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38 nips-2009-Augmenting Feature-driven fMRI Analyses: Semi-supervised learning and resting state activity

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Author: Andreas Bartels, Matthew Blaschko, Jacquelyn A. Shelton

Abstract: Resting state activity is brain activation that arises in the absence of any task, and is usually measured in awake subjects during prolonged fMRI scanning sessions where the only instruction given is to close the eyes and do nothing. It has been recognized in recent years that resting state activity is implicated in a wide variety of brain function. While certain networks of brain areas have different levels of activation at rest and during a task, there is nevertheless signiﬁcant similarity between activations in the two cases. This suggests that recordings of resting state activity can be used as a source of unlabeled data to augment discriminative regression techniques in a semi-supervised setting. We evaluate this setting empirically yielding three main results: (i) regression tends to be improved by the use of Laplacian regularization even when no additional unlabeled data are available, (ii) resting state data seem to have a similar marginal distribution to that recorded during the execution of a visual processing task implying largely similar types of activation, and (iii) this source of information can be broadly exploited to improve the robustness of empirical inference in fMRI studies, an inherently data poor domain. 1

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 de Abstract Resting state activity is brain activation that arises in the absence of any task, and is usually measured in awake subjects during prolonged fMRI scanning sessions where the only instruction given is to close the eyes and do nothing. [sent-10, score-0.941]

2 It has been recognized in recent years that resting state activity is implicated in a wide variety of brain function. [sent-11, score-1.302]

3 While certain networks of brain areas have different levels of activation at rest and during a task, there is nevertheless signiﬁcant similarity between activations in the two cases. [sent-12, score-0.445]

4 This suggests that recordings of resting state activity can be used as a source of unlabeled data to augment discriminative regression techniques in a semi-supervised setting. [sent-13, score-1.438]

5 1 Introduction In this work we study the use of resting state activity for the semi-supervised analysis of human fMRI studies. [sent-15, score-1.129]

6 We wish to use resting state activity as an additional source of unlabeled data in a semi-supervised regression setting. [sent-16, score-1.338]

7 We analyze the weights of a trained regressor to infer brain regions that are implicated in visual processing tasks. [sent-17, score-0.37]

8 One source of such additional data is resting state activity, the brain activation that arises in the absence of any task. [sent-19, score-1.173]

9 We show in this work that the marginal distribution of resting state activity is suitable to improve regression performance when employed for semi-supervised learning. [sent-21, score-1.104]

10 In neuroscience there has been a recent surge of interest in analyzing brain activity in more natural, complex settings, e. [sent-22, score-0.489]

11 with volunteers viewing movies, in order to gain insight in brain processes and connectivity underlying more natural processing. [sent-24, score-0.492]

12 We have recently applied a semi-supervised extension of KCCA to human fMRI data [32] where the unlabeled data source was given by the subjects viewing a movie for which the labels were not known. [sent-28, score-0.645]

13 In Section 2 we discuss the generation and signiﬁcance of resting state activity. [sent-31, score-0.779]

14 In Section 6, we show empirically that resting state activity is an effective source of unlabeled data for semi-supervised learning. [sent-34, score-1.273]

15 2 Resting State Activity Resting state activity has attracted the attention of neuroscientists now for over a decade [8, 20]. [sent-35, score-0.378]

16 It is deﬁned as brain activation that arises in the absence of any task, and it is usually measured in awake subjects during prolonged fMRI scanning sessions, where no other instructions are given than to close the eyes and to do nothing. [sent-36, score-0.519]

17 The basic idea is that spontaneous ﬂuctuations of neural activity in the brain may reveal some fundamental characteristics of brain function. [sent-37, score-0.861]

18 Instead, evidence suggests that spontaneous activity changes reﬂect to some extent neural activity that may account for trial-to-trial variability of human behaviour [14, 28]. [sent-43, score-0.69]

19 Resting state activity however also has structural implications, in that temporal correlations between spatially separate regions (functional connectivity) may be indicative of underlying neural communication between them, which in turn may be mediated by anatomical connections. [sent-44, score-0.567]

20 Some recent studies also attempt to reveal that resting state connectivity directly relates to structural activity as revealed using diffusion tensor imaging [33, 19]. [sent-49, score-1.337]

21 Finally, alterations in resting state activity patterns have recently been shown to be diagnostic for clinical conditions such as neuropsychiatric disorders [18], and have been shown to alter with increasing age [34]. [sent-50, score-1.069]

