A mathematical framework for minimally invasive tumor ablation therapies

Minimally invasive tumor ablations (MITAs) are an increasingly important tool in the treatment of solid tumors across multiple organs. The problems experienced in modeling different types of MITAs are very similar, but the development of mathematical models is mostly performed in isolation according to modality. Fundamental research into the modeling of specific types of MITAs is indeed required, but to choose the optimal treatment for an individual the primary clinical requirement is to have reliable predictions for a range of MITAs. In this review of the mathematical modeling of MITAs 4 modalities are considered: radiofrequency ablation, microwave ablation, cryoablation, and irreversible electroporation. The similarities in the mathematical modeling of these treatments are highlighted, and the analysis of the models within a general framework is discussed. This will aid in developing a deeper understanding of the sensitivity of MITA models to physiological parameters and the impact of uncertainty on predictions of the ablation zone. Through robust validation and analysis of the models it will be possible to choose the best model for a given application. This is important because many different models exist with no objective comparison of their performance. The collection of relevant in vivo experimental data is also critical to parameterize such models accurately. This approach will be necessary to translate the field into clinical practice.