Full Length ArticlesState-space model with deep learning for functional dynamics estimation in resting-state fMRI
Introduction
A human brain can be understood as a complex system with different structural regions dedicated for different functions, which are locally segregated but globally integrated to process various types of information. Over the last decades, it has been one of the major concerns to investigate the underlying functional mechanism of a human brain in the fields of basic and clinical neuroscience. The functional Magnetic Resonance Imaging (fMRI) that measures the changes of Blood Oxygen Level-Dependent (BOLD) signal in a non-invasive manner has become one of the most successful investigative tools to explore the functional characteristics or properties of a brain.
In the meantime, ever since Biswal et al. (1995) discovered that different brain regions still actively interact with each other while a subject is at rest, i.e., not performing any cognitive task, resting-state fMRI (rs-fMRI) has been widely used as one of the major tools to investigate regional associations or brain networks (Rombouts et al., 2005, Fox et al., 2005, Buckner et al., 2008). The rs-fMRI provides insights to explore the brain's functional organization and to examine altered or aberrant functional networks possibly caused by brain disorders such as Alzheimer's Disease (AD) (Greicius et al., 2004, Li et al., 2002), Mild Cognitive Impairment (MCI) (Rombouts et al., 2005, Sorg et al., 2007, Wang et al., 2007, Zhang et al., 2012, Chase, 2014), autism spectrum disorder (Monk et al., 2009, Khan et al., 2013), schizophrenia (Liang et al., 2006, Zhou et al., 2007, Garrity et al., 2007, Lynall et al., 2010), and depression (Anand et al., 2005, Greicius et al., 2007, Craddock et al., 2009). In this work, we focus on the early diagnosis of MCI based on the computational analysis of rs-fMRI. Due to a high rate of progression from MCI to AD in one year, approximately 10 to 15% according to Alzheimer's Association's's (2012)), it has been of great importance for early detection or diagnosis of MCI and seeking a proper treatment to prevent from progressing to AD. From a clinical point of view, it is advantageous to use rs-fMRI to investigate functional characteristics in the rs-fMRI of patients, who may not be able to perform complicated cognitive tasks during scanning. In these regards, the analysis of functional characteristics inherent in rs-fMRI is playing a core role for brain disease diagnosis or prognosis (Handwerker et al., 2012, Li et al., 2012, Leonardi et al., 2013, Hjelm et al., 2014, Wee et al., 2014, Suk et al., 2015c).
To date, the functional characteristics in a brain have been studied in two different approaches. The effective connectivity (Friston et al., 1993) investigates the causal relations between regions, e.g., one region exerts over another. The functional connectivity (Van Dijk et al., 2010), the other type of approach, measures functional associations between regions by means of temporal coherence or correlation. In this paper, we mainly consider the functional connectivity, which is computationally less intensive for whole-brain network analysis. It is worth noting that recent studies investigating the complex brain functions have observed the phenomenon that functional connectivity spontaneously changes over time (Chang and Glover, 2010, Bassett et al., 2011, Hutchison et al., 2013), i.e., dynamic rather than stationary. Functional dynamics include changes in the strength of connection between regions, and also the number of connections linked to regions. Motivated by those studies, there have been efforts to estimate temporal changes in functional connectivities and then use functional properties extracted from the estimated dynamic functional connectivities for disease diagnosis.
To our best knowledge, many existing methods for MCI diagnosis with rs-fMRI typically assumed stationarity on a functional network over time and explicitly modelled it by different methods such as Pearson's correlation, partial correlation (Liang et al., 2012), independent component analysis (Jafri et al., 2008, Li et al., 2012), and sparse linear regression (Wee et al., 2014). Recently, (Faisan et al., 2007, Hutchinson et al., 2009), and (Janoos et al., 2011) independently devised different types of state-space models to explore the dynamic characteristics of functional activation and applied for event-related fMRI data analysis. Due to the use of variables related to external stimulus, i.e., event, those models are not suitable for rs-fMRI data analysis. Meanwhile, Leonardi et al. devised an Eigen-decomposition based method to model functional dynamics with a sliding-window technique (Leonardi et al., 2013) and Eavani et al. proposed to model sparse basis learning within a Hidden Markov Model (HMM) framework (Eavani et al., 2013).
