However, subject20 and 51 had very similar overall SAR distributions, maximum 1 g SAR values and locations.The maximum 1 g SAR of subject 20 and 51 were 0.2659 and 0.2532 W kg−1 respectively,and were located 1 cm apart ([2.4, 3.4, −0.9] cm for subject 20 and [3.0, 4.1, −1.3] cm forsubject 51).
The results suggested that, if a random model were to be used for patient SAR prediction,it is possible that very large errors will result. The similar SAR values between subject 51 andsubject 20 indicated, however, that if the matching model for a patient was used, SAR valuedcan be predicted within a reasonable range. Therefore, it is important to have a metric, whichcan be used to evaluate the models’ similarity and to guide the selection of the matching modelfor a patient.
3.2.2. Patient-specific models for SAR prediction. In order to test the subject-specific modelsfor SAR prediction, the registration models were used in SAR calculations. As illustrated infigure 7, the SAR values of subject 51, subject 20 and the estimated model of subject 20 fromregistering subject 51 to subject 20 were displayed. In the case shown, the resolution of thetarget image was reduced by a factor of 3 (R = 3). This was equivalent to using 1/33 = 3.7%
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Figure 5. The magnitude and phase of B+1 of different patient models. The coronal (top two rows)
and sagittal (bottom two rows) slices that pass the centre of the coordinate system are shown.
of the total image data. As can be seen from figure 7, the constructed subject-specific model(middle column) was able to improve the SAR estimation drastically. It had SAR distributionnearly identical to that of the target (subject 20, rightmost column). Comparing with themaximum 1 g SAR of 0.2659 W kg−1 for subject 20, the registered model had maximum 1 gSAR of 0.2624 W kg−1. Remarkably, the location of the maximum 1 g SAR of the registeredmodel coincided exactly with that of subject 20 at [2.43, 3.38, −0.90] cm. The agreement inSAR levels and distributions were consistent with the high MTO measures between subject 20and 51 (figure 4), indicating that MTO is a viable candidate to evaluate the similarities amongsubject voxel distributions for the purpose of SAR calculations at 7T.
Other registered models were also tested in SAR calculations with varied improvementsin prediction accuracy, which signifies the importance of having a good matching source forthe registration. It is thus indicated that a patient-specific voxel model that facilitates accurateSAR prediction of the patient can be created by registering the high-resolution database image
Improving SAR estimations in MRI using subject-specific models 8165
Figure 6. SAR distributions of the four patient models. The coronal (top) and sagittal (bottom)slices of the maximum 1 g SAR for each subject are shown. Yellow texts in the graph indicatemaximum 1 g SAR of the corresponding model.
Figure 7. The SAR distributions of subject 51 (left), subject 20 (right) and the estimated model ofsubject 20 from registering subject 51 to subject 20 (middle). The resolution of the target imagewas reduced by a factor of 3 (R = 3). The coronal (top) and sagittal (bottom) slices of the maximum1 g SAR for each model are shown. Yellow texts in the graph indicate maximum 1 g SAR of thecorresponding model.
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to low-resolution pilot scans of the patient, provided that the database and the patient are ofsimilar sizes.
3.2.3. Patient positioning. The maximum 1 g SAR was 0.4301 W kg−1 at [5.0, 2.6, −5.2]cm and 0.3450 W kg−1 at [2.1, 3.8, 1.0] cm before and after shifting the voxel NORMANmodel along the y axis by 2.5 cm, respectively. Not only did the small geometrical shift changethe maximum 1 g SAR by approximately 20%, but also move its location dramatically by6.9 cm to the centre of the head. The SAR distributions of the x–z and y–z slices that pass themaximum 1 g SAR of the original and the shifted birdcage model are illustrated in figures 3(B)and (C), respectively. The geometrical shift reduced the 1 g SAR of the original hot spot byaround 30%, and increased that of the second hot spot by over 110%, making the latter theposition with the highest 1 g SAR value. This study exemplified the dramatic changes in SARlevels and distributions that can occur due to small changes in patient model positioning. Thisissue is however readily accounted for by using the subject-specific models constructed by theproposed method, in that, the patient positioning information is embedded in the model whenthe database is registered to the patient.
4. Discussion
4.1. The accuracy of the voxel models versus the accuracy of the SAR predictions
As shown, the SAR levels and distributions were highly sensitive to both the positioningand the anatomical details of the patient. A small geometrical shift of 2.5 cm of the patientwas able to shift the maximum hot spot by 6.9 cm in head and change its magnitude by20%. When the four patient models were compared, the largest difference in intensity was16% (subject 06 compared with subject 51), whereas the largest distance between hot spotswas 12.1 cm (between subject 20 and subject 46). Local SAR levels and distributions areexpected to have even more sensitivity to variation in patient positioning and anatomicaldetails when transmitting using surface coils, which typically have stronger interactions withthe patient. Therefore, the accuracy of the numerical models is very important for accurateSAR predictions.
4.2. MTO—a viable metric for measuring patient similarity. Using large safety margins toaccommodate the potentially large errors in SAR predication has become a major limitingfactor in realizing the full potential of high-field MRI. Therefore, SAR monitoring/predictionhas become one of the research focuses of high-field systems. To accurately estimate SARvalues for high-field MRI, a recent study (Homann et al 2011) postulated that various voxelmodels and their corresponding SAR calculations can be collected to form a database, so thatthe SAR results of the voxel model that best matches the patient can be extracted for patient RFpulse planning. However, the authors did not propose a means of constructing such a databaseor a method to select a matching model from the database for a patient.
