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Citation

Kiddie G, McLean DR, van Ooyen A & Graham B (2005) Biologically plausible models of neurite outgrowth. In: van Pelt J, Kamermans M, Levelt C, van Ooyen A, Ramakers G & Roelfsema P (eds.) Development, dynamics and pathology of neuronal networks: from molecules to functional circuits. Progress in Brain Research, 147. Amsterdam: Elsevier Science, pp. 67-80. http://www.sciencedirect.com/science/article/pii/S007961230447006X

Abstract
Mathematical modeling and computer simulation are valuable tools in unraveling the complexities underlying the morphological development of neurons. The chapter describes the biologically plausible mathematical models of neurite initiation, elongation, and branching. These models attempt to describe the intra- and extra-cellular environments of a developing neuron and to determine the limiting factors in neurite outgrowth. This typically involves modeling the production, degradation, and transport of one or more chemicals in one or two spatial dimensions. The numerical solution of even one- or two-dimensional models is computationally demanding and requires considerable care in specifying appropriate temporal and spatial discretization. As the neuronal morphology changes over time, the spatial discretization representing the neuron must also change.