Insights from mathematical modelling for T cell migration into the central nervous system

The migration of immune cells from peripheral immune organs into the central nervous system (CNS) through the blood–brain barrier (BBB) is a tightly regulated process. The complex interplay between cells of the BBB and immune cells coordinates cell migration as a part of normal immune surveillance while its dysregulation is critically involved in the pathogenesis of various CNS diseases. To develop tools for a deeper understanding of distribution and migratory pattern of immune cells regulated by the BBB, we made use of a mathematical modelling approach derived from Markov chain theory. We present a data-driven model using a derivation of kinetic differential equations from a particle game. According to the theory of gases, these equations allow one to predict the mean behaviour of a large class of cells by modelling cell–cell interactions. We used this model to assess the distribution of naive, central memory and effector memory T lymphocytes in the peripheral blood and cerebrospinal fluid. Our model allows us to evaluate the impact of activation status, migratory capacity and cell death for cell distribution in the peripheral blood and the CNS.