Optimal control for bio-heat equation due to induced microwave

Abstract

A distributed optimal control problem for a system described by a bio-heat equation for a homogeneous plane slab of tissue is analytically investigated. The required tissue temperature at a particular location of the tumour in hyperthermia can be attained within the total operation time of the process due to induced microwave radiation which is taken as control. The tissue temperature against the tissue length at different operation time of the process is considered to attain the desired temperature of the tumor.

Estimation of surface heat flux in a one-dimensional hyperbolic bio-heat conduction problem with temperature-dependent properties during thermal therapy

“…Solve the direct problem given by Eqs. (9)(10)(11)(12) and obtain the temperature data at the measurement location, T(x m , t).…”

“…Majchrzak and Paruch [10] used both the gradient method and evolutionary algorithm to identify the electric potential of the electrodes and number of nanoparticles introduced to the tumor region. Dhar and Dhar [11] extended the inverse bio-heat conduction based on the conjugate gradient method to determine the heat source in such a way that the desired temperature of the tumor is attained. Yang [12] estimated the boundary condition in hyperbolic bio-heat conduction by using a sequential method.…”

Optimal control solution for Pennes' equation using strongly continuous semigroup

“…A thermal dose optimization problem in hyperthermia was studied analytically by Loulou and his co-author [13] using conjugate gradient method via the numerically solutions of the direct, adjoint and variation problems in finite control volume method. With the aid of conjugate gradient method, a distributed optimal control problem for a system described by bioheat equation in a homogeneous plane tissue due to induced microwave was investigated by Dhar et al [6,7,8] via the numerical solution of the corresponding problem in finite sin transform method. An inverse problem of temperature optimization in hyperthermia was investigated numerically by Aghayan et al [1] via controlling the overall heat transfer coefficient of the cooling system using conjugate gradient method.…”