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Jan Verwer CWI and Univ. of Amsterdam

Centrum voor Wiskunde en Informatica. A Scientific Computing Framework for Studying Axon Guidance. Jan Verwer CWI and Univ. of Amsterdam. Computational Neuroscience Meeting, NWO, December 9, 2005. Scientific Computing. Scientific Computing. Computer based applied mathematics.

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Jan Verwer CWI and Univ. of Amsterdam

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  1. Centrum voor Wiskunde en Informatica A Scientific Computing Framework for Studying Axon Guidance Jan Verwer CWI and Univ. of Amsterdam Computational Neuroscience Meeting, NWO, December 9, 2005

  2. Scientific Computing

  3. Scientific Computing Computer based applied mathematics

  4. Scientific Computing • Computer based applied mathematics, involving • Modelling • Analysis • Simulation

  5. 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

  6. Scientific Computing • Computer based applied mathematics, involving • Modelling Prescription of a given problem in formulas, • relations, equations. Approximating reality. • Here the application is prominent. • AnalysisStudy of mathematical and numerical issues • (stability, conservation rules, etc). • Here the mathematics is prominent. • Simulation

  7. Scientific Computing • Computer based applied mathematics, involving • Modelling Prescription of a given problem in formulas, • relations, equations. Approximating reality. • Here the application is prominent. • AnalysisStudy 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.

  8. Scientific Computing • Computer based applied mathematics, involving • Modelling Prescription of a given problem in formulas, • relations, equations. Approximating reality. • Here the application is prominent. • AnalysisStudy 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.

  9. Scientific Computing • Computer based applied mathematics, involving • Modelling This is critical. • AnalysisThis is fun. • Simulation This is hard work.

  10. Axon Guidance

  11. Axon Guidance 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

  12. Axon Guidance 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 Joint project between CWI (Verwer), NIBR (van Pelt) and VU (van Ooyen), carried out at CWI and funded by

  13. Axon Guidance

  14. Axon Guidance

  15. Axon Guidance Modelling

  16. Axon Guidance Modelling

  17. 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

  18. 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

  19. 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

  20. 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 Krottje generalized their model and has developed the Matlab package: AG-tools

  21. Axon Guidance Modelling

  22. Mathematical Framework

  23. Mathematical Framework • Three basic ingredients • Domain • States • Fields

  24. 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

  25. Mathematical Framework • Three basic ingredients • Domain Physical environment of axons, neurons, • chemical fields. Domain in 2D with smooth • complicated boundary, possibly with holes. • StatesGrowth cones, target cells, axon properties, • locations. Particle dynamics modelled by • ordinary differential equations. • Fields

  26. Mathematical Framework • Three basic ingredients • Domain Physical environment of axons, neurons, • chemical fields. Domain in 2D with smooth • complicated boundary, possibly with holes. • StatesGrowth 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.

  27. Mathematical Framework • Three basic ingredients • Domain • States • Fields

  28. Mathematical Framework • Three basic ingredients • Domain • States • Fields

  29. Mathematical Framework • Three basic ingredients • Domain • States • Fields

  30. Mathematical Framework • Local function • approximations • - Arbitrary node sets • - Unstructured • Voronoi grids • - Local refinement • Implicit-explicit • Runge-Kutta • integration • Three basic ingredients • Domain • States • Fields

  31. AGTools Example

  32. AGTools Example Ilustration of topographic mapping with 5 guidance fields (3 diffusive and 2 membrane bound) and 200 growth cones

  33. Topographic Mapping Equations

  34. Topographic Mapping Equations No hard laws. Phenomenal setup.

  35. Neuro Scientific Computing Challenges • Modelling • Analysis • Simulation

  36. Neuro Scientific Computing Challenges • Modelling Here major steps are needed: • Analysis • Simulation

  37. 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

  38. 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

  39. 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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