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This article is part of the supplement: Problems and tools in the systems biology of the neuronal cell

Open Access Review

Mathematical modelling and numerical simulation of the morphological development of neurons

Bruce P Graham1* and Arjen van Ooyen2

Author affiliations

1 Department of Computing Science and Mathematics, University of Stirling, Stirling FK9 4LA, UK

2 Department of Experimental Neurophysiology, Vrije Universiteit, De Boelelaan 1085, 1081 HV Amsterdam, The Netherlands

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Citation and License

BMC Neuroscience 2006, 7(Suppl 1):S9  doi:10.1186/1471-2202-7-S1-S9

Published: 30 October 2006



The morphological development of neurons is a very complex process involving both genetic and environmental components. Mathematical modelling and numerical simulation are valuable tools in helping us unravel particular aspects of how individual neurons grow their characteristic morphologies and eventually form appropriate networks with each other.


A variety of mathematical models that consider (1) neurite initiation (2) neurite elongation (3) axon pathfinding, and (4) neurite branching and dendritic shape formation are reviewed. The different mathematical techniques employed are also described.


Some comparison of modelling results with experimental data is made. A critique of different modelling techniques is given, leading to a proposal for a unified modelling environment for models of neuronal development.


A unified mathematical and numerical simulation framework should lead to an expansion of work on models of neuronal development, as has occurred with compartmental models of neuronal electrical activity.