1. Jean LAURENS Bayesian Modelling of Visuo-Vestibular Interactions with Jacques DROULEZ Laboratoire de Physiologie de la Perception et de l'Action, CNRS, Collège de France, Paris Laurens, Droulez, Biol. Cyber. 2006

2. Bayesian model Probabilistic computation Semicircular Canals (noisy) Otoliths (ambiguous) Priors P(motion) P(sensory inputs | motion) Internal model of sensors Motion estimates P(motion | sensory inputs) = P(sensory inputs | motion).P(motion) a Plausible Improbable G A F

3. A priori ● VOR dynamic ● Somatogravic effect

4. Geometrical aspects Angular acceleration ∫∫ Otolith signal Canal signal Linear acceleration Linear velocity Head position ∫∫ Angular velocity Head orientation Double integration H -1

5. Noise issues Angular acceleration ∫∫ Otolith signal Canal signal Linear acceleration Linear velocity ∫∫ Noise Angular velocity Head orientation Head position Double integration ? ? H -1

6. A priori Angular acceleration ∫∫ Otolith signal Canal signal Linear acceleration Linear velocity ∫∫ A priori Angular velocity Head orientation A priori Head position Double integration H -1 Noise

7. Visual informations Angular acceleration ∫∫ Otolith signal Canal signal Linear acceleration Linear velocity ∫∫ A priori Angular velocity Head orientation A priori Head position Double integration H -1 Noise Visual signal Noise

8. Plan ● Introduction to Bayesian inference ● Visuo-vestibular interactions (Monkey) ● 3D Stimulations (Monkey, Human)

9. Bayesian inference ● Probability exam: normal and pronged dice (Gezinkter Würfel) D1 : normalD2 : pronged 6 in 50% throws

10. Bayesian inference P(6 | D1) = 1/6 P(6 | D2) = 3/6 Likelihood : P(D1 | 6) = 1/4 P(D2 | 6) = 3/4 ?

11. Bayesian inference ● A priori: P(D1) = 9/10 P(D2) = 1/10

12. Bayesian inference ● Bayes formula P(6 | D2).P(D2) P(6) P(D2 | 6) = LikelihoodA priori

13. Bayesian inference Likelihood : P(6 | D1) = 1/6 P(6 | D2) = 3/6 A priori : P(D1) = 9/10 P(D2) = 1/10 A posteriori : P(D1 | 6) = k * 1/6 * 9/10 = 3/4 P(D2 | 6) = k * 3/6 * 1/10 = 1/4 ?

14. Bayesian inference ● More observations P(2 | D2).P(6 | D2).P(D2) P(6,2) P(D2 | 6,2) = Likelihood A priori

15. Bayesian inference and vestibular information Likelihood : P(Vest. Signal| Motion) A priori : P(Motion) F V = 0 P(Motion | Vest. Signal) = P(Vest. Signal| Motion).P(Motion)

16. Rotations around a vertical axis Angular acceleration ∫ Canal signal A priori 40 °/s Angular velocity Noise η 10 °/s Visual signal Noise η 7 °/s τ = 4 s H -1

17. Results: rotation in dark 050100 -0.5 0 0.5 1 RotationStop Rotation Vel. Estimated vel. (τ = 20 s) Vest. Signal (τ = 4 s) Velocity Storage time (s)

18. Optokinetic stimulation LightDark OKANOKN 020406080 0 0.5 1 Stimulation velocity(Ω) Estimated velocity (Ω) Raphan, Matsuo, Cohen, 1979

19. Optokinetic stimulation LightDark 020406080 0 0.5 1 No velocity storage Normal No canals Raphan, Cohen, Matsuo 1977 Stimulation velocity (°/s) OKN velocity (°/s)

20. Optokinetic stimulation LightDark 020406080 0 0.5 1 020406080 0 0.5 1 No canals Normal

21. Canals plugging Optokinetic stimulation RotationStop Light Dark Rotation in dark 01020 0 1 01020 0 0.5 1 Angelaki & al. 1996 τ = 0.1 s

