Specific Absorption Rates and Induced Current Densities for an Anatomy-Based Model of the Human for Exposure to Time-Varying Magnetic Fields of MRI

Transcription

1 Specific Absorption Rates and Induced Current Densities for an Anatomy-Based Model of the Human for Exposure to Time-Varying Magnetic Fields of MRI Om P. Gandhi* and Xi Bin Chen Magnetic Resonance in Medicine 41: (1999) A 6-mm resolution, 30-tissue anatomy-based model of the human body is used to calculate specific absorption rate (SAR) and the induced current density distributions for radiofrequency and switched gradient magnetic fields used for MRI, respectively. For SAR distributions, the finite-difference timedomain (FDTD) method is used including modeling of 16- conductor birdcage coils and outer shields of dimensions that are typical of body and head coils and a new high-frequency head coil proposed for the band. SARs at 64, 128, and 170 have been found to increase with frequency (f ) as f k where k is on the order of The tables of the calculated maximum 1 kg and 100 g SAR may be used to calculate the maximum RF currents and/or magnetic fields that may be used in order not to exceed the safety guidelines. Because of the low frequencies associated with switched gradient magnetic fields, a quasi-static impedance method is used for calculation of induced current densities that are compared with the safety guidelines. Magn Reson Med 41: , Wiley- Liss, Inc. Key words: specific absorption rates; induced current densities; anatomic model; FDTD method Magnetic resonance imaging (MRI) is becoming an increasingly important tool for medical diagnostic applications. Newer techniques are leading to the use of higher static magnetic fields, more rapidly switched gradient fields, and higher radio frequency (RF) magnetic fields. Although use of the increasingly stronger electromagnetic fields is causing concern about patient safety (1), in the past, only simplified homogeneous spherical, cylindrical, and disc models have been used to obtain rates of energy absorption (specific absorption rates or SARs) due to RF magnetic fields (2 4). These models are, naturally, not capable of providing information on SAR distributions or the peak values that may occur for the critical regions of the body. In order to alleviate this obvious weakness of using simplistic models, the finite element method has recently been used to obtain SAR distributions in a 3256 element anatomically based representation of the human head in the saddleshaped head coil, typical of MRI (5). The biconjugate gradient (BCG) algorithm in combination with fast Fourier transform (FFT) previously used for the analysis of the absorption of electromagnetic power by the human body (6) has also been used to calculate coupling to the MRI head coil for a model of the human body truncated at the Department of Electrical Engineering, University of Utah, Salt Lake City, Utah. Grant sponsor: National Institute of Environmental Health Sciences; Grant number: ES *Correspondence to: Professor Om P. Gandhi, Department of Electrical Engineering, University of Utah, 50 S Central Campus Dr., Room 3280, Salt Lake City, UT gandhi@ee.utah.edu Received 17 April 1998; revised 30 October 1998; accepted 2 November Wiley-Liss, Inc. 816 neck (7). As acknowledged by Jin et al. (7), the high SAR in the region close to the neck may, however, be due to the artificially truncated model used for these calculations. We have developed anatomically based models of the human body with resolutions of 2.62, 1.31, and cm and have recently developed a new model based on the MRI scans of a male human volunteer with voxel dimensions of mm along horizontal and vertical axes, respectively (8). We have also recently modified the finite-difference time-domain (FDTD) method and have used it to calculate SAR distributions of bird cage coils of dimensions typical of body and head coils used for the present day MRIs operating at the radio frequency of 64 (9). Since the FDTD method (10,11) is based on the complete set of Maxwell s equations, it is usable at any RF frequency that is likely to be of interest. In addition to SAR distributions at 64, in this paper, we also give the calculated SAR distributions at the planned higher RF frequencies of 128 and 170 and for the newly proposed head coils operating at (12,13). For calculations of currents induced due to switched gradient fields, we have used the low-frequency quasi-static impedance method which has previously