Minimax optimization-based inverse treatment planning for interstitial thermal therapy

The following work represents the development and evaluation of a minimax optimization-based inverse treatment planning approach for interstitial thermal therapy of cancer and benign disease. The goal is to determine a priori optimal applicator placements and power level settings to maintain the minimum tumour temperature, Tmin, and maximum normal tissue temperature, Tmax within a prescribed therapeutic temperature range. The temperature distribution is approximated by a finite element method (FEM) solution of a bioheat transfer equation on a nonuniform finite element mesh. Lower and upper therapeutic temperature thresholds are specified in the tumour and surrounding normal tissues. A constrained minimax optimization problem is formulated to determine optimal applicator positions and power level settings that minimize the maximum (rather than average) temperature errors in the target tumour region and surrounding normal tissues. The optimization problem is formulated for two general classes of interstitial heating applicators, those with and without a surface cooling mechanism. The viability and sensitivity of this approach is investigated in the two-dimensional setting for various tumour shapes and blood perfusion levels using surface-cooled and direct-coupled interstitial ultrasound applicator power deposition models. These preliminary results indicate the utility of this approach for meeting a prescribed Tmin/Tmax-based clinical objective criterion, and its potential for generating optimal treatment plans that can withstand variations or uncertainty in blood perfusion levels.