inverse problems in functional brain...
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Inverse problems in functional brain imaging
Joint detection-estimation in fMRI
Ph. Ciuciu1,2
[email protected] www.lnao.fr
1: CEA/NeuroSpin/LNAO 2: IFR49
May 7, 2010 GDR -ISIS Spring school@Porquerolles
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Outline
● Limits of the classical fMRI data analysis
● Within-parcel detection-estimation of brain activity
● Extension to whole brain 3D analysis
● Alternative on the cortical surface
● Conclusions and perspectives
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1. Detect and localise brain activationsEx: In SPM [Friston et al, 1994], the BOLD response is modelled with:
2. Estimate the dynamics of activation [Goutte et al, IEEE TMI 2000; Marrelec et al, HBM 2003]
or
Probe brain dynamics
HRF estimates
Compute statistical activation Maps
Time s
Classical fMRI analysis
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Classical fMRI analysis
● GLM limitations:
A single HRF shape is not physiologically appropriate
Studies report HRF variability:➢ within subject (between regions, sessions, conditions, trials)
– [Miezin et al., NIM 2000; Ciuciu et al., IEEE TMI 2003]–
➢ between subjects– [Handwerker et al., NIM 2004; Aguirre et al., NIM 1998]
➢ between groups (infants, patients,...) –
➢ …
Massive univariate analysis
Data spatially smoothed for SNR enhancement
[D'Esposito et al, NIM 1998, 2003; Richter and Richter, NIM 2003]
[Neumann et al, NIM 2003, 2006; Smith et al, NIM 2005]
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Detection of brain activation and estimation of brain dynamics are addressed separately
Any detection method supposes a given HRF shape
Any estimation algorithm provides relevant results in activated voxels or regions only
Two main issues in fMRITwo main issues in fMRIMotivations
[Makni et al., IEEE SP 2005, NeuroImage, 2008; Vincent et al, ICASSP'07, EMBC'07, IEEE MLSP 2009;Ciuciu et al, ISBI'08]
Address these two problems simultaneously in a joint detection-estimation (JDE) framework
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Outline
● Limits of the classical fMRI data analysis
● Within-parcel detection-estimation of brain activity
● Extension to whole brain 3D analysis
● Alternative on the cortical surface
● Conclusions and perspectives
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Spatial compromise
BOLD signal: low contrast-to-noise ratio
Not enough reproducibility in a single voxel
The HRF is nonetheless spatially variable
Consider hemodynamically homogeneous brain areas
A given parcel should be:
Big enough for reproducibilitySmall enough for homogeneity
Parcel-wise hemodynamic model
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Non-parametric HRF modelling
Explicit assumptions on the BOLD response
Hyp. 1: linearity Hyp 2: stationarity
+Convolution kernel
Hyp 3: additivity
TR 2TR3TR ...
Time in s
[Aguirre et al, 1998; McGonigle et al, 2000; Smith et al, 2005]
[Ciuciu et al, 2003; Marrelec et al, 2004]
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Parcel-based BOLD signal model
Temporal hypotheses: for standard ISIs➢ Hyp. 1: linearity Hyp 2: stationarity
+Convolution kernel
Hyp 3: additivity
TR 2TR3TR ...
Time in s
Stimulus-varying NRLs:
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Parcel-based BOLD signal modelSpatial hypotheses: functionally homogeneous ROI➢ Single HRF shape
➢ Voxel-dependent magnitudes of the BOLD response
Neural Response Levels
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Forward BOLD signal modelSpatial hypotheses: functionally homogeneous ROI➢ Single HRF shape
➢ Voxel-dependent magnitudes of the BOLD response
[Makni, Ciuciu et al., IEEE SP 2005; Makni et al, Ciuciu, NeuroImage, 2008]
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NRL in and for condition
Forward BOLD signal model
Orthonormal basisfor low frequency drift modelling
Known parameters
Unknown parameters
Noise statistics in voxel
BOLD signal measured in voxel
HRFDrift coefficients
Arrival time of stimulus
= ⊗ + += ⊗ + +
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Bayes’ rule
likelihood
How the data are generated from the parameters?
Forward modeling
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Main hypothesis: noise decorrelated in space
fMRI time series are statistically independent in space:
Temporal noise model: either white or serially correlated AR(1)
Likelihood definition
[Makni et al, Ciuciu , NeuroImage 2008]
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Bayes’ rule
Prior
What do we know about the parameters before the data are acquired?
