Materials

Material properties in NRV are encapsulated in the material class. This object stores the physical constants necessary for field computations, whether analytical or using the Finite Element Method (FEM).

Currently, a material is defined by two intrinsic properties:

• Electrical conductivity \(\sigma\), expressed in S/m. This can be a scalar value for isotropic media or an anisotropic conductivity tensor:

  \[\begin{split}\boldsymbol{\sigma} = \begin{bmatrix} \sigma_{xx} & 0 & 0 \\ 0 & \sigma_{yy} & 0 \\ 0 & 0 & \sigma_{zz} \end{bmatrix}\end{split}\]

• Relative dielectric permittivity (unitless), used for complex-domain computations.

Although it is possible to instantiate the material class manually, it is strongly recommended for users to load materials from files—typically in the .mat format. NRV includes a collection of predefined materials, and adding new custom materials is straightforward. Both use cases are described below.

To load a material, always use the function load_material(), which ensures safe and consistent initialization. This function can handle all scenarios transparently.

Predefined Materials

NRV includes a number of commonly used materials with predefined properties. To load one of these, use the corresponding name string as an argument to load_material().

Predefined materials in NRV

Material	Name	Scientific source / Notes
Axoplasm	axoplasmic_mrg	from [m1]
Non-specific bone	bone	from [m2]
Cerebrospinal fluid	cerebrospinal_fluid	from [m3]
Dura mater	dura	from [m3]
Endoneurium (Bhadra)	endoneurium_bahdra	from [m6], isotropic, not from direct measurement
Endoneurium (Horn)	endoneurium_horn	from [m5]
Endoneurium (Ranck)	endoneurium_ranck	from [m4]
Epidural space	epidural_space	from [m3]
Epineurium (Horn)	epineurium_horn	from [m5]
Epineurium (generic)	epineurium	unspecified source
Muscle (average)	muscle	average of different muscle types, from [m3]
Perineurium (Horn)	perineurium_horn	from [m5]
Perineurium (generic)	perineurium	unspecified source
Platinum	platinum	commonly cited values
Saline solution	saline	commonly cited values
Silicone	silicone	commonly cited values

All predefined materials are located in the following directory of the NRV package: nrv/_misc/materials/

Scientific References

References for the materials listed above:

• [m1] McIntyre, C. C., Richardson, A. G., & Grill, W. M. (2002). Modeling the excitability of mammalian nerve fibers: influence of afterpotentials on the recovery cycle. Journal of Neurophysiology, 87(2), 995–1006.

• [m2] Kosterich, J. D., Foster, K. R., & Pollack, S. R. (1983). Dielectric permittivity and electrical conductivity of fluid saturated bone. IEEE Transactions on Biomedical Engineering, (2), 81–86.

• [m3] Gabriel, C., & Gabriel, S. (1996). Compilation of the dielectric properties of body tissues at RF and microwave frequencies.

• [m4] Ranck Jr, J. B., & BeMent, S. L. (1965). The specific impedance of the dorsal columns of cat: an anisotropic medium. Experimental Neurology, 11(4), 451–463.

• [m5] Horn, M. R., Vetter, C., Bashirullah, R., Carr, M., & Yoshida, K. (2023). Characterization of the electrical properties of mammalian peripheral nerve laminae. Artificial Organs, 47(4), 705–720.

• [m6] Bhadra, N., Lahowetz, E. A., Foldes, S. T., & Kilgore, K. L. (2007). Simulation of high-frequency sinusoidal electrical block of mammalian myelinated axons. Journal of Computational Neuroscience, 22, 313–326.

How to Define a Custom Material Using a .mat File

It is possible to define and add custom materials to NRV by creating a .mat file. This file can either be:

• Placed directly into the nrv/_misc/materials/ folder (in which case it becomes accessible via its name), or

• Stored locally and loaded via its full path when calling the load_material() function.

When stored in the default folder, the material can be loaded simply by passing the file name without the .mat extension to load_material.

Structure of a Custom .mat File

A .mat material file must contain a dictionary of values with the following keys:

Expected content of a .mat material file

Key	Description
name	Name of the material. Important when the material defines part of a nerve (e.g., perineurium, epineurium, endoneurium).
source	Optional string for documentation or comments. Not used internally by NRV.
sigma	Electrical conductivity (in S/m) for isotropic materials.
sigma_xx	Electrical conductivity along the x-axis (longitudinal). Required for anisotropic materials.
sigma_yy	Electrical conductivity along the y-axis (radial). Required for anisotropic materials.
sigma_zz	Electrical conductivity along the z-axis (radial). Required for anisotropic materials.
epsilon_r	Relative dielectric permittivity (unitless).

Note

For anisotropic materials, you must define all three tensor components (sigma_xx, sigma_yy, sigma_zz). For isotropic materials, use only sigma.

This approach provides a flexible way to extend NRV with application-specific materials or experimentally measured data.