On the Hyperelastic Behavior of the Boar Diaphragmatic Tendon Membrane by Inflation Tests and Modeling

TL;DR

This study characterizes the hyperelastic behavior of porcine diaphragmatic tendons under biaxial loading, demonstrating that a transversely isotropic model best captures their nonlinear mechanical response.

Contribution

It introduces a transversely isotropic hyperelastic model tailored for the diaphragm tendon, improving the understanding of its anisotropic mechanical properties.

Findings

Fung model closely fit the nonlinear pressure-stretch response.

Humphrey-Yin model significantly improved data description over isotropic models.

Transversely isotropic contribution dominates the tissue's strain-energy response.

Abstract

Background: Despite the large variety of materials used to repair congenital diaphragmatic hernia (CDH), none has proven ideal due to complications and risk of recurrence. Understanding the mechanical behavior of the diaphragm's central tendon is essential for developing biomimetic prostheses. Objective: This study aims to characterize the hyperelastic behavior of the porcine diaphragmatic tendon under biaxial loading conditions. Methods: Biaxial hyperelastic response of the porcine diaphragmatic central tendon was characterized using bulge inflation tests combined with full-field stereo digital image correlation (3D-DIC). Principal stretches were extracted from the reconstructed three-dimensional geometry using a spherical-cap approximation, with corrections for clamping-induced pre-deformation. Several incompressible isotropic hyperelastic models (Neo-Hookean, Mooney-Rivlin, Yeoh and Fung) were first evaluated as phenomenological baselines. To account for the anisotropic mechanical signature of the tendon, a transversely isotropic hyperelastic formulation of the Humphrey-Yin type was implemented. This model represents an effective anisotropic response associated with the lamellar and collagen-rich structure of the tissue through its thickness, while assuming isotropy within the membrane plane. Results: The diaphragm tissue exhibited an exponential mechanical response. Neo-Hookean and Mooney-Rivlin models failed to capture the observed behavior, while the Yeoh model slightly overestimated nonlinearity. The Fung model provided the closest fit to the nonlinear pressure-stretch response, yet failed to reproduce the directional differences observed between meridional and circumferential stretches. The Humphrey-Yin model provided a markedly improved description of the experimental data over the full inflation range. Parameter identification revealed that the transversely isotropic contribution dominated the strain-energy response, highlighting the limitations of isotropic constitutive laws for modeling diaphragmatic tendon mechanics, even under macroscopically axisymmetric inflation. Despite specimen-to-specimen variability, no significant differences were observed between left and right diaphragm samples. Conclusion: Overall, this work demonstrates that effective anisotropic hyperelastic formulations are required to describe the biaxial mechanical behavior of the diaphragmatic central tendon under inflation loading. The proposed experimental-numerical framework provides a robust basis for biomechanical modeling and constitutes a first step toward the development of biomimetic prosthetic materials for diaphragmatic repair.