# In silico Assessment of Arrhythmia Inducibility Dependence on Stimulus Location using Calibrated MR-based Infarcted Heart Models

Jairo Rodríguez Padilla, Rafael Silva, Buntheng Ly, Graham Wright, Mihaela Pop, Maxime Sermesant

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## To cite this version:

Jairo Rodríguez Padilla, Rafael Silva, Buntheng Ly, Graham Wright, Mihaela Pop, et al. In silico Assessment of Arrhythmia Inducibility Dependence on Stimulus Location using Calibrated MR-based Infarcted Heart Models. FIMH 2025 - 13th Functional Imaging and Modeling of the Heart International Conference, Jun 2025, Dallas, United States. 10.1007/978-3-031-94559-5_9. hal-05119965

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Distributed under a Creative Commons Attribution 4.0 International License
In silico Assessment of Arrhythmia Inducibility
Dependence on Stimulus Location using
Calibrated MR-based Infarcted Heart Models

Jairo Rodríguez Padilla¹,²[0000-0002-2013-1898], Rafael
Silva¹[0000-0001-6254-7843], Buntheng Ly², Graham Wright³, Mihaela Pop¹,³,
and Maxime Sermesant¹,²[0000-0002-6256-8350]

¹ Centre Inria d'Université Côte d'Azur, Epione Team, Sophia Antipolis, France

² IHU-Liryc, Université de Bordeaux, France

³ Sunnybrook Research Institute, University of Toronto, Canada
jesus-jairo.rodriguez-padilla@inria.fr

**Abstract.** Personalized computer modeling is a powerful, effective and non-invasive tool, that can be used to simulate the inducibility of ventricular tachycardia (VT) in scar-related cases. In this in silico study we propose a robust pipeline for VT risk prediction based on preclinical digital twins developed and parameterized from high resolution in vivo MR images and electro-anatomical datasets acquired in 5 pigs with chronic infarction. Specifically, we employed a modified Mitchell-Schaeffer computational model and calibrated per case the key parameter that tunes the action potential duration using the recorded intracardiac ECGs. To validate the predictions, we compared the measured VT cycle length (CL) per case to the simulated VTCL obtained from each calibrated digital twin by precisely replicating the experimental inducibility protocol. We further defined 100 pacing sites on the right and left endocardial surfaces, respectively, and investigated the impact of pacing location on the VT inducibility. Overall, results demonstrated that our pipeline was able to accurately predict VT inducibility after calibration, reproducing the experimental VT with a small error in CLs (i.e., < 4% in 4 out of the 5 cases). In particular, the right ventricular pacing sites showed more susceptibility to sustained VT: (3/30 (10%), 1/30 (3.3%), 5/30 (16.7%) and 6/30 (20%) for Pigs # 1, 2, 3 and 4, respectively. Additionally, it was possible to induce sustained VT from the left ventricular surface for Pig #2 (5/70 (7.14%), #4 (3/70 (4.28%) and #5 (1/70 (1.4%), respectively. Future work will focus on implementing the numerical scheme on GPUs, to reduce the current simulation times (5h/case) and achieve clinical tractability enabling the pipeline translation into routine evaluations of VT risks in post-infarction patients.

