Mesoscale tissue properties and electric fields in brain stimulation: bridging the macroscopic and microscopic scales using layer-specific cortical conductivity

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Abstract Objective. Accurate simulations of electric fields (E-fields) in neural stimulation depend on tissue conductivity representations that link underlying microscopic tissue structure with macroscopic assumptions. Mesoscale conductivity variations can produce meaningful changes in E-fields and neural activation thresholds but remain largely absent from standard macroscopic models. Conductivity variations within the cortex are 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. Approach. We review recent efforts modeling microscopic and mesoscopic E-fields and outline approaches that bridge micro- and macroscales to derive consistent mesoscale conductivity distributions. Using simplified microscopic models, effective tissue conductivity was estimated as a function of volume fraction of extracellular space, and the conductivities of different cortical layers were interpolated based on experimental volume fraction. Main results. The effective tissue conductivities were monotonically decreasing convex functions of the cell volume fraction. They followed the theoretical power formulas 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. Due to the high relative sensitivity, the conductivity difference between layers was considerably larger than their variation in volume fraction, e.g. with layers 3 and 6 being 5% and 24% more conductive than layer 2, respectively, despite their volume fraction being only 1.3% and 5% lower than that of the latter. Significance. The review and analysis provide a foundation for accurate multiscale models of E-fields and neural stimulation. Overcoming technical limitations that microscale and macroscale methods face will allow validation to arrive at consistent conductivity distributions. Using layer-specific conductivity values within the cortex could improve the accuracy of estimations of thresholds and distributions of neural activation in E-field models of brain stimulation.

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