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On the validity of using idealised sample geometries for interpreting mechanical tests of very soft tissues

T0 review · 2 major / 5 minor · reviewed 2026-07-12 · grok-4.5

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Pith's one-line read Idealised sample shapes systematically understate brain-tissue stiffness, by about 10% in shear and nearly 50% in compression.

desk verdict Clean controlled quantification of a real methodological bias: idealised cuboids systematically under-estimate brain shear modulus (~10% shear, ~48% axial, driven by compression contact). read the letter →

arxiv 2607.03079 v1 pith:CUVV7VT5 submitted 2026-07-03 cs.CE

Sajjad Arzemanzadeh , Karol Miller , Adam Wittek This is my paper · ORCID
classification cs.CE
keywords verysofttissuebrainsamplegeometryinversefinite-elementanalysisshearmodulusOgdenmodelcontactmechanics
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Most mechanical tests of very soft tissues such as brain still treat each specimen as a perfect cube or cylinder when converting measured forces into material parameters. Real samples, however, are imperfect: their surfaces are uneven, edges are rounded, and contact with the loading platen develops only gradually. This paper shows, by imaging every ovine-brain specimen with MRI and then running identical finite-element inverse analyses on both the true geometry and its idealised cuboidal counterpart, that the idealisation systematically underestimates the shear modulus. The bias is modest in simple shear (~10%) but reaches nearly 50% under compression, because the perfect-cube models assume full, uniform contact from the first instant of loading and therefore over-predict force for any given stiffness. The authors conclude that constitutive parameters obtained from idealised geometries carry a systematic downward bias and that the actual measured geometry should be used whenever material properties of very soft tissues are identified by inverse analysis.

What carries the argument

Controlled real-versus-idealised finite-element comparison: each specimen is meshed twice—once from its MRI segmentation and once as a volume-matched cuboid—then subjected to identical inverse optimisation of a second-order Ogden model against the same experimental force-displacement curves.

What would settle it

Repeat the identical MRI-to-idealised comparison on a new set of specimens while forcing full platen contact (e.g., by pre-compressing until optical contact is complete) and check whether the ~50% compressive modulus gap disappears.

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Extended reading notes

Core claim

When the same force-displacement data from brain-tissue specimens are inverted with MRI-reconstructed geometries versus idealised cuboids, the idealised models return shear moduli that are on average 10% lower in shear and 48% lower under axial loading (driven almost entirely by compression). The discrepancy arises because idealised models cannot capture progressive, partial contact or the resulting non-uniform strain fields.

Load-bearing premise

The modulus gap is produced mainly by geometric contact and strain differences, not by residual mismatches in mesh density, boundary-condition details, or the fixed Ogden exponents chosen after a preliminary fit.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The manuscript quantifies how idealising nominally cuboidal brain-tissue samples as perfect cuboids biases the shear modulus recovered by inverse finite-element analysis. MRI-derived “real” geometries and dimension-matched idealised cuboids are each fitted, independently, to the same experimental force–displacement records from shear, tension and compression tests on ovine brain tissue using a second-order Ogden model (exponents fixed after a preliminary four-parameter fit). Idealised geometries systematically under-estimate the shear modulus—by ~10 % in shear and ~48 % under axial loading, the latter driven almost entirely by compression—because they over-estimate contact area and cannot reproduce the progressive, incomplete contact and non-symmetric strain fields observed experimentally. The authors therefore recommend that measured sample geometry be used in inverse characterisation of very soft tissues.

