nips nips2009 nips2009-110 knowledge-graph by maker-knowledge-mining

110 nips-2009-Hierarchical Mixture of Classification Experts Uncovers Interactions between Brain Regions

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Author: Bangpeng Yao, Dirk Walther, Diane Beck, Li Fei-fei

Abstract: The human brain can be described as containing a number of functional regions. These regions, as well as the connections between them, play a key role in information processing in the brain. However, most existing multi-voxel pattern analysis approaches either treat multiple regions as one large uniform region or several independent regions, ignoring the connections between them. In this paper we propose to model such connections in an Hidden Conditional Random Field (HCRF) framework, where the classiďŹ er of one region of interest (ROI) makes predictions based on not only its voxels but also the predictions from ROIs that it connects to. Furthermore, we propose a structural learning method in the HCRF framework to automatically uncover the connections between ROIs. We illustrate this approach with fMRI data acquired while human subjects viewed images of different natural scene categories and show that our model can improve the top-level (the classiďŹ er combining information from all ROIs) and ROI-level prediction accuracy, as well as uncover some meaningful connections between ROIs. 1

Reference: text

Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 edu Abstract The human brain can be described as containing a number of functional regions. [sent-6, score-0.199]

2 These regions, as well as the connections between them, play a key role in information processing in the brain. [sent-7, score-0.294]

3 However, most existing multi-voxel pattern analysis approaches either treat multiple regions as one large uniform region or several independent regions, ignoring the connections between them. [sent-8, score-0.345]

4 In this paper we propose to model such connections in an Hidden Conditional Random Field (HCRF) framework, where the classiďŹ er of one region of interest (ROI) makes predictions based on not only its voxels but also the predictions from ROIs that it connects to. [sent-9, score-0.517]

5 Furthermore, we propose a structural learning method in the HCRF framework to automatically uncover the connections between ROIs. [sent-10, score-0.49]

6 In these multi-voxel pattern analysis (MVPA) approaches, patterns of voxels are associated with particular stimuli, leading to veriďŹ able predictions about independent test data. [sent-13, score-0.126]

7 Voxels are extracted from previously known regions of interest (ROIs) [15, 31], selected from the brain by some statistical criterion [24], or deďŹ ned by a sliding window (â€œsearchlightâ€? [sent-14, score-0.189]

8 ) positioned at each location in the brain in turn [20]. [sent-15, score-0.119]

9 Neuroanatomical evidence from macaque monkeys [10] indicates that brain regions involved in visual processing are indeed highly interconnected. [sent-17, score-0.217]

10 Since research on human subjects is largely limited to non-invasive procedures, considerably less is known about interactions between visual areas in the human brain. [sent-18, score-0.233]

11 Here we demonstrate a method of learning the interactions between regions from fMRI data acquired while human subjects view images of natural scenes. [sent-19, score-0.283]

12 classifying a scene as a beach, or a forest) is important for many human activities such as navigation or object perception [30]. [sent-22, score-0.177]

13 1 Given the highly interconnected nature of the brain, however, it is unlikely that these regions encode natural scene categories independently of each other. [sent-28, score-0.322]

14 The method in [31] neither explores connections among the ROIs nor uses the connections to build a classiďŹ er on top of all ROIs. [sent-30, score-0.597]

15 In this work, we propose a method for simultaneously learning the voxel patterns associated with natural scene categories in several ROIs and their interactions in a Hidden Conditional Random Field (HCRF) [28] framework. [sent-31, score-0.392]

16 In our model, the classiďŹ er of each ROI makes predictions based on not only its voxels, but also the prediction results of the ROIs that it connects to. [sent-32, score-0.163]

17 Using the same fMRI data set, we also explore a mutual information based method to discover functional connectivity [5]. [sent-33, score-0.147]

18 Our current model differs from [5], however, by applying a generative model to concurrently estimate the structure of connectivity as well as maximize the end behavioral task (in this case, a scene classiďŹ cation task). [sent-34, score-0.284]

19 Furthermore, we propose a structural learning method to automatically uncover the structure of the interactions between ROIs for natural scene categorization, i. [sent-35, score-0.472]

20 Unlike existing models for functional connectivity, which mostly rely on the correlation of time courses of voxels [23], our approach makes use of the patterns of activity in ROIs as well as the category labels of the images presented to the subjects. [sent-38, score-0.254]

21 Built in the hierarchical framework of HCRF, our structural learning method utilizes information in the voxel values at the bottom layer of the network as well as categorical labels at the top layer. [sent-39, score-0.237]

