Surrogate modeling in irreversible electroporation towards real-time treatment planning

In this paper, we develop surrogate models that can replace expensive predictive models and account for uncertainties in real-time treatment planning for irreversible electroporation of liver tumors. Standard non-intrusive surrogate modeling techniques that account for the model uncertainty and reduce the computational cost, such as polynomial chaos expansion and Gaussian process regression with conventional kernels, often do not capture the true physical behavior of the treatment outcome as required in the context of treatment planning. We improve the Gaussian process regression model by modifying the kernel function to a non-stationary Gibbs kernel with a support vector machine-based classifier in its length scale definition. This proposed model is compared with the standard surrogates in terms of their performance and accuracy. Our model is able to accurately replicate the behavior of the biophysics-based predictive model. There is a decrease of at least 81% in the overall root-mean-square error for treatment outcome when compared to the Gaussian process regression model with conventional kernels. Furthermore, we illustrate the application of the proposed surrogate model in treatment planning to address a voltage optimization problem for complete tumor ablation. Surrogate-assisted treatment planning exhibited good performance while maintaining similar levels of accuracy in comparison to treatment planning based on biophysical models. Finally, the effect of uncertainty in tissue electrical conductivities on the optimal voltage value is discussed.