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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
Concepts Magn Reson Part B Magn Reson Eng. Author manuscript; available in PMC 2012 May 24.
Published in final edited form as:
Concepts Magn Reson Part B Magn Reson Eng. 2007 April; 31B(2): 127–131.
Published online 2007 April 5. doi:  10.1002/cmr.b.20085
PMCID: PMC3359701

Calculation of SAR for Transmit Coil Arrays


Transmit coil arrays allowing independent control of individual coil drives facilitate adjustment of the B1 field distribution, but when the B1 field distribution is changed the electric field and SAR distributions are also altered. This makes safety evaluation of the transmit array a challenging problem because there are potentially an infinite number of possible field distributions in the sample. Local SAR levels can be estimated with numerical calculations, but it is not practical to perform separate full numerical calculations for every current distribution of interest. Here we evaluate superposition of separate electric field calculations—one for each coil—for predicting SAR in a full numerical calculation where all coils are driven simultaneously. It is important to perform such an evaluation because the effects of coil coupling may alter the result. It is shown that while there is good agreement between the superimposed and simultaneous drive results when using current sources in the simulations, the agreement is not as good when voltage sources are used. Finally, we compare maximum local SAR levels for B1 field distributions that are either unshimmed or shimmed over one of three regions of interest. When B1 field homogeneity is improved in a small region of interest without regard for SAR, the maximum local SAR can become very high.

Keywords: MRI, transmit array, RF shimming, SAR, simulations, electric field


Recent development of RF hardware with multiple variable voltage or current sources for MRI has allowed for unprecedented control of the RF magnetic (B1) field distribution (1-4). But though specified individual coil currents can produce specifically tailored RF magnetic field distributions, they also alter the electric field and SAR distributions (5). Safety evaluation of such arrays becomes a challenging task because an infinite number of current distributions are possible in the array, and thus an infinite number of field and SAR distributions are possible in a given sample.

Though it should be possible to estimate the average SAR in the region of the subject exposed to the RF fields in an array experimentally much as it is done for RF coils currently, evaluation of the maximum local SAR levels is not straightforward. Numerical calculations can be used to evaluate SAR distributions and maximum local SAR levels (6), but a full numerical calculation of each current distribution of interest is impractical. Here we evaluate the accuracy of evaluating the SAR distribution induced by the array by superimposing electric fields from each individual coil at 300 MHz. Because coupling between coils can result in a complicated relationship between the drive of a certain coil at its terminals and the field it ultimately produces, this evaluation is necessary. We evaluate the accuracy of using this method of superposition both when using current sources and when using voltage sources. Finally, we present the SAR distributions of a transmit array when driven with four different current distributions of interest.


A 3D digital human head model consisting of 23 different tissue types with a 5-mm isometric resolution was created with methods described previously (7). Two elliptical array coils containing 16 stripline TEM elements (8) were modeled and driven at 300 MHz. The coil geometries were identical to those modeled previously (9, 10). The array geometry is shown in Fig. 1. As described previously (9), in each element of the array two current or voltage sources were used to connect the conductive element to the shield element, one at each end of each element.

Figure 1
The geometry of the array modeled (left) and the magnitude of the circularly polarized component of the B1 field pertinent to excitation (B1+) field when driving a single coil alone (center) and when driving all coils simultaneously (right). Linear color ...

To examine the accuracy of superimposing separate field calculations to calculate the SAR distribution induced when driving coils simultaneously, the RF field created while driving each element in the 16-element array separately with unit current or voltage sources was calculated using the finite-difference time-domain (FDTD) method with commercially available software (xFDTD; REMCOM; State College, PA). Then the resulting complex magnetic and electric fields from these 16 separate field calculations were added together and compared with another case where all elements were driven simultaneously in a single FDTD simulation. Here the phases of the sources followed the azimuthal angle positions of the coil elements. The comparison was performed both for using voltage sources and for using current sources in all 17 simulations.

