# Impact of Geometry on the Mechanical Behavior of Atrial Appendage Tissue: A Novel Experimental and Numerical Approach

Kundry Reibel, Claudia Cino, Baptiste Pierrat, Stéphane Avril, Nicolas Curt, Fanette Chassagne

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Kundry Reibel, Claudia Cino, Baptiste Pierrat, Stéphane Avril, Nicolas Curt, et al.. Impact of Geometry on the Mechanical Behavior of Atrial Appendage Tissue: A Novel Experimental and Numerical Approach. Multidisciplinary Biomechanics Journal, 2025, 50th congress of the.., 10.46298/mbj.16147. hal-05191699v2

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# Impact of Geometry on the Mechanical Behavior of Atrial Appendage Tissue: A Novel Experimental and Numerical Approach

Kundry Reibel<sup>a*</sup>, Claudia Cino<sup>b</sup>, Baptiste Pierrat<sup>a</sup>, Stéphane Avril<sup>a</sup>, Nicolas Curt<sup>a</sup>, Fanette Chassagne<sup>a</sup>

a Mines Saint-Etienne, INSERM, U1059 Sainbiose, F-42023 Saint-Etienne, France

b Università degli Studi di Palermo, Palermo, Italia

* Corresponding author: Kundry.reibel@emse.fr

Received date: 02/04/2025

Accepted date: 27/06/2025

Publication date: 27/10/2025

**Keywords:** atrial appendage, mechanical characterization, uniaxial testing, inverse identification

© 2025 The Authors

Licence CC-BY 4.0

Published by Société de Biomécanique

## 1. Introduction

Stroke is the third leading cause of mortality in France and is strongly associated with atrial fibrillation (AF), which increases the risk of thrombus formation in the left atrial appendage (LAA) by promoting blood stasis (N. M. Al-Saady, Obel, & Camm, 1999). The irregular shape and trabeculated structure of the LAA contribute to this phenomenon, making it a key target for stroke prevention strategies such as LAA closure. Finite element models have been developed to study the mechanical response of the left atrium and LAA, but most assume identical material properties for both (Zhang & Gay, 2008a). Although limited, experimental data on LAA mechanics show significant disparities. This variability is thought to arise mainly from three factors: tissue macrostructure (geometrical heterogeneities), microstructure (compositional heterogeneities, structural anisotropy), and inter-individual differences. However, these aspects have not been fully considered in the existing literature. This work aims to propose a new approach that combines experimental and numerical methods to assess the impact of geometry on the mechanical behavior of LAA tissue.

## 2. Methods

### 2.1 Uniaxial testing

Uniaxial tensile tests were performed on 80 samples from 20 fresh porcine hearts, with four samples per heart (proximal and distal from the right and left atrial

appendages). Samples (~15x15 mm²) were first measured with a caliper, then scanned optically in 3D to capture thickness heterogeneity. Half were tested longitudinally, the others transversely. Experiments were conducted in a saline bath using a tensile machine with a 20 N force sensor. A speckle pattern was applied for displacement tracking using custom Python scripts. Samples underwent eight preconditioning cycles up to 35% strain or 2N force at 1%/s strain rate, with final cycle data recorded at 10 Hz.

### 2.2 Inverse analysis using finite element modelling

For each sample, two finite element (FE) models were developed in FEBio Studio: an “idealized” model with homogeneous thickness based on caliper measurements, and a “scan” model incorporating heterogeneous thickness from 3D scans.

One side was fixed, while a prescribed displacement was imposed to the other side. The Veronda-Westmann (VW) isotropic constitutive law (1) was selected for its ability to capture nonlinearity using only two coefficients. This isotropic formulation enables assessment of the extent to which the observed anisotropy can be attributed to geometry alone.

$$ \psi = C_1 [e^{c_2(\tilde{T}_1 - 3)} - 1] - \frac{C_1 C_2}{2} (\tilde{T}_2 - 3) + U(J) \quad (1) $$

Inverse identification was conducted on **longitudinal samples** (separately for idealized and scan geometries)
by fitting the simulated force-displacement response to the corresponding experimental force data. The optimized material parameters $C_1^{\text{long}}$ and $C_2^{\text{long}}$ were then used to model the tensile test of the corresponding transverse models, to evaluate their predictive capability.

For comparison, an independent inverse identification was also performed on the transverse models.