22 In our method, the connections between each pair of ROIs are evaluated for their potential to improve prediction accuracy, and only those that show improvement will be added to the ďŹ nal structural map. [sent-40, score-0.479]

23 In the remaining part of this paper, we ďŹ rst elaborate on our model and structural learning approach in Section 2. [sent-41, score-0.148]

24 2 Modeling Interactions of Brain Regions: a HCRF Representation The brain is highly interconnected, and the nature of the connections determines to a large extent how information is processed in the brain. [sent-44, score-0.394]

25 We model the connections of brain regions in a Hidden Conditional Random Field (HCRF) framework for the task of natural scene categorization and propose a structural learning method to uncover the pattern of connectivity. [sent-45, score-0.879]

26 In the ďŹ rst part of this section we assume that the structural connections between brain regions are already known. [sent-46, score-0.592]

27 1 Integrating Information across Brain Regions Suppose we are given a set of regions of interest (ROIs) and connections between these regions (see the intermediate layer of Fig. [sent-50, score-0.497]

28 Existing ROI-based MVPA approaches build a classiďŹ er for each ROI independently [15, 24, 18, 16, 31], neglecting the connections between ROIs. [sent-52, score-0.322]

29 It is our objective here to explore the structure of the connections between ROIs to improve prediction accuracy for decoding viewed scene category from fMRI data. [sent-53, score-0.58]

30 In this framework, the classiďŹ er for one ROI makes prediction based on the voxels in this region as well as the results of the classiďŹ ers of its connected ROIs, thereby improving the accuracy of each ROI. [sent-56, score-0.254]

31 Consider an fMRI data set whose individual brain acquisitions are associated with one of đ? [sent-63, score-0.144]

32 2 Z Top-layer Type-III Potentials Type-II Potentials Y3 Y4 Intermediate-layer Y1 3 4 Bottom-layer Type-I Potentials Y2 1 2 Figure 1: Illustration of the HCRF model for modeling connections between ROIs. [sent-97, score-0.295]

33 The weights of all connections and connectivity pattern of the type-II potentials are estimated by the model. [sent-113, score-0.488]

34 To remedy this, our model allows collaborative error-correction over the ROIs by using the given structure of connections (the intermediate layer of Fig. [sent-129, score-0.377]

35 ‘™ are connected in the given structure (the intermediate layer in Fig. [sent-146, score-0.118]

36 1, there are three types of potentials which describe different edges in the model: Type-I Potential đ? [sent-227, score-0.144]

37 Allowing connected ROIs to interact with each other makes our model signiďŹ cantly different from existing MVPA methods [15, 24, 18, 16], and can improve the prediction accuracy of each ROI. [sent-355, score-0.168]

38 In such situations it is possible for the classiďŹ er for one ROI to make better predictions if it can use the information in its connected ROIs. [sent-362, score-0.133]

39 2 Learning the Structural Connections of the Hidden Layer in HCRF Model We have described a method that models the connections between ROIs to build a classiďŹ cation predictor on top of all ROIs. [sent-364, score-0.275]

40 scene categorization), one critical scientiďŹ c goal is to uncover which ROIs are functionally connected for that task. [sent-367, score-0.247]

41 There are 6 possible connections between the ROIs, so in order to investigate whether all possible combinations of connections are present, we need to evaluate 26 = 64 different models. [sent-370, score-0.55]

42 Therefore, our structural learning starts from a graphical model containing only type-I and type-III potentials, without any interactions between ROIs. [sent-386, score-0.239]

43 As we have described in Section 1, connections among ROIs play a key role in information processing. [sent-388, score-0.294]

44 , scene categorization) activates certain ROIs as well as rely on connections between some of them. [sent-391, score-0.443]

45 Algorithm 1: The algorithm for uncovering structural connections between ROIs in the HCRF model. [sent-495, score-0.403]

46 Although some useful information might be lost compared to evaluating all possible combinations of connections, approximating the algorithm in this way can enable the evaluation of many possible connections in a reasonable amount of time, making this algorithm much more practical. [sent-517, score-0.295]

47 The structural learning algorithm is shown in Algorithm 1, and an illustration of evaluating the connection between ROI 2 and 4 is in Fig. [sent-518, score-0.224]

48 3 Model Learning and Inference Learning In the step of structural learning, we need to estimate model parameters to compare the models with or without a type-II connection (see Fig. [sent-521, score-0.195]

49 which type-II potentials should be set, we would like to ďŹ nd out the strength of these connections as well as type-I and III potentials. [sent-525, score-0.387]