**Keywords:** Electrophysiology · Modeling · Simulations · Finite Element · Personalization
# 1 Introduction

Recent advances in cardiac imaging and computational tools have led to the development of new in silico methods, allowing researchers to explore in great detail many complex electrophysiology (EP) phenomena by employing person- alized heart models. For instance, models have been proposed to tackle critical issues relevant to arrhythmia management, helping us better understand the ac- tion potential dynamics [1, 2], role of fiber anisotropy [3], genesis of scar-related ventricular tachycardia (VT) [4–9] - a major cause of sudden cardiac death, while also providing more effective guidance for ablation therapy planning [10] [11]. However, such 3D cardiac digital twins are often built from MR images acquired at a poor clinical spatial resolution [12], or from X ray-based CT scans which often cannot identify scar involvement within the right ventricle, RV [13]. Several of these models represent the EP phenomena at (sub)cellular level and thus need expensive computational resources to solve sophisticated equations describing the action potential propagation and VT wave genesis. Moreover, the parameters in these complex physiologial (subcellular/ionic) models cannot be calibrated from clinical measurements recorded at organ scale. On the other side, the parameter calibration in the macroscopic models could be affected by the sparsity and noise present in clinical EP signals, such as those obtained by non-contact catheters [14]. Thus, to accurately predict in silico the VT risk, it is essential not only to acquire structural imaging data using adequate spatial resolution for constructing detailed 3D anatomical models, but also to carefully calibrate the EP model parameters from proper measurements of tissue electrical properties.

Clinically, a critical burden in the EP lab is the invasiveness of the VT risk evaluation protocol performed in scar-related patients, along with the limited surfacic information. The VT substrate is comprised of viable cells with altered functionality and located at the interface between scar and healthy tissue. These tissue zones create anatomic 'reentry circuits' allowing rapid VT waves to override normal propagation of action potentials and triggering fast heart beats. Using catheter-based electro-anatomical maps, the healthy and heterogeneous infarct tissues are differentiated based on bipolar voltage amplitude: dense unexcitable scars (<0.5mV), VT substrate (0.5-1.5mV) and healthy myocarium (>1.5mV). This catheter-based procedure takes hours and employs a mapping procedure to identify the VT substrate followed by a rapid pacing of the heart, typically only from one site (e.g. the endocardial RV-apex) which is often ineffective. With this respect, high fidelity virtual models that simulate VT inducibility from various pacing locations may help the operator positon the pacing catheter onto precise sites that lead to VT.

The aim of this work was to implement a robust computational pipeline to build and calibrate digital twins able to accurately predict VT inducibility using high-resolution preclinical MRI-EP datasets. Novel aspects of the work include: i) a data-driven macroscopic model personalization method using intracardiac electrograms (iECGs) from very dense contact catheter-based electro-anatomical maps - focusing on the parameter tunning the AP duration, which strongly
controls arrhythmogenesis; ii) integration of an atlas of fiber directions (instead of rule-based fibers) into the 3D heart models; iii) a fully Phyton-coded FEM implementation for the numerical solver in FEniCSx. We validated the pipeline by comparing the recorded VT cycle lengths to those obtained via simulations in which we precisely replicated the experimental VT inducibility protocol. We then further studied the impact of pacing location on the induced VT, by selecting 100 equidistant stimulation points on the RV and LV endocardial surfaces. Our pipeline may help in identification of cases at risk of potentially lethal scar-related VT.

## 2 Methodology

Figure 1 presents a schematic diagram of our modelling pipeline to predict VT risk. Briefly, the main steps of the workflow were the following: i) 3 main tissue types (healthy, scar and VT substrate) were segmented in MR images; ii) the segmented stacks were used to construct anatomic meshes with 3 zones integrated and the model parameter tuning the action potential duration was calibrated from iECGs recordings; iii) comprehensive in silico study of VT inducibility using a precise stimulation protocol as in the EP experiment, with the virtual VT induction being performed from a total of 101 pacings sites defined on the LV and RV endocardial surfaces, one at a time (note that the first simulation replicated the site used in the real EP study); iv) analysis and classification of the VTs (sustained vs non-sustained) induced from the different stimulation points.

