# Numerical Modeling and Simulations of Pulsed Field Ablation for Cardiac Ablation

Simon Bihoreau, Annabelle Collin, Michael Leguèbe, Clair Poignard

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Simon Bihoreau, Annabelle Collin, Michael Leguèbe, Clair Poignard. Numerical Modeling and Simulations of Pulsed Field Ablation for Cardiac Ablation. WC2024 - 5th World Congress on Electroporation, Sep 2024, Rome, Italy. pp.1-1, 2024. [hal-04847693](https://hal.science/hal-04847693v1)

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Submitted on 19 Dec 2024

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# Numerical Modeling and Simulations of Pulsed Field Ablation for Cardiac Ablation

We present a new model of cardiac ablation with irreversible electroporation (PFA) on a tissue level. It contains non-linear effective conductivities depending locally on the electric field, in accordance with the experimental observations, and has a physiological origin. We compare it with the electroporation standard model on an applicative case.

S. Bihoreau¹,², A. Collin¹, M. Leguèbe¹,², C. Poignard¹

(1) INRIA, Univ. Bordeaux, CNRS, Bordeaux INP, CNRS, IMB, UMR 5251, 200 Avenue de la Vieille Tour, 33405 Talence cedex, France.

(2) IHU LIRYC, Electrophysiology and Heart Modeling Institute, Fondation Bordeaux Université, 33600 Pessac, France.

## Context & Numerical model

### Clinical context

* **Cardiac ablation** to eliminate sites of arrhythmias origin as atrial fibrillation (AF) or ventricular tachycardia (VT)

* **Pulsed electric Field Ablation (PFA)** based on irreversible electroporation

<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /></figure>

### Objectives of this work

* A new mathematical/numerical tissue-scale model that integrates the non-linearity depending on the **electric field** and has a **physiological origin**

* Comparison of it with the standard model on an applicative case

<figure><img src="image_4.png" /></figure>

Numerical simulations of the reentry of transmembrane voltage in a channel between two scars in the left ventricle. Evolution in time from top to bottom. View from the epicardium (left), section of ventricles (right).

Credits to Simone Nati Poltri.

### Part of a project in collaboration with IHU Liryc

* Sheep experiments: **PFA for VT** using Affera™ [1] catheter (monopolar configuration) and software

* Data pre-processing

* Various available **data** (before, immediately & 2 weeks after): MRI, activation maps & voltage maps

* Mesh generation and scar segmentation from MRI

* Catheter geometry including deformation

* Numerical simulations - confronted to experimental data - to determine the impact of **fibrotic areas** on VT and on ablation and to **determine the ablated zone**

## Simulations

<figure><img src="image_5.png" /></figure>

### Numerical simulations

* **Static** simulations

* Study of the **impact of fibrosis** (valvular plane) close to the **conduction system** (His bundle)

* **Comparison** between our new model and the standard model

* **Illustrations** of two quantities that can be used to determine the ablated regions: the electrical field (EF) & the power.

### Results from a clinical point of view:

* even if the results are still **qualitative** due to some uncertainties,

* it can be seen that both models show that low conductivity regions affect the **EF distribution** even after one pulse,

* which makes it **difficult** to determine the ablated region by intuition and could explain the **damage observed** near the AV node.

### Results from a modeling point of view:

* the correction plays a **non-negligible** role in the estimation of the ablated zone, especially in some directions,

* most of the time, the estimated ablated zone appears **bigger** with the correction than without it.

### The electroporation standard model at tissue scale

$$-\nabla \cdot (\sigma \nabla u) = f$$

* $u$ is the electric potential, $\sigma$ the electrical conductivity, $f$ a source term

* Widely used in oncology [2]

* Sufficient for **qualitative results** but cannot determine accurately the ablated zone

* The non linear version - conductivity depending on the electric field $\sigma(|\nabla u|)$ - is **phenomenological** and has no physical origin

### Our model

* Determines the **intra-cellular potential**, the **extra-cellular potential** and the **transmembrane potential** $v_m$ as it is linked, through mathematical homogenization, to the bidomain model (a very classical **cardiac electrophysiology** model [3]).

* Is physiological:

* the cellular model describes electroporation as an increase in the cell membrane conductance: $S_m(v_m)$,

* leading to a macroscopic conductance depending on the electric field: $S_m(\epsilon|\chi| \cdot \nabla u + v_m^1)$.

* Takes into account **cardiac fibers** as some terms in the model account for cell geometry.

* Can be compared with the standard model as it is a correction of it writing: $u + \epsilon u_e^1$, where $u$ is the solution of the standard model, $u_e^1$ the first order correction* and $\epsilon$ the ratio between the cell diameter and the heart dimension (= 0.01).

### *First order correction

$$1. \text{ Compute the transmembrane voltage } v_m^1 \\ - \nabla \cdot (\Sigma_i \nabla u) = S_m^{\text{eff},2} \cdot \nabla u + S_m^{\text{eff},1} v_m^1$$

$$2. \text{ Compute the extracellular potential } u_e^1 \\ - \nabla \cdot \left( (\Sigma_i + \Sigma_e) \nabla u_e^1 \right) = \nabla \cdot \left( \Sigma_i \nabla v_m^1 \right) \\ + \nabla \cdot \left( S_m^{\text{eff},3} \cdot \nabla u \right) + \nabla \cdot \left( S_m^{\text{eff},2} v_m^1 \right)$$

Effective conductivities

$$S_m^{\text{eff},1} = \int_{\Gamma} S_m (\epsilon |\chi| \cdot \nabla u + v_m^1) dA \\ S_m^{\text{eff},2} = \int_{\Gamma} S_m (\epsilon |\chi| \cdot \nabla u + v_m^1) dA [\chi] \\ S_m^{\text{eff},3} = \int_{\Gamma} S_m (\epsilon |\chi| \cdot \nabla u + v_m^1) dA [\chi] : [\chi]$$

<figure><img src="image_6.png" /><figcaption>Simulations with the standard model (thin) and the new model (bold)</figcaption></figure>

Left - far from the valvular plane. Right - in the vicinity of the valvular plane. Top - 2D view along the y-axis, centered on the catheter. Bottom - 2D view along the x-axis, centered on the his bundle

<figure><img src="image_7.png" /><figcaption>Isolines of the **power** of the system at 1.5W/mm³ (red) and at 0.5W/mm³ (black)</figcaption></figure>

## Perspectives

* **Numerical estimation of the ablated area** using sheep data

* Numerical study of some parameters (contact force, fibers orientation, patch orientation, ...)

* Which quantity to assess ablated area? Make use of the effective conductivities?

* Study the impact of pulse frequency?

<footnote>[1] I. Kawamura et al. Pulsed field ablation of the porcine ventricle using a focal lattice-tip catheter. Circulation: Arrhythmia and Electrophysiology 2022.</footnote>

<footnote>[2] Jankowiak G et al. Comparison and calibration of different electroporation models. Application to rabbit livers experiments. ESAIM : Proc. and Surveys, 2020.</footnote>

<footnote>[3] A. Collin, S. Imperiale. *Mathematical Analysis and 2-Scale Convergence of a Heterogeneous Microscopic Bidomain Model*. Math. Mod. and Meth. in App. Sc., 2018.</footnote>