50 In the case of natural scene categorization, evidence from neuroscience studies have postulated that 7 regions are likely to play critical roles in this task [31]. [sent-607, score-0.283]

51 ’´ 5 (9) 3 Related Work In this paper, we model the dependencies between ROIs in an HCRF framework, which improves the ROI-level as well as the top-level decoding accuracy by allowing ROIs to exchange information. [sent-632, score-0.156]

52 Other approaches to inferring connections between brain regions from fMRI data can be broadly separated into effective connectivity and functional connectivity [11]. [sent-633, score-0.712]

53 Models for effective connectivity, such as Granger causality mapping [14] and dynamic causal modeling [13], model directed connections between brain regions. [sent-634, score-0.456]

54 Model-driven methods usually test a prior hypothesis by correlating the time courses of a seed voxel and a target voxel [12]. [sent-637, score-0.141]

55 Datadriven methods, such as Independent Component Analysis [8], are typically used to identify spatial modes of coherent activity in the brain at rest. [sent-638, score-0.148]

56 The structural learning method proposed in this paper offers an entirely new way to assess the interactions between brain regions based on the exchange of information between ROIs so that the accuracy of decoding experimental conditions from the data is improved. [sent-640, score-0.511]

57 Furthermore in contrast with the conventional model comparison approaches of trying to optimize the evidence of each model [2], our method relates the connectivity structure to observed brain activities as well as the classes of stimuli that elicited the activities. [sent-641, score-0.26]

58 In this experiment, 5 subjects were presented with color images of 6 scene categories: beaches, buildings, forests, highways, industry, and mountains. [sent-645, score-0.208]

59 Photographs were chosen to capture the high variability within each scene category. [sent-646, score-0.143]

60 Images were presented in blocks of 10 images of the same category lasting for 16 seconds (8 brain acquisitions). [sent-647, score-0.178]

61 We use 7 ROIs that are likely to play critical roles for natural scene categorization. [sent-650, score-0.213]

62 In the inner loop, we use 10 of the 11 training runs to train an SVM classiďŹ er for each ROI and each subject, and the remaining run to learn the connections between ROIs and train the HCRF model by using outputs of the SVM classiďŹ ers. [sent-658, score-0.342]

63 2 Scene ClassiďŹ cation Results and Analysis In order to comprehensively evaluate the performance of the proposed structural learning and modeling approach, we consider different settings of the intermediate layer of our HCRF model. [sent-668, score-0.21]

64 While always keeping all type-I and type-III potentials connected, we consider ďŹ ve different dependencies between the ROIs as shown in Fig. [sent-669, score-0.145]

65 3(e) possesses all properties of our method: the connections between ROIs are determined by structural learning, and the weights of the connections are obtained by estimating model parameters in Equ. [sent-672, score-0.698]

66 In order to estimate the effectiveness of our structural learning method, we compare this setting with the situations where no connections exists between any of the ROIs (Fig. [sent-674, score-0.422]

67 (d,e) The connections between ROIs are obtained by structural learning. [sent-686, score-0.403]

68 Table 1: Recognition accuracy for predicting natural scene categories with different methods (chance is 1/6). [sent-690, score-0.256]

69 Note that the model with no type-II potentials (Fig. [sent-716, score-0.132]

70 From Table 1 it becomes clear that learning both the structure of the connections and their strengths leads to more improvement in decoding accuracy than either one of these alone. [sent-718, score-0.358]

71 The overall, toplevel classiďŹ cation rate increases from 31% for the variant of the model without any connections (Fig. [sent-719, score-0.295]

72 3 Structural Learning Results and Analysis Having established that our full HCRF model outperforms other comparison models in the recognition task, we now investigate how our model can shed light on learning connectivity between brain regions. [sent-726, score-0.26]

73 In the nested cross validation procedure, 12Ă—11=132 structural maps are learned for each subject. [sent-727, score-0.128]

74 2 reports for each subject which connections are present in what fraction of these structural maps. [sent-729, score-0.428]

75 A connection is regarded as a strong connection for a subject if it presents in at least half of the models learned for this subject. [sent-730, score-0.157]

76 2 we use larger font size to denote the connections which are strong on more subjects. [sent-732, score-0.336]

77 Connections that are strong for all subjects are marked in bold. [sent-733, score-0.116]

78 We see that both LOC and PPA show strong interactions between the contralateral counterparts, which makes sense for integrating information across the visual hemiďŹ elds. [sent-734, score-0.185]