been used for a number of applications from power frequency magnetic field sources such as hair dryers, hair clippers to radio frequency sources such as induction heaters, etc. (8,14 16). THE FINITE-DIFFERENCE TIME-DOMAIN METHOD The finite-difference time-domain method has been described in several publications and a couple of recent textbooks (10,11). This method has also been used successfully to obtain specific absorption rates for anatomically based models of the human body for whole-body or partial-body exposures to spatially uniform or nonuniform (far-field or near-field) electromagnetic fields from ELF to microwave frequencies (8,14). In this method, the timedependent Maxwell s curl equations E H t, E H E are implemented for a lattice of subvolumes or cells that may be cubical or parallelepiped with different dimensions x, y, z,inx-, y-, or z-directions, respectively. The details of the method are given in several of the above referenced publications and will, therefore, not be repeated here. In the FDTD method, it is necessary to represent not only the scatterer/absorber such as the human body or a part thereof, but also any near-field source(s) such as 16-rung t [1]

2 SAR and Induced Currents for an Anatomic Model 817 shielded birdcage coils that are used in the MR imagers of today. The source-body interaction volume is subdivided into the Yee cells for which the volume-averaged electrical properties ( r, ) are prescribed for each of the cells of volume x y z. The interaction space consisting of several hundred thousand to several million cells is truncated by means of absorbing boundaries. For our calculations, we have assumed retarded-time boundary conditions (17) at the absorbing boundaries that were assumed separated by five to 10 cells in each direction from the modeled volume. Sixteen rungs of the birdcage coil were modeled by voxels representing the respective conductors for which the current sources were prescribed by means of magnetic fields H x and H y around the boundaries of the cell such that consistent with Ampere s law For the FDTD cells this corresponds to I H dl [2] I (H x x H y y ) 2H x x or 2H y x [3] since x y. In order to obtain circularly polarized RF magnetic fields with the birdcage coils, progressive relative phase shifts of 22.5 were used between the adjacent rungs (18). We also used these relative phase shifts in prescribing the H x and H y for the cells representing each of the rungs. We, furthermore, assumed that the rungs were made of a highly conducting material such as copper and prescribed a conductivity S/m for each of the voxels representing the rungs. Also, assumed for the calculations was that the current passing through each of the rungs is constant and in phase from one end to the other which is justified since the length of the rung is small compared to wavelength at the lower frequencies of 64, 128, and even 170. For the higher-frequency head coils at , a sinusoidally varying RF current distribution over the length of the rung was, however, taken as suggested in Vaughan et al. (12,13). The initial fields thus defined and assumed to be sinusoidally varying in time were tracked in the time-domain for all voxels of the interaction space. The problem was considered completed when a sinusoidal steady-state behavior for E and H was observed for the interaction space. This generally involved four to five RF cycles at the various frequencies of interest. THE QUASI-STATIC IMPEDANCE METHOD Because of fairly low frequencies up to a few kilohertz involved with switched gradient fields, we have used the quasi-static impedance method for calculations of induced current densities. For low-frequency dosimetry problems, the impedance method has been found to be highly efficient as a numerical procedure for calculations of internal current densities and induced electric fields for exposure to time-varying magnetic fields (8,15,16). In this method, the biological body or the exposed part thereof is represented by a three-dimensional (3-D) network of impedances whose individual values are obtained from the complex conductivities j for the various locations of the body. Since : for low frequencies of a few kilohertz characteristic of switched gradient fields, the network at these frequencies may be approximated by a 3-D grid of resistances whose values are given by R m i,j,k m n p m i,j,k where i, j, k indicate the cell indices; m is the direction which can be x, y, or z for which the resistance is