Inverse problems in functional brain imaging

Joint detection-estimation in fMRI

Ph. Ciuciu1,2

philippe.ciuciu@cea.fr 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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References

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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