Prior modeling
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HRF prior modeling
Information about the HRF shapenonparametric approachesAveraging: [Buckner et al, 1996]
Selective averaging: [Dale et al, HBM 1997]
FIR (Finite Impulse Response)Regularized FIR (smoothing prior):
[Marrelec, Ciuciu et al, IPMI’03; Ciuciu et al., IEEE TMI 2003]
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NRL prior modeling
Spatial information
Independence between conditions:
Spatial mixture model (SMM) for each
[Vincent, Ciuciu et al, ICASSP'07]
~~
~~
Hidden MarkovRandomField
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NRL prior modeling
~~
~~
Ising or Potts field:
~~~
~~~~
~ ~~~
~ ~~~
~
=0
=0.5
=2
0.25 0.25 0.25 0.25
0.46 0.28 0.16 0.100.46 0.28 0.16
0.0020.87 0.118 0.01 → adaptive estimation
Partition function:
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Typical instance: 2-class GSMM
Two-class Gaussian mixture [Vincent et al., ICASSP' 07]
Non-activating voxels:Activating voxels:
Influence of
Unknown hyper-parameters:
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Bayes’ rule
What do we know about the HRF, the NRLs and thehyper-parameters given the data?
Keystone of learning scheme:- Simulating realizations of using MCMC
- Approximating using variational EM
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Simulated datasets
Time in s.
Non-activating voxel
Activating voxel
BO
LD
fM
RI
data
BO
LD
fM
RI
data
[Vincent et al, IEEE TMI 2010]
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Simulation results
SMM SMM SMM
True activations True inactivations
SMM SMMSMM
Strong influence of regularization parameter
SMM
SMM
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Simulation results
SMM SMM=0.7 SMM
dash/continuous line: density of inactivating/activating voxels
SMM SMMSMM =0.7SMM =0.2
SMM =0.2
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Simulation results
SMM SMM SMM
True activations True inactivations
SMM SMMSMM
SMM
SMM
lower SNR for Best tuning: larger
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Simulation results
SMM SMM SMM
dash/continuous line: density of inactivating/activating voxels
SMM SMMSMMSMM
SMM
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Hyper-parameter inference
Random walk Metropolis-Hastings step for
Special case:
Alternative: mean-field approximation
[Forbes and Peyrard, IEEE PAMI 2003]
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Partition function estimation
RW Metropolis-Hastings step for sampling
Preliminary estimation of the partition function
Importance sampling identity:
Practical implementation: Tabulate over a fine grid
For ➢ Generate of (SW scheme)➢ Compute
[Meng and Rubin, Biometrika 1998]
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Supervised vs. unsupervised
SMM =0.7 USMMSMM
SMM =0.7 USMM
USMM
SMM
Interest of unsupervised spatial mixture models
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Supervised vs. unsupervised
SMM USMMSMM =1.1
SMM =1.1 USMMSMM =1.1
lower SNR for Best tuning: larger
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Area under R0C curves
Are
a u
nder
RO
C c
urv
e
Are
a u
nder
RO
C c
urv
e
nearly optimal unsupervised settings
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Robustness to SNR fluctuations
Are
a u
nder
RO
C c
urv
e
Are
a u
nder
RO
C c
urv
e
- - IMM– USMM
Improved robustness to noise level for USMM
- - IMM– USMM
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Impact of HRF modeling
Roi-based HRF modeling increases statistical sensitivity
HRF shape variability tested in two regions:Fixed HRF Single HRF estimateRegion-based HRF estimate
Time in s.Time in s.
%∆
BO
LD
sig
nal
%∆
BO
LD
sig
nal
ROI mask
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Extension to 3-color Potts modelSMM USMM
USMMSMM
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Extension to 3-color Potts modelSMM USMM
USMMSMM
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Real data sets
Experimental conditions under study: auditory and visual stimuli
Event-related paradigm :- Short stimuli duration- Inter-stimulus interval : ~3s to 10s- Randomised sequence
125 scans with TR = 2.4s, scanning at 3T
● Localizer fMRI experiment:
ROIs located in the primary auditory
cortices
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SPM vs. JDE
Auditory – Visual contrast:
Bilateral activation detected along the gray matterfrom raw data sets (spatially unsmoothed)
% Δ B
OLD
sig
nal
% Δ B
OLD
sig
nal
Time in s.
Time in s.
