A model of tissue contraction during thermal ablation

Abstract

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.

A thermoelastic deformation model of tissue contraction during thermal ablation

“…A three state model was considered here for the thermal denaturation process with the thermal reaction rate being dependent on the Arrhenius equation. The equations and parameters to determine the strain can be found in Appendix 1, with the theory and the values of the parameters involved given in full in Park et al [20].…”

“…In addition to this effect, several ex vivo experiments have associated contraction of tissue exposed to elevated temperatures with effects such as protein denaturation and dehydration [6,18,19]. Studies have developed mathematical models based on physiology to determine the behaviour of tissue contraction as a result of protein denaturation during hyperthermic ablation [20,21]. This was achieved using state models with first order reaction kinetics describing the transition of molecules between the different states.…”

“…The purpose of this study was to estimate the degree of tissue contraction as a result of heating during typical ablation procedures, and thus to improve the accuracy of mathematical simulations for treatment planning. A previously developed three state model of protein denaturation [20] was coupled with the thermoelastic wave equation, which determines the deformation due to the internal forces. A typical temperature distribution during hyperthermic ablation therapies was considered to solve for the coupled equations using a finite difference method.…”

Coupled thermo-electro-mechanical models for thermal ablation of biological tissues and heat relaxation time effects

“…The kinetic parameters (A and ΔE) account for the morphological changes in the tissue related to thermal degradation of proteins. With the constraint that the sum of all the three states is equal to one (i.e., N+U+D=1), the three-state death model can be mathematically described by following system of equations [45]:…”

Numerical simulation of microwave ablation incorporating tissue contraction based on thermal dose

“…Multiple groups have performed quantitative measurements of tissue contraction spatially or temporally on different organs (Liu and Brace, 2014; Sommer et al , 2013), and some studies have proposed mathematical models to describe temperature dependent tissue shrinkage (Chen et al , 1998; Rossmann et al , 2014; Park et al , 2016). However, previous studies have not incorporated the numerical models into a simulation environment that also predicts the energy-tissue interaction leading to ablation growth.…”