calculated; m i,j,k is the electrical conductivity for the cell i, j, k in the mth direction, and n, p are the widths of the cell in directions at right angles to the mth direction. For exposure to time- and space-varying magnetic fields, voltages or electromotive forces (EMFs) are induced for the various loops of the 3-D resistance network whose values are given by the following expression [4] V m i,j,k d dt Bi,j,k ds 1 d dt B m i,j,k 2 n p [5] The initial value of the loop currents were set to zero assuming that the external electric field is negligible. In addition to the current densities, the x-, y-, and z-components of electric fields inside each cell can also be evaluated as E i,j,k x,y,z J i,j,k x,y,z [6] i,j,k In the impedance method formulation, the conductivity for a given cell can be directionally dependent. This feature is important for calculations at ELF where highly anisotropic conductivities have been reported, particularly for the skeletal muscle (19,20). For the calculations reported in this paper, the dielectric properties ( r, ) taken for the various RF frequencies are given in Table 1. Also, given in the same table are the frequency-independent conductivities taken for the various tissues of the body that have been used for calculations of induced currents due to switched-gradient magnetic fields. These properties have been compiled from a number of references (19 24). MILLIMETER-RESOLUTION MODEL BASED ON MRI SCANS OF THE HUMAN BODY A millimeter-resolution model of the human body has been developed from the magnetic resonance imaging (MRI) scans of a male volunteer of height cm and weight 64 kg (8). The MRI scans were taken with a resolution of 3 mm along the height of the body and mm for the orthogonal axes in the cross-sectional planes. Even though the height of the volunteer was quite appropriate for an average adult male, the weight was somewhat lower than an average of 71 kg, which is generally assumed for an average male. This problem was ameliorated by assuming that the pixel dimensions for the cross sections are larger than mm by the ratio of (71/64) 1/ By taking the larger pixel dimensions mm for the cross-sectional axes, the volume of the model was increased by (1.053) , i.e., by about

3 818 Gandhi and Chen Table 1 Tissue Properties Assumed for the mm Resolution Anatomically Based Model (19 24) Tissue Mass density 10 3 kg/m 3 Low frequencies Muscle (horz.) (vert.) Fat Bone Cartilage Skin Nerve Intestine Spleen; pancreas Heart Blood Parotid gland Liver Kidney Lung Bladder CSF Eye humor Eye sclera Eye lens Stomach Erectile tissue Prostate gland; spermatic cord; testicle Compact bone Ligament Brain; pineal gland; pituitary gland r S/m r S/m r S/m r S/m 10.9% which resulted in an increase of its weight to approximately 71 kg. The MRI sections were converted into images involving 30 tissue types (listed in Table 1) whose electrical properties were prescribed at the exposure frequencies. For the highest frequency of 400 used for the present calculations, it is not necessary to use the abovedescribed mm resolution model. We, therefore, combined cells along x-, y-, and z-axes, respectively, to obtain a new model with somewhat larger size voxels each of dimension mm. This new model with volume-averaged electrical properties ( r, ) at radio frequencies and directionally averaged conductivities at low frequencies was used for all of the calculations given in this paper. TESTS RUNS For RF Magnetic Fields For calculations of the SAR distributions with the mm anatomically based model of the human body described in the previous section, we have used the dimensions of the birdcage coils that are given in Table 2. Accuracy of the FDTD code was validated by calculating the magnetic field distributions for coils A, B, and C (defined in Table 2) in air as well as for coaxially placed dielectric cylinders of diameter 40 cm for coil A and 20 cm for coils B and C, respectively, for which properties corresponding to two-thirds muscle were taken. The salient features of the calculated results are summarized in Table 3. Because of the limitation of space, only a few of the calculated results are shown as Figures 1 and 2. Shown in Figure 1 are the variations of the axial ratio H y /H x or H x /H y and the relative phase difference between H y and H x that are calculated for the central transverse plane (xy plane) for the unloaded body coil A at 64. As expected, the RF magnetic fields created for this central plane are nearly