<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Workflow of 3D MR-based biventricular model construction and the in silico testing of stimulation protocols from different pacing sites to study VT inducibility. GZ: Grey zone.</figcaption></figure>

The following sections describe each of the steps comprising our pipeline.
## 2.1 MRI-EP data collection and 3D heart model generation

All imaging and interventional studies were carried out under general anesthesia, with Sunnybrook Research Ethics Board approval. Cardiac magnetic resonance (MR) imaging data was acquired in n = 5 swine with chronic infarction (resembling human pathophysiology), by employing a 3D late gadolinium enhanced (LGE) method at 1.4mm isotropic spatial resolution. The VT substrate was defined in LGE images by a grey zone (GZ) of intermediate signal intensity (SI) between healthy myocardium and dense scar. The three tissue types (i.e., scar, GZ, and healthy) forming anatomic VT circuits, were segmented using a conventional full width at half maximum (FWHM) method [15, 16], which is clinically accepted. For each LGE slice, a ROI was manually drawn on the infarcted area that visually coresponded to a maximum SI (Matlab). To output tissue maps, we used the following definitions: SI(scar) > 0.5*peak(scar) and peak(remote) < SI(GZ) < 0.5*peak(scar), where peak(scar) is the peak of SI of all infarcted pixels while remote refers to healthy myocardium remote from the scar (e.g. in the free wall).

Next, we generated 3D biventricular digital twin models from the segmented images. Fine meshes of ≈ 800K elements (average element size of 0.45 mm) were created using Mmg<fnref n="4" /> plattform. For myocardial anisotropy (i.e., fiber directions), we integrated into meshes an atlas of fiber directions constructed from ex vivo diffusion tensor MR images of pig hearts [17].

In each animal, a CARTO3 system (Biosense Webster, J&J, USA) was used to perform an x-ray guided catheter-based electroanatomical mapping of the LV-endocardium during sinus rhythm, along with a VT inducibility study mimicking clinical protocols (i.e., fast S1 pacing followed by one or more extra-stimuli with decreasing coupling interval).

## 2.2 Mathematical equations and numerical schemes

To simulate the propagation of action potential (AP) wave we used a monodomain formulation of a modified Mitchell-Schaeffer (MS) model as in [18]. This modification of the original MS model introduces an additional parameter, λ, that allows us to control the degree of excitability in a region of interest (i.e., tissue type). The evolution equations of the system are given by:

$$ \begin{aligned} \frac{\partial u}{\partial t} &= \nabla \cdot (D \nabla u) + \frac{hu(u-\lambda)(u_{max}-u)}{\tau_{in}} - \frac{u}{\tau_{out}} + J_{stim}, \\ \frac{\partial h}{\partial t} &= \epsilon(u, h)(h_{\infty}(u) - h), \end{aligned} \quad (1) $$

$$ \epsilon(u, h) = \frac{1}{\tau_{close}} + \frac{\tau_{close} - \tau_{open}}{\tau_{close} \cdot \tau_{open}} h_{\infty}(u), $$

$$ h_{\infty}(u) = \frac{1}{2}(1 - \operatorname{sgn}(u - u_{gate})) $$

<footnote n="4">⁴ http://www.mmgtools.org/</footnote>
where $u$ is the normalized transmembrane voltage (i.e., the action potential) variable, $h$ is the gating variable which makes the gate open and close (corresponding to depolarization and repolarization phases), $J_{stim}$ is the stimulation current at the pacing location. The parameters $\tau_{in}$ and $\tau_{out}$ define the repolarization phase, whereas the constants $\tau_{open}$ and $\tau_{close}$ regulate the gate opening or closing depending on the changeover voltage $u_{gate}$ and $u_{max}$ controls the maximum amplitude of AP. $D = \Lambda A \Lambda^T$ is the diffusion tensor, with $A = \text{diag}(d_{11}, d_{22}, d_{33})$ the diagonal matrix having the diffusion coefficient values parallel with and perpendicular to the fibers; $\Lambda$ the basis representing the fiber directions from the atlas. The anisotropy ratio used in our study was 1:2.7 [19].

