Two-compartment mathematical modeling in RF tumor ablation: New insight when irreversible changes in electrical conductivity are considered.

Dora Luz Castro-López,Ricardo Romero-Mendez,Enrique Berjano,Macarena Trujillo

doi:10.3934/mbe.2020405

Abstract

The objective was to explore variations of temperature distribution and coagulation zone size computed by a two-compartment radiofrequency ablation (RFA) model when including simultaneously reversible changes in the tissue electrical conductivity (σ) due to temperature and irreversible changes due to thermal coagulation. Two-compartment (tumor and healthy tissue) models were built and simulated. Reversible change of σ was modeled by a piecewise function characterized by increments of +1.5%/℃ up to 100 ℃, and a 100 times smaller value from 100 ℃ onwards. Irreversible changes of σ were modeled using an Arrhenius model. We assumed that both tumor and healthy tissue had a different initial σ value (as suggested by the experimental data in the literature) and tended towards a common value as thermal damage progressed (necrotized tissue). We modeled a constant impedance protocol based on 90 V pulses voltage and three tumor diameters (2, 3 and 4 cm). Computer simulations showed that the differences between both models were only 0.1 and 0.2 cm for axial and transverse diameters, respectively, and this small difference was reflected in the similar temperature distributions computed by both models. In view of the available experimental data on changes of electrical conductivity in tumors and healthy tissue during heating, our results suggest that irreversible changes in electrical conductivity do not have a significant impact on coagulation zone size in two-compartment RFA models.

Highlights

Computer modeling has been widely used to study temperature distributions during radiofrequency (RF) tumor ablation (RFA)
In view of the available experimental data on changes of electrical conductivity in tumors and healthy tissue during heating, our results suggest that irreversible changes in electrical conductivity do not have a significant impact on coagulation zone size in two-compartment radiofrequency ablation (RFA) models
Our goal was to explore how temperature distribution and coagulation zone size computed from a two-compartment model could vary in the case of including simultaneously reversible changes due to temperature, as suggested in Figure 1E, and irreversible changes due to thermal coagulation as suggested in Figure 1F in the specific case of assuming that the differences in between healthy and tumor tissue disappear as tissue passes from native state to denatured state

Summary

Introduction

Computer modeling has been widely used to study temperature distributions during radiofrequency (RF) tumor ablation (RFA). Up to now, this method involved solving an electrical-thermal coupled problem using a mathematical framework based on the Laplace equation to solve the electrical problem and the Pennes' equation for the thermal problem. The first computer models mimicked an RFA on non-tumor tissue, i.e. the tissue sub-domain was assumed to be homogeneous and constituted by a ‘single compartment’ [1−3]. Computer modeling was later used to explore temperature distributions in tumors with non-healthy tissue properties, for which two-compartment models were proposed: one compartment (or sub-domain) representing the tumor and the other the healthy tissue. About the RF applicator, some studies considered a multi-prong [6,7] while others modeled a single-needle RF applicator as the Cool-tip model [10−12]

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