In this paper, we propose a novel method of modelling functional dynamics inherent in rs-fMRI by means of probabilistic models. Specifically, rather than computing correlation matrices and extracting graph-theoretic features (Rubinov and Sporns, 2010) such as clustering coefficients and modularity as commonly performed in the literature, we explicitly model dynamic changes of functional characteristics obtained from regional mean time series of rs-fMRI. In a testing phase, our model estimates the likelihood of a testing sample as MCI and Normal healthy Control (NC), based on which we diagnose MCI. Note that, compared to Eavani et al.'s work, where they utilized the original high-dimensional features, in our method, we devise a Deep Auto-Encoder (DAE) that hierarchically discovers non-linear relations among regional features and helps circumvent the problem of high dimensionality, a common in neuroimaging analysis, and then train a dynamic state-space model, i.e., HMM. While Leonardi et al.'s method fails to reflect the spontaneous changes due to the use of a sliding window strategy, the proposed method probabilistically determines the spontaneous changes based on an observation.
It should be noted that the preliminary version of this work was presented in (Suk et al., 2015a). Compared to the preliminary version of this manuscript, we have extended our work by: 1) carrying out more extensive experiments with an additional dataset from the ADNI2 cohort and 2) analyzing the learned models and the estimated functional connectivities in various perspectives. Although, in this paper, we deal with MCI data only, our method can be also used to understand the functional characteristics of other diseases such as autism, schizophrenia, and depression. In addition, thanks to its capability of estimating dynamic functional connectivities from rs-fMRI, our method can be used for neuroscientific studies on functional organization in a brain.
Section snippets
Materials and preprocessing
In this work, we use two independent rs-fMRI datasets, namely, an ADNI2 dataset publicly available online1 and an in-house dataset.
Proposed method
In this section, we propose a novel probabilistic method of modelling functional dynamics inherent in rs-fMRI and estimating the data likelihood of a test subject as NC and MCI for diagnosis. Fig. 1 illustrates the overall framework of our method for MCI identification. Given rs-fMRI images, we first extract mean time series of ROIs, preceded by preprocessing images as described in Preprocessing section. We then train a Deep Auto-Encoder (DAE), which takes the mean intensities of ROIs in a
Experimental settings and results
In this section, we validate the effectiveness of the proposed method for MCI diagnosis with rs-fMRI by comparing with the state-of-the-art methods in the literature, which assume stationarity or non-stationarity (i.e., dynamic) in functional connectivity. As described in Materials and preprocessing section, we conducted experiments on two different datasets, i.e., ADNI2 and in-house cohorts.
Performance interpretation
In our experiments on the ADNI2 and in-house datasets, the proposed method achieved the best diagnostic accuracy of 72.58% (ADNI2) and 81.08% (in-house), respectively.
It is noteworthy that the methods of sDFN and our method considering the potential dynamics inherent in rs-fMRI showed better performance than the methods of Baseline and gSR that ignored the functional dynamics. As for HMM + SDL, it achieved the lowest performance among the competing methods except for Baseline on both datasets. As
Conclusion
In this paper, we focused on computational modelling of functional dynamics inherent in rs-fMRI. Specifically, we proposed a novel method of combining a deep architecture model, i.e., deep-auto encoder, with a state-space model, i.e., hidden Markov model, in a unified framework to investigate the underlying functional dynamics in rs-fMRI and ultimately to identify subjects with MCI. The rationale of using DAE is to discover the latent non-linear relations among brain regions, which are
Acknowledgement
This research was supported by Institute for Information & communications Technology Promotion (IITP) grant funded by the Korea government (MSIP) (No. B0101-15-0307, Basic Software Research in Human-level Lifelong Machine Learning (Machine Learning Center)). This research was also partially supported by NIH grants (EB006733, EB008374, EB009634, AG041721, AG049371, AG042599).
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