To numerically solve system (1), we used an IMEX scheme, specifically, a second-order, semi-implicit scheme (modified Adam-Bashford and Crank-Nicolson, equation 15 in [20]). The diffusion term is implicitly integrated, whereas the reaction term is explicitly computed. The resulting discretized system thus takes the following form:

$$ \frac{u^{n+1}-u^n}{\Delta t} = \left( \frac{9}{16}\nabla \cdot (D\nabla u^{n+1}) + \frac{3}{8}\nabla \cdot (D\nabla u^n) + \frac{1}{16}\nabla \cdot (D\nabla u^{n-1}) \right) + \frac{3}{2} \left( \frac{h^n(u^n)^2(1-u^n)}{\tau_{in}} - \frac{u^n}{\tau_{out}} \right) - \frac{1}{2} \left( \frac{h^{n-1}(u^{n-1})^2(1-u^{n-1})}{\tau_{in}} - \frac{u^{n-1}}{\tau_{out}} \right) + J_{stim}, \quad (2) $$

$$ \frac{h^{n+1}-h^n}{\Delta t} = \frac{3}{2} \left( \epsilon(u^n, h^n)(h_\infty(u^n) - h^n) - \frac{1}{2} \left( \epsilon(u^{n-1}, h^{n-1})(h_\infty(u^{n-1}) - h^{n-1}) \right) \right). $$

Let us consider the following spaces:

$$ V = \{v \in H^1(\Omega) | \frac{\partial v}{\partial n} = 0 \text{ on } \partial\Omega\}, $$

$$ \hat{V} = \{v \in H^1(\Omega) | v = 0 \text{ on } \partial\Omega\}, $$

where $H^1(\Omega)$ denotes the Sobolev space containing functions $v$ such that $v^2$ and $|\nabla v|^2$ have finite integrals over $\Omega$. Let $v_1, v_2 \in \hat{V}$ be two test functions. Multiplying the first and second equations of system (2) by $v_1$ and $v_2$, respectively, and after using integration by parts to treat the diffusion part of the first equation and the fact that we use Neumann boundary conditions $(\frac{\partial u}{\partial n} = 0, \frac{\partial h}{\partial n} = 0 \forall u, h \in \partial\Omega)$,
solving system (1) translates into finding $(u^{n+1}, h^{n+1}) \in V \times V$ such that:

$$
\begin{align}
F = \int_{\Omega} \Delta t^{-1}(u^{n+1} - u^n)v_1 dx &+ \int_{\Omega} (\Delta t^{-1}(h^{n+1} - h^n)v_2) dx \nonumber \\
&+ \frac{9}{16} \int_{\Omega} D \nabla u_1^{n+1} \nabla v_1 dx + \frac{3}{8} \int_{\Omega} D \nabla u_1^n \nabla v_1 dx + \frac{1}{16} \int_{\Omega} D \nabla u_1^{n-1} \nabla v_1 dx \nonumber \\
&+ \frac{3}{2} \int_{\Omega} \left( -\frac{h^n(u^n)^2(1-u^n)}{\tau_{in}} + \frac{u^n}{\tau_{out}} \right) v_1 dx \nonumber \\
&- \frac{1}{2} \int_{\Omega} \left( -\frac{h^{n-1}(u^{n-1})^2(1-u^{n-1})}{\tau_{in}} + \frac{u^{n-1}}{\tau_{out}} \right) v_1 dx \tag{3} \\
&+ \frac{3}{2} \int_{\Omega} \left( -\epsilon(u^n, h^h)(h_{\infty}(u^n) - h^n) \right) v_2 dx \nonumber \\
&- \frac{1}{2} \int_{\Omega} \left( -\epsilon(u^{n-1}, h^{h-1})(h_{\infty}(u^{n-1}) - h^{n-1}) \right) v_2 dx \nonumber \\
&+ \int_{\Omega} J_{stim} v_1 dx = 0, \nonumber
\end{align}
$$

$\forall v_1, v_2 \in \hat{V} \times \hat{V}$, with $V, \hat{V}$, trial and test functions spaces, respectively. The implementation was done in FEniCSx<fnref n="5" /> [21–23]. This implementation leverages on MPI paralellization. Another advantage is that the code is written entirely in the Python language, thus being very flexible and easy to adapt to different scenarios. All simulations in our study were run on a PC equipped with an intel Xeon Gold 6138 CPU (40 cores). Simulating a sustained reentry (at least 10 seconds of simulation) takes approximately 5 hours four the biventricular geometries.

