Geometry-Driven Flow Analysis of Brain Sulcal Pattern

Abstract

Cortical folding reflects coordinated neurodevelopmental processes and is increasingly recognized as a sensitive marker of neurological disease. However, most existing analyses rely on indirect scalar summaries that do not explicitly model folding geometry itself. In juvenile myoclonic epilepsy (JME), a common genetic epilepsy, cortical abnormalities are often subtle, spatially distributed, and difficult to detect using conventional morphometric measures. We introduce a Poisson-equation-based framework that models cortical folding as a geometry-driven flow derived from mean curvature on the cortical manifold. By treating folding patterns as a stationary source-sink structure, the proposed approach yields a smooth, globally balanced potential field whose surface gradient defines a physically interpretable flux. This framework enables spatially coherent analysis of sulcal-gyral folding organization and provides a principled representation of geometry-driven cortical structure in JME.