Содержание
- 2. Overview Forward Models for M/EEG Variational Bayesian Dipole Estimation (ECD) Empirical Bayesian Distributed Estimation Multimodal integration
- 3. Overview Forward Models for M/EEG Variational Bayesian Dipole Estimation (ECD) Empirical Bayesian Distributed Estimation Multimodal integration
- 4. Likelihood Prior Posterior Evidence Bayesian Perspective Forward Problem Inverse Problem Data Parameters Model
- 5. Likelihood Forward Problem: Physics Kirkoff’s law: Electrical potential Quasi-static Maxwell’s Equations: Orientation Location Current density: (EEG)
- 6. Likelihood Forward Problem: Physics Orientation Location depends on: Can have analytic or numerical form… location (orientation)
- 7. Forward Problem: Head Models Concentric Spheres: Pros: Analytic; Fast to compute Cons: Head not spherical; Conductivity
- 8. Forward Problem: Meshes 3 important surfaces for BEMs are those with large changes in conductivity: Scalp
- 9. Forward Problem: Canonical Meshes Rather than extract surfaces from individuals MRIs, why not warp Template surfaces
- 10. fMRI time-series Motion Correct Anatomical MRI Coregister Deformation Estimate Spatial Norm Spatially normalised Smooth Smoothed Template
- 11. Forward Problem: Canonical Meshes Rather than extract surfaces from individuals MRIs, why not warp Template surfaces
- 12. Likelihood Forward Problem: ECD vs Distributed Orientation Location For small number of Equivalent Current Dipoles (ECD)
- 13. Overview Forward Models for M/EEG Variational Bayesian Dipole Estimation (ECD) Empirical Bayesian Distributed Estimation Multimodal integration
- 14. Inverse Problem: VB-ECD Standard ECD approaches iterate location/orientation (within a brain volume) until fit to sensor
- 15. Inverse Problem: VB-ECD Maximising the (free-energy approximation to the) model evidence offers a natural answer to
- 16. Inverse Problem: DCM Dynamic Causal Modelling (DCM) can be seen as a source localisation (inverse) method
- 17. Overview Forward Models for M/EEG Variational Bayesian Dipole Estimation (ECD) Empirical Bayesian Distributed Estimation Multimodal integration
- 18. Y = Data n sensors J = Sources p>>n sources L = Leadfields n sensors x
- 19. Phillips et al (2002), Neuroimage Inverse Problem: Standard L2-norm “Minimum Norm” “Loreta” (D=Laplacian) “Depth-Weighted” “Beamformer” “Tikhonov
- 20. Phillips et al (2005), Neuroimage Likelihood: C(e) = n x n Sensor (error) covariance Prior: C(j)
- 21. Specifying (co)variance components (priors/regularisation): 1. Sensor components, (error): C = Sensor/Source covariance Q = Covariance components
- 22. Henson et al (2007) Neuroimage When multiple Q’s are correlated, estimation of hyperparameters λ can be
- 23. Henson et al (2007) Neuroimage When multiple Q’s are correlated, estimation of hyperparameters λ can be
- 24. Friston et al (2008) Neuroimage Fixed Variable Data Source and sensor space Inverse Problem: Full (DAG)
- 25. Friston et al (2002) Neuroimage 1. Obtain Restricted Maximum Likelihood (ReML) estimates of the hyperparameters (λ)
- 26. Hyperpriors allow the extreme of 100’s source priors, or MSP Inverse Problem: Multiple Sparse Priors …
- 27. Hyperpriors allow the extreme of 100’s source priors, or MSP Inverse Problem: Multiple Sparse Priors Friston
- 28. Summary: Automatically “regularises” in principled fashion… …allows for multiple constraints (priors)… …to the extent that multiple
- 29. Overview Forward Models for M/EEG Variational Bayesian Dipole Estimation (ECD) Empirical Bayesian Distributed Estimation Multi-modal and
- 30. Multi-subject Integration (Group Inversion) Specifying (co)variance components (priors/regularisation): 1. Sensor components, (error): C = Sensor/Source covariance
- 31. Specifying (co)variance components (priors/regularisation): 1. Sensor components, (error): C = Sensor/Source covariance Q = Covariance components
- 32. Litvak & Friston (2008) Neuroimage Fixed Variable Data Source and sensor space Multi-subject Integration (as before)
- 33. Litvak & Friston (2008) Neuroimage Fixed Variable Data Source and sensor space Multi-subject Integration
- 34. Concatenate data across subjects Common source-level priors: Subject-specific sensor-level priors: Litvak & Friston (2008) Neuroimage …having
- 35. Litvak & Friston (2008) Neuroimage MMN MSP MSP (Group) Multi-subject Integration: Results
- 36. Multi-modal Integration 1. Symmetric integration (fusion) of MEG + EEG 2. Asymmetric integration of M/EEG +
- 37. fMRI MEG ? (future) Data: Causes (hidden): Generative (Forward) Models: Balloon Model Head Model ? EEG
