Jan Verwer
CWI and
Univ. of Amsterdam
A Scientific Computing Framework for Studying Axon Guidance
Computational Neuroscience Meeting, NWO, December 9, 2005
Centrum voor Wiskunde en Informatica
Scientific Computing
Computer based applied mathematics, involving
• Modelling
• Analysis
• Simulation
Scientific Computing
Computer based applied mathematics, involving
• Modelling Prescription of a given problem in formulas, relations, equations. Approximating reality.
Here the application is prominent. • Analysis
• Simulation
Scientific Computing
Computer based applied mathematics, involving
• Modelling Prescription of a given problem in formulas, relations, equations. Approximating reality.
Here the application is prominent. • Analysis Study of mathematical and numerical issues (stability, conservation rules, etc).
Here the mathematics is prominent.
• Simulation
Scientific Computing
Computer based applied mathematics, involving
• Modelling Prescription of a given problem in formulas, relations, equations. Approximating reality.
Here the application is prominent. • Analysis Study of mathematical and numerical issues (stability, conservation rules, etc).
Here the mathematics is prominent.
• Simulation Programming, benchmark selection, testing, visualization, interpretation.
Here the computer is prominent.
Scientific Computing
Computer based applied mathematics, involving
• Modelling Prescription of a given problem in formulas, relations, equations. Approximating reality.
Here the application is prominent. • Analysis Study of mathematical and numerical issues (stability, conservation rules, etc).
Here the mathematics is prominent.
• Simulation Programming, benchmark selection, testing, visualization, interpretation.
Here the computer is prominent.
Scientific Computing
Computer based applied mathematics, involving
• Modelling This is critical.
• Analysis This is fun.
• Simulation This is hard work.
Results from the PhD thesis of J. Krottje (CWI):On the numerical solution of diffusion systems with localized, gradient-driven moving sources, UvA, November 17, 2005
Axon Guidance
Joint project between CWI (Verwer), NIBR (van Pelt) and VU (van Ooyen), carried out at CWI and funded by
Results from the PhD thesis of J. Krottje (CWI):On the numerical solution of diffusion systems with localized, gradient-driven moving sources, UvA, November 17, 2005
Axon Guidance
A first PDE model was built by Hentschel & van Ooyen ‘99
The model moves particles (axon heads) in attractant-repellent gradient fields
Axon Guidance Modelling
A first PDE model was built by Hentschel & van Ooyen ‘99
The model moves particles (axon heads) in attractant-repellent gradient fields
Axon Guidance Modelling
A first PDE model was built by Hentschel & van Ooyen ‘99
The model moves particles (axon heads) in attractant-repellent gradient fields
Axon Guidance Modelling
A first PDE model was built by Hentschel & van Ooyen ‘99
The model moves particles (axon heads) in attractant-repellent gradient fields
Axon Guidance Modelling
Krottje generalized their model and has developed the Matlab package: AG-tools
Mathematical Framework
Three basic ingredients
• Domain Physical environment of axons, neurons, chemical fields. Domain in 2D with smooth complicated boundary, possibly with holes. • States
• Fields
Mathematical Framework
Three basic ingredients
• Domain Physical environment of axons, neurons, chemical fields. Domain in 2D with smooth complicated boundary, possibly with holes. • States Growth cones, target cells, axon properties,
locations. Particle dynamics modelled by ordinary differential equations.
• Fields
Mathematical Framework
Three basic ingredients
• Domain Physical environment of axons, neurons, chemical fields. Domain in 2D with smooth complicated boundary, possibly with holes. • States Growth cones, target cells, axon properties,
locations. Particle dynamics modelled by ordinary differential equations.
• Fields Changing concentrations of guidance molecules due to diffusion, absorption, moving sources. Modelled by partial differential equations.
Three basic ingredients
• Domain
• States
• Fields
Mathematical Framework
- Local function approximations- Arbitrary node sets- Unstructured Voronoi grids- Local refinement- Implicit-explicit Runge-Kutta integration
AGTools Example
Ilustration of topographic mapping with 5 guidance fields(3 diffusive and 2 membrane bound) and 200 growth cones
Neuro Scientific Computing Challenges
• Modelling Here major steps are needed:
• Analysis
• Simulation
Neuro Scientific Computing Challenges
• Modelling Here major steps are needed: - e.g., dimensioned wires instead of point particles,
- in general, a less phenomenal setup, - realistic data (coefficients, parameters).
• Analysis
• Simulation
Neuro Scientific Computing Challenges
• Modelling Here major steps are needed: - e.g., dimensioned wires instead of point particles,
- in general, a less phenomenal setup, - realistic data (coefficients, parameters).
• Analysis Higher modelling level will require participation of PDE analysts.
• Simulation
Neuro Scientific Computing Challenges
• Modelling Here major steps are needed: - e.g., dimensioned wires instead of point particles,
- in general, a less phenomenal setup, - realistic data (coefficients, parameters).
• Analysis Higher modelling level will require participation of PDE analysts.
• Simulation 3D-model with many species and axons. Will require huge computer resources,
and presumably a different grid approach.
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