THEORETICAL GAS CONCENTRATIONS ACHIEVING 100% FILL OF THE VITREOUS CAVITY IN THE POSTOPERATIVE PERIOD: A Gas Eye Model Study.

Purpose: To determine the concentrations of different gas tamponades in air to achieve 100% fill of the vitreous cavity postoperatively and to examine the influence of eye volume on these concentrations.

Methods: A mathematical model of the mass transfer dynamics of tamponade and blood gases (O2, N2, and CO2) when injected into the eye was used. Mass transfer surface areas were calculated from published anatomical data.

A thermoelastic deformation model of tissue contraction during thermal ablation.

Purpose: Thermal ablation is an energy-based ablation technique widely used during minimally invasive cancer treatment. Simulations are used to predict the dead tissue post therapy. However, one difficulty with the simulations is accurately predicting the ablation zone in post-procedural images due to the contraction of tissue as a result of exposure to elevated temperatures.

Mathematical model of the post-ablation enhancement zone as a tissue-level oedematic response.

Purpose: A hyperdense rim is commonly observed at the periphery of ablation zones during post-ablation imaging (e.g. ultrasound) in tumours.

A model of tissue contraction during thermal ablation.

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.

Cell death, perfusion and electrical parameters are critical in models of hepatic radiofrequency ablation.

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.

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.