A highly accurate Augmented Matched Interface and Boundary method for heat dissipation in tumor anatomies

Abstract

Hyperthermia therapy stands out as a promising complementary cancer treatment because it targets tumor cells by their thermal sensitivity. Accurate simulation of heat distribution in complex tumor geometries is critical for treatment planning and delivery. Pennes' bioheat equation provides a widely-used framework to describe thermal transport in perfused biological tissues, but applying it to complex tumor geometries remains computationally challenging. We developed an advanced computational framework by combining Pennes' bioheat model and a new adaptive Augmented Matched Interface and Boundary (AMIB) method to accurately simulate heat dissipation in realistic tumor anatomies. CT scans are processed through edge-detection algorithms to identify the tumor boundary. A pair of coupled parametric cubic splines is created from a set of selected boundary points to reconstruct the tumor outline. Numerical schemes for boundary calculations are designed to support the AMIB method in solving Pennes' bioheat equation within the tumor. The AMIB method functions on Cartesian grids, achieving a second-order convergence in time and fourth-order convergence in space without requiring complex mesh generation. Numerical experiments demonstrate unconditional stability, high-order convergence rates, and high efficiency of the AMIB method in simulating hyperthermia treatments. The proposed computational pipeline offers a generalizable approach for image-guided thermal therapy simulations involving irregular tissue geometries. This study helps progress towards thermal modeling platforms that support hyperthermia cancer therapy through image-guided clinical applications.

Keywords: Augmented Matched Interface and Boundary (AMIB) method; Cancer treatments; Hyperthermia therapy (HT); Pennes’ bioheat equation.