Numerical modeling and optimization of the cryosurgery operations (Q492094)

The authors present a Pennes bioheat transfer model accounting for cryosurgery operations and posed as \(\rho C\frac{\partial T}{\partial t}=- \text{div}(-\kappa \nabla T)+\rho _{b}\omega _{b}C_{b}(T_{b}-T)\) in the domain \((0,\infty )\times H\), where \(H\) is the tissue containing a cancer tumor \(U\). Here \(\rho C\) takes three expressions according to the value of the temperature \(T\) with respect to a lower value \(-8^\circ C\) and an upper value \(-1^\circ C\). The coefficient \(\rho _{b}\omega _{b}C_{b}\) and the temperature \(T_{b}\) refer to the blood characteristics. The boundary conditions \(-\kappa \nabla T=0\) are imposed on the boundary \(\Gamma \) of \(H\) and the temperature starts from \(T_{body}\) at \(t=0\). The authors also add cryoprobes at a finite number of points in the tissue where the temperature must satisfy the Dirichlet condition \(T=-150^\circ C\). They first propose a numerical resolution of this problem combining a finite difference discretization with respect to the time parameter and a finite volume discretization with respect to the space variable. They finally propose an optimization procedure considering a cryosurgery impact and try to find a Pareto solution for the location of the cryoprobes. The paper ends with a presentation of the results they obtain through this method.