Significance. If the reported bias is robust, the result is of immediate practical importance: the large majority of published soft-tissue constitutive parameters have been obtained with idealised geometries and may therefore contain a systematic under-estimate of stiffness, especially under compression. The experimental design is clean (identical force data, identical constitutive form and optimiser; only geometry differs), the compression-only first-order Ogden check isolates the dominant source of the discrepancy, and the contact/strain-field explanation is directly supported by the MRI segmentations and FE strain maps. The work supplies a concrete, falsifiable quantitative bound rather than a qualitative caution, and therefore has clear value for experimental biomechanics protocols.

major comments (2)
  1. §2.4.2–2.4.3 and Fig. 7: mesh-independence and contact fidelity for the irregular real geometries are asserted but not demonstrated. An element size of 0.5 mm is stated to be “consistent with MRI resolution and ensures mesh-independent converged solution,” yet no refinement study (or even a single coarser/finer comparison) is reported for either geometry class. Because the central claim rests on differences in progressive contact and localised strain, a short mesh-convergence check on at least one real-geometry compression case is needed to confirm that the ~48 % modulus gap is not an artefact of under-resolved contact on the irregular surface.
  2. §2.4.3 and §3.2: boundary-condition implementation is not identical across loading modes. Tension and shear apply prescribed displacements to video-selected top-surface nodes, while compression uses rigid-plate contact. The authors correctly note that nodal prescription would be inappropriate for real geometries at large compression, but the mixed BC strategy leaves open a residual confound when comparing the shear (~10 %) and axial (~48 %) discrepancies. A brief sensitivity test—e.g., applying the same rigid-plate contact formulation to one tension or shear specimen—would strengthen the claim that geometry, rather than BC formulation, is the dominant driver.
minor comments (5)
  1. §2.2: two different MRI scanners and resolutions (0.25×0.25×0.5 mm vs 0.6 mm isotropic) were used for axial versus shear samples. A short statement on whether the coarser shear resolution systematically under- or over-estimates top-surface area would help the reader judge comparability of the two cohorts.
  2. Table 1 and Table 2: the difference formula is written as (μIdeal − μReal)/μReal × 100, which correctly yields negative values; the abstract and text, however, speak of “lower” moduli without always quoting the signed percentage. Adding the signed mean ± SD in the abstract would remove any ambiguity.
  3. Fig. 5 and Fig. 6: force–displacement curves are shown with every fiftieth experimental point; residual plots or an R²/RMSE table would make the quality of the fits more transparent, especially given that the objective is absolute area between curves.
  4. §2.4.4, Eq. (1): the second-order Ogden form is standard, but the decision to freeze α1 = −8, α2 = 16 after a four-parameter pilot is only briefly justified. A one-sentence note that re-optimising the exponents on a subset of samples left the modulus gap essentially unchanged would close the residual concern about model-form sensitivity.
  5. References [18,19] are listed as “in press” / “2025–2026”; if they are the authors’ own related work, a brief parenthetical clarification would help the reader place the present contribution.

Circularity Check

0 steps flagged · score 1.0 of 10

No load-bearing circularity: real and idealised geometries are independently inverse-fitted to identical experimental force–displacement data; the reported modulus discrepancy is an observed output, not an input or forced prediction.

full rationale

The paper’s central claim is an empirical comparison, not a first-principles derivation. For each sample the same experimental force–displacement curves are supplied to two otherwise identical inverse FE optimisations (second-order Ogden, fixed α1=−8/α2=16 after a preliminary four-parameter run, identical SLSQP objective and bounds); only the mesh geometry differs. The resulting shear-modulus difference (Tables 1–2) is therefore an output of that controlled comparison, not a quantity that has been fitted or defined into existence. Contact-area and strain-field explanations (Figs. 2, 7) are post-hoc observations drawn from the MRI segmentations and the FE solutions themselves. Material-model form, Poisson ratio and experimental protocol are taken from the broader literature (including some author self-citations of prior methods papers), but none of those citations supplies the numerical discrepancy that constitutes the paper’s result. Consequently the derivation chain contains no self-definitional loop, no fitted-input-called-prediction, and no uniqueness theorem imported from the authors’ own prior work. A residual score of 1 reflects only the presence of ordinary methodological self-citation that is not load-bearing for the geometry-bias claim.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on standard continuum-mechanics and FE assumptions plus a small set of domain choices (Ogden form, fixed exponents, Poisson 0.49, no-slip contact, strain cut-offs). No new physical entities are postulated. Free parameters are the per-sample shear moduli that are deliberately fitted; the geometry-induced difference between those fitted values is the measured quantity, not an extra free parameter.

