A stochastic approach to serotonergic fibers in mental disorders.

Virtually all brain circuits are physically embedded in a three-dimensional matrix of fibers that release 5-hydroxytryptamine (5-HT, serotonin). The density of this matrix varies across brain regions and cortical laminae, and it is altered in some mental disorders, including Major Depressive Disorder and Autism Spectrum Disorder. We investigate how the regional structure of the serotonergic matrix depends on the stochastic behavior of individual serotonergic fibers and introduce a new framework for the quantitative analysis of this behavior. In particular, we show that a step-wise random walk, based on the von Mises-Fisher probability distribution, can provide a realistic and mathematically concise description of these fibers. We also consider other stochastic models, including the fractional Brownian motion. The proposed approach seeks to advance the current understanding of the ascending reticular activating system (ARAS) and may also support future theory-guided therapeutic approaches.