## 2.3 Statistical analysis

A statistical analysis was conducted to evaluate the influence of four key sample parameters on the mechanical response of the tissue, by performing a one-way ANOVA test on the material coefficients obtained from the inverse identification. These parameters were: (1) heart specimen (N=20), (2) anatomical side (right vs. left appendage), (3) sampling location (proximal vs. distal), and (4) trabeculae orientation relative to loading (longitudinal vs. transverse).

## 3. Results and discussion

Force-displacement curves (Figure 1b) show good agreement between the experimental and numerical results in the longitudinal direction, indicating that the Verona-Westmann constitutive law effectively captures the nonlinear behavior of the response.

However, the transverse numerical model shows deviations from the experimental results. The model based on the 3D scan geometry provides a better fit than the idealized version, with a lower mean RMSE (63.6 [3.7; 389.5] mN) compared to the idealized model (81.4 [8.2; 496.4] mN). These findings highlight the significant impact of geometry on tissue mechanics. However, the geometry alone is not sufficient to explain the anisotropic response of the tissue, as for some samples the discrepancies between the experimental and numerical results are large. Future work will explore simultaneous inverse identification for both orientations to optimize parameter fitting and better capture anisotropic effects. Additional efforts will focus on evaluating the statistical significance of discrepancies between experimental and the numerical models. Future work will investigate the tissue's microstructural composition and organization to inform the use of adapted anisotropic constitutive laws and assess the role of fiber orientation.

Preliminary ANOVA results showed no significant influence of heart specimen, anatomical side, trabeculae orientation, or sampling position on identified parameters. Trabeculae orientation had a marginal effect on

<figure><img src="image_2.png" /><figcaption>**Figure 1:** Example on one appendage. a) The idealized and scan geometries of the longitudinal sample (top) and the transverse sample (bottom). b) Force-displacement curves for longitudinal data (black), and transverse data (pink). Experimental data (circles) are compared with numerical results from both idealized (dotted lines) and scan (continuous lines) models.</figcaption></figure>

$C_1$ (p=0.116) but was not statistically significant. Future analyses will incorporate all 80 samples to refine statistical models and investigate potential interactions. Additionally, trabeculae orientation definition remains challenging due to trabecular misalignment. To address this, an image analysis of the thickness distribution could be performed to assess the primary orientation of the trabeculae.

## 4. Conclusions

This work highlights the variability observed in AA tissues mechanics and introduces a novel experimental- numerical approach assessing the influence of thickness distribution. The findings demonstrate that considering geometry is crucial for accurate mechanical analysis. Future work will investigate multiscale fibrous architecture of the tissue through histology and microCT imaging.

### Contributor Roles

Kundry Reibel: Conceptualization, Methodology, Writing original draft, Writing – review & editing,
Software, Investigation, Visualization, Supervision, Formal analysis; Claudia Cino: Conceptualization, Methodology, Software, Writing – review & editing; Baptiste Pierrat: Conceptualization, Methodology, Software, Supervision, Writing – review & editing; Stéphane Avril: Conceptualization, Resources, Supervision, Writing – review & editing; Nicolas Curt: Conceptualization, Methodology, Resources, Writing – review & editing; Fanette Chassagne: Conceptualization, Methodology, Investigation, Supervision, Resources, Funding acquisition, Project administration, Writing – review & editing.

## References

Al-Saady, N., Obel, O., & Camm, A. (1999). Left atrial appendage: Structure, function, and role in thromboembolism. *Heart, 82*(5), 547–554. https://doi.org/10.1136/hrt.82.5.547

Bellini, C., & Di Martino, E. S. (2012). A mechanical characterization of the porcine atria at the healthy stage and after ventricular tachypacing. *J Biomech Eng, 134*(2), 021008. https://doi.org/10.1115/1.4006026

Javani, S. (2016). *Regional mechanical properties and microstructure of ovine heart chambers* (PhD Thesis, University of Denver). University of Denver.

Jernigan, S. R., Buckner, G. D., Eischen, J. W., & Cormier, D. R. (2007a). Finite element modeling of the left atrium to facilitate the design of an endoscopic atrial retractor. *Journal of biomechanical engineering, 129*(6), 825–837. https://doi.org/10.1115/1.2801650

Zhang, L. T., & Gay, M. (2008a). Characterizing left atrial appendage functions in sinus rhythm and atrial fibrillation using computational models. *Journal of Biomechanics, 41*(11), 2515–2523. https://doi.org/10.1016/j.jbiomech.2008.05.012