79 We also observe strong interactions between PPA and RSC across hemispheres, which underscores the importance of acrosshemiďŹ eld integration of visual information. [sent-735, score-0.157]

80 We see a similar effect in the interactions between LOC and PPA: strong contralateral interactions. [sent-736, score-0.157]

81 For each subject we have 132 learned structural maps (12-fold cross-validation, each one has 11 models). [sent-739, score-0.153]

82 Larger font size denotes connections that are strong on more subjects. [sent-741, score-0.336]

83 76 The strong interactions between PPA and RSC are not surprising, since both are typically associated with the processing of natural scenes [25], albeit with slightly different roles [7]. [sent-812, score-0.18]

84 Together with the strong improvement of decoding accuracy for natural scene categories from LOC when it is allowed to interact with other ROIs (see above), this suggests a role for LOC in scene categorization. [sent-814, score-0.511]

85 , a car) helps with determining the scene category (e. [sent-817, score-0.183]

86 On the other hand, it is also possible that information ďŹ‚ows the other way, that scene-speciďŹ c information in PPA and RSC feeds into LOC to bias object detection based on the scene category (see [3, 1]), and that the classiďŹ er decodes this bias signal in LOC. [sent-820, score-0.23]

87 4 shows the connections which are strong on at least two subjects. [sent-822, score-0.313]

88 left right RSC RSC Figure 4: Schematic illustration of the connections between the seven ROIs obtained by our structural learning method. [sent-823, score-0.432]

89 The connections shown in this ďŹ gure are strong on at least two of the three subjects. [sent-825, score-0.313]

90 Connections that are strong for all three subjects (marked with bold in Table 2) are marked with thicker lines in this ďŹ gure. [sent-826, score-0.144]

91 left PPA right PPA left LOC right LOC 5 V1 Conclusion In this paper we modeled the interactions between brain regions in an HCRF framework. [sent-827, score-0.28]

92 We also presented a structural learning method to automatically uncover the connections between ROIs. [sent-828, score-0.49]

93 Experimental results showed that our approach can improve the top-level as well as ROI-level prediction accuracy, as well as uncover some meaningful connections between ROIs. [sent-829, score-0.382]

94 approach [20] to automatically discover ROIs, and apply our structural learning and modeling method to those ROIs. [sent-831, score-0.147]

95 Exploring functional connectivities of the human brain using multivariate information analysis. [sent-876, score-0.199]

96 Differential parahippocampal and retrosplenial involvement in three types of scene recognition. [sent-891, score-0.191]

97 Investigating directed cortical interactions in time-resolved fMRI data using vector autoregressive modeling and granger causality mapping. [sent-945, score-0.156]