22. Velocity storage 050100 -0.5 0 0.5 1 020406080 0 0.5 1 RotationStopLightDark Stimultation velocity Estimated velocity (Ω) ^ Vest. signal 'Velocity storage' (Ω t 0 ) ^ Optokinetic stimulation Rotation in Dark Raphan, Cohen

23. Equivalence with Raphan-Cohen model +

24. Conclusion ● Probabilistic modelling:  noise on vestibular signal σ = 10°/s  noise on visual signal σ = 7°/s  A priori on velocity σ = 40°/s LightDark 020406080 0 0.5 1

25. 3D model Acceleration Tilt F ≈ G Gravito-inertial ambiguity G A F

26. 3D model Angular acceleration ∫∫ Otolith signal Canal signal Linear acceleration Linear velocity ∫∫ A priori 40 - 30 °/s Angular velocity Head orientation A priori 3 - 5 m/s² Head position Double integration Noise η 10 °/s Implementation: particle filter

27. Somatogravic effect Acceleration A Y (m/s²) -20246810 0 2 4 Tilt roll (°) -20246810 0 20 30 G -A F

28. Somatogravic: canals plugged A Y (m/s²) -20246810 0 2 4 roll (°) -20246810 0 20 30 G -A F Acceleration Tilt

29. Tilt/translation discrimination Acceleration (m/s²) 051015 -4 -2 0 2 4 tilt (°) temps (s) 051015 -20 0 20 Acceleration (m/s²) 051015 -4 -2 0 2 4 tilt (°) 051015 -20 0 20 Normal Angelaki, 1999

30. Tilt/translation discrimination 051015 -4 -2 0 2 4 time (s) 051015 -20 0 20 051015 -4 -2 0 2 4 051015 -20 0 20 Canals plugged Angelaki, 1999 Acceleration (m/s²) tilt (°) Acceleration (m/s²) tilt (°)

31. Post-rotatory tilt Angular velocity  y (°/s) time (s) 020406080100120 -50 0 50 Angelaki, 1994

32. Post-rotatory tilt 6080100120 -60 -40 -20 0 20 6080100120 -20 0 20 time (s) 6080100120 -20 0 20 Angelaki, 1994

33. Centrifugation G A F Roll  r (°) 050100150 -20 0 20 40 60 time (s)

34. OVAR Benson, Bodin, 1965 Guedry, 1974 after Guedry, 1974 60 °/s 180 °/s

35. OVAR Head tilt  (°) 050100150200 0 100 time (s) 050100150200 0 100 200 α 180 °/s 050100150200 0 20 40 60 60 °/s Angular velocity (°/s)

36. OVAR F G F G -A Guedry, 1974 60 °/s 180 °/s

37. OVAR Ang. vel. a priori: σ Ω = 30°/s Acceleration a priori :σ A = 5 m/s² 60 °/s 78°/s180 °/s Rotation 2 σ Ω 2.6 σ Ω 6 σ Ω Acceleration (13 m/s²) 2.6 σ A 2.6 σ A 2.6 σ A Correia 1966, Lackner 1978, Mittelstaedt 1989, Bos 2002 (90°/s) Guedry 1965, Benson 1966, Correia 1966, Wall 1990

38. OVAR Denise, Darlot, Droulez, Berthoz 1989 Angular velocity (°/s) 050100150200 0 20 40 60 Angular velocity (°/s) time (s) 050100150200 0 20 40 60 Angelaki 2000, Kushiro 2002

39. OVAR time (s) Angelaki 2000, Kushiro 2002 020406080 0 20 40 60 Yaw velocity (°/s)

40. Motion sickness 0204060 10 -2 10 0 2 4 accélération linéaire rotation inclinaison post-rotatoire time (s) k.P(Sensory Signal)

41. Conclusion ● 3 hypothesis  Sensory signals uncertainty  A priori  Bayesian inference ● Lesion modelling (observer theory) ● Bayesian approach ● Extensions ● Predictions Laurens, Droulez, Biol. Cyber. 2006

42. Thanks !