A blind deconvolution approach to recover effective connectivity brain networks from resting state fMRI data

G. Wu; W. Liao; S. Stramaglia; J. Ding; H. Chen; D. Marinazzo

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A blind deconvolution approach to recover effective connectivity brain networks from resting state fMRI data

G. Wu, W. Liao, S. Stramaglia, J. Ding, H. Chen, D. Marinazzo

arXiv:1208.3766v1Aug 18, 2012q-bio.NCq-bio.QM

TL;DR

The paper addresses HRF confounding and conditioning difficulties in Granger-causality analysis of resting-state fMRI. It combines blind deconvolution based on spontaneous pseudo-events with partial conditioning, and reports improved NetSim sensitivity and specificity alongside differences in local but not long-range network organization.

Problem
Granger-causality analysis of BOLD fMRI is limited by HRF confounding, short noisy time series, overfitting, redundant variables, and absent explicit resting-state inputs.
Method
The study combines blind deconvolution using spontaneous pseudo-events and a region-specific HRF with partially conditioned Granger causality.
Results
On the 50-node NetSim dataset, sensitivity increased from 20% to 30% and specificity from 88% to 94% after deconvolution.
Takeaways & Limitations
BOLD and deconvolved-BOLD effective-connectivity networks both showed small-world attributes, while deconvolution affected local properties at longer TR but not long-range organization.
Takeaways & Limitations
The method was limited to stability validation because fMRI ground truth lacks general consensus and the usefulness of HRF deconvolution remains unresolved.

Abstract

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A great improvement to the insight on brain function that we can get from fMRI data can come from effective connectivity analysis, in which the flow of information between even remote brain regions is inferred by the parameters of a predictive dynamical model. As opposed to biologically inspired models, some techniques as Granger causality (GC) are purely data-driven and rely on statistical prediction and temporal precedence. While powerful and widely applicable, this approach could suffer from two main limitations when applied to BOLD fMRI data: confounding effect of hemodynamic response function (HRF) and conditioning to a large number of variables in presence of short time series. For task-related fMRI, neural population dynamics can be captured by modeling signal dynamics with explicit exogenous inputs; for resting-state fMRI on the other hand, the absence of explicit inputs makes this task more difficult, unless relying on some specific prior physiological hypothesis. In order to overcome these issues and to allow a more general approach, here we present a simple and novel blind-deconvolution technique for BOLD-fMRI signal. Coming to the second limitation, a fully multivariate conditioning with short and noisy data leads to computational problems due to overfitting. Furthermore, conceptual issues arise in presence of redundancy. We thus apply partial conditioning to a limited subset of variables in the framework of information theory, as recently proposed. Mixing these two improvements we compare the differences between BOLD and deconvolved BOLD level effective networks and draw some conclusions.

1. Introduction

Granger causality is data-driven but faces HRF confounding and conditioning problems in short, high-dimensional fMRI time series. The paper motivates partial conditioning to address these issues while distinguishing direct from mediated influences.

Granger causality relies on statistical prediction and temporal precedence rather than specific anatomical or physiological hypotheses.
BOLD-fMRI Granger analysis is confounded by regionally variable hemodynamic response function latency.Earlier analyses assumed homogeneous hemodynamic processes, but studies reported latency differences across physiological processes and brain regions.
Bivariate analysis can produce false positives, whereas fully multivariate conditioning may overfit short time series and mishandle redundant variables.
The study applies partial conditioning to a limited subset of variables for reconstructing BOLD and deconvolved-BOLD effective connectivity networks.

2. Materials and methods

The method estimates neural activity from resting-state BOLD signals by identifying spontaneous pseudo-events, fitting a regional HRF, and applying blind deconvolution. It then uses the resulting signals for effective-connectivity analysis without requiring event timing or prior spatial information.

Blind-deconvolution in resting-state fMRI data: Resting-state BOLD data are modeled as neural states convolved with an HRF under a linear time-invariant transformation assumption.The measured signal also includes white measurement noise.
Blind-deconvolution in resting-state fMRI data: The procedure models neural activation with an on-off pseudo-event process and fits a canonical HRF with temporal and dispersion derivatives.
Blind-deconvolution in resting-state fMRI data: A Wiener filter uses the estimated HRF and observed BOLD data to approximate the underlying neural signal.
Blind-deconvolution in resting-state fMRI data: Resting-state fMRI is treated as spontaneous event-related because relatively large-amplitude BOLD peaks may reflect specific neural events or states.
Blind-deconvolution in resting-state fMRI data: Pseudo-event onsets are selected by searching candidate timing values and choosing the one with the smallest noise error covariance.
Blind-deconvolution in resting-state fMRI data: The approach can deconvolve BOLD signals without timing information or a priori spatial information about events.