circularly polarized in the plane at right angle to the axis of the coil. A perfect circularly polarized magnetic field would have had an axial ratio of 1.0 and a relative phase difference of 90 between H y and H x. The calculated values are certainly very close to this requirement for circularly polarized fields. Shown in Figure 2 are the calculated variations of the total magnetic field H t (H x 2 H y 2 H z 2 ) 1/2 with radius r for z 0, i.e. the central plane, and for the H t for points along the central z-axis (r 0) for the high frequency coil C. Also shown for comparison are the measured values given by Zhang et al. (13). Similar to the design of the high-frequency coils (12,13), we have taken 16 rungs for which the sinusoidally varying currents given by Eq. 7 have been assumed for the calculations. I(z) I o cos k (z l /2) [7] where l is the length of the rung for the bird cage coil C and k 2/ with being the wavelength at the RF frequency of excitation. It should be noted that as suggested by Vaughan et al. (12), this current distribution is similar to that for a half wavelength dipole. Also, like the cases of

4 SAR and Induced Currents for an Anatomic Model 819 Table 2 Dimensions of the 16-Rung Birdcage Coils Considered for the SAR Calculations Body coil A (18,25) cm Head coil B (18,25) cm High frequency head coil C (10,11) cm Diameter of the cage with rungs Diameter of the shield Length of the rungs Length of the shield Frequencies () 64, 128, , 128, , 350, 400 lower frequency birdcage coils, a 22.5 progressive phase shift is assumed for the various rungs in order to obtain circularly polarized RF magnetic fields. As seen in Figure 2, agreement between the calculated and experimentally measured variations of RF magnetic fields along radial and axial directions is quite good. For Switched Gradient Magnetic Fields As aforementioned, the quasi-static impedance method (8,15,16) has been used for calculations of induced internal current densities for the three-dimensional spatially varying switched magnetic fields typical of MRI machines. This method, detailed above, has been tested thoroughly and previously used for a number of bioelectromagnetic problems, some of which have been detailed (8,15,16). As suggested by Dr. D.J. Schaefer of GE Medical Systems, for the present calculations, we have considered a Maxwell pair of single-turn loops with radii m placed at axial locations z m through which equal and opposite currents I A flow with trapezoidal timedomain variation shown as the insert of Figure 3. Note that as desired for the Maxwell pair, the axial distance is 3 r o where r o is the radius for each of the loops (25). From the Biot-Savart law of electromagnetics (26), we can write the FIG. 1. The axial ratio H y /H x or H x /H y and the relative phase difference between H x and H y for the unloaded body coil A (see Table 2) at 64. expressions for the vector magnetic fields (B x, B y, and B z ) that are set up for the space between the Maxwell pair as well as the other regions occupied by the patient. Shown in Figure 3 is the variation of the total magnetic field for various axial locations z for all of the period corresponding to the top of the I(t) curve shown as the insert of Figure 3. The magnetic field is purely z-directed for all of the axial locations, and, as expected, shows a reversal in direction because of the oppositely directed currents in the two single-turn loops. These magnetic fields calculated for maximum equal and opposite currents of A should, of course, be multiplied by the time-domain variation given for I(t) to obtain the switched gradient magnetic fields for the various axial locations inside and outside the Maxwell pair of loops. Three dimensional variations of vector magnetic fields (B x, B y, B z ) have similarly been obtained for all locations occupied by the patient from the Biot-Savart law and used for calculations of induced current densities. Table 3 Salient Features of the FDTD-Calculated Data for 16-Rung Birdcage Coils A, B, C of Table 2 Body coil A Head coil B Head coil C Frequency () Empty coils H 0 with no shield (A/m) center H 0 from Biot-Savart Law (A/m) (26) center H 0 with outer shield (A/m) center Coils filled with 2/3 muscle-equivalent cylinder Diameter of cylinder (cm) Length of cylinder (cm) Max. layer-averaged SAR (W/kg) Assumed for the calculations is a current of 1.0 A (RMS) for each of the rungs which are fed with a progressive phase shift of 22.5 between adjacent rungs.

