An estimation of the HRF in resting state fMRI:methodology and applications

Guo-Rong Wu1 2 Daniele Marinazzo1

1Ghent University, Belgium2Southwest University, China

November 30, 2016

7 @dan marinazzohttp://users.ugent.be/~dmarinaz/

Statistical analysis of fMRI data

Two main objectives

I Establishing the link between neural activity and the measuredsignal

I Determining distributed brain networks that correspond to brainfunction

Statistical methods

I General linear model (GLM)

I Functional and effective connectivity

BOLD Signal: General linear model (GLM)

Linear Time Invariant

The processed BOLD signal at time t, y(t) (partial out confounds:motion parameters etc.), is modeled as the convolution of neuralstate s(t) and hemodynamic response function h(t), i.e.

y(t) = s(t)⊗ h(t) + c + ε(t)

where c indicates the baseline magnitude.

I ε(t) can be modelled by AR(p) to account for the temporalcorrelation.

I in task-related fMRI, s(t) could be substituted by stimulus func-tion s(t) =

∑Ki=1 αiδ(t − t i )

I in resting-state fMRI there is no explicit stimulus and timingfor HRF onset

Point Process

Specific BOLD events govern the dynamics of the brain at rest(Tagliazucchi et al. 2012, Petridou et al. 2013)

Figure: from Tagliazucchi et al. 2012. BOLD point process: Sb(t)

Figure: Simultaneous BOLD peaks reproduce whole series FC patterns

From neuronal pseudo-events to BOLD peaks

we assume the peak of BOLD response lags behind the peak ofspontaneous point process event is L = κ · TR/N seconds(0 <L <PST).

Figure: Time lag from stimulus to BOLD peak. To obtain the time lag κ,we search all integer values in the interval [0,PST ·N/TR], where PST isthe peristimulus time, choosing the one for which the noise squared erroris smallest (i.e. min∀0<L<PST | y(t)− sb(t − L)⊗ h(t) |2), indicating thespontaneous event onset.

HRF basis vectors

I Reduce the bias in the linear estimation framework especiallyfor the low signal noise ratio dataset.

I Decrease computational cost.

We assume that the hemodynamic responses for all resting statespontaneous point process events and at all locations in the brainare fully contained in an d-dimensional linear subspace H of Rd .then, any hemodynamic response h can be represented uniquely asthe linear combination of the corresponding basis vectors, such as:

I Canonical HRF with its delay/dispersion derivatives (canon2dd),

I (smoothed) Finite Impulse Response (sFIR)

Recap of the procedure

Once the RS-HRF is retrieved it can be used to:

I deconvolve BOLD data in order to eliminate confounders ontemporal precedence

I map it onto the brain surface and use it as a pathophysiologicalbiomarker

Physiological Simulation Test

Balloon model (Buxton et al. 1998)

BOLD signal y(t) = λ(v , q,E0) is taken to be a static nonlinearfunction of normalized venous volume (v), normalized totaldeoxyhemoglobin voxel content (q) and resting net oxygenextraction fraction by the capillary bed (E0).

y(t) = V0(k1(1− q) + k2(1− q/v) + k3(1− v))k1 = 7E0, k2 = 2, k3 = 2E0 − 0.2.

Simulation

TR=2s, default parameters in SPM, and varying transit time(τ0 = V0/F0) = 0.98, 1.3, 1.6, 2, where V0 is resting blood volumefraction and F0 is resting flow. The physiology of the relationshipbetween flow and volume is determined by the evolution of thetransit time (Friston et al. 2000). ε(t): AR(1).

Two types of internal stimulus → simulate the BOLD signal

1. Event-related (ER) design (0.1s on) with fixed inter-stimulus-interval (ISI) of 40 s,

2. Jittered ER design with non-uniform ISI (average ISI = 19s).SNR := σsignal/σnoise , where σ is the SD. 20 runs

Figure: Left panel: Ground truth (Balloon: green) and estimated HRFs(canon2dd: red, sFIR: blue) for jittered ER design (mean ISI=33.3s,TR=2s) with different SNR, the colored shadow indicates the standarddeviation. Right panel: the relative error for jittered ER design (meanISI=33.3s, TR =1s (star), TR=2s(square), TR=3s(circle)) with differentSNR

Relation with baseline cerebral blood flow: pCASLdataset(n=108)

Figure: figure from Havlicek et al. 2015

resting state HRF vs CBF (1), (BOLD fMRI TR=2s)

Figure: Mean maps of CBF and HRF parameters across subjects. A:CBF; B: response height, canon2dd; C: response height, sFIR; D: re-sponse height-PSC, canon2dd; E: response height-PSC, sFIR; F: baseline,canon2dd; G: baseline, sFIR; H: FWHM, canon2dd; I: FWHM, sFIR; J:time to peak, canon2dd; I: time to peak, sFIR)

resting state HRF vs CBF (2)

Figure: Scatterplot of the spatial correlations across voxels between CBFand HRF parameters. X-axis is the CBF, Y-axis are HRF parameters

Figure: Correlations between CBF and HRF parameters at voxel level acrosssubjects, p <0.05 FDR corrected. Left column is for canon2dd HRF, rightcolumn is for sFIR HRF.

Relation with EEG power

Simultaneous EEG-fMRI, eyes closed - eyes open.

BOLD-fMRI TR=1s, 7 Tesla. Thalamus and Occipital lobe: individual

voxel p <10−6, cluster size >50.

Applications

Looking at modulations of the HRF parameters across conditions

Eyes closed (1) - open - closed again (2), Eyes closed (1) - closed again(2) - openTR=2s, 48 healthy subjects (fcon1000 project, Beijing) Group-levelrepeated-measures ANCOVA

Loss of consciousness

I Awake (W1) - Mild sedation (S1) - Deep sedation (S2) - Re-covery (W2), TR=2.46 s, 21 healthy subjects

I 12 Vegetative State (VS) patients and 25 Healthy Controls(HC), TR=2.46 s

(Coma Science Group, Liege)

HRF parameters across conditions

HRF shape is modulated by consciousness

Correlation HRF height - consciousness in anesthesia

p <0.05, topo FDR corrected

Differences in HRF height between W1 and S2

p <0.05, topo FDR corrected

Differences in HRF width between W1 and S2

p <0.05, topo FDR corrected

Differences in HRF height between controls and VS

Conjunction map of (W1-S2) and (Cont-VS) height

Correlation with self-generated thoughts - NYCQ scores

Significant canonical correlation between NYCQ and HRFparameters, p¡0.05 FDR corrected. Left column is for canon2ddHRF, right column is for sFIR HRF.Dafa from Gorgolewski, Mendes et al. 2015

Improving the estimation of Granger causality

Conclusions

I We have proposed a way to identify the HRF in resting statefMRI using point processes

I The procedure has been validated with simulations and ASLdata

I The retrieved RS-HRF is modulated by several psycho-physiologicalfactors

I Deconvolving the retrieved RS-HRF from BOLD time seriesimproves the estimation of lagged influences

Thanks

Collaborators

Philippe Ciuciu, Neurospin, FranceSteven Laureys, C. Di Perri, ULG, BelgiumGopikrishna Deshpande, Auburn University, USA

Contact

Matlab code is available athttps://github.com/guorongwu/rsHRF

email: daniele.marinazzo@ugent.be

Refs

Wu et al., Med. Im. Anal. 2013 PMID 23422254Wu and Marinazzo, Phil. Trans. R. Soc. A 2016 PMID 27044997Wu and Marinazzo, PeerJ preprint 1317, 2015