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An estimation of the HRF in resting state fMRI:methodology, applications, and the effect of
autonomic nervous system fluctuations
Guo-Rong Wu1 2 Daniele Marinazzo1
1Ghent University, Belgium2Southwest University, China
March 3, 2017
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 analysis of fMRI data
I General linear model (GLM)
I Functional and effective connectivity
fMRI: brain activity is measured through oxygenated bloodlevel
So, apart from making the signal possible, how does heartrate affect recorded brain activity in fMRI?
Variance explained..
... by the Respiratory Response Function (Birn et al. 2008),Respiratory Variability (RV), Heart Rate (HR) and Respiratoryvariability + Heart Rate (RVHR)
HR and RV filters
Effects on connectivity
Correlation between connectivity and HRV
Correlation with LF- and HF-HRV
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 analysis of fMRI data
I General linear model (GLM)
I Functional and effective connectivity
BOLD Signal: General linear model (GLM)
Figure: cartoon of the BOLD signal resulting from blocked and event-related stimuli, without noise
BOLD Signal: General linear model (GLM)
Linear Time Invariant model
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 pathophysiologicalindicator
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
CBF-HRF correlation across subjects
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.
But never forget the physiology behind it
Fluctuation models
I Cardiac phase (CP) and heart rate (HR)
I Respiratory phase (RP) and interaction between CP and RP(InterCRP)
I Respiratory volume per unit time (RVT)
Different combinations of these regressors
I RP RVT (RPV-model)
I RP RVT CP InterCRP (RPVC-model)
I RP RVT HR (RPVH-model)
I RP RVT CP InterCRP HR (RPVCH-model)
Variance explained by quasi-periodic and non-periodiccardiac fluctuation regressors
Spatial modulations of HRF: median maps
Preprocessing
Processing steps ..
I Despiking (D)
I Physiological noise correction (C)
I Slice timing correction (T)
I Registration (R)
I Normalization (N)
.. in different orders
I DCTRN
I DRCTN
I DTRCN
Preprocessing
Processing steps ..
I Despiking (D)
I Physiological noise correction (C)
I Slice timing correction (T)
I Registration (R)
I Normalization (N)
.. in different orders
I DCTRN
I DRCTN
I DTRCN
Different HRF estimation across models
Correlation maps between HRV and HRF parameters
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.Data 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: [email protected]
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