JDE SPM
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Outline
● Limits of the classical fMRI data analysis
● Within-parcel detection-estimation of brain activity
● Extension to whole brain 3D analysis
● Alternative on the cortical surface
● Conclusions and perspectives
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Whole brain analysis
First step:Segmentation of the gray/white matter interface from the T1 MRI
Second step : brain parcellation based upon functional similarities and spatial connectivty [Flandin et al, ISBI'02; Thirion et al, HBM 2006]
[Makni et al, NeuroImage 2008]
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Adaptive spatial regularization
Remarks:
Extrapolation methods required for ROI of variable sizeand shape
Parcel-dependent regularization factor
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Linear extrapolation of
Linear extrapolation technique: [Trillon et al, Eusipco 2008]
Reference parcels:
Linear regression (c= # neighbour voxels in the parcel):
Application of linear interpolation to non-reference parcels:
Strong limitations for small and irregular grids
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Bilinear dependence of
At a fixed number of , the larger the larger
c = # neighbour voxels in the parcels = # voxels in the parcel
[Risser et al, ICIP'09]
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Bilinear extension:
Bilinear regression:
Application of bilinear interpolation to test grid:
Still homogeneous reference set but applicable toirregular gridsMultiple PFs involved in the extrapolation process
Bilinear extrapolation of
[Risser et al, ICIP'09]
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Min/max extrapolation of
● Fast extrapolation technique:Reference grids:
Grid selection: Min/max approximation criterion
The form of guarantees that:
➢
➢
[Risser et al, MICCAI'09;Risser et al, JSPS 2010]
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Min/max extrapolation of Additional constraints
Remarks➢ Single PF estimate involved in the extrapolation➢ inhomogeneous reference grids are acceptable
x
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Half whole brain analysis
=0.8IMM SSMM USMM
Activations enhanced in the parietal cortex using U/SSMMCoherence with sulcal anatomy & literature
Normalized contrast: Audit. (Computation – Sentence)
[Vincent et al, IEEE TMI 2010]
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Adaptive spatial regularization
Auditory sentence Auditory computation
Time in s.
%∆
BO
LD
sig
nal
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Half whole brain analysis
=0.8IMM SSMM USMM
Activations enhanced in the parietal cortex using U/SSMMCoherent with sulcal anatomy
Normalized contrast: Audit. (Computation – Sentence)
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Half whole brain analysis
=0.8IMM SSMM USMM
Normalized contrast: right – left “auditory clicks”
Only USMM provides more sensitive activation in themotor cortex
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Adaptive spatial regularization
Left click Right click
Time in s.
%∆
BO
LD
sig
nal
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Outline
● Limits of the classical fMRI data analysis
● Within-parcel detection-estimation of brain activity
● Extension to whole brain 3D analysis
● Alternative on the cortical surface
● Conclusions and perspectives
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Cortical surface analysis
Segmentation of the gray/white matter interface from the T1 MRI
BOLD signal projection
Parcellation on the cortical surface
JDE on the cortical surface
[Operto et al, NeuroImage 2008]
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Surface analysis - localizer
Gyrii parcellation
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Surface analysis - localizer
Effect maps
Auditory sentence Vertical checker-board
[Ciuciu et al, SfS 2010]
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Surface analysis – detection maps
Audit. (Computation – Sentence)
Normalized contrast[Ciuciu et al, SfS 2010]
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Hemodynamic parameter maps
Estimated hemodynamic parameters
Time-to-peak
Full Width atHalf Maximum
[Ciuciu et al, SfS 2010]
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Outline
● Limits of the classical fMRI data analysis
● Within-parcel detection-estimation of brain activity
● Extension to whole brain 3D analysis
● Alternative on the cortical surface
● Conclusions and perspectives
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Summary The joint detection-estimation framework:
directly accounts for different sources of variability
provides both region-based HRF time courses and contrast maps
embeds unsupervised spatial regularization
avoids using spatial filtering of fMRI datasets
depends on an input parcellation: [Vincent et al, ISBI'08]
Second release of Pyhrf package (v 2.0)
downloadable at http://launchpad.net (nipy project)WIP: integration in the BrainVISA-fMRI toolbox
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Acknowlegdments
This work was partly supported by grants from Région Ile-de-France
Special thanks to:
Thomas VincentSalima Makni Anne-Laure FouqueLaurent RisserSolveig BadilloStéphane Sockeel
Jérôme IdierAlexis RocheSophie DonnetFlorence ForbesJean-François Giovannelli
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Forward model with habituation
15 t-scores5
L
R
Activation in response to the first sentence detected in the STS/G
[Rabrait et al, JMRI 2008]
[Ciuciu et al, ICASSP 2009]
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Habituation phenomenon● Response variation to a stimulus after repeated exposure
to that stimulus [Naccache et Dehaene, Science, 2001]
Causes : - Strategy, tiredness, attentional effects, learning...
- Repetition suppression effect...
Effects : - Decreased NRLs - Shorter response delays
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Introduction of habituation parameters
Forward model with habituation
We assume that for non-activating voxels
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Forward model with habituation
Stimulus trials Stimulus trials
BO
LD m
ag
nit
ud
e
Tim
e in s
.
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Main hypothesis: noise decorrelated in space
fMRI time series are statistically independent in space:
Temporal noise model: either white or serially correlated AR(1)
Likelihood definition
[Makni et al, NeuroImage 2008]
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Aguirre et al (1998). Neuroimage 8:360–369.Birn et al (2000). Neuroimage 14:817–826.Birn et al (2005). Neuroimage 27:70–82Boynton et al (1996). J Neurosci 16(13):4207–4221.Buckner et al (1996). Proc Natl Acad Sci U.S.A. 93:14878–14883.Buckner (1998). Hum Brain Mapp 6:373–377.Burock & Dale (2000). Hum Brain Mapp 11:249–260.Buxton et al (2004). Neuroimage 23:S220–S233.Chen et al (2004). Neurcomputing 61:395–400.Ciuciu et al (2003). IEEE Trans Medical Imag 22:1235–1251.
