Sparse SPM: Group Sparse-dictionary learning in SPM framework for resting-state functional connectivity MRI analysis

doi:10.1016/j.neuroimage.2015.10.081

NeuroImage

Volume 125, 15 January 2016, Pages 1032-1045

https://doi.org/10.1016/j.neuroimage.2015.10.081 Get rights and content

Abstract

Recent studies of functional connectivity MR imaging have revealed that the default-mode network activity is disrupted in diseases such as Alzheimer's disease (AD). However, there is not yet a consensus on the preferred method for resting-state analysis. Because the brain is reported to have complex interconnected networks according to graph theoretical analysis, the independency assumption, as in the popular independent component analysis (ICA) approach, often does not hold. Here, rather than using the independency assumption, we present a new statistical parameter mapping (SPM)-type analysis method based on a sparse graph model where temporal dynamics at each voxel position are described as a sparse combination of global brain dynamics. In particular, a new concept of a spatially adaptive design matrix has been proposed to represent local connectivity that shares the same temporal dynamics. If we further assume that local network structures within a group are similar, the estimation problem of global and local dynamics can be solved using sparse dictionary learning for the concatenated temporal data across subjects. Moreover, under the homoscedasticity variance assumption across subjects and groups that is often used in SPM analysis, the aforementioned individual and group analyses using sparse dictionary learning can be accurately modeled by a mixed-effect model, which also facilitates a standard SPM-type group-level inference using summary statistics. Using an extensive resting fMRI data set obtained from normal, mild cognitive impairment (MCI), and Alzheimer's disease patient groups, we demonstrated that the changes in the default mode network extracted by the proposed method are more closely correlated with the progression of Alzheimer's disease.

Introduction

Spontaneous low-frequency fluctuations (< 0.1 Hz) of blood oxygen level-dependent (BOLD) signals during resting states have been shown to represent cognitive functions and neural physiology (Biswal et al., 1995, Cordes et al., 2001, Damoiseaux et al., 2006). Spatiotemporally distinct resting-state networks have been consistently identified in the primary visual network, default mode network, salience network, fronto-parietal network, and sensory motor network, among others (De Luca et al., 2006). Among the various resting-state subnetworks, the default mode network (DMN), which significantly deactivates during cognitive task-related experiments, has been studied extensively in functional connectivity analyses. It has been shown that the DMN is closely involved with episodic memory processing (Lustig et al., 2003, Greicius et al., 2004). Furthermore, previous works have provided evidence that the PCC, which shows a neural deactivation in early Alzheimer's disease (AD), is the first brain region to exhibit decreased metabolism in AD patients (Minoshima et al., 1997).

Seed-based approaches (Lowe et al., 1998, Rombouts et al., 2003, Fransson, 2005, Fox et al., 2009) and independent component analysis (ICA)-based approaches (van de Ven et al., 2004, Beckmann et al., 2005) are the most commonly used analysis methods in resting-state functional connectivity studies. The seed-based approach extracts BOLD signal time courses from a region of interest (ROI), called a “seed” region, and computes the cross-correlation between time course signals from the ROI and all other voxels in the brain to obtain a map of neuronal connectivity (Fox and Raichle, 2007). Despite their popularity, seed-based correlation analyses have limitations such that they require a prior determination of the seed's location. On the other hand, ICA automatically decomposes the entire BOLD dataset into maximally independent components. However, the brain networks are not independent of each other due to their complex, interconnected regions. Another issue in using ICA is that the individual analysis is usually not sensitive in detecting networks compared to seed-based analysis. Moreover, the unified theory that links the individual analysis results to group analysis is still not fully established. Additionally, graph theory-based quantitative analyses of brain connectivity have been developed to study structural and functional brain networks and their interactions (Bullmore and Sporns, 2009). However, graph theory-based analysis is dependent on pre-defined parcellations. Therefore, parcellation-independent graph theoretical analyses are required.

Unlike the conventional approaches, here we present a novel parcellation-free functional connectivity analysis that is inspired by the graph theoretical approach for brain networks. More specifically, our method is derived from signal decomposition based on a sparse graph model that regards the temporal dynamics at each voxel as a sparse combination of unknown global information flow. Interestingly, we can show that the sparse dictionary learning algorithm and the concept of a spatially adaptive design matrix used for our fMRI analysis in Lee et al. (2011b) can be used to represent local connectivities based on the sparse graph model. However, one of the technical difficulties of using Lee et al. (2011b) for functional connectivity fMRI analysis is that the extracted temporal dynamics corresponding to each network highly depend on the individual. Moreover, subject-dependent regressors should be estimated, after which the group-level statistical inferences should be performed using group average activation maps that are extracted using the subject-specific regressors. This complicates the group sparse learning and statistical inference. Similar difficulties have been observed in other data-driven approaches, such as ICA. In group ICA, the problem has been addressed by concatenating the data or by using tensor factorization. However, even though group-wise activation maps can be detected using these types of approaches, more advanced group analyses, such as a two-sample t-test, or an analysis of variance (ANOVA), are often difficult. There are some recent methods for ICA to obtain such components, such as dual regression (Zuo et al., 2010), and GRAICAR (generalized ranking and averaging independent component analysis by reproducibility) (Yang et al., 2012). However, a unified framework from individual to group level using standard statistical analysis tools still appears to be lacking.

