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arxiv: 2605.19547 · v1 · pith:6DGQYI3Vnew · submitted 2026-05-19 · ⚛️ physics.med-ph · physics.class-ph

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

R. Anwar (UFE , LMGC) , J. Vasquez-Villegas , S. Le Floc'h (LMGC) , P. Royer (LMGC) , N. Bahlouli (ICube) , Christiane Wagner-Kocher (LMGC , BBB) This is my paper

Pith reviewed 2026-05-20 02:28 UTC · model grok-4.3

classification ⚛️ physics.med-ph physics.class-ph
keywords hyperelasticitydiaphragmatic tendoninflation testtransversely isotropicHumphrey-Yin modelbiaxial loadingporcine diaphragmbiomechanical modeling
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The pith

The Humphrey-Yin transversely isotropic hyperelastic model captures the biaxial hyperelastic response of the porcine diaphragmatic tendon better than isotropic models.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper characterizes the mechanical properties of the central tendon in the porcine diaphragm using bulge inflation tests and digital image correlation. It evaluates several hyperelastic models and finds that isotropic ones like Neo-Hookean and Mooney-Rivlin fail to describe the exponential response and directional differences, while the Humphrey-Yin transversely isotropic model fits the data much better across the full range of inflation. A sympathetic reader would care because this understanding is needed to create better biomimetic materials for repairing congenital diaphragmatic hernias, where current patches have high complication rates. The work shows that anisotropy must be accounted for even in macroscopically symmetric loading due to the tissue's lamellar structure.

Core claim

The diaphragm tissue exhibited an exponential mechanical response. While isotropic models struggled, particularly in reproducing directional differences between meridional and circumferential stretches, the Humphrey-Yin transversely isotropic hyperelastic model provided a markedly improved description of the experimental data over the full inflation range, with the transversely isotropic contribution dominating the strain-energy response.

What carries the argument

The Humphrey-Yin transversely isotropic hyperelastic formulation, which represents an effective anisotropic response associated with the lamellar and collagen-rich structure through the thickness while assuming isotropy within the membrane plane.

If this is right

  • The tissue shows exponential stiffening under biaxial loading.
  • Isotropic hyperelastic models are insufficient for accurate modeling of this tendon.
  • The transversely isotropic contribution dominates the strain energy.
  • No significant mechanical differences exist between left and right diaphragm samples.
  • This framework can support biomechanical modeling for prosthetic development.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This suggests that similar anisotropic modeling may be necessary for other collagen-rich membranes in the body.
  • Future work could test the model under different loading conditions like uniaxial tension to confirm its generality.
  • Improved material models could reduce recurrence rates in CDH repairs by better matching native tissue mechanics.
  • Validating the spherical cap approximation with more advanced strain mapping techniques would strengthen the results.

Load-bearing premise

The spherical-cap approximation for extracting principal stretches from the reconstructed 3D geometry, along with corrections for clamping-induced pre-deformation, accurately represents the local deformation state throughout the test.

What would settle it

If full-field strain measurements without the spherical-cap approximation show that the Humphrey-Yin model no longer fits the pressure-stretch data significantly better than isotropic models, the claim of its superiority would be challenged.

read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reports bulge inflation tests on porcine diaphragmatic central tendon using 3D-DIC to measure biaxial hyperelastic response. Isotropic models (Neo-Hookean, Mooney-Rivlin, Yeoh, Fung) are fitted to pressure-stretch data but fail to capture observed directional differences between meridional and circumferential stretches; a transversely isotropic Humphrey-Yin formulation is shown to provide a markedly improved description over the full inflation range, with parameter identification indicating that the transversely isotropic term dominates the strain-energy response. The work concludes that anisotropic constitutive laws are required even under macroscopically axisymmetric loading and provides a framework for biomimetic prosthesis design, noting no significant left-right differences despite specimen variability.