## 2.3 Model calibration and simulations set-up

There are eight model parameters in total: $\tau_{in}$, $\tau_{out}$, $\tau_{open}$, $\tau_{close}$, $u_{gate}$, $u_{max}$, $\lambda$ and $d_{11}$. A sensitivity analysis performed for each parameter allowed us to identify that the parameter $\tau_{close}$ is the one predominantly controling APD (the duration of AP). Thus, we fixed the other parameters $\tau_{in}$, $\tau_{out}$, $\tau_{open}$ and $u_{gate}$ in all cases. Additionally, for healthy tissue zone we assigned $u_{max} = 1$ and $\lambda = 0.01$, whereas for GZ we used $u_{max} = 0.9$ and $\lambda = 0.2$ in order to reduce tissue excitability. The diffusion coefficient $D$ ($d_{11}$) was initially calibrated per case using recorded CARTO3 activation maps. The coefficient for the sheet and cross-sheet directions are obtained by dividing by 2.7 ($d_{11}/2.7$).

From each recorded endocardial iEGM we extracted activation-recovery interval (ARI), a clinical surrogate of action potential duration (APD), which we further used to calibrate our model parameters for prediction of accurate AP waves per individual case. Figure 2 shows a snapshot of an annotated iEGM (left panel), and the resulting calibrated APD (right panel).

We calibrated APDs by modifying $\tau_{close}$ in the model, based on ARI values extracted from the recorded intracardiac ECGs, as in [24–26]. We then conducted

<footnote n="5">⁵ https://fenicsproject.org/</footnote>
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Left panel: Example of ARI extraction from an iEGM signal; top plot: iEGM signal with annotated activation (green points) and repolarization (blue points) times; middle plot: Derivative of the iEGM signal used for the annotation of the activation part; bottom plot: Lead II and the detected fiducials, namely the R-peaks (green crosses) and W-wave limits (blue crosses). Right panel: Calibrated APDs.</figcaption></figure>

an in silico study, replicating exactly the VT stimulation protocol performed in the EP experiment. Table 1 summarizes the VT stimulation protocol per case and Table 2 shows the final calibrated parameters. Once we induced VT in the model using the same stimulation protocol and pacing site as in the real EP experiment, we repeated the same VT protocol for each virtual pacing site. In total, we defined 70 equally spaced points on the LV surface and 30 points on the RV, respectively. The CL of simulated VTs were recorded per case, along with the VT type: sustained or not sustained (hereto, sustained VT was defined by reentry wave self-perpetuating for at least 10s, as in [27]).

**Table 1.** Stimulation protocols used to induce VT per case in the preclinical EP experiments, mimicking typical inducibility tests performed in the clinical cath-lab. Note that the same stimulation protocols consisting in rapid pacing by 8xS1 stimulus followed by combinations of extrastimuli (i.e., S2, S2-S3, or S2-S3-S4 with decreased coupling interval) were then used in the in silico computational study, in order to precisely replicate the experimental conditions.

