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

Abstract

In this paper, an optimal control problem subject to an energy transfer equation in thermally significant blood vessel coupled with the Pennes governing equation is solved. The proposed dynamical system is modeled by a system of conduction-reaction and convection-conduction equations. Chebyshev–Gauss–Lobatto (CGL) and Legendre–Gauss–Lobatto (LGL) points are applied to discretize optimal control problem. Then, the problem transferred into a quadratic programming problem using domain decomposition and matching the solution and its first derivative across the related interfaces. The Tikhonov regularization method is used to compute the optimal regularization parameter for the objective function. Some theories have been discussed to prove that the discrete problem has a solution and it is also consistent with the continuous problem. Numerical results are compared and numerical convergent is shown. Optimal and non-optimal external heat source is compared and it is shown that the mathematical modeling is effective in saving the external heat energy. Numerical results show that by this process of heating at the final time, the temperature is very close to the desired temperature without damaging the vessel domain. Numerical results and corresponding graphs are depicted.

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.…”