We examined the SAR distribution of four current distributions of interest for the 16-element array. The desired current distributions were found using an optimization routine that capitalized on the superposition of the different magnetic fields (9, 10). During optimization, the magnitude and phase of the separate coil currents were varied to produce a homogeneous distribution of the magnitude of the pertinent circularly polarized component of the B1 field ([mid ]B1+[mid ]) over three different regions: (1) the entire head portion of the model, excluding neck and shoulders (optimizing whole head), (2) the entire brain including white matter, gray matter, and CSF (optimizing whole brain), and (3) a single axial slice of the brain (optimizing brain slice). After each optimization of [mid ]B1+[mid ] homogeneity was performed, the resulting magnitudes and phases for all coils were used in a single FDTD calculation to determine the SAR with standard methods (11). For comparison, the [mid ]B1+[mid ] and SAR distributions of an array with elements driven with a current pattern similar to that expected for a volume coil (standard drive) were also calculated.


The relative difference between the field distribution resulting from superposition of the separate field calculations and the field from a single calculation including all sources is shown in Fig. 2 on a single axial slice. The superimposed field is significantly different from the field of the array when using voltage sources, but they are almost identical when using current sources. As shown in Table 1, the average difference is less than 1% when current sources are used.

Figure 2
Relative difference between superimposed magnetic fields (B1s+) and superimposed electric fields (Es) from 16 separate field calculations (with only one coil driven in each) and their counterparts (B1+ and E) from a single calculation when all 16 coils ...
Table 1
Relative Difference of Magnetic Field and Electric Field Between Superimposed Fields From 16 Coils and a 16-Coil Array Under Different Driving Sources

Figure 3 illustrates the normalized signal intensity distribution for a gradient echo image with a long TR (9, 10) and SAR distribution during the pulse for the standard drive, whole-head optimized drive, whole-brain optimized drive, and single axial slice-optimized drive. The SAR can be high in some regions when using some optimized drive configurations. Table 2 lists the relative standard deviation of the B1 field (standard deviation divided by the average) and average and maximum SAR values in the head model during the standard and optimized pulses. Because the average B1+ in the head portion of the model changes during optimization, the SAR values for field distributions like those in Table 2 and Fig. 3 but normalized as if to have the same average B1+ in the head are given in Table 3.

Figure 3
Signal intensity distribution and SAR levels (in each 5-mm-cubed voxel) on an axial plane through the center of the brain for four different field distributions of interest.
Table 2
Summary of SAR (W/kg) for a 16-Coil Array With Different Drives
Table 3
Summary of SAR (W/kg) Normalized for 2 μT average B1+ in Head Portion of Model


RF fields can be manipulated by adjusting the driving current amplitude and phase of each coil individually. However, if the only objective is improvement of RF magnetic field homogeneity within a portion of the sample, other quantities may reach undesirable values. It has been observed that when the RF magnetic field is shimmed over a certain region, the RF magnetic field outside that region can become inhomogeneous (9). SAR should be taken into account as well. When the RF magnetic field homogeneity is optimized over a region the size of the brain or smaller, the maximum local SAR levels can reach extremely high levels, as seen in Table 2. The regions of highest SAR usually occur in a region with a highly inhomogeneous RF magnetic field. Where the RF magnetic field is homogeneous, the electric field tends to vary more gradually. Thus, when the RF magnetic field is shimmed over the entire head, rather than the brain or a single slice, the maximum local SAR levels tend to be lower (Table 2), though the field homogeneity is not as good (see Fig. 3, Table 2).

The calculated SAR extremes indicate that it would be valuable to consider the SAR or electric field when the driving condition of an array coil is optimized. Using the principle of superposition, both electric fields and magnetic fields can be calculated during a fast optimization routine, but this approach may not accurately account for coil coupling in general. In experiment, coils can be essentially decoupled for transmission purposes with a variety of methods, including the use of current sources (12). In simulations, when the electric fields driven by voltage sources are linearly summed, the mutual impedances between elements will lead to significant errors (see Fig. 1, Table 1). However, using current sources results in much lower error in use of the principal of superposition.

Though at least one initial attempt to consider SAR while optimizing magnetic field homogeneity with numerical calculations looks promising (13), the general application of such an approach is yet uncertain as local SAR levels and locations are patient specific (14, 15) and it is not practical to create patient-specific numerical models of every patient before MRI imaging. The results in this article demonstrate that the superposition of electric and magnetic fields is valid when using current source driving methods, a fundamental step toward future developments of considering SAR for transmit arrays.


Funding for this work was provided by the National Institutes of Health through R01 EB 000454.


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