(17) Cell Volume Fraction Determines Layer-specific Tissue Conductivity in the Cortex

Introduction: Electric field modeling of neuromodulation allows computational dosing of stimulation strength and simulation of neural responses. These models mostly utilize homogenous conductivity for each tissue volume; however, conductivity variation within the cortex is expected given the differences in cell density and volume fraction across layers. We sought to estimate layer-specific conductivity within the cortex using computational models.

Methods: Finite element models were generated in COMSOL to represent different microscopic neural tissue structures with cellular volume fraction varying between 5% up to 95% inside a cubic block of tissue. To achieve the high volume fraction, hexagonal prisms placed in a hexagonal grid were used to represent parallel axon fibers, truncated octagons placed in a body-centered cubic lattice [1] were used to represent packing of cell bodies, and lattices of 3D-crosses with square cross-section were used to represent densely interleaved neural branches in the neuropil, respectively. Conductivities of cell membranes and the intra- and extra-cellular spaces were assigned according to literature. Current was applied through a pair of electrodes on the opposite sides of the tissue block and the resulting electrode voltages were evaluated. For each volume fraction, the effective tissue conductivity was calculated and averaged for various rotational orientations of the tissue structure inside. The conductivities of different cortical layers (layer 2 to 6) were interpolated based on experimental volume fraction in the range of 70% to 90% [2].

Results: The effective tissue conductivities for the three modeled tissue structures were monotonically decreasing convex functions of the cell volume fraction. They followed the theoretical power formula [3] only for small volume fractions ( < 20%), and deviated to higher values for larger volume fractions. With decreasing cell volume fraction, the conductivity of cortical layers increased with depth from layer 2 to 6. Although the variation of conductivity within the cortex was small when compared to the conductivity of cerebrospinal fluid (9% to 15%), the conductivity difference was considerably larger when compared between layers, e.g., with layer 3 and 6 being 20% and 50% more conductive than layer 2, respectively.

Conclusion: The study demonstrated a simple method to evaluate tissue conductivity using cell volume fraction data, which can be obtained from microscopic tissue samples. Using layer-specific conductivity values within the cortex could improve the accuracy of electric field models for brain stimulation, especially for intracortical microstimulation with high electric field gradient due to the electrode location within the cortex.