Designing weighted correlation kernels in convolutional neural networks for functional connectivity based brain disease diagnosis

Highlights

• A new wc-kernel to measure the correlation of brain regions, with weights learned in a data-driven manner to characterize specific contributions of different time points, is proposed.

• A unified wc-kernel-based CNN framework to define functional connectivity networks and extract hierarchical connectivities for disease diagnosis is developed.

• Achieving an accuracy of 84.6%, 88.0% and 57.0 for eMCI (early MCI) vs. HC (healthy control), AD vs. HC, and AD vs. lMCI (later MCI) vs. eMCI vs. HC classifications, respectively.

Abstract

Functional connectivity networks (FCNs) based on functional magnetic resonance imaging (fMRI) have been widely applied to analyzing and diagnosing brain diseases, such as Alzheimer’s disease (AD) and its prodrome stage, i.e., mild cognitive impairment (MCI). Existing studies usually use Pearson correlation coefficient (PCC) method to construct FCNs, and then extract network measures (e.g., clustering coefficients) as features to learn a diagnostic model. However, the valuable observation information in network construction (e.g., specific contributions of different time points), as well as high-level and high-order network features are neglected in these studies. In this paper, we first define a novel weighted correlation kernel (called wc-kernel) to measure the correlation of brain regions, by which weighting factors are learned in a data-driven manner to characterize the contributions of different time points, thus conveying the richer interaction information among brain regions compared with the PCC method. Furthermore, we build a wc-kernel based convolutional neural network (CNN) (called wck-CNN) framework for learning the hierarchical (i.e., from local to global and also from low-level to high-level) features for disease diagnosis, by using fMRI data. Specifically, we first define a layer to build dynamic FCNs using our proposed wc-kernels. Then, we define another three layers to sequentially extract local (brain region specific), global (brain network specific) and temporal features from the constructed dynamic FCNs for classification. Experimental results on 174 subjects (a total of 563 scans) with rest-state fMRI (rs-fMRI) data from ADNI database demonstrate the efficacy of our proposed method.

Introduction

Accurate diagnosis of brain diseases, such as Alzheimer’s disease (AD) and its prodromal stage, i.e., mild cognitive impairment (MCI), is very important for early treatment and possible delay of disease progression. As a complex network, the human brain contains a large number of functional regions. The functional interaction among these regions provides an important insight into the basic mechanism and cognitive processes of the brain (Greicius et al., 2003). In the context of neuroimaging, functional magnetic resonance imaging (fMRI) provides a non-invasive way to map the functional interaction of the brain. Based on fMRI data, functional connectivity networks (FCNs), which characterize functional interactions among brain regions, have been applied to brain disease analysis, and thus helping us better understand the pathology of neurological disorders. Recently, FCNs constructed based on resting-state fMRI (rs-fMRI) have been widely applied in the task of automated brain diseases diagnosis (Guye, Bettus, Bartolomei, Cozzone, 2010, Jie, Zhang, Gao, Wang, Wee, Shen, 2014, Wee, Yap, Zhang, Denny, Browndyke, Potter, Welsh-Bohmer, Wang, Shen, 2012).

Up to now, studies on FCNs typically focus on two aspects: 1) traditional FCN, which usually implicitly assumes that functional connectivity is temporally stationary throughout recording period in fMRI (Sporns, 2011). However, these studies ignore the changing properties of FCNs over time. 2) dynamic FCN, which focuses on the temporal changes of functional connectivity between specific brain regions. Existing studies have suggested that the changing properties of functional connectivity over time may be associated with cognitive and vigilance state (Thompson, Magnuson, Merritt, Schwarb, Pan, McKinley, Tripp, Schumacher, Keilholz, 2013, Chang, Liu, Chen, Liu, Duyn, 2013), which are critical for better understanding the pathology of brain diseases (Hutchison, Womelsdorf, Allen, Bandettini, Calhoun, Corbetta, Della Penna, Duyn, Glover, Gonzalez-Castillo, et al., 2013, Zhang, Small, 2006, Kiviniemi, Vire, Remes, Elseoud, Starck, Tervonen, Nikkinen, 2011). Also, some studies have found that brain diseases (e.g., AD/MCI) are related with temporal changes of functional connectivities (Jones, Vemuri, Murphy, Gunter, Senjem, Machulda, Przybelski, Gregg, Kantarci, Knopman, et al., 2012, Wee, Yang, Yap, Shen, Initiative, et al., 2016).

