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

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 (