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arxiv: 2601.09660 · v1 · submitted 2026-01-14 · ⚛️ physics.bio-ph · q-bio.TO

Constitutive parameter inference using physics-based data-driven modeling in full volume datasets of intact and torn rotator cuff tendons

Carla Nathaly Villac\'is N\'u\~nez , Siddhartha Srivastava , Ulrich Scheven , Asheesh Bedi , Krishna Garikipati , Ellen M. Arruda This is my paper

Pith reviewed 2026-05-16 14:03 UTC · model grok-4.3

classification ⚛️ physics.bio-ph q-bio.TO
keywords rotator cuff tendonconstitutive parameter inferencevariational system identificationfull volume strainHGO modeltendon injuryneo-Hookean model
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The pith

Modified HGO and three-term polynomial models match full-volume strains in intact and torn rotator cuff tendons while neo-Hookean fails on shear

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

The paper uses full three-dimensional displacement fields from tension tests on intact and injured animal rotator cuff tendons to infer constitutive parameters via variational system identification. It compares three models and finds that a modified Holzapfel-Gasser-Ogden formulation and a reduced polynomial model both reproduce the observed volumetric, tensile, and shear deformations reasonably well. The neo-Hookean model cannot capture the shear patterns, especially in the damaged tissue. The authors conclude that homogeneous models still track the main trends despite complex geometry and fiber structure.

Core claim

Variational system identification applied to full-volume displacement data from fiber-direction tension experiments on intact and torn tendons yields parameters for neo-Hookean, modified HGO, and reduced polynomial constitutive models. The modified HGO and polynomial models reproduce internal deformation mechanisms with reasonable accuracy while the neo-Hookean model fails to match shear behavior in the injured state, showing that current homogeneous models capture key trends but require further refinement for precise internal mechanics.

What carries the argument

Variational system identification solving the weak form of stress equilibrium directly from full-volume displacements, followed by adjoint-based PDE-constrained optimization to refine constitutive parameters.

If this is right

  • Homogeneous constitutive models can capture the principal deformation trends in both intact and damaged tendon under fiber-aligned tension.
  • A reduced polynomial model with only three terms performs comparably to the modified HGO model.
  • Neo-Hookean models are inadequate for reproducing shear behavior observed in injured tendons.
  • Further constitutive development is required to enable accurate clinical-grade simulations of tendon injury and repair.

Where Pith is reading between the lines

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

  • Extending the same full-volume inference method to human rotator cuff specimens could support patient-specific repair planning.
  • Testing additional loading directions with VSI might expose when isotropic or homogeneous assumptions break down in fiber-reinforced soft tissue.
  • The comparable performance of low-order polynomial forms suggests opportunities for computationally cheaper constitutive laws in large-scale biomechanical models.

Load-bearing premise

A single homogeneous set of material parameters throughout the tendon volume is sufficient to match the measured full-volume strain fields in both intact and torn states.

What would settle it

Forward simulation of the tendon using the inferred parameters and direct comparison of predicted internal shear strain distributions in the injured tendon against the experimental full-volume measurements; large mismatches would falsify the model adequacy or homogeneity assumption.

Figures

Figures reproduced from arXiv: 2601.09660 by Asheesh Bedi, Carla Nathaly Villac\'is N\'u\~nez, Ellen M. Arruda, Krishna Garikipati, Siddhartha Srivastava, Ulrich Scheven.

Figure 1
Figure 1. Figure 1: Representative full volume displacement maps obtained with MRI-based strain acquisition protocol. a) [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Mechanisms activated with our quasi-uniaxial tensile experimental setup. Normal strain components shown [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Boundary conditions applied to the intact and torn states of a representative sample. Equations of [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Procedure to find fiber directions in each 1-2 slice of high-resolution datasets. a) A representative 1-2 slice [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Full volume displacement maps of a representative tendon (right shoulder). Each frame depicts the [PITH_FULL_IMAGE:figures/full_fig_p021_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Full volume displacement error maps of a representative tendon (right shoulder). Each frame depicts the [PITH_FULL_IMAGE:figures/full_fig_p022_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Full volume strain maps of a representative tendon. Each frame depicts the experimental response on [PITH_FULL_IMAGE:figures/full_fig_p023_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Full volume invariant error maps of a representative tendon. Each frame depicts the forward prediction [PITH_FULL_IMAGE:figures/full_fig_p025_8.png] view at source ↗
read the original abstract

