Purpose: A sensitivity analysis has been performed on a mathematical model of radiofrequency ablation (RFA) in the liver. The purpose of this is to identify the most important parameters in the model, defined as those that produce the largest changes in the prediction. This is important in understanding the role of uncertainty and when comparing the model predictions to experimental data. Materials and methods: The Morris method was chosen to perform the sensitivity analysis because it is ideal for models with many parameters or that take a significant length of time to obtain solutions. A comprehensive literature review was performed to obtain ranges over which the model parameters are expected to vary, crucial input information. Results: The most important parameters in predicting the ablation zone size in our model of RFA are those representing the blood perfusion, electrical conductivity and the cell death model. The size of the 50 °C isotherm is sensitive to the electrical properties of tissue while the heat source is active, and to the thermal parameters during cooling. Conclusions: The parameter ranges chosen for the sensitivity analysis are believed to represent all that is currently known about their values in combination. The Morris method is able to compute global parameter sensitivities taking into account the interaction of all parameters, something that has not been done before. Research is needed to better understand the uncertainties in the cell death, electrical conductivity and perfusion models, but the other parameters are only of second order, providing a significant simplification.

A model of a globular protein is used to describe the contraction of tissue exposed to elevated temperatures. This will be useful in predicting the contraction of tissue that is observed during thermal ablation of tumours, which is a problem when trying to determine the ablation zone in post-operative images. The transitions between the states of the protein can be related to a change in the length of the molecule, which can be directly observed as a change in the length of the tissue. A three state model of a globular protein is used to describe the contraction of tissue exposed to elevated temperatures. A nonlinear fitting algorithm is considered here to fit available experimental data and thus to obtain the values of the model parameters. A sensitivity analysis of the proposed mathematical model is performed to determine the most important parameters in the model. The model parameters were obtained from experimental data of isothermal free shrinkage experiments. The predictions of the complete model show similar agreement with the data, well within the experimental error of 10%. The overall activation energy and frequency factor were found to be 201 kJ mol(-1) and [Formula: see text] s(-1) respectively. The results show that the experimental data were well described by the three state model considered here. Furthermore, it was possible to determine the most sensitive parameters in the model. The model presented here will allow predictions of thermal ablation to be corrected for tissue shrinkage, thus improving mathematical simulations for treatment planning, although clinical translation will require adapting the model from experimentally obtained tendon data to soft tissue data.

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.

The model presented here will allow predictions of thermal ablation to be corrected for tissue contraction, which is an important effect, during comparison with post-procedural images, thus improving the accuracy of mathematical simulations for treatment planning.