Tissue mechanics — evidence & validation

Open the laboratory · Equations & limitations

Show the evidence, including the failures.

These static curves come from the Living Matter Lab CANN data release, attributed there to Budday 2017. They are not synthetic validation curves. The separate viscoelastic presets reproduce Tables 4 and 6 of Budday et al., Viscoelastic parameter identification of human brain tissue.

Two different questions: numerical verification asks whether the equations are solved correctly. Experimental comparison asks whether those equations describe measured tissue. A converged finite-element result is not evidence that a material law is biologically accurate.

Three laws, four regions, three loading modes

Each fit uses compression, tension and shear together. Nonzero indices 4, 8, 12 and 16 are held out; the other points train the model, with each mode weighted by its training peak stress. The reported error is held-out RMSE divided by that mode's full observed peak magnitude. Zero is not treated as an independent successful prediction. The script also performs leave-one-loading-mode-out checks.

Ogden: solid line. Neo-Hookean: dashed. Mooney–Rivlin: dotted. Filled circles: training measurements. Open circles: held-out measurements. Stress is nominal stress in kPa; the horizontal axis is stretch λ or shear γ.

The fits can be selected under “Material & evidence” in both laboratories. Static curve fits contain no inferred viscosity and cannot be used as published viscoelastic fits. Choosing another law or changing parameters marks a modified model.

What the comparison does not establish

These are distributed average curves, not independent donor-level samples. Neighboring held-out points are correlated with the training curve. Neither curve holdouts nor loading-mode holdouts establish patient-specific accuracy. No confidence intervals are fabricated: the laboratory's 0.75× and 1.25× settings are sensitivity scenarios only. Some published all-mode viscoelastic fits have negative tension R²; the laboratory displays those values explicitly.

Numerical acceptance tests

The independent reference reconstructs the mesh and energy in Python/JAX, differentiates it automatically, and solves the nonlinear system with SciPy trust-region Newton. Four compression cases compare the mixed and full-volume formulations using neo-Hookean and Mooney–Rivlin energies. Both displacement relative L₂ error and reaction relative error must remain below 10⁻⁴. Ogden stresses are checked independently by NumPy energy differences; the finite viscoelastic law is checked against continuous-time DOP853 integration, including a timestep-halving sequence. These are bounded tests, not validation of every geometry or loading history.

On the recorded finite-Maxwell material test, peak-normalized stress error was approximately 2.11%, 1.08% and 0.55% at 0.5, 0.25 and 0.125 s respectively. The interactive timestep is a speed/accuracy setting, not a universal error guarantee. Mesh sweeps expose remaining reaction-force sensitivity and the artificial stiffening of displacement-only tetrahedra near incompressibility.

Provenance and reproduction

Workbook blob: 6e7bc72c317a29d24064eaf38c6f5951c226abcb. SHA-256: 701f9c7d4495bc55e78f69189719a448b1de81cdf1941e9c556995fa30d4c2bb. The CI input stage verifies the workbook hash and checks all 408 extracted x/y values against the pinned source. A duplicate sheet is deliberately excluded.

node --test tests/tissue-mechanics.mjs tests/tissue-phase2.mjs
node scripts/tissue-phase2/validate.mjs --full
python scripts/tissue-phase2/reference.py
python scripts/tissue-phase2/calibrate.py

Full results, software versions, failed statuses and timings are retained as CI artifacts. Browser/network/EM loading are excluded from numerical timing. There is no claim of pia rupture, puncture, poroelastic fluid transport, tract anisotropy, cell-specific mechanics or injury prediction.