Validation

Validation

golgi is validated layer by layer — the FEM solver against analytic and COMSOL references, the fiber models against canonical electrophysiology, and end-to-end recruitment against published in-vivo and cross-platform studies. The validation scripts live in paper_figs/ (validate_*.py).

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What is checked against what

Layer	Script(s)	Reference	Check
FEM solver	validate_fem_analytic.py	analytic point source V(r)=I/(4πσ)(1/r−1/R)	FEniCSx solution accuracy
FEM (cross-platform)	comsol_validation_fig.py, _m1_golgi_cylinder.py	COMSOL (M1 monopole, M2 idealized cuff w/ anisotropy + perineurium CI, M3 swine, M4 human)	point-for-point lead fields (S15)
Conduction velocity	validate_fiber.py, validate_mrg.py	Hursh 1939, McIntyre 2002 (MRG)	CV-vs-diameter; MRG interpolation vs discrete
Strength–duration	validate_fiber.py	Weiss/Lapicque (rheobase, chronaxie)	threshold vs pulse width
Dog cervical VNS	validate_dogvns_native.py	Yoo 2013 (in-vivo, via ASCENT)	A/B/C thresholds, LivaNova helical cuff, perineurium CI
Cat tibial LIFE	validate_nrv*.py	NRV / Couppey 2024, Nannini-Horch 1991, Yoshida-Horch 1993	intrafascicular recruitment
Multi-fascicle cuff	validate_bucksot.py, fig_bucksot.py	Bucksot 2019 (via ASCENT)	per-fascicle recruitment, circumferential vs inverted cuff

Digitized literature reference curves are stored as JSON (save_bucksot_ref.py → bucksot_reference.json; save_nrv_ref.py → nrv_reference.json) for the overlays. The integrated Fig 4 combines the analytic/COMSOL, dog-VNS, NRV-LIFE, and Bucksot checks into one figure; S8 (supp_foundations) and S15 (supp_comsol_validation) are the supplementary validation figures. See Reproducing the Paper.

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Why this matters

• The analytic and COMSOL checks establish that golgi's open FEniCSx solver matches both a closed form and the field most peripheral-nerve studies have historically used (COMSOL) — so dropping the commercial solver costs no accuracy. See Finite-Element Solver.
• The Hursh / McIntyre checks establish that the fiber backends reproduce textbook conduction velocity and strength–duration behaviour. See Fiber Models & Activation.
• The Yoo / Bucksot / NRV checks establish end-to-end recruitment against independent in-vivo and cross-platform data, including the perineurium contact-impedance model. See Conductivity & Tissue Properties.

Regression tests

Beyond the paper validation, the repository ships fast automated tests (Contributing): source/attribute guards that the headless API stays wired to its pipeline drivers, a full import_nerve → run_mesh → run_fem → run_fibers → run_sweep integration test (auto-skips without the solver stack), and pure-numpy unit tests of the CNAP cable math.

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References

Fiber-model foundations

• Hursh JB (1939). Conduction velocity and diameter of nerve fibers. Am J Physiol 127:131.
• McIntyre CC, Richardson AG, Grill WM (2002). Modeling the excitability of mammalian nerve fibers. J Neurophysiol 87:995.
• Weiss G (1901). Sur la possibilité de rendre comparables entre eux les appareils servant à l'excitation. Arch Ital Biol 35:413. — strength–duration.
• Lapicque L (1907). Recherches quantitatives sur l'excitation électrique des nerfs. J Physiol Pathol Gén 9:620. — chronaxie.

FEM cross-validation

• Bossetti CA, Birdno MJ, Grill WM (2008). Analysis of the quasi-static approximation for calculating potentials generated by neural stimulation. J Neural Eng 5:44.
• Pelot NA, Thio BJ, Grill WM (2019). On the parameters used in finite element modeling of compound peripheral nerves. J Neural Eng 16:016007.
• COMSOL Multiphysics (commercial; used only as an external cross-check, not by golgi).

End-to-end recruitment

• Yoo PB, et al. (2013). High-resolution measurement of electrically-evoked vagus nerve activity. J Neural Eng. — dog cervical VNS.
• Bucksot JE, et al. (2019). Flat electrode contacts for vagus nerve stimulation. PLOS ONE. — multi-fascicle cuff.
• Nannini N, Horch K (1991). Muscle recruitment with intrafascicular electrodes. IEEE Trans Biomed Eng. — LIFE.
• Yoshida K, Horch K (1993). Selective stimulation of peripheral nerve fibers using dual intrafascicular electrodes. IEEE Trans Biomed Eng. — LIFE.
• Couppey T, et al. (2024). NRV: an open framework for in silico evaluation of peripheral nerve stimulation. PLOS Comput Biol. — cross-platform LIFE.
• Musselman ED, Cariello JE, Grill WM, Pelot NA (2021). ASCENT: a pipeline for sample-specific computational modeling of electrical stimulation of peripheral nerves. PLOS Comput Biol. — reference masks/pipeline for the dog-VNS and Bucksot checks.

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See also

Reproducing the Paper · Finite-Element Solver · Fiber Models & Activation · Contributing