5 820 Gandhi and Chen FIG. 2. The FDTD-calculated variations of total magnetic field H t vs. radius r or axial position z for unloaded high-frequency coil C at 350. Current I 1 A and frequency 300. Also shown for comparison are the data measured by Zhang et al. (13). SAR DISTRIBUTIONS FOR THE ANATOMICALLY BASED MODEL FOR MAGNETIC FIELDS As described above, we have developed an anatomically based model from the MRI scans of a male human volunteer for which we have identified each of the voxels of dimensions mm with one of 30 tissues given in Table 1. In order to reduce computer memory requirements, we developed another model with somewhat coarser cells by combining voxels of the higher resolution model such that the new model has voxel dimensions of mm (nominal 6.0 mm resolution) along x-, y-, and z-directions, respectively. This requires that we store the new volume-averaged electrical properties r, and mass densities for each of the larger voxels of this model. The SARs thus obtained for the individual larger voxels were used to calculate the layeraveraged SARs for each of the coils of interest (see Figs. 4 6). Since SARs in various tissues were also of interest, FIG.4. ThelayeraveragedSARdistributionfora6mmresolution anatomically based model of the human body exposed to the birdcage body coil A. Each rung is assumed to be fed by a 1.0 A (RMS) current. The location of the coil vis à vis the body is indicated by points M N along the ordinate. we identified each of the larger voxels with the majority tissue in that subvolume. This naturally altered the weights of some of the tissues and organs in the nominal 6.0 mm resolution model. However, the weights of important tissues/organs in the nominal 6.0 mm resolution model were found to be within 5% of the corresponding weights in the original mm MRI-based model. This nominal 6.0 mm resolution anatomically based model was used to obtain SAR distributions for the body coil A of dimensions given in Table 2 for RF frequencies of 64, 128, and 170. For these calculations, the body coil was assumed to be centered at a plane that is cm above the bottom of the feet of the model, and the man model was truncated at the two planes that are 70.8 and cm above the bottom of the feet, respectively. The salient features of the calculated results are summarized in FIG. 3. Axial variation of magnetic fields calculated for a Maxwell pair of oppositely directed current-carrying single-turn loops coaxially placed at z m. I A. The trapezoidal variation of current as a function of time is shown as the insert of the figure. FIG.5. ThelayeraveragedSARdistributionfora6mmresolution anatomically based model of the human body exposed to the head coil B. Each rung is assumed to be fed by a 1.0 A (RMS) current. The location of the coil vis à vis the body is indicated by points M N along the ordinate.

6 SAR and Induced Currents for an Anatomic Model 821 Table 4, and the section-averaged SAR values for the various cross sections of the body are plotted in Figure 4. As expected, the higher the frequency the higher the SARs. An f 1.1 type dependence, rather an than f k (k 2) type dependence predictable from quasi-static considerations (27,28), is observed for the calculated whole-body-averaged SARs. This result is interesting since considerably higher SARs increasingly approximately as f 2 with frequency were previously projected both by us (28) and by others (7,27). Most of these projections were, however, made with quasi-static methods that are valid strictly at lower frequencies, whereas full-wave analysis using the FDTD method has been used for the present calculations, and this approach is certainly valid for all of the frequencies presently used or projected for MRI. Given in Table 5 are the salient features of the results calculated for the head coil B of dimensions given in Table 2 for RF frequencies of 64, 128, and 170. The head coil of axial length 39.3 cm was assumed to be placed such that its central plane was coincident with the top of the head (assumed to be cm above the bottom of the feet). Shown in Figure 5 are the layer-averaged SAR distributions for this head coil at frequencies of 64, 128, and 170, respectively. As