A One-Dimensional Model For Neuronal Growth
Abstract: A mathematical model for neuronal growth is presented, describing the process of axonal elongation. The main construction material is a protein called tubulin, which is produced in the soma (core body of the cell), and transported inside the axon to a structure known as the growth cone on its tip, where the construction process occurs. The concentration of tubulin is modelled by a convection-diffusion PDE along the axon and by an ODE in the small tip. The length of the axon as a function of time is given by another ODE which models the building process in the growth cone. The entire model constitutes a coupled moving-boundary problem for which a numerical method is described and investigated. Simulation are also presented with parameter values from literature in the case of the squid (Loligo pealeii).
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