To overcome such technical difficulties in group analysis, one of the main contributions of this paper is to propose a novel unified mixed-effect model framework where group-level sparse dictionary learning and group inference can be performed in a unified linear mixed model and the restricted maximum likelihood (ReML) variance estimation framework. More specifically, to estimate the unknown global dynamics and local network structures at a group level, we first concatenated the time series across the subject and performed a group sparse dictionary learning for the concatenated temporal data. We showed that the sparse learning for the concatenated time series is equivalent to imposing a constraint that the network structures within a group are similar. Using this constraint, a global dictionary was estimated from the concatenated data, after which the dictionaries from the concatenated time series were separated to obtain each subject-level sparse dictionary. Then, the SPM-type analysis was performed using individualized dictionaries. Under the homoscedasticity variance assumption, we showed that the aforementioned group sparse dictionary learning and inference can be rigorously derived using the unified linear mixed model framework and the restricted maximum likelihood (ReML) variance estimation.

As the mathematical framework for inference turns out to be similar to that of a standard statistical parameter mapping (SPM) analysis with only the exception of a spatially adaptive design matrix (which still retains the homogeneous degree of the freedom), rich statistical analysis tools, such as p-value correction using random field theory and hypothesis-driven inference, can be used. Accordingly, we call the proposed method as sparse SPM (SSPM).

To confirm the validity of the proposed method, we provide extensive comparisons using group data from normal, MCI, and Alzheimer subjects from both our clinical data set and the ADNI (Alzheimer's Disease Neuroimaging Initiative) data set (http://www.loni.usc.edu/ADNI).

Section snippets

Theory

Throughout the paper, xⁱ and x_j correspond to the i-th row and the j-th column of matrix X, respectively. When S is an index set, X^S and A_S correspond to a submatrix collecting the corresponding rows of X and columns of A, respectively; x_S denotes a subvector collecting the corresponding elements of X. The superscripts ' and ^† denote the adjoint operator and pseudo-inverse, respectively. A vector 1_L denotes a L-dimensional vector with elements of ones, and I_k × k is a k × k identity matrix.

Data acquisition

We collected three groups of resting-state fMRI data: 1) 22 normal subjects (8 male, mean age 70 years), 2) 37 MCI patients (21 male, mean age 72 years), and 3) 20 AD patients with CDR 0.5 (5 male, mean age 72 years). During the task period, subjects were instructed to be awake and alert but not actively involved in a task and with eye closed. A 3.0 T fMRI system (Philips, Netherlands) was used to measure the BOLD response. The echo planar imaging (EPI) sequence was used with TR/TE = 3000/35 ms, flip

Parameter selection

The determination of the number of atoms in a dictionary is an important issue, because it represents the number of linearly independent temporal dynamics across the whole brain. Group results with various dictionary numbers are shown in Fig. 5. In general, when a small number of dictionary components are chosen, they tend to aggregate different networks. On the other hand, a large dictionary size tends to segregate a subnetwork into multiple fragments. We tested various dictionary component

Discussion

The ANOVA results in Fig. 9 clearly indicate progression of Alzheimer's disease. The results imply that the PCC is the first area to deteriorate and is followed by MPFC and IPL areas. These findings with SSPM coincide with the biological findings that the posterior components of the default network, including the precuneus and posterior cingulate, are particularly vulnerable to early deposition of amyloid β-protein, one of the hallmark pathologies of AD (Sperling et al., 2009). This clearly

Conclusion

In this paper, we developed a unified mixed model called sparse SPM for group sparse dictionary learning and inference for resting-state fMRI analysis. Unlike ICA methods, the new algorithm exploits the fact that temporal dynamics at each voxel can be represented as a sparse combination of global dynamics because of the property of small-worldness of brain networks. In addition, the sparse coding step in the sparse dictionary learning step of our proposed method enabled SSPM for

Acknowledgment

JCY was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (NRF-2014R1A2A1A11052491). YJ was supported by the Brain Research Program (NRF-2010-0018843), Basic Science Research Program (NRF-2012R1A1A2044776) through the National Research Foundation of Korea funded by the Ministry of Science, ICT and Future Planning.

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²: Data used in the preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database (http://www.loni.usc.edu/ADNI). As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in analysis or writing of this report. ADNI investigators include (complete listing available at http://www.loni.usc.edu/ADNI/Collaboration/ADNIAuthorshiplist.pdf).

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Sparse SPM: Group Sparse-dictionary learning in SPM framework for resting-state functional connectivity MRI analysis

Abstract

Introduction

Section snippets

Theory

Data acquisition

Parameter selection

Discussion

Conclusion

Acknowledgment

NeuroImage

NeuroImage

NeuroImage

NeuroImage

NeuroImage

NeuroImage

Neuron

NeuroImage

NeuroImage

Fast and incoherent dictionary learning algorithms with application to fmri

SIViP

K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation

IEEE Trans. Signal Process.

Investigations into resting-state connectivity using independent component analysis

Philos. Trans. R. Soc. B Biol. Sci.

Functional connectivity in the motor cortex of resting human brain using echo-planar mri

Magn. Reson. Med.

Complex brain networks: graph theoretical analysis of structural and functional systems

Nat. Rev. Neurosci.

Frequencies contributing to functional connectivity in the cerebral cortex in “resting-state” data

Am. J. Neuroradiol.

Consistent resting-state networks across healthy subjects

Proc. Natl. Acad. Sci.

Sparse dictionary learning of resting state fMRI networks

Spontaneous fluctuations in brain activity observed with functional magnetic resonance imaging

Nat. Rev. Neurosci.

The global signal and observed anticorrelated resting state brain networks

J. Neurophysiol.

Spontaneous low-frequency BOLD signal fluctuations: an fMRI investigation of the resting-state default mode of brain function hypothesis

Hum. Brain Mapp.

Statistical Parametric Mapping: The Analysis of Functional Brain Images: The Analysis of Functional Brain Images