Significance. If the deformation-state extraction is accurate, the demonstration that isotropic phenomenological models are insufficient while a transversely isotropic Humphrey-Yin model captures both nonlinearity and directional signatures supplies useful experimental data and modeling guidance for diaphragmatic-tendon biomechanics. The finding that the anisotropic contribution dominates the strain energy directly supports the need for directionally sensitive constitutive descriptions in congenital-diaphragmatic-hernia repair applications.

major comments (2)
  1. [Methods] Methods section: Principal stretches are obtained via spherical-cap fit to the reconstructed 3D geometry plus clamping pre-deformation corrections. Under true material anisotropy or non-uniform boundary effects the deformed surface need not remain spherical, so the extracted meridional and circumferential stretches may contain systematic error. This error could artifactually generate the directional differences that isotropic models cannot fit while the Humphrey-Yin form can, thereby weakening the claim that the transversely isotropic contribution dominates the strain-energy response.
  2. [Results] Results section: The abstract states that the Humphrey-Yin model yields a markedly improved description and that the transversely isotropic term dominates, yet no quantitative fit residuals, R^{2} values, or specimen counts are referenced in the provided text. Without these metrics it is impossible to judge whether the reported superiority is robust or sensitive to data selection and parameter choices.
minor comments (2)
  1. The abstract and conclusion refer to 'boar' and 'porcine' interchangeably; consistent terminology should be used throughout.
  2. Figure legends and axis labels should explicitly state whether plotted stretches are meridional or circumferential and whether they include the clamping correction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We are grateful to the referee for their thorough review and valuable suggestions. Below we respond to each major comment and indicate the changes we will make to the manuscript.

read point-by-point responses

  1. Referee: Methods section: Principal stretches are obtained via spherical-cap fit to the reconstructed 3D geometry plus clamping pre-deformation corrections. Under true material anisotropy or non-uniform boundary effects the deformed surface need not remain spherical, so the extracted meridional and circumferential stretches may contain systematic error. This error could artifactually generate the directional differences that isotropic models cannot fit while the Humphrey-Yin form can, thereby weakening the claim that the transversely isotropic contribution dominates the strain-energy response.

    Authors: This is an important point. The spherical cap approximation is a standard approach in bulge inflation tests for membranes, but we recognize that anisotropy could lead to deviations. We will add to the methods and results sections a quantitative assessment of the fit accuracy, such as the average deviation from sphericity in the analyzed region. We maintain that the observed stretch differences reflect the tissue's true mechanical behavior, as supported by the histological structure, but will include this additional check to rule out methodological artifacts. revision: yes

  2. Referee: Results section: The abstract states that the Humphrey-Yin model yields a markedly improved description and that the transversely isotropic term dominates, yet no quantitative fit residuals, R^{2} values, or specimen counts are referenced in the provided text. Without these metrics it is impossible to judge whether the reported superiority is robust or sensitive to data selection and parameter choices.

    Authors: We agree that the absence of specific quantitative metrics in the text makes it difficult to fully assess the model performance. We will revise the results section to include the number of specimens tested, as well as R² and residual error values for the different models. This will provide concrete evidence for the superiority of the Humphrey-Yin model and the dominance of the transversely isotropic term. revision: yes

Circularity Check

0 steps flagged

No significant circularity; standard experimental model fitting

full rationale

The paper conducts bulge inflation experiments on porcine diaphragmatic tendon, reconstructs 3D geometry via stereo DIC, applies a spherical-cap approximation plus pre-deformation corrections to obtain principal stretches, and then performs parameter identification for several hyperelastic constitutive models against the measured pressure-stretch data. The Humphrey-Yin transversely isotropic form is shown to fit better than the isotropic baselines, with the anisotropic term contributing most to the strain energy. This workflow is direct fitting of model parameters to independent experimental inputs; the reported dominance of the transversely isotropic contribution is a post-fit diagnostic, not a quantity that equals the fitting procedure by construction. No self-citation chain, uniqueness theorem, or ansatz smuggling is invoked to justify the central claim. The geometric approximation is an explicit modeling assumption whose validity can be checked against the data but does not render the subsequent model comparison circular.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The modeling rests on several standard continuum-mechanics assumptions plus two tissue-specific modeling choices whose validity is not independently verified in the provided abstract.

free parameters (1)
  • Humphrey-Yin material constants (C1, C2, C3, k1, k2, kappa)
    Multiple coefficients in the strain-energy function are identified by fitting to the inflation data; their specific numerical values are not stated in the abstract.
axioms (2)
  • domain assumption The diaphragmatic tendon is incompressible.
    Standard assumption for soft biological tissues invoked to reduce the constitutive model to two principal stretches.
  • domain assumption The tissue is transversely isotropic with the plane of isotropy lying within the membrane.
    Introduced to capture the lamellar collagen structure through the thickness while treating the in-plane response as isotropic.

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Reference graph

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