# Standardized numerical simulations of cardiac electrical stimulation devices

Valentin Pannetier, Yves Coudière, Michael Leguèbe

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## To cite this version:

Valentin Pannetier, Yves Coudière, Michael Leguèbe. Standardized numerical simulations of cardiac electrical stimulation devices. Journée annuelle de l'EDMI, Apr 2023, Bordeaux (France), France. hal-04384583

HAL Id: hal-04384583

https://inria.hal.science/hal-04384583v1

Submitted on 10 Jan 2024

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Distributed under a Creative Commons Attribution 4.0 International License
# Standardized numerical simulations of cardiac electrical stimulation devices

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SIM CARDIO TEST

Valentin Pannetier, Yves Coudière, Michael Leguèbe

Université de Bordeaux, IMB, Inria and IHU Liryc

## CONTEXT

The **SimCardioTest** project aims to improve the interest and benefits of **insilico simulations** in the case of cardiovascular diseases.

We work on the electrical part with **MicroPort CRM pacemakers** manufacturers.

An **interface** separates the electrode from the tissue, where several **biochemical** effects occur. We want to understand the impact of contact **impedance** during a stimulation and quantify the **energy** actually applied to the tissue.

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## ODE – 0D MODEL

### Why

- Basic study on electrical properties of **contacts**.

- Test some algorithms, and simplified **nonlinear** effects.

- First comparison with **experimental** data.

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◆ **Device** equation (equivalent RC circuit)

$$ \frac{dI}{dt} + \frac{I}{\tau} = \frac{1}{R} \left( \frac{V_1}{\tau_1} + \frac{V_2}{\tau_2} + \frac{I_{\text{ion}}}{C_m} + \frac{V_m}{\tau_m} \right) $$

◆ **Contact** equations (tip and ring)

$$ \frac{dV_i}{dt} + \frac{V_i}{\tau_i} = \frac{I}{C_i} $$

◆ **0D cell** equation with **ionic terms** from literature

$$ \frac{dV_m}{dt} + \frac{I_{\text{ion}}}{C_m} + \frac{V_m}{\tau_m} = \frac{I}{S C_m} $$

$$ \frac{dh}{dt} + g(v_m, h) = 0 $$

**How to choose and determine** contact and scaling parameters... ?

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## STIMULATIONS

Parametrized by their **amplitude** and **duration** of pulse.

◆ Efficient stimulations lead to a capture, and the other ones fail.

◆ The plane of stimulations is split in two parts by the **Lapicque** curve

$$ A(d) = A_{\text{rh}} \left( 1 + \frac{t_{\text{ch}}}{d} \right) $$

with two parameters called rheobase and chronaxie.

## PDE – 3D MODEL

### WHY

- Take geometry into account (electrode distances, front wave propagation...).

- Compare **experimental** data with our solution.

◆ **Bidomain** equations in the tissue

$$ - \text{div} (\sigma_i \nabla u_i) = -C_m \partial_t v_m - j_{\text{ion}} $$

$$ - \text{div} (\sigma_e \nabla u_e) = C_m \partial_t v_m + j_{\text{ion}} $$

$$ \partial_t h + g(v_m, h) = 0 $$

◆ **Poisson** equation in the blood

$$ - \text{div} (\sigma_e \nabla u_e) = 0 $$

◆ At **boundaries** with **electrodes** (tip and ring)

$$ - \sigma_e \nabla u_e \cdot \mathbf{n} = j_{-} $$

$$ - \sigma_e \nabla u_e \cdot \mathbf{n} = j_{+} $$

◆ At **exterior boundaries**, a transmissive b.c.

$$ - \sigma_e \nabla u_e \cdot \mathbf{n} = \mu_e u_e $$

$$ - \sigma_i \nabla u_i \cdot \mathbf{n} = \mu_i u_i $$

**Proof of existence on the way!**

**How to adjust** conductivities, ionic model, all parameters... ?

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## RINGER TESTS

Measurements in saline solution

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MicroPort

### CONTEXT

These experiments were done in a laboratory of the industrial partner company **MicroPort**.

### PRINCIPLE

A lead is **submersed** in a salt bath, **voltage** and **current** passing through between the two electrodes are measured.

### SHAPE OF DATA OBTAINED

<figure><img src="image_10.png" /></figure>

### DISCHARGE

Phase to counterbalance capacitive effects of contacts.

## RESULTS

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### CONTACT CALIBRATION

◆ Several **contact models** tested (different ODE systems).

◆ We are confronted with the **non identifiability** of parameters.

◆ Still a **large variability** even with R/C.

◆ **Accurate** enough to reproduce measures in saline solution.

### SCALING PARAMETERS

◆ Great influence of parameter *S* (surface membrane).

◆ *S* and *τ*<sub>m</sub> are **surrogates** of the geometry.

### LAPICQUE CURVES

◆ Obtained by 2D dichotomy for now.

◆ Not accurate enough for **ex-vivo comparison**.

◆ Order of magnitude and results **relevant for exploration**.

### CONTEXT

These experiments were done at **IHU Liryc** with MicroPort leads.

### PRINCIPLE

A **sheep**'s ventricle is placed in a bath with two **cameras** pointing at it (endocardial and epicardial sides). A lead is then **implanted** and **stimulates** the tissue. An **activation map** is calculated from the fluorescence captured by the cameras.

### EX-VIVO DATA FROM 2 ANIMALS

◆ Activation map by optical mapping.

◆ Measured voltage at lead terminal.

◆ Geometries and some tissue characteristics by MRI 9.4T.

## OPTICAL MAPPING

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liryc
L'Institut des maladies du rythme cardiaque

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MicroPort

## NO RESULTS IN 3D FOR LAPICQUE STUDIES YET

But some works on bidomain coupled with an extracardiac domain already done.

### OBJECTIVES

◆ Reproduce 0D studies in 3D.

◆ **Quantify** influence of **tissue variability** and **geometric properties** on results.

For that we need to exploit experimental data, and several **calibrations** will be required.

### ALL THIS WORK TO

◆ Take into account **pacemaker** in models.

◆ Create a web platform with a design tool for lead manufacturers.

## RESULTS

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Université de BORDEAUX

Institut de Mathématiques de Bordeaux

BORDEAUX

cnrs

Inria

liryc
L'Institut des maladies du rythme cardiaque

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This project received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 101016496