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

Abstract

Conventional temperature optimisation in Hyperthermia Treatment Planning aims to maximise tumour temperature (e.g., T90; the temperature reached in at least 90% of the tumour) while enforcing hard constraints on normal tissue temperature (max(Ttissue)≤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 optimisation in clinical applications, we developed new robust optimisation strategies to reduce the impact of tissue/perfusion property uncertainties.
Approach: Within the software package Plan2Heat, temperature calculations during optimisation 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 average T-matrix(Tavg) and a covariance matrix C to account for uncertainties in tissue/perfusion properties. Three new strategies were implemented using Tavg and C during optimisation:

(1) Tavg90 maximisation, hard constraint on max(Ttissue),
(2) Tavg90 maximisation, hard constraint on max(Ttissue) variation, and
(3) combined Tavg90 maximisation and variation minimisation, hard constraint on max(Ttissue). 

Conventional and new optimisation strategies were tested in a cervical cancer patient. One-hundred test cases were generated, randomly sampling tissue-property probability distributions. Tumour T90 and hotspots (max(Ttissue)>45°C) were evaluated for each sample.

Main Results: Conventional optimisation had 28 samples without hotspots, with a median T90 of 39.7°C. For strategies (1), (2) and (3), the number of samples without hotspots was increased to 33, 41 and 36, respectively. Median T90 was reduced lightly, by ~0.1-0.3°C, for strategies (1-3). Tissue volumes exceeding 45°C and variation in max(Ttissue) were less for the novel strategies.
Significance: Optimisation strategies that account for tissue-property uncertainties demonstrated fewer, and reduced in volume, normal tissue hotspots, with only a marginal reduction in tumour T90. This implies a potential clinical utility in reducing the need for, or the impact of, device setting adjustments during hyperthermia treatment.&#xD.

Keywords: Hyperthermia; bioheat; optimization; perfusion; robust optimization; tissue properties; uncertainties.