A One-Dimensional Model For Neuronal Growth
(2013) In Master's Theses in Mathematical Sciences 2013:E10 FMA820 20122Mathematics (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:
http://lup.lub.lu.se/student-papers/record/3563796
- author
- Perna, Stefano LU
- supervisor
-
- Stefan Diehl LU
- organization
- course
- FMA820 20122
- year
- 2013
- 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}}, }