2.2. Partially conditioned Granger causality

The method computes Granger causality while conditioning on a limited set of variables selected for their informativeness, reducing the burden of fully multivariate conditioning.

2.2. Partially conditioned Granger causality: Partial conditioning selects a limited subset of variables to remove indirect interactions in sparse connectivity patterns.The selected variables are chosen as the most informative for the candidate driver variable.
2.2. Partially conditioned Granger causality: The variables are modeled as n covariance-stationary time series represented by state vectors.The model order m determines the lagged components included in each state vector.
2.2. Partially conditioned Granger causality: The partially conditioned Granger causality index compares prediction errors for the target variable with and without the candidate driver’s past.The prediction error ǫ(xα|Y ) is defined as the mean squared error based on vectors Y.
2.2. Partially conditioned Granger causality: The conditioning set Z contains nd variables excluded from the candidate driver and selected by an approximate information-gain strategy.Starting from Zk−1, the procedure repeatedly adds the variable with the greatest information gain until nd variables are selected.

2.3. Simulation Datasets: NetSim

The study evaluates deconvolution on the 50-node NetSim benchmark, while noting that no general ground truth method for fMRI data has been established.

2.3. Simulation Datasets: NetSim: After deconvolution, sensitivity increased from 20% to 30% and specificity increased from 88% to 94%.The authors present these changes as indicative of the usefulness of deconvolving the BOLD signal, not as establishing GC as the preferred method for NetSim.
2.3. Simulation Datasets: NetSim: The analyzed NetSim dataset contained 50 nodes.The dataset was described as the largest of the benchmark datasets considered in the cited discussion.
2.3. Simulation Datasets: NetSim: No general consensus has been reached on how to establish ground truth for fMRI data.The authors also note that NetSim is simulated under DCM, lacks reciprocal connections, and contains only Gaussian noise.

2.4. Resting-State fMRI Datasets

The resting-state fMRI analyses investigate repetition time using publicly released datasets with different temporal and spatial resolutions and standard acquisition durations.

2.4. Resting-State fMRI Datasets: The analyses examined the role of repetition time in deconvolution and effective network reconstruction.The data came from the publicly released 1000 Functional Connectomes Project resting-state fMRI dataset.
2.4. Resting-State fMRI Datasets: Participants had no history of neurological or psychiatric disorders and provided informed consent approved by a local Institutional Review Board.During scanning, participants were instructed to keep their eyes closed.
2.4. Resting-State fMRI Datasets: Two datasets used TR=1.4s and TR=0.645s acquisitions on Siemens 3T Trio Tim scanners.Both were acquired with multiplexed echo planar imaging.
2.4. Resting-State fMRI Datasets: The TR=0.645s dataset provided optimal temporal resolution, whereas the TR=1.4s dataset provided optimal spatial resolution.The corresponding acquisitions used 3mm isotropic voxels and 2mm isotropic voxels, respectively, with 10 minutes of scanning for each.
2.4. Resting-State fMRI Datasets: A third dataset used TR=3, 4mm isotropic voxels, and a 5-minute acquisition on a 4T scanner.This dataset consisted of standard resting-state fMRI acquisitions.

2.5. Data preprocessing

Resting-state images were preprocessed with SPM8 through timing, motion, normalization, and resampling corrections before subsequent analysis.

2.5. Data preprocessing: Preprocessing used SPM8 and included slice-timing correction, head-motion correction, spatial normalization, and resampling to 3-mm isotropic voxels.Slice timing was corrected relative to the middle axial slice, and normalization used Montreal Neurological Institute stereotaxic space.
2.5. Data preprocessing: Eight or nine subjects were excluded from the dataset with TR=0.645s.The supplied passage reports the exclusion count as “8(9)” without resolving the notation.

2.6. Anatomical parcellation and analysis

Resting-state fMRI images were parcellated into anatomical regions, and regional time series were extracted and cleaned by regression before deconvolution.