<table><thead><tr><th>Pig #</th><th>VT protocol: 8xS1 followed by extra-stimuli at varying coupling intervals</th></tr></thead><tbody><tr><td>1</td><td>8 S1 at 400 ms, 1 S2 at 210 ms, 1 S3 at 180 ms</td></tr><tr><td>2</td><td>8 S1 at 350 ms, 2 S2 at 220 ms, 1 S3 at 210 ms</td></tr><tr><td>3</td><td>8 S1 at 300 ms, 2 S2 at 190 ms, 1 S3 at 180 ms</td></tr><tr><td>4</td><td>8 S1 at 300 ms, 4 S2 at 180 ms</td></tr><tr><td>5</td><td>8 S1 at 290 ms, 1 S2 at 230 ms, 2 S3 at 190 ms, 1 S4 at 180 ms</td></tr></tbody></table>
<table><caption>**Table 2.** Values of parameters $\tau_{close}$ and $d_{11}$ per case, while the other parameters were fixed in all simulations: $\tau_{in} = 0.0003$, $\tau_{out} = 0.006$, $\tau_{open} = 0.12$, $u_{gate} = 0.13$. In all cases, $\lambda$ was set to 0.01 in healthy tissue and 0.2 in GZ, while $u_{max}$ was set to 1 in healthy tissue and 0.9 in GZ, respectively. AVG denotes the average values of all 5 subjects.</caption><thead><tr><th>Pig #</th><th>Parameter</th><th>Value for Healthy</th><th>Value for GZ</th></tr></thead><tbody><tr><td>1</td><td>τ<sub>close</sub></td><td>0.093</td><td>0.175</td></tr><tr><td>1</td><td>d<sub>11</sub></td><td>3.54</td><td>0.25</td></tr><tr><td>2</td><td>τ<sub>close</sub></td><td>0.101</td><td>0.206</td></tr><tr><td>2</td><td>d<sub>11</sub></td><td>2.55</td><td>0.25</td></tr><tr><td>3</td><td>τ<sub>close</sub></td><td>0.093</td><td>0.235</td></tr><tr><td>3</td><td>d<sub>11</sub></td><td>2.95</td><td>0.05</td></tr><tr><td>4</td><td>τ<sub>close</sub></td><td>0.081</td><td>0.162</td></tr><tr><td>4</td><td>d<sub>11</sub></td><td>5.85</td><td>0.45</td></tr><tr><td>5</td><td>τ<sub>close</sub></td><td>0.106</td><td>0.211</td></tr><tr><td>5</td><td>d<sub>11</sub></td><td>1.83</td><td>0.05</td></tr><tr><td>AVG</td><td>τ<sub>close</sub></td><td>0.095</td><td>0.198</td></tr><tr><td>AVG</td><td>d<sub>11</sub></td><td>3.34</td><td>0.21</td></tr></tbody></table>

Comparison between simulated and measured (i.e., ground truth) VT cycle length per case, and the corresponding percent error.

<table><thead><tr><th>Pig #</th><th>Simulated</th><th>Measured</th><th>Error</th></tr></thead><tbody><tr><td>1</td><td>192 ms</td><td>190 ms</td><td>2 ms (1.1 %)</td></tr><tr><td>2</td><td>218 ms</td><td>226 ms</td><td>8 ms (3.5 %)</td></tr><tr><td>3</td><td>186 ms</td><td>193 ms</td><td>7 ms (3.6 %)</td></tr><tr><td>4</td><td>190 ms</td><td>170 ms</td><td>20 ms (11.7 %)</td></tr><tr><td>5</td><td>204 ms</td><td>210 ms</td><td>6 ms (2.8 %)</td></tr></tbody></table>

## 3 Results and Discussion

In Table 2.3, we report the measured VTCL for each case, as well as the simulated VTCL obtained with the stimulation protocols listed in Table 1. Overall the % error was less than 4% in four pigs (i.e., 1.1% in Pig #1; 3.5% in Pig #2; 3.6% in Pig #3; and 2.8% in Pig #5) and quite large 11.7% in Pig #4. The large discrepancy in VTCL for Pig #4 could be caused by heterogeneities in regional CV values, requiring further refinement of d-values per AHA regions.

