# The Open Biomedical Engineering Journal

ISSN: 1874-1207 ― Volume 13, 2019

# Mathematical Models Based on Transfer Functions to Estimate Tissue Temperature During RF Cardiac Ablation in Real Time

Jose Alba-Martínez1, Macarena Trujillo2, Ramon Blasco-Gimenez3, Enrique Berjano1, *
1 Biomedical Synergy, Electronic Engineering Department, Universitat Politècnica de Valencia, Spain
2 Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de Valencia, Spain
3 Dpto. Ingeniería de Sistemas y Automática, Universitat Politècnica de Valencia, Spain

## Abstract

Radiofrequency cardiac ablation (RFCA) has been used to treat certain types of cardiac arrhythmias by producing a thermal lesion. Even though a tissue temperature higher than 50ºC is required to destroy the target, thermal mapping is not currently used during RFCA. Our aim was thus to develop mathematical models capable of estimating tissue temperature from tissue characteristics acquired or estimated at the beginning of the procedure (electrical conductivity, thermal conductivity, specific heat and density) and the applied voltage at any time. Biological tissue was considered as a system with an input (applied voltage) and output (tissue temperature), and so the mathematical models were based on transfer functions relating these variables. We used theoretical models based on finite element method to verify the mathematical models. Firstly, we solved finite element models to identify the transfer functions between the temperature at a depth of 4 mm and a constant applied voltage using a 7Fr and 4 mm electrode. The results showed that the relationships can be expressed as first-order transfer functions. Changes in electrical conductivity only affected the static gain of the system, while specific heat variations produced a change in the dynamic system response. In contrast, variations in thermal conductivity modified both the static gain and the dynamic system response. Finally, to assess the performance of the transfer functions obtained, we conducted a new set of computer simulations using a controlled temperature protocol and considering the temperature dependence of the thermal and electrical conductivities, i.e. conditions closer to those found in clinical use. The results showed that the difference between the values estimated from transfer functions and the temperatures obtained from finite element models was less than 4ºC, which suggests that the proposed method could be used to estimate tissue temperature in real time.

Keywords: Cardiac ablation, closed loop control, finite element method, radiofrequency ablation, temperature controlled ablation, theoretical model..

### Article Information

#### Identifiers and Pagination:

Year: 2012
Volume: 6
First Page: 16
Last Page: 22
Publisher Id: TOBEJ-6-16
DOI: 10.2174/1874120701206010016

#### Article History:

Revision Received Date: 2/2/2012
Acceptance Date: 3/2/2012
Electronic publication date: 8/3/2012
Collection year: 2012

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© Alba-Martínez et al.; Licensee Bentham Open.

open-access license: This is an open access article licensed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted, non-commercial use, distribution and repr oduction in any medium, provided the work is properly cited.

* Address correspondence to this autor at the Biomedical Synergy, Electronic Engineering Department, Universitat Politècnica de Valencia, Spain; Tel: 34-963877607; Fax: 34-963877609; Email: eberjano@eln.upv.es

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