In this work, we characterized the material properties of an animal model of the rotator cuff tendon using full volume datasets of both its intact and injured states by capturing internal strain behavior throughout the tendon. Our experimental setup, involving tension along the fiber direction, activated volumetric, tensile, and shear mechanisms due to the tendon's complex geometry. We implemented an approach to model inference that we refer to as variational system identification (VSI) to solve the weak form of the stress equilibrium equation using these full volume displacements. Three constitutive models were used for parameter inference: a neo-Hookean model, a modified Holzapfel-Gasser-Ogden (HGO) model with higher-order terms in the first and second invariants, and a reduced polynomial model consisting of terms based on the first, second, and fiber-related invariants. Inferred parameters were further refined using an adjoint-based partial differential equation (PDE)-constrained optimization framework. Our results show that the modified HGO model captures the tendon's deformation mechanisms with reasonable accuracy, while the neo-Hookean model fails to reproduce key internal features, particularly the shear behavior in the injured tendon. Surprisingly, the simplified polynomial model performed comparably to the modified HGO formulation using only three terms. These findings suggest that while current constitutive models do not fully replicate the complex internal mechanics of the tendon, they are capable of capturing key trends in both intact and damaged tissue, using a homogeneous modeling approach. Continued model development is needed to bridge this gap and enable clinical-grade, predictive simulations of tendon injury and 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

3 major / 2 minor

Summary. The manuscript introduces a variational system identification (VSI) method to infer constitutive parameters directly from full-volume displacement fields in intact and torn rotator cuff tendons under tension. Three models are compared: neo-Hookean (which fails to capture shear), a modified Holzapfel-Gasser-Ogden (HGO) model with higher-order invariant terms, and a reduced polynomial model using only three terms; the latter two are reported to reproduce key internal strain features, including shear in the injured state, under a single homogeneous parameter set per tissue state after adjoint-based refinement.

Significance. If the quantitative validation and independence of predictions can be established, the work demonstrates the feasibility of physics-constrained parameter inference from 3D imaging data for soft tissues and highlights that surprisingly simple polynomial forms can match more complex anisotropic models for tendon mechanics. This could support improved predictive simulations of injury and repair, though the homogeneous assumption limits immediate clinical translation.

major comments (3)
  1. [Abstract] Abstract and Results: the central claim that the modified HGO and reduced polynomial models 'capture the tendon's deformation mechanisms with reasonable accuracy' and reproduce 'key internal features' is unsupported by any reported quantitative error metrics (e.g., L2 residuals on displacement or strain fields), cross-validation scores, or out-of-sample prediction errors, leaving open whether the reported agreement is merely a restatement of the fitted data.
  2. [Methods] Methods and Results: the inference solves the weak-form equilibrium equation with spatially constant parameters for the torn tendon; given the complex geometry-driven shear and potential localized fiber disruption, this homogeneous assumption risks averaging over sub-volume heterogeneity, and the manuscript provides no sub-region residual analysis or comparison against heterogeneous parameter fields to confirm that key trends are not simply traded off.
  3. [Results] Results: the adjoint-based refinement step is described, yet no convergence diagnostics, final residual norms of the weak-form equilibrium, or independent validation against withheld displacement data are shown, which is required to establish that the 'predictions' are not circular reproductions of the input fields used for inference.
minor comments (2)
  1. Explicitly state the precise functional form of the modified HGO model (including the higher-order terms in I1 and I2) and the three-term reduced polynomial, preferably with equation numbers.
  2. Clarify the number of biological samples, loading increments, and imaging resolution used to generate the full-volume datasets.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed comments, which have helped us identify areas where the manuscript can be strengthened with additional quantitative support and clarifications. We address each major comment below and will incorporate revisions accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract and Results: the central claim that the modified HGO and reduced polynomial models 'capture the tendon's deformation mechanisms with reasonable accuracy' and reproduce 'key internal features' is unsupported by any reported quantitative error metrics (e.g., L2 residuals on displacement or strain fields), cross-validation scores, or out-of-sample prediction errors, leaving open whether the reported agreement is merely a restatement of the fitted data.

