Multifidelity Uncertainty Quantification for Focused Ultrasound Breast Cancer Therapies Using Reduced Order Models

Focused ultrasound (FUS) is a thermal therapy used to noninvasively destroy diseased tissues. Computational tools are being explored to plan faster, safer, and more effective focused ultrasound treatments by using simulations to predict their outcomes. For simulations to be used with confidence, the uncertainties in their predicted outcomes must be characterized. This is challenging because the simulations have a large computational cost and performing uncertainty quantification (UQ) typically requires evaluating the simulations many times. Multifidelity uncertainty quantification uses techniques that aim to reduce the computational cost of uncertainty quantification. This is done by combining results from computationally expensive and accurate high-fidelity models with lower-fidelity models that sacrifice some accuracy to reduce computational expense. In this work, a multifidelity uncertainty quantification technique using projection-based reduced order models (ROMs) as the low-fidelity model is used on thermal simulations of two focused ultrasound sonications performed as part of breast cancer treatments. The errors in mean response estimates of multiple quantities of interest (QoIs) using this multifidelity uncertainty quantification technique are compared against those using traditional Monte Carlo uncertainty quantification. The mean, standard deviation, and skewness estimated using the multifidelity and Monte Carlo techniques are fit to Pearson Type III distributions to compare their predictions of quantity of interest distributions. It is found that multifidelity uncertainty quantification predicts the mean response of the quantities of interest with up to 50% lower error while maintaining similar accuracy in distribution predictions when compared to Monte Carlo.