Optimal Control for Pennes' Bioheat Equation

Abstract

The problem of Pennes' bioheat boundary control through a skin with its inner medium kept at a constant steady‐state temperature where the outer surface subjected to conductive condition is solved by different methods. Analytical and mild solutions of Pennes' boundary control problem yield a discrete optimization problem for temperature profile at the specific depth point as well as temperature profile at all points of the skin in the final time. The pointwise optimal control problem has been solved by discretized form of the unconstrained optimization problem using analytical solution for Pennes' boundary control problem. The analytical solution has been used to solve the optimal control problems via an unconstrained/constrained optimization in Methods I and II. In Method III first, Pennes' boundary control problem is solved using mild solution by strongly continuous semigroup theory. Then, nonlinear optimization problem with linear constraints is proposed to calculate the corresponding piecewise optimal control function. All methods, have been applied to a homogeneous tissue. Mathematical simulation is done to show the optimal controls for the related states when minimum effort is used.

Optimal Control of Anti-Angiogenesis and Radiation Treatments for Cancerous Tumor: Hybrid Indirect Solver

“…According to World Health Organization reports for the year 2019, cancer diseases are considered the main cause of death and the most important cause of life expectancy reduction [1]. Malek and Abbasi [2][3][4][5] in years 2016, 2019, 2020, and 2022 introduced some mathematical models to simulate and solve optimal control problems for cancer therapy. Cancer cells form and reproduce abnormal cells irregularly, while the proliferation of adult normal cells is based on the division and replacement of dying cells.…”

Solving two-dimensional bioheat optimal control problem in solid and vessel domain by pseudospectral discretization

“…In the year 2014, a direct solution for the Pennes equation is presented in the literature (Malek and Abbasi, 2014). Malek and Abbasi used strongly continuous semigroup for solving optimal control subject to PBE (Malek and Abbasi, 2015, 2016). Direct solution for linear and nonlinear dual-phase-lag bioheat transfer model is presented in the literature (Kumar et al, 2016) and (Kumar et al, 2017), respectively.…”