for the case of the body coil A (see Table 4), here, too, the total power absorbed by the head and the head-averaged SAR varies approximately as f 1.2 rather than as f k (k 2) which would have been predicted from quasi-static considerations (27,28). Given in Table 6 are the results calculated for the high-frequency head coil C proposed by Vaughan et al. (12) of dimensions given in the last column of Table 2. For this coil, we have calculated SARs at the planned frequencies of 300, 350, and 400. Shown in Figure 6 are the layer-averaged SAR distributions for the high-frequency head coil C at frequencies of 300, 350, and 400, respectively. The salient features of the organ-averaged SARs obtained for this frequency head coil C are summarized in Table 6. It is, however, interesting to note that contrary to expectations, the SARs here do not increase with frequency. This is likely due to the cosinusoidal current distribution of Eq. 7 (12,13) that was assumed at these frequencies. Since the assumed current was normalized to a maximum value of 1.0 A at the center of the rungs, a reducing spatially averaged I 2 varying as 1:0.957:0.909 was thus assumed for frequencies of 300, 350, and 400, respectively. This may be a part of the reason why somewhat lower SARs have been calculated at 350 and 400 as compared to the values at 300. Nevertheless, as expected, the SARs in Table 6 are considerably higher than those in Table 5. This was to be expected since the frequencies here are considerably higher than the highest frequency of 170 used for coil B (Table 5). FIG. 6. The layer averaged SAR distribution for a 6 mm resolution anatomically based model of the human body exposed to the head coil C. Each rung is assumed to be fed by a 1.0 A (RMS) current. The location of the coil vis à vis the body is indicated by points M N along the ordinate. CURRENTS INDUCED IN THE HUMAN BODY MODEL FOR SWITCHED GRADIENT B-FIELDS This 6 mm resolution anatomy-based model of the human body was also used to calculate the distribution of induced current densities for switched-gradient magnetic fields of the axial variation shown in Figure 3. Such fields are generated by a Maxwell pair of single-turn loops with oppositely directed currents varying in the time-domain as shown in the insert of Figure 3. For this case, as seen in Figure 3, db/dt 22 T/sec occurs for axial locations z m. The induced current densities were calculated using the quasi-static impedance method de- Table 4 Salient Features of the Calculated Organ-Averaged SARs for the 6 mm Resolution Anatomically Based Model of the Human Body Exposed to the Body Coil A Tissue Organ-averaged SAR (W/kg) Intestine Spleen Pancreas Heart Blood Parotid gland Liver Kidney Lungs Bladder Cerebrospinal fluid (CSF) Aqueous humour Stomach Prostate gland Pineal gland Brain Calculated SARs (W/kg) Whole body averaged SAR Maximum SAR for 1 kg a tissue 0.37 (1.0 kg) 0.83 (0.98 kg) 2.17 (0.98 kg) Maximum SAR for 100 g a tissue 1.52 (101 g) 2.13 (90 g) 4.37 (102 g) a Actual weights given in parentheses. Each of the rungs is assumed to be fed with a current of 1.0 A (RMS) with progressive phase shifts of 22.5 to obtain circular polarization. A duty cycle of 1/25 is assumed for the calculations.

7 822 Gandhi and Chen Table 5 Salient Features of the Calculated Organ-Averaged SARs for the Region of the Truncated Body for the Head Coil B at Frequencies of 64, 128, and 170 Tissue Organ-averaged SAR (W/kg) Heart Blood Parotid gland Liver Lungs Cerebrospinal fluid (CSF) Aqueous humour Stomach Pineal gland Brain Calculated SARs (W/kg) Whole body averaged SAR Maximum SAR for 1 kg a tissue 3.47 (1.0 kg) 4.72 (0.96 kg) 6.78 (1.03 kg) Maximum SAR for 100 g a tissue 7.21 (100 g) 7.92 (96 g) 9.90 (100 g) a Actual weights given in parentheses. Each of the rungs is assumed to be fed with a current of 1.0 A (RMS) with progressive phase shifts of A duty cycle of 1/25 is assumed for the calculations. scribed above. The properties of the various tissues were assumed to be frequency-independent for the low kilohertz frequencies that are involved for switched-gradient magnetic fields. For the assumed time-domain variation of currents and the corresponding