Optimal control of hyperthermia thermal damage based on tumor configuration

Improvement and optimization of hyperthermia as one of the most effective and conventional cancer treatments have been tackled by many researchers in recent years. The main benchmark for hyperthermia treatment is to elevate the cancerous tissue temperature to a specified level to initiate damage or ablation and simultaneously to prevent any irreversible thermal damage to the surrounding healthy cells. Therefore, the heat source pattern for hyperthermia treatment should be adjusted according to the distribution of cancerous cells. To do this, in the present study the fractional bioheat equation with unknown heat source term is implemented. Two different hyperthermia scenarios with single and dual tumors are considered and the appropriate damage level at both healthy and cancerous tissues is planned according to the Arrhenius model. Moreover, the optimal control criterion is set to simultaneously produce the goal temperature level and minimize the thermal power consumption. The mentioned task is accomplished by the definition of a priority coefficient as a weight function which determines whether the establishment of desired thermal field or the reduction of applied thermal power is more important. Based on the results, the optimal control approach can precisely determine the heat source distribution for single and dual tumor cases (with 1.03 and 0.13% deviation error, respectively). Whereas, by shifting the priority to the minimization of applied energy, up to 23.1 and 38.7% deviation is observed in formation of the desired temperature field (while the overall cost function is minimized). In order to investigate the numerical results, a computational method based on the Legendre cardinal functions is proposed. The main advantage of the proposed method is that it transforms solving such fractional models into solving systems of algebraic equations which greatly simplify the problem.