Jan Verwer CWI and Univ. of Amsterdam
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Transcript of Jan Verwer CWI and Univ. of Amsterdam
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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
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Scientific Computing
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Scientific Computing
Computer based applied mathematics
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Scientific Computing
Computer based applied mathematics, involving
• Modelling
• Analysis
• Simulation
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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
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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
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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.
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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.
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Scientific Computing
Computer based applied mathematics, involving
• Modelling This is critical.
• Analysis This is fun.
• Simulation This is hard work.
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Axon Guidance
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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
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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
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Axon Guidance
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Axon Guidance
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Axon Guidance Modelling
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Axon Guidance Modelling
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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
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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
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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
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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
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Axon Guidance Modelling
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Mathematical Framework
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Mathematical Framework
Three basic ingredients
• Domain
• States
• Fields
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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
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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
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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.
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Three basic ingredients
• Domain
• States
• Fields
Mathematical Framework
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Three basic ingredients
• Domain
• States
• Fields
Mathematical Framework
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Three basic ingredients
• Domain
• States
• Fields
Mathematical Framework
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Three basic ingredients
• Domain
• States
• Fields
Mathematical Framework
- Local function approximations- Arbitrary node sets- Unstructured Voronoi grids- Local refinement- Implicit-explicit Runge-Kutta integration
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AGTools Example
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AGTools Example
Ilustration of topographic mapping with 5 guidance fields(3 diffusive and 2 membrane bound) and 200 growth cones
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Topographic Mapping Equations
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Topographic Mapping Equations
No hard laws.Phenomenal setup.
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Neuro Scientific Computing Challenges
• Modelling
• Analysis
• Simulation
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Neuro Scientific Computing Challenges
• Modelling Here major steps are needed:
• Analysis
• Simulation
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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
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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
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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.