The statistical analysis in the current study suggested that high MTO measures indicatehigh conformity of tissues and high similarity in size and weight, when a pair of models iscompared. Furthermore, an excellent correlation between high MTO and agreeing SAR valuesbetween two subjects (subject 20 and 51) has been demonstrated. It is therefore suggestedthat MTO can be used as a viable metric for measuring the similarity between a pair of voxelmodels for the purpose of high-field SAR prediction. Additionally, MTO can be employed tostudy what biological attributes, such as age, gender, racial and etc, are more indicative of thepatients’ tissue agreement. Such a study can therefore assist in the construction of a patient
Improving SAR estimations in MRI using subject-specific models 8167
database that covers the majority of the populations and in the selection of the best matchingmodel for a patient’s pulse planning.
4.3. Accurate coil models
Undoubtedly, the accuracy of the coil model also plays an important role in accurate SARpredictions. As the authors’ previous study indicated, the accuracy of the coil models can beconsiderably improved by a calibration method using phantom imaging (Jin et al 2010, 2012).This calibration method, namely the inverse field-based approach or IFA, may prove useful inaccurately modelling the RF coils.
Briefly, with an approximate geometry of the coil and phantom available, one could createa parametric numerical model that represents the RF coil and the phantom. Based on the modelcreated, the transmit and receive magnetic field (B+
1 and B−1 ) profiles were calculated. The
magnetic fields were then used to evaluate the signal intensity (SI) that would result froman experiment (Hoult 2000, Collins et al 2002). By adjusting the geometry- and sequence-related variables, an optimization process was employed to minimize the difference betweenthe calculated SI image and that acquired from the calibration scan, yielding an optimal set ofgeometrical parameters. The geometric information of the RF coil can therefore be extractedand used for subsequent SAR calculations. Please refer to Jin et al (2012) for more detailson the IFA method. The IFA method would suit the calibration of volume coil and rigid arraycoils that can be bolted to the scanner and do not change position from each scan. These coils,as opposed to flexible surface coils, are typically used for RF transmission.
4.4. Custom voxel models via image registration
In this study, we have drawn our focus on improving the accuracy of patient modelsemploying image registration techniques. The purpose of the registration is to determine aspatial transformation that warps the source images to the target images, so that the sametransformation can warp the tissue distribution of the source to the target. Comparing tocreating target voxel models from segmenting the high-resolution scans, the proposed methodis a more practical approach. In contrast with the segmentation approach, the proposed methodonly requires low-resolution scans of the patient, making this pilot scan more easily designedwithout violating SAR limits. Furthermore, the amount of data required from the pilot scan isfurther reduced, as only the body region with significance to RF illumination is imaged. Therest of the body model can be extracted from generic models to create correct overall loading,as was done in the current study.
A variety of in vivo methods has been proposed to acquire tissue dielectric properties.These methods include electrical impedance tomography (EIT) (Metherall et al 1996, Kerneret al 2002), in which electrical properties are inversely determined from surface potentialmeasurements. The resolution of EIT is usually limited by the small number of measurementsand ill-posed condition of the inverse problem. Particularly motivated by the need to predictSAR for high-field MRI application, electric properties tomography (EPT) (Katscher et al2009, 2012, Xiaotong et al 2010, Voigt et al 2011b) has seen rapid development. EPT relates thedielectric properties in the human body with the RF magnetic fields. It could potentially providehigh-resolution dielectric property maps at the operational Larmor frequency. However, suchmapping relies heavily on the reliable, high-resolution mapping of both the magnitude andthe phase of the B+
1 fields. The approximation that negatively circularly polarized componentof the transmit magnetic field is negligible requires strategic RF excitation and is not easilyachieved especially with heterogeneous subject. Moreover, the assumption that the longitudinal
component of the magnetic fields is small may hold on average yet can vary substantially inspatial domain. This suggests that the proposed method provides a practical alternative to thein vivo approaches.
The current study is focused on the development of voxel models of human head. It is arelatively challenging anatomy for SAR prediction and for image registration, thanks to thepresence of fine and complex structures. The study of the head bodes well for the adaptationof the method to other parts of the body.
4.5. Computational complexity
More accurate patient anatomy was obtained using the proposed method at the cost of highercomputational complexity. The nonlinear deformations took roughly 30 min to complete ona Dell Optiplex 980 computer (with Core i7 CPU at 2.8 GHz and 8 G RAM). We may,however, expect a reduction in solution time by exploring more efficient registration methodsand employing graphics processing units (GPU). A recent study has reported registering high-resolution 3D images using a single Nvidia GTX 8800 GPU under 1 min (Modat et al 2010).The high-resolution FDTD-based SAR calculations were typically computation-intensive andpotentially prohibitively time-consuming for clinical practice. Parallelization with GPU isthe direction currently being investigated. By means of employing multi-GPU and multi-resolution, the MRI-dedicated FDTD algorithms (Chi et al 2011, Wei et al 2005) can achieveup to three orders acceleration in solution time, which should make the proposed methodfeasible for clinical timeframes.
5. Conclusion
To regulate global or local RF energy deposition in high-field MRI applications, this proof-of-concept study presented a new patient modelling method that can be used for accurateSAR predictions. The method is based on image registration techniques that warp the tissuevolumes of an image library to the pre-scan data of a patient. The FDTD-based EM simulationdemonstrated that a patient’s maximum 1 g SAR value and its location can be predicted withremarkable accuracy. Integrated with the author’s previously proposed coil modelling method,the proposed SAR prediction method was able to accurately predict the safety margins for7T applications. Therefore, various standard/novel RF pulsing techniques can be facilitatedwhile achieving the full capacity of high-field MRI systems. Aiming for practical high-fieldapplications, future studies will focus on the development of a dedicated patient database andthe improvement of the efficiency and effectiveness of the method.
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