E. F. Meliado^{1,2,3}, A. Sbrizzi^{1,2}, C.A.T. van den Berg^{2,4}, B. R. Steensma^{1,2}, P.R. Luijten^{1}, and A. J. E. Raaijmakers^{1,2,5}

^{1}Department of Radiology, University Medical Center Utrecht, Utrecht, Netherlands, ^{2}Computational Imaging Group for MR diagnostics & therapy, Center for Image Sciences, University Medical Center Utrecht, Utrecht, Netherlands, ^{3}Tesla Dynamic Coils BV, Zaltbommel, Netherlands, ^{4}Department of Radiotherapy, Division of Imaging & Oncology, University Medical Center Utrecht, Utrecht, Netherlands, ^{5}Biomedical Image Analysis, Dept. Biomedical Engineering, Eindhoven University of Technology, Eindhoven, Netherlands

The introduction of a linear safety factor to address peak local SAR uncertainties (e.g. inter-subject variation and modeling inaccuracies) bears one considerable drawback: it often results in over-conservative scanning constraints. In this work, we present a more efficient and probabilistic approach to define a variable safety margin based on the conditional probability density function of the true peak local SAR value given the estimated peak local SAR value. Results show that the proposed approach leads to a reduction of peak local SAR overestimation up to 30%.

$$f_{T|E}(pSAR^T|pSAR^E)=\frac{f_{E,T}(pSAR^E,pSAR^T)}{f_E(pSAR^E)}$$ [1]

Now the probability $$$P_{underest}$$$ that pSAR

$$P_{underest}=P(pSAR^T>E_1|pSAR^E=E_1)=\int_{E_1}^{\infty} f_{T|E}(pSAR^T|pSAR^E=E_1)dpSAR^T$$ [2]

For each of the 23 models, driving the array with uniform input power (8×1W) and random phase settings, 250 pSAR

The pairs (pSAR

$$$Find$$$ $$$pSAR^{E,C}$$$ $$$such$$$ $$$that$$$

$$P(pSAR^T>pSAR^{E,C}|pSAR^E=E_1)=\int_{pSAR^{E,C}}^{\infty} f_{T|E}(pSAR^T|pSAR^E=E_1)dpSAR^T=\epsilon$$ [3]

This corrected pSAR

To assess the performance of the conditional safety margin, a larger test set (23×1000=23000 test samples) is generated and the mean overestimation of the conditional safety margin is evaluated and compared to the mean overestimation of the corrected pSAR values using the linear safety factor (LSF)

Figure 3.a shows the scatter plot pSAR

Figure 3 clearly shows that the suggested approach is reducing overestimation because the green line remains closer to the distribution of actually expected pSAR

Results show that the conditional safety margin allows to reduce the mean overestimation from 108% to 89% using the generic model (18% reduction), from 104% to 83% using the model library (20% reduction) and from 57% to 41% with the deep learning method (28% reduction). Note that these are averaged values. For individual cases with high pSAR

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