free parameters (3)
  • μ1, μ2 (or μ) per sample and geometry
    Shear parameters of the Ogden model are optimised independently for each real and each idealised mesh to match experimental force–displacement curves; they are the quantities whose difference constitutes the main result.
  • α1 = −8, α2 = 16 (fixed after preliminary fit)
    Exponents were observed to be nearly constant in a four-parameter optimisation and then locked; the choice affects absolute moduli but is shared by both geometries, so the relative bias is less sensitive.
  • Poisson’s ratio ν = 0.49
    Taken from literature to enforce near-incompressibility; not fitted to the present force data.
assumptions (4)
  • domain assumption Second-order (or first-order) Ogden hyperelasticity adequately represents brain tissue response up to the chosen strain limits (0.25 tension, 0.3 compression/shear).
    Stated in §2.4.4; literature precedent is cited, but the form is assumed rather than discovered from the present data.
  • domain assumption No-slip contact between sample and platens (glue or sandpaper) is correctly captured by the Abaqus contact algorithm or by fully constrained nodes.
    Boundary-condition idealisation in §2.4.3; any residual slip would affect both geometries but may interact with surface roughness present only in real meshes.
  • domain assumption MRI segmentation followed by 0.5 mm hexahedral meshing yields a geometry and discretisation accurate enough that the modulus difference is not a mesh artefact.
    §2.4.1–2.4.2; mesh size is justified by MRI resolution and claimed convergence, but no formal mesh-convergence study is shown.
  • standard math Finite-deformation continuum mechanics and the explicit dynamics FE solver with hourglass control are valid for the tested strain rates and nearly incompressible tissue.
    Standard computational solid mechanics; invoked throughout §2.4.

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Pith. "Pith review of On the validity of using idealised sample geometries for interpreting mechanical tests of very soft tissues." pith.science (2026). https://pith.science/paper/CUVV7VT5

@misc{pith2026260703079,
  author       = {Pith},
  title        = {Pith review of: On the validity of using idealised sample geometries for interpreting mechanical tests of very soft tissues},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CUVV7VT5}},
  note         = {Machine review of arXiv:2607.03079}
}
read the original abstract

Mechanical characterisation of soft tissues often relies on inverse analysis of experimental data in which constitutive models are calibrated to match experimental force-displacement curves, yet the vast majority of such studies use idealised (nominal) sample geometries even though experimental samples unavoidably deviate from these nominal shapes because of imperfections in excision and mounting. The influence of these geometric simplifications on the material parameters determined through inverse analysis remains poorly quantified. We investigate the appropriateness of using idealised sample geometries in mechanical characterisation of brain tissue. Magnetic resonance imaging (MRI) was used to reconstruct the exact (real) geometry of each nominally cuboidal tissue sample. We determined a stress parameter (the shear modulus) by modelling, using the finite element method, tensile, compressive, and shear tests of brain tissue samples with both the MRI-based (real) and idealised cuboidal geometries, enabling a controlled comparison of geometry. Idealised geometries consistently yielded a lower stress parameter. The discrepancy in shear modulus between the real and idealised geometries varied across loading modes, averaging approximately 10% in shear and 48% under axial loading, predominantly arising from the compressive response. These discrepancies can be attributed to the inability of idealised-geometry models to accurately represent contact interactions and predict strain distributions, particularly under compressive loading. Idealisation of sample geometry may introduce systematic bias in the mechanical characterisation of very soft tissues; therefore, the actual measured sample geometry should be used in inverse analysis to identify constitutive models and their parameters.

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