3D-specific absorption rate estimation from high-intensity focused ultrasound sonications using the Green's function heat kernel

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PurposeTo evaluate a numerical inverse Green's function method for deriving specific absorption rates (SARs) from high-intensity focused ultrasound (HIFU) sonications using tissue parameters (thermal conductivity, specific heat capacity, and mass density) and three-dimensional (3D) magnetic resonance imaging (MRI) temperature measurements.MethodsSAR estimates were evaluated using simulations and MR temperature measurements from HIFU sonications. For simulations, a “true” SAR was calculated using the hybrid angular spectrum method for ultrasound simulations. This “true” SAR was plugged into a Pennes bioheat transfer equation (PBTE) solver to provide simulated temperature maps, which were then used to calculate the SAR estimate using the presented method. Zero mean Gaussian noise, corresponding to temperature precisions between 0.1 and 2.0°C, was added to the temperature maps to simulate a variety of in vivo situations. Experimental MR temperature maps from HIFU sonications in a gelatin phantom monitored with a 3D segmented echo planar imaging MRI pulse sequence were also used. To determine the accuracy of the simulated and phantom data, we reconstructed temperature maps by plugging in the estimated SAR to the PBTE solver. In both simulations and phantom experiments, the presented method was compared to two previously published methods of determining SAR, a linear and an analytical method. The presented numerical method utilized the full 3D data simultaneously, while the two previously published methods work on a slice-by-slice basis.ResultsIn the absence of noise, SAR distribution estimates obtained from the simulated heating profiles match closely (within 10%) to the initial true SAR distribution. The resulting temperature distributions also match closely to the corresponding initial temperature distributions (<0.2°C RMSE). In the presence of temperature measurement noise, the SAR distributions have noise amplified by the inverse convolution process, while the resulting temperature distributions still match closely to the initial “true” temperature distributions. In general, temperature RMSE was observed to be approximately 20–30% higher than the level of the added noise. By contrast, the previously published linear method is less sensitive to noise, but significantly underpredicts the SAR. The analytic method is also less sensitive to noise and matches SAR in the central plane, but greatly underpredicts in the longitudinal direction. Similar observations are made from the phantom studies. The described numerical inverse Green's function method is very fast — at least two orders of magnitude faster than the compared methods.ConclusionThe presented numerical inverse Green's function method is computationally fast and generates temperature maps with high accuracy. This is true despite generally overestimating the true SAR and amplifying the input noise.

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