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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/f50c6428-f0a5-4f91-bde3-f332753fe894
- author
- Diehl, Stefan
LU
; Henningsson, Erik
LU
and Heyden, Anders
LU
- organization
- publishing date
- 2016-08
- 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
- pmid:27121476
- wos:000379186900004
- 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
- 2023-09-11 17:20:18
@article{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}},
keywords = {{Neurite elongation; Partial differential equation; Numerical simulation; Peaceman–Rachford splitting scheme; Polymerization; Microtubule cytoskeleton}},
language = {{eng}},
number = {{1}},
pages = {{45--63}},
publisher = {{Springer}},
series = {{Journal of Computational Neuroscience}},
title = {{Efficient simulations of tubulin-driven axonal growth}},
url = {{http://dx.doi.org/10.1007/s10827-016-0604-x}},
doi = {{10.1007/s10827-016-0604-x}},
volume = {{41}},
year = {{2016}},
}