Robust stochastic optimisation strategies for locoregional hyperthermia treatment planning using polynomial chaos expansion.

Abstract

Objective.Conventional temperature optimization in hyperthermia treatment planning aims to maximize tumour temperature (e.g.T90; the temperature reached in at least 90% of the tumour) while enforcing hard constraints on normal tissue temperature (max(T_tissue) ⩽45 °C). This method generally incorrectly assumes that tissue/perfusion properties are known, typically relying on average values from the literature. To enhance the reliability of temperature optimization in clinical applications, we developed new robust optimization strategies to reduce the impact of tissue/perfusion property uncertainties.Approach.Within the software package Plan2Heat, temperature calculations during optimization apply efficient superposition of precomputed distributions, represented by a temperature matrix (T-matrix). We extended this method using stochastic polynomial chaos expansion models to compute an averageT-matrix (T_avg) and a covariance matrixCto account for uncertainties in tissue/perfusion properties. Three new strategies were implemented usingT_avgandCduring optimization: (1)T_avg90 maximization, hard constraint on max(T_tissue), (2)T_avg90 maximization, hard constraint on max(T_tissue) variation, and (3) combinedT_avg90 maximization and variation minimization, hard constraint on max(T_tissue). Conventional and new optimization strategies were tested in a cervical cancer patient. 100 test cases were generated, randomly sampling tissue-property probability distributions. TumourT90 and hot spots (max(T_tissue) >45 °C) were evaluated for each sample.Main Results.Conventional optimization had 28 samples without hot spots, with a medianT90 of 39.7 °C. For strategies (1), (2) and (3), the number of samples without hot spots was increased to 33, 41 and 36, respectively. MedianT90 was reduced lightly, by ∼0.1 °C-0.3 °C, for strategies (1-3). Tissue volumes exceeding 45 °C and variation in max(T_tissue) were less for the novel strategies.Significance.Optimization strategies that account for tissue-property uncertainties demonstrated fewer, and reduced in volume, normal tissue hot spots, with only a marginal reduction in tumourT90. This implies a potential clinical utility in reducing the need for, or the impact of, device setting adjustments during hyperthermia treatment.