98 Review of methods for functional brain connectivity detection using fmri. [sent-1006, score-0.266]

99 Mental imagery of faces and places activates corresponding stimulusspeciďŹ c brain regions. [sent-1018, score-0.144]

100 Natural scene categories revealed in distributed patterns of activity in the human brain. [sent-1060, score-0.283]

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Abstract: Recent advances in neuroimaging techniques provide great potentials for effective diagnosis of Alzheimer’s disease (AD), the most common form of dementia. Previous studies have shown that AD is closely related to the alternation in the functional brain network, i.e., the functional connectivity among different brain regions. In this paper, we consider the problem of learning functional brain connectivity from neuroimaging, which holds great promise for identifying image-based markers used to distinguish Normal Controls (NC), patients with Mild Cognitive Impairment (MCI), and patients with AD. More specifically, we study sparse inverse covariance estimation (SICE), also known as exploratory Gaussian graphical models, for brain connectivity modeling. In particular, we apply SICE to learn and analyze functional brain connectivity patterns from different subject groups, based on a key property of SICE, called the “monotone property” we established in this paper. 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Learning functional brain connectivity from neuroimaging data holds great promise for identifying image-based markers used to distinguish among AD, MCI (Mild Cognitive Impairment), and normal aging. Note that MCI is a transition stage from normal aging to AD. Understanding and precise diagnosis of MCI have significant clinical value since it can serve as an early warning sign of AD. Despite all these, existing research in functional brain connectivity modeling suffers from limitations. A large body of functional connectivity modeling has been based on correlation analysis [2]-[3], [5]. However, correlation only captures pairwise information and fails to provide a complete account for the interaction of many (more than two) brain regions. Other multivariate statistical methods have also been used, such as Principle Component Analysis (PCA) [8], PCA-based Scaled Subprofile Model [9], Independent Component Analysis [10]-[11], and Partial Least Squares [12]-[13], which group brain regions into latent components. The brain regions within each component are believed to have strong connectivity, while the connectivity between components is weak. One major drawback of these methods is that the latent components may not correspond to any biological entities, causing difficulty in interpretation. In addition, graphical models have been used to study brain connectivity, such as structural equation models [14]-[15], dynamic causal models [16], and Granger causality. However, most of these approaches are confirmative, rather than exploratory, in the sense that they require a prior model of brain connectivity to begin with. This makes them inadequate for studying AD brain connectivity, because there is little prior knowledge about which regions should be involved and how they are connected. This makes exploratory models highly desirable. In this paper, we study sparse inverse covariance estimation (SICE), also known as exploratory Gaussian graphical models, for brain connectivity modeling. Inverse covariance matrix has a clear interpretation that the off-diagonal elements correspond to partial correlations, i.e., the correlation between each pair of brain regions given all other regions. This provides a much better model for brain connectivity than simple correlation analysis which models each pair of regions without considering other regions. Also, imposing sparsity on the inverse covariance estimation ensures a reliable brain connectivity to be modeled with limited sample size, which is usually the case in AD studies since clinical samples are difficult to obtain. From a domain perspective, imposing sparsity is also valid because neurological findings have demonstrated that a brain region usually only directly interacts with a few other brain regions in neurological processes [ 2]-[3]. Various algorithms for achieving SICE have been developed in recent year [ 17]-[22]. In addition, SICE has been used in various applications [17], [21], [23]-[26]. In this paper, we apply SICE to learn functional brain connectivity from neuroimaging and analyze the difference among AD, MCI, and NC based on a key property of SICE, called the “monotone property” we established in this paper. Unlike the previous study which is based on a specific level of sparsity [26], the monotone property allows us to study the connectivity pattern using different levels of sparsity and obtain an order for the strength of connection between pairs of brain regions. In addition, we apply bootstrap hypothesis testing to assess the significance of the connection. Our experimental results on PET data of 42 AD, 116 MCI, and 67 NC subjects enrolled in the Alzheimer’s Disease Neuroimaging Initiative project reveal several interesting connectivity patterns consistent with literature findings, and also some new patterns that can help the knowledge discovery of AD. 2 S ICE : B ack grou n d an d th e Mon oton e P rop erty An inverse covariance matrix can be represented graphically. If used to represent brain connectivity, the nodes are activated brain regions; existence of an arc between two nodes means that the two brain regions are closely related in the brain's functiona l process. Let be all the brain regions under study. We assume that follows a multivariate Gaussian distribution with mean and covariance matrix . Let