Characterization of the electrical properties of mammalian peripheral nerve laminae

The intrinsic electrical material properties of the laminar components of the mammalian peripheral nerve bundle are important parameters necessary for the accurate simulation of the electrical interaction between nerve fibers and neural interfaces. Improvements in the accuracy of these parameters improve the realism of the simulation and enables realistic screening of novel devices used for extracellular recording and stimulation of mammalian peripheral nerves. This work aims to characterize these properties for mammalian peripheral nerves to build upon the resistive parameter set established by Weerasuriya et al. in 1984 for amphibian somatic peripheral nerves (frog sciatic nerve) that is currently used ubiquitously in the in-silico peripheral nerve modeling community.

A custom designed characterization chamber was implemented and used to measure the radial and longitudinal impedance between 10 mHz and 50 kHz of freshly excised canine vagus nerves using four-point impedance spectroscopy. The impedance spectra were parametrically fitted to an equivalent circuit model to decompose and estimate the components of the various laminae. Histological sections of the electrically characterized nerves were then made to quantify the geometry and laminae thicknesses of the perineurium and epineurium. These measured values were then used to calculate the estimated intrinsic electrical properties, resistivity and permittivity, from the decomposed resistances and reactances. Finally, the estimated intrinsic electrical properties were used in a finite element method (FEM) model of the nerve characterization setup to evaluate the realism of the model.

The geometric measurements were as follows: nerve bundle (1.6 ± 0.6 mm), major nerve fascicle diameter (1.3 ± 0.23 mm), and perineurium thickness (13.8 ± 2.1 μm). The longitudinal resistivity of the endoneurium was estimated to be 0.97 ± 0.05 Ωm. The relative permittivity and resistivity of the perineurium were estimated to be 2018 ± 391 and 3.75 kΩm ± 981 Ωm, respectively. The relative permittivity and resistivity of the epineurium were found to be 9.4 × 10⁶  ± 8.2 × 10⁶ and 55.0 ± 24.4 Ωm, respectively. The root mean squared (RMS) error of the experimentally obtained values when used in the equivalent circuit model to determine goodness of fit against the measured impedance spectra was found to be 13.0 ± 10.7 Ω, 2.4° ± 1.3°. The corner frequency of the perineurium and epineurium were found to be 2.6 ± 1.0 kHz and 368.5 ± 761.9 Hz, respectively. A comparison between the FEM model in-silico impedance experiment against the ex-vivo methods had a RMS error of 159.0 ± 95.4 Ω, 20.7° ± 9.8°.

Although the resistive values measured in the mammalian nerve are similar to those of the amphibian model, the relative permittivity of the laminae bring new information about the reactance and the corner frequency (frequency at peak reactance) of the peripheral nerve. The measured and estimated corner frequency are well within the range of most bioelectric signals, and are important to take into account when modeling the nerve and neural interfaces.