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

Abstract

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 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. The effective tissue conductivities were monotonically decreasing convex functions of the cell volume fraction. 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 extracellular 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. The review and analysis provide a foundation for accurate multiscale models of E-fields and neural stimulation. 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.