Definition of perineurium

The perineurium is a thin highly resistive layer of connective tissue and has a profound impact on thresholds of activation and block. Our previous modeling work demonstrates that representing the perineurium with a thin layer approximation (Rm = rho*peri_thk), rather than as a thinly meshed domain, reduces mesh complexity and is a reasonable approximation [1]. Therefore, perineurium can be modeled with a thin layer approximation (except with “peanut” fascicles; see an example in Fig 2), termed “contact impedance” in COMSOL (if Model’s “use_ci” parameter is true (S8 Text)), which relates the normal component of the current density through the surface $(\vec{n}\cdot\vec{J_{1}})$ to the drop in electric potentials $(V_{1}-V_{2})$ and the sheet resistance $(\rho_{s})$ :

$\vec{n}\cdot\vec{J_{1}}=\frac{1}{\rho_{s}}(V_{1}-V_{2})$

The sheet resistance $(\rho_{s})$ is defined as the sheet thickness $(\d_{s})$ divided by the material bulk conductivity $(\sigma_{s})$ :

$\rho_{s}=\frac{d_{s}}{\sigma_{s}}$

Our previously published work quantified the relationship between fascicle diameter and perineurium thickness [2] (Table A).

Table A. Previously published relationships between fascicle diameter and perineurium thickness.

Species	peri_thk: f(species, d_fasc)	References
Rat	peri_thk = 0.01292*d_fasc + 1.367 [um]	[2]
Pig	peri_thk = 0.02547*d_fasc + 3.440 [um]	[2]
Human	peri_thk = 0.03702*d_fasc + 10.50 [um]	[2]

The “rho_perineurium” parameter in Model can take either of two modes:

“RHO_WEERASURIYA”: The perineurium conductivity value changes with the frequency of electrical stimulation (for a single value, not a spectrum, defined in Model as “frequency”) and temperature (using a Q10 adjustment, defined in Model as “temperature”) based on measurements of frog sciatic perineurium [1,3]. The equation is defined in src/core/Waveform.py in the rho_weerasuriya() method.
“MANUAL”: Conductivity value assigned to the perineurium is as explicitly defined in either materials.json or Model without any corrections for temperature or frequency.

References

Pelot NA, Behrend CE, Grill WM. On the parameters used in finite element modeling of compound peripheral nerves. J Neural Eng [Internet]. 2019;16(1):16007. Available from: http://dx.doi.org/10.1088/1741-2552/aaeb0c
Pelot NA, Goldhagen GB, Cariello JE, Musselman ED, Clissold KA, Ezzell JA, et al. Quantified Morphology of the Cervical and Subdiaphragmatic Vagus Nerves of Human, Pig, and Rat. Front Neurosci [Internet]. 2020;14:1148. Available from: https://doi.org/10.3389/fnins.2020.601479
Weerasuriya A, Spangler RA, Rapoport SI, Taylor RE. AC impedance of the perineurium of the frog sciatic nerve. Biophys J. 1984 Aug;46(2):167–74. Available from: https://dx.doi.org/10.1016%2FS0006-3495(84)84009-6