1. 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

2. Scientific Computing

3. 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. Analysis Study 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. 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.

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. 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.

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

10. Axon Guidance

11. 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

12. 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

15. Axon Guidance Modelling

17. 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

18. 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

19. 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

20. 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

21. Axon Guidance Modelling

22. Mathematical Framework

23. 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. States Growth 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. 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.

27. Three basic ingredients Domain States Fields Mathematical Framework

28. Three basic ingredients Domain States Fields Mathematical Framework

29. Three basic ingredients Domain States Fields Mathematical Framework

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

31. AGTools Example

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

33. Topographic Mapping Equations

35. No hard laws. Phenomenal setup.

36. Neuro Scientific Computing Challenges Modelling Analysis Simulation

37. Neuro Scientific Computing Challenges Modelling Here major steps are needed: 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 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

40. 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.