db/dt of 22 T/sec, the induced currents for the man model are maximum for time Table 6 Salient Features of the Calculated Organ-Averaged SARs for the Region of the Truncated Body for the High-Frequency Head Coil C at Frequencies of 300, 350, and 400 Tissue Organ-averaged SAR (W/kg) Blood Parotid gland Lungs Cerebrospinal fluid (CSF) Aqueous humour Stomach Pineal gland Brain Calculated SARs (W/kg) Whole body averaged SAR Maximum SAR for 1 kg a tissue 2.67 (1.11 kg) 2.57 (1.11 kg) 2.20 (1.13 kg) Maximum SAR for 100 g a tissue 4.17 (116 g) 3.88 (112 g) 3.29 (115 g) a Actual weights given in parentheses. Each of the rungs is assumed to be fed with a current of 1.0 A (RMS) with progressive phase shifts of A duty cycle of 1/25 is assumed for calculation. durations 0 t 100 sec and 400 t 500 sec, for the latter the induced currents being maximum but oppositely directed since db/dt 22 T/sec. For anisotropic conductivities assumed for skeletal muscle and isotropic conductivities for all other tissues (see Table 1), the calculated maximum induced current densities for each of the layers of the model are plotted in Figure 7. For these calculations, the Maxwell pair was assumed centered at a layer cm from the bottom of the feet. The physical locations M and N corresponding to the two single-turn loops used for the Maxwell pair are shown along the ordinate in Figure 7. As expected, some of the highest current densities were calculated for layers close to the axial locations M and N for these loops. Maximum induced current densities as high as 386 ma/m 2 were calculated for some of the layers under the top loop of the Maxwell pair. COMPARISON WITH SAFETY GUIDELINES It is informative to compare the calculated SARs for RF magnetic fields and the induced peak current densities with the safety guidelines proposed by U.S. Food and Drug Administration (29) and National Radiological Protection Board (NRPB, UK) (30). The NRPB safety guidelines for peak SARs in any 1 kg of tissue and for maximum local induced current densities are summarized in Table 7. By comparing the numbers obtained for maximum 1 kg SARs in Tables 4 6 with the SAR guidelines in Table 7, one can estimate the duty cycles (assumed to be 1 25 for Tables 4 6) or the RF currents (assumed to be 1 A rms for each of the rungs) that must not be exceeded to be within the SAR safety guidelines. Similarly, we can compare the peak-induced current density J max of 400 ma/m 2 obtained for an axial db/dt 22 T/sec (see Fig. 7) with the maximum current densities that should not be exceeded according to the NRPB safety guidelines (Table 7). Note that for the switched-gradient fields assumed for the present calculations, 100 sec and J 480 ma/m 2 from Table 7. The calculated J max of 386 ma/m 2 is less than this prescribed upper limit for the FIG. 7. Peak-induced current densities for the various layers of a 6 mm resolution anatomically based model of the human body. db/ dt 0 center 22 T/sec.

8 SAR and Induced Currents for an Anatomic Model 823 Table 7 The NRPB Safety Guidelines for Maximum SARs for RF Magnetic Fields and Induced Current Densities for Switched- Gradient Magnetic Fields Duration of exposure (min) induced current density implying that somewhat higher db/dt on the order of 27.4 T/sec could indeed be used for 100 sec switched gradient fields. This compares favorably with db/dt 2400/(sec) for sec suggested in the FDA safety guidelines (29). REFERENCES Peak SARs in any 1 kg a of tissue Head Trunk Limbs 30 (W/kg) (W min/kg) (W/kg) a Averaged over any 6-min period. Peak induced current densities for switched-gradient magnetic fields: J 400 ma/m 2 for 120 µsec; J ma sec/m 2 for 120 µsec. 1. Magin RL, Liburdy RP, Persson B, editors. Biological effects and safety aspects of nuclear magnetic resonance imaging and spectroscopy. Ann NY Acad Sci 1992; Bottomley PA, Redington RW, Edelstein WA, Schenck JF. Estimating radiofrequency power Deposition in body NMR imaging. Magn Reson Med 1985;2: Buchli R, Saner M, Meier D, Boskamp EB, Boesiger P. Increased RF power absorption in MR imaging due to RF coupling between body coil and surface coil. Magn Reson Med 1989;9: Keltner JR, Carlson JW, Roos MS, Wang STS, Wang