Optimal Control of Thermal Damage to Targetted Regions in a Biological Material

A numerical technique with potential applications in hyperthermia treatment planning is presented. The treatment is simulated using a 2D transient computational model of the Pennes bioheat equation within an optimization algorithm. The algorithm recovers the heating protocol which will lead to a desired damage field. The relationship between temperature, time and thermal damage is expressed as a first order rate process using the Arrhenius equation. The objective function of the control problem is based on this thermal damage model. The adjoint method in conjunction with the conjugate gradient algorithm is used to minimize the objective function. The results from a numerical simulation show good agreement between the optimal damage field and the damage field recovered by the algorithm. A comparison between the recovered damage field and the commonly used thermal dose is also made.