be the inverse covariance matrix. Suppose we have samples (e.g., subjects with AD) for these brain regions. Note that we will only illustrate here the SICE for AD, whereas the SICE for MCI and NC can be achieved in a similar way. We can formulate the SICE into an optimization problem, i.e., (1) where is the sample covariance matrix; , , and denote the determinant, trace, and sum of the absolute values of all elements of a matrix, respectively. The part “ ” in (1) is the log-likelihood, whereas the part “ ” represents the “sparsity” of the inverse covariance matrix . (1) aims to achieve a tradeoff between the likelihood fit of the inverse covariance estimate and the sparsity. The tradeoff is controlled by , called the regularization parameter; larger will result in more sparse estimate for . The formulation in (1) follows the same line of the -norm regularization, which has been introduced into the least squares formulation to achieve model sparsity and the resulting model is called Lasso [27]. We employ the algorithm in [19] in this paper. Next, we show that with going from small to large, the resulting brain connectivity models have a monotone property. Before introducing the monotone property, the following definitions are needed. Definition: In the graphical representation of the inverse covariance, if node to by an arc, then is called a “neighbor” of . If is connected to chain of arcs, then is called a “connectivity component” of . is connected though some Intuitively, being neighbors means that two nodes (i.e., brain regions) are directly connected, whereas being connectivity components means that two brain regions are indirectly connected, i.e., the connection is mediated through other regions. In other words, not being connectivity components (i.e., two nodes completely separated in the graph) means that the two corresponding brain regions are completely independent of each other. Connectivity components have the following monotone property: Monotone property of SICE: Let components of with and and be the sets of all the connectivity , respectively. If , then . Intuitively, if two regions are connected (either directly or indirectly) at one level of sparseness ( ), they will be connected at all lower levels of sparseness ( ). Proof of the monotone property can be found in the supplementary file [29]. This monotone property can be used to identify how strongly connected each node (brain region) to its connectivity components. For example, assuming that and , this means that is more strongly connected to than . Thus, by changing from small to large, we can obtain an order for the strength of connection between pairs of brain regions. As will be shown in Section 3, this order is different among AD, MCI, and NC. 3 3.1 Ap p l i cati on i n B rai n Con n ecti vi ty M od el i n g of AD D a t a a c q u i s i t i o n a n d p re p ro c e s s i n g We apply SICE on FDG-PET images for 49 AD, 116 MCI, and 67 NC subjects downloaded from the ADNI website. We apply Automated Anatomical Labeling (AAL) [28] to extract data from each of the 116 anatomical volumes of interest (AVOI), and derived average of each AVOI for every subject. The AVOIs represent different regions of the whole brain. 3.2 B r a i n c o n n e c t i v i t y mo d e l i n g b y S I C E 42 AVOIs are selected for brain connectivity modeling, as they are considered to be potentially related to AD. These regions distribute in the frontal, parietal, occipital, and temporal lobes. Table 1 list of the names of the AVOIs with their corresponding lobes. The number before each AVOI is used to index the node in the connectivity models. We apply the SICE algorithm to learn one connectivity model for AD, one for MCI, and one for NC, for a given . With different ’s, the resulting connectivity models hold a monotone property, which can help obtain an order for the strength of connection between brain regions. To show the order clearly, we develop a tree-like plot in Fig. 1, which is for the AD group. To generate this plot, we start at a very small value (i.e., the right-most of the horizontal axis), which results in a fully-connected connectivity model. A fully-connected connectivity model is one that contains no region disconnected with the rest of the brain. Then, we decrease by small steps and record the order of the regions disconnected with the rest of the brain regions. Table 1: Names of the AVOIs for connectivity modeling (“L” means that the brain region is located at the left hemisphere; “R” means right hemisphere.) Frontal lobe Parietal lobe Occipital lobe Temporal lobe 1 Frontal_Sup_L 13 Parietal_Sup_L 21 Occipital_Sup_L 27 T emporal_Sup_L 2 Frontal_Sup_R 14 Parietal_Sup_R 22 Occipital_Sup_R 28 T emporal_Sup_R 3 Frontal_Mid_L 15 Parietal_Inf_L 23 Occipital_Mid_L 29 T emporal_Pole_Sup_L 4 Frontal_Mid_R 16 Parietal_Inf_R 24 Occipital_Mid_R 30 T emporal_Pole_Sup_R 5 Frontal_Sup_Medial_L 17 Precuneus_L 25 Occipital_Inf_L 31 T emporal_Mid_L 6 Frontal_Sup_Medial_R 18 Precuneus_R 26 Occipital_Inf_R 32 T emporal_Mid_R 7 Frontal_Mid_Orb_L 19 Cingulum_Post_L 33 T emporal_Pole_Mid_L 8 Frontal_Mid_Orb_R 20 Cingulum_Post_R 34 T emporal_Pole_Mid_R 9 Rectus_L 35 T emporal_Inf_L 8301 10 Rectus_R 36 T emporal_Inf_R 8302 11 Cingulum_Ant_L 37 Fusiform_L 12 Cingulum_Ant_R 38 Fusiform_R 39 Hippocampus_L 40 Hippocampus_R 41 ParaHippocampal_L 42 ParaHippocampal_R For example, in Fig. 1, as decreases below (but still above ), region “Tempora_Sup_L” is the first one becoming disconnected from the rest of the brain. As decreases below (but still above ), the rest of the brain further divides into three disconnected clusters, including the cluster of “Cingulum_Post_R” and “Cingulum_Post_L”, the cluster of “Fusiform_R” up to “Hippocampus_L”, and