Geometry-Driven Flow Analysis of Brain Sulcal Pattern

2026-06-06

AI Summary

This study addresses the challenge of detecting subtle and spatially dispersed abnormalities in cortical folding associated with juvenile myoclonic epilepsy, which are poorly captured by conventional methods relying on local scalar metrics. To overcome this limitation, the work proposes a novel approach that models cortical folding as a geometric flow driven by mean curvature. By solving a Poisson equation on the cortical manifold, the method constructs a globally balanced potential field and its surface gradient, yielding a physically interpretable and globally consistent representation of cortical geometry. This framework transcends the constraints of traditional local morphometry, enabling spatially coherent analysis of sulcal and gyral structures and significantly enhancing sensitivity to fine-grained cortical anomalies in patients.

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.

Problem

• cortical folding
• juvenile myoclonic epilepsy
• geometry-driven analysis
• sulcal pattern
• neurodevelopmental abnormalities

Innovation

• Poisson equation
• geometry-driven flow
• cortical folding
• mean curvature
• sulcal pattern