Numerical simulation of cryosurgeries and optimization of probe placement
The authors apply a numerical scheme for the resolution of a model accounting for cryosurgery with 1, 2 or 3 probes whose positions can be chosen. They start with the heat equation \(\rho C\frac{\partial T}{\partial t }=\text{div}(\kappa \nabla T)\) posed in an overall domain including the unknown tumor zone. The transmission conditions \(T\mid _{S-0}=T\mid _{S+0}=T_{cr}\) and \(Q\mid _{S-0}=Q\mid _{S+0}=\rho LV_{S}\) are imposed on the interface. Here, \(Q=-\kappa \nabla T\) is the heat flux. On the outer boundary (far away from the tumor), the flux is imposed equal to 0 and the temperature of the body and at the probe positions is known. The authors present a quasi-delta functional combination for the coefficient \(\rho C\). For the numerical scheme, the authors suppose that the overall domain and the tumor are cubes and they apply a finite volume method with an enthalpy approach. They test their numerical scheme first in a 1D situation, then very briefly in the 3D case with the values of chicken tissues and with 1 or 3 probes. In the last part of the paper, the authors discuss an optimization procedure for the probe position. They use nonparametric multiple criteria optimization techniques through the notion of Pareto front. They finally present results of this optimization procedure for 1, 2 or 3 probes.
scientific article; zbMATH DE number 6526861