Functional images were segmented into 90 AAL regions of interest, with each representative time series obtained by voxel averaging.
Preprocessing regressed six head-motion parameters and signals from cerebrospinal-fluid and white-matter regions to remove possible spurious variance.
The regional time series were subsequently deconvolved into neural-state signals using the proposed approach.

2.7. Effective connectivity network analysis

Effective connectivity was represented as a thresholded directed graph whose incoming and outgoing topology were analyzed separately.

The effective connectivity network was defined as a 90 × 90 binary directed graph of nodes and directed edges.
An edge eij denotes a directed connection from ROI i to ROI j, and its presence is determined by threshold T.
Because directed edges need not be reciprocal, graph properties were calculated separately for incoming and outgoing matrices using the Brain Connectivity Toolbox.

2.8. Threshold selection

Network comparisons used matching strategies and multiple cost thresholds to control for differences in edge number and weighting across subjects.

A matching strategy was applied because effective connectivity networks can differ across subjects in both edge number and edge weighting.
Global and local network efficiencies tend to increase with edge number, so sparsity differences can alter graph structure and confound comparisons.
Overall topological and nodal properties were calculated at each cost threshold, with small-worldness, efficiency, degree, and nodal efficiency assessed.

3. Results

The proposed blind deconvolution and partial-conditioning framework was evaluated on resting-state fMRI across acquisition times and network scales. Deconvolution produced robust HRF maps, reduced causality-matrix variance, and changed effective-network organization, while global-signal regression preserved HRF spatial distributions.

3.1. Reconstruction of HRF: 4–6 s: the estimated time-deviation κ peaked in this range, consistent with reported gray-matter latency delays of 4–8 s.Lower TR may allow more accurate lag estimation.
3.1. Reconstruction of HRF: 81.7 ± 2.9%: the first HRF-map component explained response-height variance, compared with 98.1 ± 1.2% for time to peak and 95.6 ± 3.5% for FWHM.Spatial patterns were similar across subjects and TRs.
3.2. Variance stability of causality matrix: Much lower variance: causality matrices from deconvolved signals showed lower across-subject variance than BOLD-level matrices for all TR values.PCGC also maintained lower variance than full conditional GC, including at the 1024-node scale.
3.3. Global signal regression: r=0.97, r=0.90, and r=0.88: global-signal regression preserved HRF spatial distributions for response height, time to peak, and FWHM, respectively.
3.4. Effective connectivity network recovery with partial conditioning: Six variables: the mutual-information-gain curves reached their knee when six conditioning variables were considered across alternative prior templates.The authors selected nd = 10 as the most appropriate conditioning size after considering the curves, sensitivity, and specificity.
3.5. Global characteristics of ECN: TR=1.4s: differences between deconvolved-BOLD and BOLD networks were more numerous, with prominent changes in AUC-based global and nodal topological measures.Shorter-TR data showed additional outgoing-network differences in characteristic path length and global efficiency.

4. Discussion

The study combines resting-state BOLD deconvolution with partially conditioned Granger causality and compares effective connectivity networks across signal representations and sampling rates. Results indicate differences in local and nodal organization, while validation is limited by the absence of ground truth and unresolved HRF-deconvolution debates.

Method: The proposed joint approach deconvolves resting-state BOLD using spontaneous pseudo-events and applies partially conditioned Granger causality to infer effective connectivity.The method uses a simpler generic linear canonical HRF rather than a biophysically informed state-space approach.
Limitations: The authors limited validation to method stability and topological comparisons because fMRI effective-connectivity ground truth is unavailable and HRF-deconvolution usefulness remains debated.The comparison covered deconvolved BOLD-level versus BOLD-level networks and the effects of TR=0.645s and TR=1.4s.
Global topology: Both BOLD and deconvolved effective connectivity networks exhibited prominent small-world attributes across shorter and longer TR conditions.Small-worldness reflects a balance between segregated and integrated network organization.
Local topology: For longer TR, deconvolution produced significant differences in clustering and normalized clustering coefficients, indicating altered local-scale network properties.These measures quantify local cliquishness or local information-transfer efficiency.
Global topology: The study found no differences in long-range network organization between BOLD and deconvolved effective connectivity networks.Characteristic path length and global efficiency were used as measures associated with long-range information propagation.