This paper proposes an estimation method for maximum local SAR in parallel transmission. In order to estimate maximum local SAR with fewer evaluation points, the evaluation points are selected by iterative SAR calculation under a restricted random initial input signal condition. It is shown
Figure 1 shows local SAR evaluation point number with maximum local SAR extracted by iterative SAR calculation with human model Duke (Sime4Life, ZMT, Zurich, Switzerland) while randomly changing the initial input condition at every eight feeding points of a whole-body coil. The maximum local SAR occurs repeatedly in particular points. In consideration of this result, we propose a maximum local SAR estimation method with the evaluation points selected by iterative SAR calculation under a restricted random input signal condition to estimate the maximum local SAR with fewer evaluation points. Under the restricted random condition, the input signal amplitude is set within 0.5 to 1.0, 0.7 to 1.0 or 0.9 to 1.0, and the initial input signal phase is set within θn - 30 to θn + 30 degrees, θn - 60 to θn + 60 degrees or θn - 90 to θn + 90 degrees, where θn is the fixed value at each eight input ports and θ1 = 0, θ2 = 45, … , θ8 = 315. The local SAR evaluation points are selected as follows.
Step1: Set the range of input signal amplitude and initial phase, the total number of iterative SAR calculation and the overestimation value.
Step2: At first SAR calculation, the evaluation point with maximum local SAR is selected as an evaluation point for estimating maximum local SAR.
Step3: In the second and subsequent SAR calculations, the maximum local SAR is compared with the estimation value which is the sum of the overestimation value and the maximum value among the local SAR of evaluation points selected on previous calculations. If the maximum local SAR is higher than estimation value, the evaluation point with the maximum local SAR is selected.
Step4: End when the trial number of SAR calculation reaches the total number.
In each SAR calculation in Step 2 and Step 3, the amplitude and initial phase are randomly set to a different value within the range set at Step 1. The overestimation value is 10 % of the maximum local SAR in the worst case, where the electric fields generated by the input signals to eight ports are combined with the same phase.
Figure 2 shows the maximum local SAR estimation results after 5000 trials using the amplitude range as a parameter. Dots on the diagonal reflect that the actual maximum local SAR and the estimated maximum local SAR are equal, while dots below the diagonal mean that the maximum local SAR is underestimated. Dots between the diagonal and the upper line indicates that the maximum local SAR is estimated within the tolerance. From these results, it is found that all estimation values of maximum local SAR are within a tolerance determined by the overestimation value. It also can be seen that the amplitude range when selecting the evaluation point may be narrower than that of the supposed input signal.
Figure 3 shows the maximum local SAR estimation results after 5000 trials using the initial phase range as a parameter. There are many underestimation results when the initial phase range in selecting the evaluation point is narrower than that of the supposed input signal. From these results, the remitted random condition in selecting the maximum local evaluation points should be a wider initial phase range than that of the supposed input signal.
Figure 4 shows maximum local SAR estimation results where the restricted random condition in selecting maximum local SAR evaluation points is a wider initial phase range than that of the supposed input signal. All estimated maximum local SAR is within a desired tolerance. The total number of selected evaluation points is 10 while the total number of evaluation points using conventional method under the same condition is 323.
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