the cluster of the other regions. As continuously decreases, each current cluster will split into smaller clusters; eventually, when reaches a very large value, there will be no arc in the IC model, i.e., each region is now a cluster of itself and the split will stop. The sequence of the splitting gives an order for the strength of connection between brain regions. Specifically, the earlier (i.e., smaller ) a region or a cluster of regions becomes disconnected from the rest of the brain, the weaker it is connected with the rest of the brain. For example, in Fig. 1, it can be known that “Tempora_Sup_L” may be the weakest region in the brain network of AD; the second weakest ones are the cluster of “Cingulum_Post_R” and “Cingulum_Post_L”, and the cluster of “Fusiform_R” up to “Hippocampus_L”. It is very interesting to see that the weakest and second weakest brain regions in the brain network include “Cingulum_Post_R” and “Cingulum_Post_L” as well as regions all in the temporal lobe, all of which have been found to be affected by AD early and severely [3]-[5]. Next, to facilitate the comparison between AD and NC, a tree-like plot is also constructed for NC, as shown in Fig. 2. By comparing the plots for AD and NC, we can observe the following two distinct phenomena: First, in AD, between-lobe connectivity tends to be weaker than within-lobe connectivity. This can be seen from Fig. 1 which shows a clear pattern that the lobes become disconnected with each other before the regions within each lobe become disconnected with each other, as goes from small to large. This pattern does not show in Fig. 2 for NC. Second, the same brain regions in the left and right hemisphere are connected much weaker in AD than in NC. This can be seen from Fig. 2 for NC, in which the same brain regions in the left and right hemisphere are still connected even at a very large for NC. However, this pattern does not show in Fig. 1 for AD. Furthermore, a tree-like plot is also constructed for MCI (Fig. 3), and compared with the plots for AD and NC. In terms of the two phenomena discussed previously, MCI shows similar patterns to AD, but these patterns are not as distinct from NC as AD. Specifically, in terms of the first phenomenon, MCI also shows weaker between-lobe connectivity than within-lobe connectivity, which is similar to AD. However, the degree of weakerness is not as distinctive as AD. For example, a few regions in the temporal lobe of MCI, including “Temporal_Mid_R” and “Temporal_Sup_R”, appear to be more strongly connected with the occipital lobe than with other regions in the temporal lobe. In terms of the second phenomenon, MCI also shows weaker between-hemisphere connectivity in the same brain region than NC. However, the degree of weakerness is not as distinctive as AD. For example, several left-right pairs of the same brain regions are still connected even at a very large , such as “Rectus_R” and “Rectus_L”, “Frontal_Mid_Orb_R” and “Frontal_Mid_Orb _L”, “Parietal_Sup_R” and “Parietal_Sup_L”, as well as “Precuneus_R” and “Precuneus_L”. All above findings are consistent with the knowledge that MCI is a transition stage between normal aging and AD. Large λ λ3 λ2 λ1 Small λ Fig 1: Order for the strength of connection between brain regions of AD Large λ Small λ Fig 2: Order for the strength of connection between brain regions of NC Fig 3: Order for the strength of connection between brain regions of MCI Furthermore, we would like to compare how within-lobe and between-lobe connectivity is different across AD, MCI, and NC. To achieve this, we first learn one connectivity model for AD, one for MCI, and one for NC. We adjust the in the learning of each model such that the three models, corresponding to AD, MCI, and NC, respectively, will have the same total number of arcs. This is to “normalize” the models, so that the comparison will be more focused on how the arcs distribute differently across different models. By selecting different values for the total number of arcs, we can obtain models representing the brain connectivity at different levels of strength. Specifically, given a small value for the total number of arcs, only strong arcs will show up in the resulting connectivity model, so the model is a model of strong brain connectivity; when increasing the total number of arcs, mild arcs will also show up in the resulting connectivity model, so the model is a model of mild and strong brain connectivity. For example, Fig. 4 shows the connectivity models for AD, MCI, and NC with the total number of arcs equal to 50 (Fig. 4(a)), 120 (Fig. 4(b)), and 180 (Fig. 4(c)). In this paper, we use a “matrix” representation for the SICE of a connectivity model. In the matrix, each row represents one node and each column also represents one node. Please see Table 1 for the correspondence between the numbering of the nodes and the brain region each number represents. The matrix contains black and white cells: a black cell at the -th row, -th column of the matrix represents existence of an arc between nodes and in the SICE-based connectivity model, whereas a white cell represents absence of an arc. According to this definition, the total number of black cells in the matrix is equal to twice the total number of arcs in the SICE-based connectivity model. Moreover, on each matrix, four red cubes are used to highlight the brain regions in each of the four lobes; that is, from top-left to bottom-right, the red cubes highlight the frontal, parietal, occipital, and temporal lobes, respectively. The black cells inside each red cube reflect within-lobe connectivity, whereas the black cells outside the cubes reflect between-lobe connectivity. While the connectivity models in Fig. 4 clearly show some connectivity