    Authors: We agree that quantitative metrics are necessary to substantiate claims of model accuracy and to distinguish true predictive capability from data reproduction. In the revised manuscript, we will add explicit L2 residual norms computed on both the displacement and strain fields for all three constitutive models. We will also perform a cross-validation study by partitioning the full-volume displacement data, inferring parameters on a training subset, and reporting out-of-sample prediction errors on the withheld portion. These additions will provide objective evidence for the relative performance of the modified HGO and reduced polynomial models. revision: yes

  2. Referee: [Methods] Methods and Results: the inference solves the weak-form equilibrium equation with spatially constant parameters for the torn tendon; given the complex geometry-driven shear and potential localized fiber disruption, this homogeneous assumption risks averaging over sub-volume heterogeneity, and the manuscript provides no sub-region residual analysis or comparison against heterogeneous parameter fields to confirm that key trends are not simply traded off.

    Authors: The homogeneous-parameter assumption is a deliberate modeling choice that still reproduces the dominant observed strain patterns across the entire volume. To address concerns about potential averaging of heterogeneity, we will add a sub-region residual analysis in the revised Results section, partitioning the tendon into regions proximal and distal to the tear and reporting local L2 residuals in each. This will demonstrate that the homogeneous model captures consistent trends without obvious trade-offs. A full heterogeneous-parameter inference lies outside the present scope and would require substantial additional methodological development; we will note this limitation explicitly in the Discussion while emphasizing the utility of the homogeneous approach for the current data. revision: partial

  3. Referee: [Results] Results: the adjoint-based refinement step is described, yet no convergence diagnostics, final residual norms of the weak-form equilibrium, or independent validation against withheld displacement data are shown, which is required to establish that the 'predictions' are not circular reproductions of the input fields used for inference.

    Authors: We will augment the Results section with convergence diagnostics for the adjoint-based optimization, including plots of the objective function and weak-form residual norms versus iteration count. In addition, we will conduct an independent validation by withholding a spatially distributed subset of the displacement measurements, performing inference on the remaining data, and reporting prediction errors on the held-out points. These diagnostics and validation metrics will be included to confirm that the refined parameters are not merely reproducing the input fields. revision: yes

Circularity Check

0 steps flagged

No circularity: parameters inferred from data via weak-form VSI; model comparisons are standard fit validation

full rationale

The derivation infers constitutive parameters directly from full-volume experimental displacement fields by solving the weak-form stress equilibrium using variational system identification (VSI), then refines them via adjoint PDE-constrained optimization. The central results compare how well the fitted modified HGO, 3-term polynomial, and neo-Hookean models reproduce the observed internal strains (including shear in the injured state). This is ordinary post-fit validation against the same dataset rather than any 'prediction' that reduces to the inputs by construction. No load-bearing step relies on a self-citation chain, uniqueness theorem imported from the authors' prior work, or an ansatz smuggled via citation; the homogeneous modeling assumption is stated explicitly as a modeling choice without circular justification. The paper therefore remains self-contained against the experimental benchmarks.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central claim rests on continuum-mechanics assumptions plus the specific constitutive forms chosen; no new physical entities are postulated.

free parameters (3)
  • neo-Hookean mu
    Shear modulus fitted to displacement data
  • modified HGO parameters (C1, C2, k1, k2, kappa)
    Multiple material constants inferred from full-volume strains
  • reduced polynomial coefficients (three terms)
    Coefficients for I1, I2, and fiber-invariant terms fitted to data
axioms (2)
  • domain assumption Tendon tissue can be modeled as a homogeneous, hyperelastic continuum
    Invoked to justify single set of parameters throughout the volume
  • standard math Stress equilibrium holds in the weak form throughout the imaged volume
    Basis for the variational system identification step

pith-pipeline@v0.9.0 · 5618 in / 1641 out tokens · 29076 ms · 2026-05-16T14:03:10.532210+00:00 · methodology

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Reference graph

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