Studying topographic organization of the brain with directional derivatives of connectivity

Motivation: The currently available tools to describe changes in structural connectivity preclude an in-depth topography study of the brain’s white matter. We sought to quantify the degree of change in structural connectivity through the mathematical notion of directional derivatives. Goal(s): To define and compute the directional derivatives of tractograms. Approach: We defined a measure of connectivity at a point in the brain, that is expressed on the brain's surface. By using numerical differentiation, we computed directional derivatives of connectivity. Results: Our directional derivative method allows a comprehensive topographic study of the brain and highlights potential topographic patterns in structural organization. Impact: Directional derivatives quantify connectivity changes, enabling systematic topographic study of the brain. The computational neuroimaging tool developed may aid in neurosurgical planning, precise brain stimulation, and biomarkers identification. This versatility may contribute significantly to both neuroscience research and clinical practice.