- 38. Asymmetric Integration fMRI MEG ? (future) Data: Causes (hidden): Generative (Forward) Models: Balloon Model Head Model
- 39. Multi-modal Integration 1. Symmetric integration (fusion) of MEG + EEG 2. Asymmetric integration of M/EEG +
- 40. Specifying (co)variance components (priors/regularisation): 1. Sensor components, (error): C = Sensor/Source covariance Q = Covariance components
- 41. Specifying (co)variance components (priors/regularisation): 1. Sensor components, (error): Ci(e) = Sensor error covariance for ith modality
- 42. Henson et al (2009) Neuroimage Fixed Variable Data Source and sensor space Single Modality (as before)
- 43. Henson et al (2009) Neuroimage Fixed Variable Data Source and sensor space Multiple modalities
- 44. Henson et al (2009) Neuroimage Stack data and leadfields for d modalities: Where data / leadfields
- 45. ERs from 12 subjects for 3 simultaneously-acquired Neuromag sensor-types: RMS fT/m μV Faces Scrambled fT Magnetometers
- 46. MEG mags MEG grads EEG FUSED +31 -51 -15 +19 -48 -6 +43 -67 -11 +44
- 47. Henson et al (2009) Neuroimage Fusing magnetometers, gradiometers and EEG increased the conditional precision of the
- 48. Multi-modal Integration 1. Symmetric integration (fusion) of MEG + EEG 2. Asymmetric integration of M/EEG +
- 49. Asymmetric Integration of M/EEG+fMRI Specifying (co)variance components (priors/regularisation): 1. Sensor components, (error): C = Sensor/Source covariance
- 50. Henson et al (2010) Hum. Brain Map. Specifying (co)variance components (priors/regularisation): 1. Sensor components, (error): C
- 51. Friston et al (2008) Neuroimage Fixed Variable Data Source and sensor space Asymmetric Integration of M/EEG+fMRI
- 52. Henson et al (2010) Hum. Brain Map. Fixed Variable Data Source and sensor space Asymmetric Integration
- 53. T1-weighted MRI Anatomical data {T,F,Z}-SPM Gray matter segmentation Cortical surface extraction 3D geodesic Voronoï diagram Functional
- 54. SPM{F} for faces versus scrambled faces, 15 voxels, p 5 clusters from SPM of fMRI data
- 55. (binarised, variance priors) Magnetometers (MEG) * * * * None Global Local (Valid) Local (Invalid) Valid+Invalid
- 56. (binarised, variance priors) Magnetometers (MEG) * * * * Gradiometers (MEG) None Global Local (Valid) Local
- 57. (binarised, variance priors) Magnetometers (MEG) * * * * Gradiometers (MEG) None Global Local (Valid) Local
- 58. 3.2 Fusion of MEG+fMRI (Application) (binarised, variance priors) Magnetometers (MEG) * * * * Gradiometers (MEG)
- 59. (binarised, variance priors) Magnetometers (MEG) * * * * Gradiometers (MEG) None Global Local (Valid) Local
- 60. None Global Local (Valid) Local (Invalid) Magnetometers (MEG) Gradiometers (MEG) Electrodes (EEG) IID sources and IID
- 61. None Global Local (Valid) Local (Invalid) Magnetometers (MEG) Gradiometers (MEG) Electrodes (EEG) IID sources and IID
- 62. 3.2 Fusion of MEG+fMRI (Application) fMRI priors counteract superficial bias of L2-norm None Global Local (Valid)
- 63. fMRI priors counteract superficial bias of L2-norm None Global Local (Valid) Local (Invalid) Magnetometers (MEG) Gradiometers
- 64. Prior 4. Prior 5. NB: Priors affect variance, not precise timecourse… R L Gradiometers (MEG) (5
- 65. Adding a single, global fMRI prior increases model evidence Adding multiple valid priors increases model evidence
- 66. Multi-modal Integration 1. Symmetric integration (fusion) of MEG + EEG 2. Asymmetric integration of M/EEG +
- 67. Fusion of fMRI and MEG/EEG? fMRI MEG ? (future) Data: Causes (hidden): Balloon Model Head Model
- 68. Fusion of fMRI and MEG/EEG? Fixed Variable Data Source and sensor space Henson Et Al (2011)
- 69. Fusion of fMRI and MEG/EEG? Henson Et Al (2011) Frontiers Fixed Variable Data Source and sensor
- 70. Overall Conclusions SPM offers standard forward models (via FieldTrip)… (though with unique option of Canonical Meshes)
- 71. The End
- 72. Likelihood Forward Problem: Physics Ohm’s law: Continuity equation: Maxwell’s Equations: Orientation Location Current (nA):
- 73. Inverse Problem: Simulations Mattout et al (2006) Multiple constraints: Smooth sources (Qs), plus valid (Qv) or
- 74. Inverse Problem: Simulations Mattout et al (2006) Multiple constraints: Smooth sources (Qs), plus valid (Qv) or
- 75. Inverse Problem: Temporal Friston et al (2006) V typically Gaussian autocorrelations… In general, temporal correlation of
- 76. Inverse Problem: Temporal Friston et al (2006)
- 77. 3.2. Fusion of MEG+fMRI Prior 4. Prior 5. fMRI hyperparameters ln(λ)+32 ln(λ)+32 Participant Participant Magnetometers (MEG)
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