Folded tissue geometry adds an electrodiffusive slowing term to cortical spreading depolarization

Cortical spreading depolarization (CSD) propagates across cortex at millimeters per minute and can slow in sulcal regions, but the contribution of folded geometry remains unresolved. We tested whether sulcal dipole alignment adds a measurable electrodiffusive delay in a reduced surface model in which extracellular diffusion remains the dominant transport process. The model included overlapping extracellular and intracellular surface compartments, explicit K⁺, Na⁺, and Cl^- concentrations, Goldman-Hodgkin-Katz membrane voltage, activation-dependent membrane sources, Na⁺/K⁺ pump dynamics, dynamic extracellular-space restriction, and a quasi-static screened potential. A nonlocal dipole kernel coupled membrane-current deviations through geodesic distance and surface-normal opposition. We compared paired simulations with dipole alignment disabled or enabled in one representative folded surface, 12 synthetic folded geometries plus a flat control, and 8 sulcal versus 8 flatter fsaverage6 patches. In the representative simulation, cross-fold speed decreased from 2.609 to 2.537 mm/min and the region-of-interest E1-E2 delay increased from 128.0 to 131.6 s. Across the synthetic sweep, all folded geometries slowed, whereas the flat control did not. Mean slowdown was 0.136 mm/min (95% bootstrap CI 0.106-0.170), corresponding to a 4.88% speed reduction, and mean delay increased by 6.81 s (95% CI 5.31-8.26). Null kernels and atlas patches supported geometry specificity. In this reduced surface model, folded cortical anatomy adds an orientation-dependent electrodiffusive slowing term to diffusion-driven CSD propagation.