Direct Reconstruction of DC Cortical Conductivity from Large-Scale Electron Microscopy Data

Electrical conductivity of cortical gray matter governs the magnitude and spatial distribution of electric fields generated by brain stimulation and intrinsic neuronal activity measured with M/EEG and intracortical recordings. However, reported macroscopic conductivity values vary by more than threefold, limiting the fidelity of bioelectromagnetic models and leaving unresolved whether this variability reflects measurement uncertainty or genuine structural heterogeneity of cortical tissue. Here, we present a multiscale computational framework that, for the first time, attempts to derive mesoscale conductivity maps of mouse visual cortex at 50-{micro}m resolution directly from large-volume, segmented nanometer-scale electron microscopy data. The Minnie 65 subvolume of the MICrONS dataset is accurately subdivided into 1,224 50-{micro}m cubic blocks. Each block contains, on average, 40-50 million membrane facets of a highly convoluted and dense cellular structure. Three orthogonal electrode pairs are applied to each isolated block to estimate the three principal components of the conductivity tensor. Quasistatic electric modeling is enabled by an iterative boundary-element fast multipole method (BEM-FMM) under the approximation of non-conducting membranes (DC conductivity). Spatially averaged conductivity values predicted by our framework agree well with prior low-resolution measurements in rats, validating the approach. At the same time, the resulting mesoscale maps reveal pronounced conductivity granularity at 50-100 {micro}m scales as well as significant variations in both radial and tangential directions. These results indicate that mesoscale conductivity heterogeneity could be an intrinsic structural property of the cortex. Limitations and extensions of this study are discussed in detail.