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A One-Dimensional Model For Neuronal Growth

Perna, Stefano LU (2013) In Master's Theses in Mathematical Sciences 2013:E10 FMA820 20122
Mathematics (Faculty of Engineering)
Abstract
A mathematical model for neuronal growth is presented, describing the process of axonal elongation. The main construction material is a protein called tubulin, which is produced in the soma (core body of the cell), and transported inside the axon to a structure known as the growth cone on its tip, where the construction process occurs. The concentration of tubulin is modelled by a convection-diffusion PDE along the axon and by an ODE in the small tip. The length of the axon as a function of time is given by another ODE which models the building process in the growth cone. The entire model constitutes a coupled moving-boundary problem for which a numerical method is described and investigated. Simulation are also presented with parameter... (More)
A mathematical model for neuronal growth is presented, describing the process of axonal elongation. The main construction material is a protein called tubulin, which is produced in the soma (core body of the cell), and transported inside the axon to a structure known as the growth cone on its tip, where the construction process occurs. The concentration of tubulin is modelled by a convection-diffusion PDE along the axon and by an ODE in the small tip. The length of the axon as a function of time is given by another ODE which models the building process in the growth cone. The entire model constitutes a coupled moving-boundary problem for which a numerical method is described and investigated. Simulation are also presented with parameter values from literature in the case of the squid (Loligo pealeii). (Less)
Please use this url to cite or link to this publication:
author
Perna, Stefano LU
supervisor
organization
course
FMA820 20122
year
type
H2 - Master's Degree (Two Years)
subject
publication/series
Master's Theses in Mathematical Sciences 2013:E10
report number
LUTFMA-3241-2013
ISSN
1404-6342
other publication id
2013:E10
language
English
id
3563796
date added to LUP
2013-05-29 14:55:09
date last changed
2013-05-29 14:55:09
@misc{3563796,
  abstract     = {A mathematical model for neuronal growth is presented, describing the process of axonal elongation. The main construction material is a protein called tubulin, which is produced in the soma (core body of the cell), and transported inside the axon to a structure known as the growth cone on its tip, where the construction process occurs. The concentration of tubulin is modelled by a convection-diffusion PDE along the axon and by an ODE in the small tip. The length of the axon as a function of time is given by another ODE which models the building process in the growth cone. The entire model constitutes a coupled moving-boundary problem for which a numerical method is described and investigated. Simulation are also presented with parameter values from literature in the case of the squid (Loligo pealeii).},
  author       = {Perna, Stefano},
  issn         = {1404-6342},
  language     = {eng},
  note         = {Student Paper},
  series       = {Master's Theses in Mathematical Sciences 2013:E10},
  title        = {A One-Dimensional Model For Neuronal Growth},
  year         = {2013},
}