Exemplary simulation results from one case (Pig #5) are shown in Fig. 3. The first row shows the simulated action potential output at four time frames selected from a simulated sustained VT with reentrant pattern, for which the stimulus site was placed on the anterior side of the LV endocardium, near the heart base. The second row shows an example of a non-sustained reentry where the stimulus site was placed on the apex of LV-endocardial surface. Typically, non-sustained VTs were self-terminated due to wave breaks or wave annihilation. The third row shows an example of a non-inducible VT, for which the stimulus location was placed on the free wall of the RV-endocardium. Lastly, the bottom
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Exemplary results of simulated AP wave, selected from one case (Pig #5). First row: sustained VT pacing from the anterior side of LV-endocardium, near the base; Second row: non-sustained VT, pacing site located near the endocardial LV-apex; Third row: Non-inducible VT, pacing from the RV free wall. The yellow star indicates the location of pacing stimulus. Bottom row: AP waves output at the same location corresponding to the simulations shown in the above three rows (i.e., sustained VT, non-sustained VT and non-inducible VT). The dotted vertical line indicates the end of stimulation protocol.</figcaption></figure>

row shows three examples of computed AP waves (all traces recorded from the same node), corresponding to the simulations illustrated in the first three rows. Notably, simulations performed after the APD in the model was calibrated based on the average ARI value (computed from the extracted ARIs in all cases), did not lead to inducible VT. This result highlights the essential requirement of subject-specific calibrations.

Pacing from the LV endocardial surface in Pigs #1 and #3 it was only possible to induce a non-sustained VT from one stimulus location. On the contrary, in Pigs #2, #4 and #5 there were five, three and one sites, respectively, from which a sustained VT could be virtually induced. Remarkably, Pig #5 showed the most susceptibility to induce reentries (40 out of 70 locations, 55.71%). Table 3 summarizes the results obtained by defining the pacing sites on the LV-endocardium.
<table><caption>**Table 3.** Summary of the VT classification per case, for the pacing sites placed on the LV-endocardial surface.</caption><thead><tr><th>Pig #</th><th># Non inducible</th><th># Reentry not sustained</th><th>Sustained reentry</th></tr></thead><tbody><tr><td>1</td><td>69 / 70 (98.58%)</td><td>1 / 70 (1.42%)</td><td>0</td></tr><tr><td>2</td><td>54 / 70 (77.15%)</td><td>11 / 70 (15.71%)</td><td>5 / 70 (7.14%)</td></tr><tr><td>3</td><td>69 / 70 (98.58%)</td><td>1 / 70 (1.42%)</td><td>0</td></tr><tr><td>4</td><td>65 / 70 (92.85%)</td><td>2 / 70 (2.85%)</td><td>3 / 70 (4.28%)</td></tr><tr><td>5</td><td>30 / 70 (42.86%)</td><td>39 / 70 (55.71%)</td><td>1 / 70 (1.4%)</td></tr></tbody></table>

<table><caption>**Table 4.** Summary of the VT classification per case, for pacing sites placed on RV.</caption><thead><tr><th>Pig #</th><th># Non inducible</th><th># Reentry not sustained</th><th>Sustained reentry</th></tr></thead><tbody><tr><td>1</td><td>27 / 30 (90 %)</td><td>0</td><td>3 / 30 (10%)</td></tr><tr><td>2</td><td>21 / 30 (70 %)</td><td>8 / 30 (26.7%)</td><td>1 / 30 (3.3%)</td></tr><tr><td>3</td><td>25 / 30 (85.3%)</td><td>0</td><td>5 / 30 (16.7%)</td></tr><tr><td>4</td><td>24 / 30 (80 %)</td><td>0</td><td>6 / 30 (20 %)</td></tr><tr><td>5</td><td>16 / 30 (53.3%)</td><td>14 / 30 (46.7 %)</td><td>0</td></tr></tbody></table>