In these previous studies, the FCNs are usually constructed by simply calculating the Pearson correlation coefficients (PCCs) between time series from brain regions, and then the low-level measures (e.g., clustering coefficients) are extracted from the constructed FCNs as features to train a diagnostic model (e.g., support vector machine, SVM). However, these studies have several critical limitations. First, during the construction of FCNs, they neglect the valuable observation information (e.g., specific contributions of different time points). Intuitively, different time points could have different contributions for characterizing interactions among brain regions. In fact, studies have demonstrated that the functional connectivity calculated at specific time points can extend the usual pairwise interaction measures both in information and interpretability (Tagliazucchi, Balenzuela, Fraiman, Chialvo, 2012, Tagliazucchi, Balenzuela, Fraiman, Montoya, Chialvo, 2011). Second, the high-level and high-order network features that could further improve the performance are also neglected by these previous studies in feature extraction step. In addition, since network construction, feature extraction and classification are separately performed, it could yield sub-optimal learning model, thus degrading the diagnosis performance.

To address these problems and motivated by recent successful applications of convolutional neural networks (CNNs) in the natural image analysis field, in this paper we first define a weighted correlation kernel (called wc-kernel) for calculating the correlation between brain regions by using learned weights to characterize the contributions of different time points. Compared with previous methods (e.g., PCC), our proposed wc-kernel can capture the specific contributions of different time points, thus conveying richer interaction information among brain regions. Furthermore, we build a wc-kernel based CNN (called wck-CNN) for constructing FCNs and extracting the hierarchical (i.e., from local and global, and also from low-level to high-level) high-order features for brain disease classification, using fMRI data. Fig. 1 shows the architecture of our proposed wck-CNN method. Specifically, we first define a layer to build dynamic FCNs using our proposed wc-kernels. Here, we build multiple dynamic FCNs using multiple wc-kernels, with each one reflecting temporal changes of FCNs, thus conveying richer dynamic information of brain network. Then, we build another three layers to sequentially extract local (brain region specific), global (brain network specific), and temporal high-level and high-order features from the constructed low-level and low-order functional connectivities for classification. We evaluate the proposed wck-CNN method on 174 subjects (a total of 563 scans) with rs-fMRI data from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database, ² which includes 48 healthy controls (HC), 50 early MCI (eMCI), 45 late MCI (lMCI) and 31 AD. The experimental results suggest that our proposed method can not only improve the diagnostic performance compared with state-of-the-art methods, but also provide novel insights into the interaction patterns of brain activities and their changes in diseases.

The main contributions of this paper are four-fold. First, we define a wc-kernel to measure the correlation of brain regions, with weights learned in a data-driven manner to characterize specific contributions of different time points. The proposed wc-kernel is different from previous methods (e.g., PCC method) that equally treat all time points. Second, we build a unified wck-CNN framework for defining FCNs and extracting hierarchical connectivities for disease diagnosis based on rs-fMRI data. To the best of our knowledge, this is among the first attempt to define the correlation kernel in CNN for characterizing the interactions among brain regions, and to build a unified CNN framework for dynamic FCN construction and analysis using fMRI data. Third, we provide an implementation for performing inference on brain network data. Finally, we investigate the changing connectivity patterns in AD/MCI patients.

The rest of the paper is organized as follows. In Section 2, we briefly review the related studies. Then, we describe the data used in the experiments, and present our proposed method and learning framework in Section 3. In Section 4, we describe conducted experiments and present corresponding results. In Section 5, we present discussions regarding the experiments and results. Finally, we conclude this paper in Section 6.