Mean Field Theories in Neuroscience

1. Mean Field Theories in Neuroscience B. Cessac, Neuromathcomp, INRIA

5. Cortical columns.

7. Cortical columns. Small cylinders, of diameter 0.1~1mm, crossing cortex layers, with about 103-104 neurons, from different types, strongly connected.

8. Cortical columns. Cortical columns are involved in elementary sensori-motor like vision.

9. Cortical columns. They are composed of neurons belonging to a small number of populations interacting together. These populations belong to different cortex layers. Inhibitory Cells Superficial layers Spiny Stellate Cells Layer IV Thalamic Input Deep layers Pyramidal Cells

10. Cortical columns. It is possible and useful to propose phenomenological models characterizing the mesoscopic activity of cortical columns, predicting the behaviour of local field potential generated by the electric activity of neurons and to relate this behavior with measures and clinical observations (epilepsy). Inhibitory Cells Superficial layers Spiny Stellate Cells Layer IV Thalamic Input Deep layers Pyramidal Cells

11. Type of cortical column OI pixel Definition Our Column Spatial scale 50-100 µm Number of neurons 150-200 neurons Courtesy. S. Chemla. Cortical column paradigm Physico-functional Functional Anatomical Cortical Area Micro-column Mini-column Macro-column or Hyper-column (V1) Neural Mass Orientation column 600 µm (and more) 40-50 µm 200-300 µm 10 mm 100XThousand neurons of the same type (pyr, stellate,…) 60-100 mini-columns 10000 neurons 80-100 neurons Several mini-columns

12. Mean field models.

13. Neurons and synapses.

14. Neurons and synapses.

15. Neurons and synapses.

16. Neurons and synapses. Pre-synaptic neuron j Post-synaptic neuron i

17. Neurons and synapses. Pre-synaptic neuron j Post-synaptic neuron i

18. Neurons and synapses. Pre-synaptic neuron j Post-synaptic neuron i

19. Neurons and synapses. Pre-synaptic neuron j Post-synaptic neuron i

20. Neurons and synapses. Pre-synaptic neuron j Post-synaptic neuron i

21. Neurons and synapses. Pre-synaptic neuron j Post-synaptic neuron i

22. Neurons and synapses. Pre-synaptic neuron j Post-synaptic neuron i

23. Neurons and synapses. Pre-synaptic neuron j Post-synaptic neuron i

24. Neurons and synapses. Pre-synaptic neuron j Post-synaptic neuron i

25. Neural mass model.

26. Neural mass model. P populations of neurons, a =1 ... P

27. Neural mass model. Voltage-based model P populations of neurons, a =1 ... P

28. Neural mass model. Voltage-based model P populations of neurons, a =1 ... P Assumptions:

29. Neural mass model. Voltage-based model P populations of neurons, a =1 ... P Assumptions: • Synapse response, current and noise depend only on the neuronal population.

30. Neural mass model. 2 Voltage-based model 1 3 P populations of neurons, a =1 ... P Assumptions: • Synapse response, current and noise depend only on the neuronal population.

31. W21 W23 W31 Neural mass model. W12 2 Voltage-based model 1 3 W32 P populations of neurons, a =1 ... P Assumptions: • Synapse response, current and noise depend only on the neuronal population.

32. W21 W23 W31 Neural mass model. W12 2 Voltage-based model 1 Synaptic weights 3 W32 (independent)‏ P populations of neurons, a =1 ... P Assumptions: • Synapse response, current and noise depend only on the neuronal population. • The probability distribution of synaptic efficacies depend only on pre- and post synaptic neuron' population

33. Neural mass model. Voltage-based model Synaptic weights (independent)‏ P populations of neurons, a =1 ... P Assumptions: • Synapse response, current and noise depend only on the neuronal population. • The probability distribution of synaptic efficacies depend only on pre- and post synaptic neuron' population

35. Dynamic mean-field theory.

36. Dynamic mean-field theory. Voltage-based model

37. Dynamic mean-field theory. Voltage-based model Stochastic (annealed)‏ Random (quenched)‏ Nonlinear

38. Dynamic mean-field theory. Voltage-based model

39. Dynamic mean-field theory. Voltage-based model

40. Dynamic mean-field theory. Voltage-based model Local interactions field.

41. Dynamic mean-field theory. Voltage-based model Local interactions field.

42. Dynamic mean-field theory. Voltage-based model Non random synaptic weights. Local interactions field.

43. Dynamic mean-field theory. Voltage-based model Non random synaptic weights. Local interactions field.

44. Dynamic mean-field theory. Voltage-based model Non random synaptic weights. Local interactions field.

45. Dynamic mean-field theory. Voltage-based model Non random synaptic weights. Local interactions field.

46. Dynamic mean-field theory. Voltage-based model Non random synaptic weights. Local interactions field. Dynamic mean-field equations.

47. Dynamic mean-field theory. Voltage-based model Non random synaptic weights. Local interactions field. Dynamic mean-field equations.

48. Dynamic mean-field theory. Voltage-based model Non random synaptic weights. Local interactions field. Naive mean-field equations.

49. Dynamic mean-field theory. Voltage-based model Non random synaptic weights. Local interactions field. Naive mean-field equations.

50. Dynamic mean-field theory. Voltage-based model Non random synaptic weights. Local interactions field. Naive mean-field equations.