Pacing from the RV endocardial surface was noticeably more prone to induce reentrant VT. In Pig #1, there were 3 sites from which sustained VT with reentry pattern was induced (representing 10 % of all points). In Pigs #2, #3 and #4, it was possible to induce a sustained VT from one, five and six out of 30 sites accounting for 3.3%, 16.7% and 20% of all locations, respectively. Again, in Pig #5 VT was generated in 14/30 (46.7%) of all locations; however, only one pacing site led to a sustained reentrant VT. Table 4 summarizes the simulation results obtained for pacing sites selected on the RV-endocardium. Finally, simulation results showed that Pig #5 was the most susceptible case to VT inducibility. Figure 4 illustrates the pacing locations used for each ventricle in the virtual study. In purple, we indicated pacing sites for which VT was not induced, while the remaining yellow points indicate the pacing sites that induced VT waves. The bottom frame in Fig 4 shows the box plot of VTCL values per case, where VTs where classified in non-sustained (blue) and sustained (red). We observed that in Pigs #1 and #4, the median VTCL values obtained for non-sustained VTs was larger (300 and 387.5 ms, respectively) than that of sustained VTs (204 and 325.34 ms, respectively). In Pigs #2, #3 and #5, the difference in the median VTCL in non-sustained VTs (268.42, 240.5 and 268 ms, respectively) vs. sustained VTs (279.16, 237.16 and 278.27 ms, respectively) was less noticeable.

Interestingly, in all cases there were pacing sites not closely located relative to GZ or scar, which still led to sustained VT. Thus, our future efforts will focus on a deeper analysis regarding the (geodesic) distance from the pacing points that induce VT to the reentry circuits, to help us better understand if there is a direct correlation between the GZ/scar and the points triggering VT.

We acknowledge that our study has several limitations. First the pipeline was tested using a small preclinical dataset; thus, precluding a deeper statisti-
cal analysis. The model parameterization per case (i.e., APD calibration from iECGs) needs invasive EP data; thus, our current digital twins cannot accurately predict the VT risk prior to the EP mapping study, as demonstrated by the simulations using average ARI values. In addition, the current computational time ( 5h/case) is not clinically tractable. This is important for translating the pipeline into routine clinical procedures. Thus, future work will implement the numerical solver on GPUs, which will considerably reduce the simulation time and may enable real-time intraprocedural predictions during the EP study.

4 Conclusion

Our in silico study highlights the importance of data-driven model personaliza-
tion when developing high-fidelity image-based digital heart twins. For compu-
tational biophysical EP models that employ macroscopic formalisms, we sug-
gest that a proper calibration of APD parameter per individual heart from EP
measurements is critical in order to enable accurate predictions of VT risk, po-
tentially lethal VT (i.e., short VTCL), as well as VT type (sustained VT vs.
non-sustained VT). Moreover, the multi-site pacing scheme demonstrated that
sustained VTs can be induced from various locations. Such schemes may help the
clinical operators by providing alternative scenarios for the navigation of pacing
catheter onto ventricular sites of easier access, in order to induce VT.

**Acknowledgments.** This work has received funding from the European Union Horizon 2020 Research and Innovation Program SimCardioTest (101016496), from the French government through the National Research Agency (ANR) projects PEPR Digital Health ChroniCardio (22-PESN-0015), 3IA Côte d'Azur and IA Cluster (ANR-19-3IA-0002 and ANR-23-IACL-0001), as well as a Canadian CIHR project grant (PJT 153212) and a Canada Foundation for Innovation research infrastructure grant.

The authors are also grateful to the OPAL infrastructure from Université Côte d'Azur for providing computational resources and associated support.

**Disclosure of Interests.** The authors have no competing interests to declare that are relevant to the content of this article.
<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Top frames: Pacing sites that induced VT (either a reentry with single or multiple rotations of the waves, or sustained VT lasting > 10s). Purple points indicate virtual pacing locations that did not induce VT, while yellow points indicate virtual sites that led to successfully inducing VT. Bottom frame: box plot showing the computed VTCL for all sustained and non-sustained reentrant VTs per case.</figcaption></figure>
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