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Ondes de dépression corticales envahissantes

Ondes de dépression corticales envahissantes. Migraine et AVC E. Grenier. Biological aspects. Spreading depression. Ionic exchanges : reaction term Ions diffuse in extracellular space Ions diffuse through « gap junctions » (small holes in the membranes of cells).

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Ondes de dépression corticales envahissantes

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  1. Ondes de dépression corticales envahissantes Migraine et AVC E. Grenier

  2. Biological aspects

  3. Spreading depression • Ionic exchanges : reaction term • Ions diffuse in extracellular space • Ions diffuse through « gap junctions » (small holes in the membranes of cells). • Reaction diffusion equations in the center of the model • Are there travelling waves ? YES: spreading depressions • observed in various species: rat, chicken, … • observed during stroke in rats • conjectured in man during migraine with aura

  4. Spreading depression In Rat cortex • Injection of KCl in some part of the brain • At injection point, depolarization of the cells • Depolarization propagates 2 – 4 mm / min • Recovery after depolarization • Progressive wave: depolarization wave • Two waves do not cross

  5. Spreading depression Occurs in • Migraine with aura • Starts in visual areas • Stop at different locations, depending of the patients • Speed of a few mm / min • Strokes in rat • Created at the border of the dying area • Propagate in the penumbra • Exhausts cells in the penumbra • Final size of the dead zone is proportionnal to the number of spreading depressions which propagate. • No evidence during stroke in human.

  6. Principaux mécanismes impliqués dans la propagation des ondes de dépolarisation de la zone infarcie vers la zone saine par un processus de diffusion des ions K+ et du glutamate dans l'espace extracellulaire et par un processus de propagation d'ondes calciques dans les astrocytes

  7. Spreading depression in a cat brain

  8. Mathematical models

  9. Spreading depression: simple model • State described by a variable u(t,x) • 0 <= u <= 1: 0 normal state / 1 fully depressed state. • Evolution of u under • Diffusion • Local reaction of the tissu f(u) ∂t u – ν∂Δ u = f(u) • In grey matter: • F(u) is negative if u is small (normal state is stable) • F(u) is positive if u is large (fully depressed state is stable, up to recovery phenomena) f(u) = a u (1 – u) (u – u0) • In white matter: recovery f(u) = - b u

  10. Spreading depression: ionic model • Introduce all extra and intracellular ionic concentrations: K+, Na+, Ca2+, Glu, Cl-, … • Extracellular ionic concentrations diffuse in extracellular space • Some species diffuse from glial cells to glial cells through gap junctions • Reaction term is given by all local ionic exchanges through voltage dependent gates, exchangers, pumps … • Very complex system ! • Still to be studied completly !

  11. Spreading depression: ionic model Simulation of a spreading depression following Shapiro (2001)

  12. Spreading depressions in migraine with aura

  13. The domain of propagation

  14. Numerical domain of propagation

  15. Discussion • Topography of grey matter may explain by itself that spreading depression do not propagate in the whole brain during stroke • Topography of grey matter may explain why spreading depressions have never been observed during stroke • Should also come from experimental difficulties • Observed in vitro on small cuts of grey substance (coherent) • Big difference with Rat, where the final size of dead area is proportional to the number of spreading depressions !

  16. Numerical computation: Rolando sulcus

  17. Simulation for Rolando sulcus

  18. Discussion • Topography of Rolando sulcus by itself may explain that spreading depressions always stop there during migraine with aura

  19. Spreading depressions in stroke:Global models

  20. Global models of stroke Very large models, combining • Ionic models: • Simple bistable equations • Complete ionic model of the first section • Oedema models • Blood flow • Death of cells (apoptosis / necrosis) • Programmed cell death : a kind of cell suicide • Energy management • Topography • Toxicity

  21. Typical simulation Dead zone Spreading depressions

  22. Influence of diffusion / apoptosis / toxicity

  23. Influence of diffusion / apoptosis / toxicity

  24. Spreading depressions • In Rat, spreading depressions are observed in vivo • Important in the progression of the dead core • Important to try to block them • In human, no spreading depressions are observed at large scales • Coherent with previous section • Remains to be checked numerically on the whole model • Explains failures of some therapeutics ? • Existence of spreading depressions for very small strokes ? • Stroke in young men • Trace of the propagations of spreading depressions ?

  25. Perspectives • To complete model • Include complete ionic model • Add free radicals • Realistic 2D geometries (in progress) • Realistic 3D geometries (very challenging) • To compare with clinical cases • Basis of clinical images already set up • Numerical challenges • Very different time scales (from 1ms to 12h) • Very complex topography (already in 2D, … 3D …) • Very expensive !

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