difference between AD, MCI, and NC, it is highly desirable to test if the observed difference is statistically significant. Therefore, we further perform a hypothesis testing and the results are summarized in Table 2. Specifically, a P-value is recorded in the sub-table if it is smaller than 0.1, such a P-value is further highlighted if it is even smaller than 0.05; a “---” indicates that the corresponding test is not significant (P-value>0.1). We can observe from Fig. 4 and Table 2: Within-lobe connectivity: The temporal lobe of AD has significantly less connectivity than NC. This is true across different strength levels (e.g., strong, mild, and weak) of the connectivity; in other words, even the connectivity between some strongly-connected brain regions in the temporal lobe may be disrupted by AD. In particular, it is clearly from Fig. 4(b) that the regions “Hippocampus” and “ParaHippocampal” (numbered by 39-42, located at the right-bottom corner of Fig. 4(b)) are much more separated from other regions in AD than in NC. The decrease in connectivity in the temporal lobe of AD, especially between the Hippocampus and other regions, has been extensively reported in the literature [3]-[5]. Furthermore, the temporal lobe of MCI does not show a significant decrease in connectivity, compared with NC. This may be because MCI does not disrupt the temporal lobe as badly as AD. AD MCI NC Fig 4(a): SICE-based brain connectivity models (total number of arcs equal to 50) AD MCI NC Fig 4(b): SICE-based brain connectivity models (total number of arcs equal to 120) AD MCI NC Fig 4(c): SICE-based brain connectivity models (total number of arcs equal to 180) The frontal lobe of AD has significantly more connectivity than NC, which is true across different strength levels of the connectivity. This has been interpreted as compensatory reallocation or recruitment of cognitive resources [6]-[7]. Because the regions in the frontal lobe are typically affected later in the course of AD (our data are early AD), the increased connectivity in the frontal lobe may help preserve some cognitive functions in AD patients. Furthermore, the frontal lobe of MCI does not show a significant increase in connectivity, compared with NC. This indicates that the compensatory effect in MCI brain may not be as strong as that in AD brains. Table 2: P-values from the statistical significance test of connectivity difference among AD, MCI, and NC (a) Total number of arcs = 50 (b) Total number of arcs = 120 (c) Total number of arcs = 180 There is no significant difference among AD, MCI, and NC in terms of the connectivity within the parietal lobe and within the occipital lobe. Another interesting finding is that all the P-values in the third sub-table of Table 2(a) are insignificant. This implies that distribution of the strong connectivity within and between lobes for MCI is very similar to NC; in other words, MCI has not been able to disrupt the strong connectivity among brain regions (it disrupts some mild and weak connectivity though). Between-lobe connectivity: In general, human brains tend to have less between-lobe connectivity than within-lobe connectivity. A majority of the strong connectivity occurs within lobes, but rarely between lobes. These can be clearly seen from Fig. 4 (especially Fig. 4(a)) in which there are much more black cells along the diagonal direction than the off-diagonal direction, regardless of AD, MCI, and NC. The connectivity between the parietal and occipital lobes of AD is significantly more than NC which is true especially for mild and weak connectivity. The increased connectivity between the parietal and occipital lobes of AD has been previously reported in [3]. It is also interpreted as a compensatory effect in [6]-[7]. Furthermore, MCI also shows increased connectivity between the parietal and occipital lobes, compared with NC, but the increase is not as significant as AD. While the connectivity between the frontal and occipital lobes shows little difference between AD and NC, such connectivity for MCI shows a significant decrease especially for mild and weak connectivity. Also, AD may have less temporal-occipital connectivity, less frontal-parietal connectivity, but more parietal-temporal connectivity than NC. Between-hemisphere connectivity: Recall that we have observed from the tree-like plots in Figs. 3 and 4 that the same brain regions in the left and right hemisphere are connected much weaker in AD than in NC. It is desirable to test if this observed difference is statistically significant. To achieve this, we test the statistical significance of the difference among AD, MCI, and NC, in term of the number of connected same-region left-right pairs. Results show that when the total number of arcs in the connectivity models is equal to 120 or 90, none of the tests is significant. However, when the total number of arcs is equal to 50, the P-values of the tests for “AD vs. NC”, “AD vs. MCI”, and “MCI vs. NC” are 0.009, 0.004, and 0.315, respectively. We further perform tests for the total number of arcs equal to 30 and find the P-values to be 0. 0055, 0.053, and 0.158, respectively. These results indicate that AD disrupts the strong connectivity between the same regions of the left and right hemispheres, whereas this disruption is not significant in MCI. 4 Con cl u si on In the paper, we applied SICE to model functional brain connectivity of AD, MCI, and NC based on PET neuroimaging data, and analyze the patterns based on the monotone property of SICE. Our findings were consistent with the previous literature and also showed some new aspects that may suggest further investigation in brain connectivity research in the future. 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