Mathematical modeling of neuroblast migration toward the olfactory bulb

This article is devoted to the mathematical modeling of the migration of neuroblasts, precursor cells of neurons, along the Rostral Migratory Stream (RMS), the pathway they usually follow before maturing. According to our model, this way is determined mainly by attraction forces to the olfactory bulb, and also by the heterogeneous mobility of neuroblasts in different regions of the brain. Carefully identifying them as solutions to partial differential equations allows us to determine the movement of neuroblasts along the RMS in a realistic fashion. For solving the equations we develop numerical schemes where the application of novel discontinuous Galerkin methods allows to maintain the properties of the continuous model such as the maximum principle. We present some successful computer tests including parameter adjustment to fit real data from rodent brains.