title: Mathematical modelling and numerical simulation of the morphological development of neurons.
abstract: BACKGROUND
  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.
  
  
  METHODS
  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.
  
  
  RESULTS
  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.
  
  
  CONCLUSIONS
  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.
authors.affiliation: Department of Computing Science and Mathematics, University of Stirling, Stirling FK9 4LA, UK. b.graham@cs.stir.ac.uk
authors.forename: Bruce P
authors.initials: BP
authors.lastname: Graham
authors.forename: Arjen
authors.initials: A
authors.lastname: van Ooyen
mesh_terms: D000818:Animals; D002454:Cell Differentiation / Q000502:physiology; D003198:Computer Simulation; D020439:Growth Cones / Q000502:physiology*; D006801:Humans; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology; D016501:Neurites / Q000502:physiology; D009474:Neurons / Q000166:cytology* / Q000502:physiology*