Numerical simulation of cryosurgeries and optimization of probe placement
type: Item
instance of: scholarly article
title: Numerical simulation of cryosurgeries and optimization of probe placement
zbMATH Open document ID: 1334.92203
DOI: 10.1134/S0965542515090092
published in: Computational Mathematics and Mathematical Physics
publication date: 2016-01-06T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 92C50
Mathematics Subject Classification ID: 80A22
Mathematics Subject Classification ID: 80M12
Mathematics Subject Classification ID: 80M50
Mathematics Subject Classification ID: 92-08
zbMATH DE Number: 6526861
zbMATH Keywords: cryosurgery
zbMATH Keywords: heat equation
zbMATH Keywords: Stefan problem
zbMATH Keywords: numerical method
zbMATH Keywords: finite volume method
zbMATH Keywords: enthalpy approach
zbMATH Keywords: multiple criteria optimization
author: Nikolai A. Kudryashov
author: K. E. Shilnikov
reviewed by: Alain Brillard
MaRDI profile type: Publication
cites work: Q5807063
cites work: An economic continuous calculation scheme for the stefan multidimensional problem
cites work: A survey of multicriteria optimization or the vector maximum problem. I: 1776-1960
description: scientific article; zbMATH DE number 6526861