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Efficient simulations of tubulin-driven axonal growth

Diehl, Stefan LU ; Henningsson, Erik LU and Heyden, Anders LU (2016) In Journal of Computational Neuroscience 41(1). p.45-63
Abstract
This work concerns efficient and reliable numerical simulations of the dynamic behaviour of a moving-boundary model for tubulin-driven axonal growth. The model is nonlinear and consists of a coupled set of a partial differential equation (PDE) and two ordinary differential equations. The PDE is defined on a computational domain with a moving boundary, which is part of the solution. Numerical simulations based on standard explicit time-stepping methods are too time consuming due to the small time steps required for numerical stability. On the other hand standard implicit schemes are too complex due to the nonlinear equations that needs to be solved in each step. Instead, we propose to use the Peaceman–Rachford splitting scheme combined with... (More)
This work concerns efficient and reliable numerical simulations of the dynamic behaviour of a moving-boundary model for tubulin-driven axonal growth. The model is nonlinear and consists of a coupled set of a partial differential equation (PDE) and two ordinary differential equations. The PDE is defined on a computational domain with a moving boundary, which is part of the solution. Numerical simulations based on standard explicit time-stepping methods are too time consuming due to the small time steps required for numerical stability. On the other hand standard implicit schemes are too complex due to the nonlinear equations that needs to be solved in each step. Instead, we propose to use the Peaceman–Rachford splitting scheme combined with temporal and spatial scalings of the model. Simulations based on this scheme have shown to be efficient, accurate, and reliable which makes it possible to evaluate the model, e.g. its dependency on biological and physical model parameters. These evaluations show among other things that the initial axon growth is very fast, that the active transport is the dominant reason over diffusion for the growth velocity, and that the polymerization rate in the growth cone does not affect the final axon length. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Neurite elongation, Partial differential equation, Numerical simulation, Peaceman–Rachford splitting scheme, Polymerization, Microtubule cytoskeleton
in
Journal of Computational Neuroscience
volume
41
issue
1
pages
19 pages
publisher
Springer
external identifiers
  • Scopus:84977079437
ISSN
1573-6873
DOI
10.1007/s10827-016-0604-x
language
English
LU publication?
yes
id
f50c6428-f0a5-4f91-bde3-f332753fe894
date added to LUP
2016-05-02 16:52:40
date last changed
2016-10-13 05:07:28
@misc{f50c6428-f0a5-4f91-bde3-f332753fe894,
  abstract     = {This work concerns efficient and reliable numerical simulations of the dynamic behaviour of a moving-boundary model for tubulin-driven axonal growth. The model is nonlinear and consists of a coupled set of a partial differential equation (PDE) and two ordinary differential equations. The PDE is defined on a computational domain with a moving boundary, which is part of the solution. Numerical simulations based on standard explicit time-stepping methods are too time consuming due to the small time steps required for numerical stability. On the other hand standard implicit schemes are too complex due to the nonlinear equations that needs to be solved in each step. Instead, we propose to use the Peaceman–Rachford splitting scheme combined with temporal and spatial scalings of the model. Simulations based on this scheme have shown to be efficient, accurate, and reliable which makes it possible to evaluate the model, e.g. its dependency on biological and physical model parameters. These evaluations show among other things that the initial axon growth is very fast, that the active transport is the dominant reason over diffusion for the growth velocity, and that the polymerization rate in the growth cone does not affect the final axon length.},
  author       = {Diehl, Stefan and Henningsson, Erik and Heyden, Anders},
  issn         = {1573-6873},
  keyword      = {Neurite elongation,Partial differential equation,Numerical simulation,Peaceman–Rachford splitting scheme,Polymerization,Microtubule cytoskeleton},
  language     = {eng},
  month        = {04},
  number       = {1},
  pages        = {45--63},
  publisher    = {ARRAY(0x96152e0)},
  series       = {Journal of Computational Neuroscience},
  title        = {Efficient simulations of tubulin-driven axonal growth},
  url          = {http://dx.doi.org/10.1007/s10827-016-0604-x},
  volume       = {41},
  year         = {2016},
}