Donnet et al (2006). NeuroImage. 31:1169-1176.Deneux & Faugeras (2006). NeuroImage. 32(4): 1669-1689.D'Esposito et al (1999). Neuroimage 10:6–14.D'Esposito et al (2003). Nat Rev Neurosci 4:863–872.Ford et al (2005). Neuroimage 26:922–931Friston et al (1994). Hum Brain Mapp 1:153–171.Friston et al (1998). Neuroimage 7:30–40Friston et al (2000). Neuroimage 12:466–477.Genovese (2000). J Amer Statist Assoc 1995:691–719.Gibbons et al (2004). Neuroimage 22:804–814.Glover et al (1999). Neuroimage 9:416-429.Gössl et al (2001a). Biometrics 57:554–562.Gössl et al (2001b). Neuroimage 14:140–148.Goutte et al (2000). IEEE Trans Medical Imag 19:1188–1201.Handwerker et al (2004). Neuroimage 21:1639–1651.Hansen et al (2004). Neuroimage 23:233–241.Henson et al (2002). Neuroimage 15:83–97.
References
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ReferencesKershaw et al (1999). IEEE Trans Medical Imag 18:1138–1153.Kruggel & Von Cramon (1999a). Magn Reson Med 42:787–797.Kruggel & Von Cramon (1999b). Hum Brain Mapp 8:259–271.Kruggel et al (2000). Neuroimage 12:173–183.Liao et al (2002). Neuroimage 16:593–606.Logothetis (2003). J Neurosci 23:3963–3971.Logothetis et al (2001). Nature 412:150–157.Makni et al (2005). IEEE Trans Signal Process 53(9):3488–3502.Marrelec et al (2003) Hum Brain Mapp 19:1–17.Marrelec et al (2004). IEEE Trans Medical Imag 23:959–967.McGonigle et al (2000). Neuroimage 11:708–734.Miezin et al (2000). Neuroimage 11:735–759.Neumann et al (2003). Neuroimage 19:784–796.Neumann et al (2006). Neuroimage 32(3): 1185-1194.Penny et al (2003). NeuroImage. 19(3): 727-744.Penny et al (2005). NeuroImage. 24(2): 350-362.Rajapakse et al (1998). Hum Brain Mapp 6:283–300.Richter & Richter (2003). Neuroimage 20:1122–1131.Riera et al (2004). NeuroImage 21(2): 547--567.Saad et al (2001). Hum Brain Mapp 13:74–93.Smith et al (2005). Hum Brain Mapp 24:248–257.Vazquez et al (1998). Neuroimage 7:108–118.Woolrich et al (2004a). Neuroimage 21:1732–1747.Woolrich et al (2004b). Neuroimage 21:1748–1761.Woolrich et al (2004c). IEEE Trans Medical Imag 23:213–231.Woolrich et al (2005). IEEE Trans Medical Imag 24(1): 1-11Worsley & Friston (1995). Neuroimage 2:173–181.Worsley et al (2002). NeuroImage. :15(1): 1-15.
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Comparison of linear/bilinear
Mean approximation error over Regular & Irregular test fields.Errors given in percentage.
Improved performance with the bilinear approach for small and irregular fieldsApproximation accuracy depends on
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Other statistical parameters
Non-activating voxels
Noise parameters [Makni et al, ISBI'06]
Mixture parameters [Makni et al, NIM 2008]
Activating voxels
Mixture probabilities [Makni et al, NIM 2008]
2-class mixture(Jeffreys prior):
3-class mixture:
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Cortical surface analysis
Towards FMRI/EEG fusion
Asymmetric approach: EEG source reconstruction informed by fMRI analysis or fMRI informed by EEG events
Onsets given by interictal spikes Constraint on the variance/covariance matrix expressed from the estimated hemodynamic parameters estimated by JDE
Symmetric approach:
Model transient neuronal signal between stimulus onset signal and the hemodynamic response + generative models (DCM)
Spatio-temporal decoupling, identify a common spatial support
[Daunizeau et al 2007]
[Makni et al 2008b; Stephan et al, 2007/08/09/10]
[Daunizeau et al 2005; Mattout et al, 2006]
[M. Dojat, GIN]
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Ongoing works Neuro-dynamics models (habituation effect)
Inference of the parcellation in a variational framework
Validation at the group level
Model comparison and selection
Application to infants and epileptic patients
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Metropolis-Hastings step to sample PF estimate required
Unsupervised SMM