# Modeling Cardiac Stimulation by a Pacemaker, with Accurate Tissue-Electrode Interface

Valentin Pannetier, Michael Leguèbe, Yves Coudière, Richard D Walton, Delphine Feuerstein, Diego Amaro, Philippe Dhiver

► To cite this version:

Valentin Pannetier, Michael Leguèbe, Yves Coudière, Richard D Walton, Delphine Feuerstein, et al. Modeling Cardiac Stimulation by a Pacemaker, with Accurate Tissue-Electrode Interface. FIMH 2023 - 12th International Conference on Functional Imaging and Modeling of the Heart, Jun 2023, Villeurbanne (Lyon), France. hal-04384661

HAL Id: hal-04384661

https://inria.hal.science/hal-04384661v1

Submitted on 10 Jan 2024

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Distributed under a Creative Commons Attribution 4.0 International License
# MODELING CARDIAC STIMULATION BY A PACEMAKER, WITH ACCURATE TISSUE-ELECTRODE INTERFACE

Valentin PANNETIER¹, Michael LEGUÈBE¹, Yves COUDIÈRE¹, Richard WALTON², Delphine FEUERSTEIN³, Diego AMARO³, and Philippe DHIVER³

1. Univ. Bordeaux, CNRS, Inria, IMB, UMR 5251, IHU Liryc F-33400, Talence, France, 2. Univ. Bordeaux, Inserm, CRCTB, U 1045, IHU Liryc, F-33000 Bordeaux, France 3. Microport CRM, Clamart, France

An implantable **pacemaker** aims to **restore a cardiac beat** when the intrinsic conduction system fails. It sends energy to the heart in the form of a **voltage pulse** and it is programmed to deliver enough energy to trigger a **cardiac depolarization** (which is called **capture**). We present a 0D model of a cardiac pacemaker with a cardiac tissue. We take into account electrochemical phenomena observed during pacing, like **electrode polarization**. To validate it, we compare numerical results with ex-vivo experimental data of stimulation threshold detection.

## › 0D model for a pacemaker

① **Pulse.** A tank capacitor $C_{\text{pulse}}$ acts as source of current. In the meantime, a second capacitor $C_{\text{oqd}}$ is charged. The **duration** (d) and the **amplitude** ($V_{\text{stim}}$) of the pulse is decided by the clinician.

② **Switch.** short transition phase (~ hundreds of µs) during which switches are open.

③ **Output Capacitor Discharge (OCD).** $C_{\text{pulse}}$ is isolated and $C_{\text{oqd}}$ discharges. This step lasts for 13 ms, and counteracts the electrode polarization that occured during the pulse.

### › Pacemaker coupled to a purely resistive medium

$$ 
\begin{aligned}
\frac{dI}{dt} + \frac{1}{\tau} I &= \frac{1}{R_{\text{tot}}} \left( \frac{V_1}{\tau_1} + \frac{V_2}{\tau_2} \right) \\
\frac{dV_1}{dt} + \frac{V_1}{\tau_1} &= \frac{I}{C_1} \\
\frac{dV_2}{dt} + \frac{V_2}{\tau_2} &= \frac{I}{C_2}
\end{aligned}
$$

► **Current** (top) and **voltage** (bottom) delivered by a pacemaker lead in a **saline solution** (black solid line). Red dashed lines are the **calibration** for 2 V and 1 ms.

**Parameters:**

* device: $R_{\text{tot}}$, $\tau=R_{\text{tot}}C_{\text{tot}}$ depend on the phase (1, 2 or 3).

* contacts: modeled by a parallel R C circuit with parameters ($C_1$, $\tau_1$) and ($C_2$, $\tau_2$).

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

## › Calibration: ringer tests

To evaluate the **accuracy of the R//C model** for the **electrode polarization**:

* We measure the current I and the voltage V delivered by a pacemaker lead directly **in a saline passive solution** without cardiac tissue.

* We use a MicroPort Vega lead to **obtain datasets of ($I_{\text{meas}}$, $V_{\text{meas}}$)** for different stimulation amplitudes and durations.

* **Method.** Weighted least square on $I_{\text{meas}}$ and $V_{\text{meas}}$.

* **Resolution.** SciPy implementation of the L-BFGS-B algorithm

→ **Identifying** properties of contacts ($C_1$, $\tau_1$) and ($C_2$, $\tau_2$).

<figure><img src="image_3.png" /><figcaption>▲ **Sketch** of the bench test used to calibrate the electrode contact model.</figcaption></figure>

## › Computer model compared to experimental data

<figure><img src="image_4.png" /><figcaption>▲ **Lapicque curve** obtained after detection of a 50% capture ratio. Blue points are for 0% capture, and red points for 100% capture.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>▲ **Comparison of Lapicque curves** (solid lines) computed with different values of S (top) and $R_1$ (bottom). The **shaded regions** indicate where the **experimental capture threshold** is located, for different stimulation sites on the tissue wedge. ▼</figcaption></figure>

<figure><img src="image_6.png" /></figure>

### › Lapicque curve

In order to save battery, the energy delivered by the pacemaker must be just above the cut-off threshold between capture and non-capture.

* **Lapicque curve:** threshold of stimulation in the voltage-duration plane [2].

* Computed from **ratio of successful captures** in the 0D model with a **2D dichotomy**.

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

### › Animal and computer experiments

* **Two** wedge preparation of **sheep hearts** in a saline solution [5].

* Testing a **range of pulse durations and stimulus amplitudes** to localize the stimulation threshold.

* Scaling parameter **S** has a **great influence** (determines the amount of current seen per cm² of membrane).

* **Little influence** of the parameter **gext**

* Study the **influence of bio-electrodes parameters** (contact with tissue, not only a bath).

## › Next

### › 3D model of tissue slab surrounded by blood

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

* Compare experimental data with our 3D solution.

<figure><img src="image_7.png" /></figure>

* Equi-potential electrodes coupled with the device [4].
* Transparent boundary conditions on the box.
* Bidomain in the tissue ($u_i, u_e$).
* With bath loading in the blood ($u_e$).

### › Additional ex-vivo data to adjust the model

* Activation by optical mapping → conductivity distribution.

* Voltage measured by the lead.

* Geometries, fibers orientation and collagen distribution from 9.4T MRI.

<figure><img src="image_8.png" /><figcaption>▲ 3D lead and electric field line between the two electrodes.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>► Example of activation map obtained from optical mapping.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>▲ Example of mesh with implanted lead into a simple ventricular model.</figcaption></figure>

## References

1. Beeler, G.W., Reuter, H.: Reconstruction of the action potential of ventricular myocardial fibres. J Physiol (1977).

2. Blair, H.: On the intensity-time relations for stimulation by electric currents. JGP (1932).

3. Grimnes, S., Ørjan G Martinsen: Bioimpedance and Bioelectricity Basics (Third Edition). Academic Press, Oxford (2015).

4. Grimnes, S., Ørjan G Martinsen: Bioimpedance and Bioelectricity Basics (Third Edition). Academic Press, Oxford (2015).

5. Somersalo, E et al: Existence and Uniqueness of Electrode Models for Electric Current Computed Tomography. SIAP (1992).

université
de BORDEAUX

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Inria

Inserm
La science pour la santé
From science to health

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MicroPort

FIMH
2023
Lyon

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SIM
CARDIO
TEST

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