Polynomial Chaos Expansion based Skull Uncertainty Analysis of Low Intensity Focused Ultrasound Modulation

Neuromodulation with low intensity focused ultrasound (LIFUS) is an emerging field that holds great promise for the non-invasive treatment of neurological disorders. The success of this technique relies heavily on an accurate targeting of the specific brain region(s). Computational modeling provides us a valuable tools to visualize the uncertainties due to uncertainties in the modeled properties. Skull speed of sound is the main source of uncertainty in transcranial focused ultrasound stimulation. While traditional methods can uncover the uncertainties, they are resource heavy. Since the traditional Monte Carlo (MC) simulations are resource heavy, we implemented and studied surrogate modeling using Polynomial Chaos Expansion (PCE). The PCE method projects the relationship between a model's output and a set of input parameters onto a basis of orthogonal polynomials. Our model evaluated with respect to Gaussian quadrature nodes (3 samples) and weights used to approximate the coefficients of orthogonal polynomial basis using the Chaospy 4.3.13 library and Python 3.9.13. Once the surrogate model is ready, we generated 200 results with randomly selected samples. As a reference, the standard deviation of the simulation was also estimated via Monte Carlo, by running 200 simulations. We have evaluated the similarity using root mean square error method. For LIFUS, we found that PCE using 3 samples enables good agreement with 200 MC samples: 0.1% error in mean and 0.5% error in standard deviation. This creates an efficient and fast alternative to the traditional methods of uncertainty assessments which relies on running large number of full-wave solvers. A possible extension of our method is to use PCE to predict temperature rise induced by the acoustic field. We will investigate the further implementations of this method for uncertainty and safety assessment.