TL, Budinger TF. Electromagnetic fields of surface coil in-vivo NMR at high frequencies. Magn Reson Med 1991;22: Simunic D, Wach P, Renhart W, Stollberger R. Spatial distribution of high-frequency electromagnetic energy in human head during MRI: numerical results and measurements. IEEE Trans Biomed Eng 1996;43: Borup DT, Gandhi OP. Fast Fourier transform method for calculation of SAR distribution in finely discretized inhomogeneous models of biological bodies. IEEE Trans Microwave Theory Tech 1984;32: Jin JM, Chen J, Chen WC, Gan H, Magin RL, Dimbylow PJ. Computation of electromagnetic fields for high-frequency magnetic resonance imaging applications. Physics Med Biol 1996;41: Gandhi OP. Some numerical methods for dosimetry: extremely low frequencies to microwave frequencies. Radio Science 1995;30: Gandhi OP, Chen XB, Yuan XJ, Chen JY. Dosimetry for time-varying magnetic fields in MRI imaging. Sixteenth Annual Meeting of the Bioelectromagnetics Society, Copenhagen, Denmark, June 12 17, Kunz KS, Luebbers RJ. The finite-difference time-domain method in electromagnetics. Boca Raton, FL: CRC Press; Taflove A. Computational electrodynamics: the finite-difference timedomain method. Dedham, MA: Artech House Vaughan JT, Hetherington HP, Otu JO, Pan JW, Pohost GM. High frequency volume coils for clinical NMR imaging and spectroscopy. Magn Reson Med 1994;32: Zhang N, Roos MS, Wang STS, Vaughan JT. An experimental study of a head coil for proton imaging and spectroscopy at 8 10 T. Second Meeting of the Society of Magnetic Resonance, San Francisco, CA, August 6 12, Lin JC, Gandhi OP. Computational methods for predicting field intensity. In: Polk C, Postow E, editors. Handbook of biological effects of electromagnetic fields, 2nd edition. Boca Raton, FL: CRC Press; 1996; Gandhi OP, DeFord JF. Calculation of EM power deposition for operator exposure to RF induction heaters. IEEE Trans Electromagnetic Compatibility 1988;30: Orcutt N, Gandhi OP. A 3-D impedance method to calculate power deposition in biological bodies subjected to time-varying magnetic fields. IEEE Trans Biomed Eng 1988;35: Berntsen S, Bajers F, Hornsleth S. Retarded time absorbing boundary conditions. IEEE Trans Antennas and Propagation 1994;42: Hayes CE, Edelstein WA, Schenck JF, Mueller OM, Eash M. An efficient, highly homogeneous radiofrequency coil for whole body NMR imaging at 1.5 Tesla. J Magn Reson 1985;63: Epstein BR, Foster KR. Anisotropy in dielectric properties of skeletal muscle. Med Biol Eng Comput 1983;21: Zheng E, Shao S, Webster JG. Impedance of skeletal muscle from 1 Hz to 1. IEEE Trans Biomed Eng 1984;31: Geddes LA, Baker LE. The specific resistance of biological material a compendium of data for the biomedical engineer and physiologist. Med Biol Eng 1967;5: Foster KR, Schwan HP. Dielectric properties of tissues. In: Polk C, Postow E, editors. Handbook of biological effects of electromagnetic fields, second edition. Boca Raton, FL: CRC Press; 1996; Gabriel C. Compilation of the dielectric properties of body tissues at RF and microwave frequencies. Report AL/OE-TR , Armstrong Laboratory (AFMC), Radiofrequency Radiation Division, Brooks AFB, TX, 78235, June Durney CH et al. Radio frequency radiation dosimetry handbook, fourth edition. USAF SAM-TR-85-73, Brooks AFB, TX, 78235, October Thomas SR. Magnets and gradient coils: types and characteristics. In: Bronskill MJ, Sprawls P, editors. The physics of MRI (1992 AAPM summer school proceedings). Woodbury, NY: American Institute of Physics; Paul CR, Nasar SA. Introduction to electromagnetic field, second edition, New York: McGraw-Hill; Roeschmann P. Radiofrequency penetration and absorption in the human body: limitations to high-field whole-body nuclear magnetic resonance imaging. Med Physics 1987;14: Gandhi OP, Chen JY. Absorption and distribution patterns of RF fields. In: Biological effects and safety aspects of nuclear magnetic resonance imaging and spectroscopy. Ann NY Acad Sci 1992;649: Athey TW. Current FDA guidance for MR patient exposure and considerations for the future. Ann NY Acad Sci 1992;649: National Radiological Protection Board, U.K. Board statement on clinical magnetic resonance diagnostic procedures. 1991;2.