22 However, the analysis of resting state activity poses a challenge, as it is not stimulus-driven, and is therefore difﬁcult to analyze or to reveal using hypothesis-driven analysis methods. [sent-51, score-1.102]

23 One common approach has been to reveal functional networks and their connectivity by measuring the temporal correlations of a seed region with the remaining voxels of the brain [8, 21, 3, 33, 19]. [sent-52, score-0.698]

24 Another approach has been to apply data-driven spatio-temporal clustering methods such as independent component analysis (ICA) to reveal distinct functional areas or networks at rest [35, 1]. [sent-53, score-0.33]

25 The over2 whelming evidence of these studies shows that groups of voxels, but also widespread networks of cortical areas that are co-engaged during task performances are also consistently co-activated during rest [35, 1, 12]. [sent-54, score-0.218]

26 We provide an alternative, computationally driven approach to assess whether and to which extent externally driven functional networks coincide with spontaneous ﬂuctuations during rest. [sent-55, score-0.331]

27 We stimulated volunteers using natural movies, and measured resting state activity during the same session in separate runs that each lasted 20 min. [sent-56, score-1.107]

28 Prior work has shown that natural movie viewing leads not only to wide-spread cortical activation, but also to a higher functional separation of distinct networks and areas compared to that obtained using traditional stimulation with controlled stimuli [23, 1, 17]. [sent-57, score-0.467]

29 This is most likely so because distinct cortical regions responded each to distinct features occurring in the movie, thus revealing the functional division of labor in cortex [2, 4, 23]. [sent-58, score-0.336]

30 In subsequent sections we show that semi-supervised learning algorithms improve when resting state data are added to aide feature-regression of movie-viewing data. [sent-59, score-0.779]

31 This improvement indicates that a similar cortical structure underlies resting state data as that underlying movie-viewing data. [sent-60, score-0.832]

32 These results thus fall in line with prior work demonstrating consistency of resting state networks across subjects [35, 12], and reveal that feature-driven activity during natural viewing induces a similar functional clustering as that occurring during rest. [sent-61, score-1.478]

33 Importantly however, this approach may also be of other methodological interest, in that data obtained at rest may actually be used to augment the performance of feature-driven regression of stimulus-driven data. [sent-62, score-0.165]

34 3 Semi-supervised Learning Semi-supervised learning makes use of a combination of labeled and unlabeled training points in order to better learn a mapping from an input space, X (in this case voxels recorded from fMRI), to an output space, Y (variables recording viewing conditions). [sent-63, score-0.361]

35 The additional unlabeled data in X allow us to better model the manifold on which the data lie. [sent-69, score-0.226]

36 In the case of fMRI acquired data, we expect that brain activity follow certain common patterns of activation. [sent-70, score-0.489]

37 In practice, in a data poor domain, we may have to resort to a source of unlabeled data that is derived by a (slightly) different process than that of the labeled samples. [sent-77, score-0.298]

38 As resting state data is a representative byproduct of the experimental design of fMRI studies, we explore the empirical performance of its employment as a source of unlabeled data. [sent-78, score-1.013]

39 4 Data Acquisition A Siemens 3TTIM scanner was used to acquire the fMRI data of 5 human volunteers and consisted of 350 time slices of 3-dimensional fMRI brain volumes. [sent-80, score-0.483]

40 5 min length, wherein one movie had labels indicating the continuous content of the movie (i. [sent-86, score-0.229]

41 The subjects additionally were recorded during a resting state of the same length of time. [sent-90, score-0.889]

42 A temporal high-pass ﬁlter with a cut-off of 512 s was applied, as well as a low-pass ﬁlter with the temporal properties of the hemodynamic response function (hrf), in order to reduce temporal acquisition noise. [sent-94, score-0.215]

43 First by using computer frame-by-frame analysis of the movie [4], and second using subjective ratings averaged across an independent set of ﬁve human observers [1]. [sent-96, score-0.223]

44 The computerderived labels indicated luminance change over time (temporal contrast), visual motion energy (i. [sent-97, score-0.165]

45 The human-derived labels indicated the intensity of subjectively experienced color, and the degree to which faces and human bodies were present in the movie. [sent-100, score-0.163]

46 In prior studies, each of these labels had been shown to correlate with brain activity in particular and distinct sets of areas specialized to process the particular label in question [1, 4]. [sent-101, score-0.599]

47 We denote the design matrix of labeled ˆ data as X and that of labeled and unlabeled data X. [sent-111, score-0.286]

48 4 Table 1: Mean holdout correlations for motion in the ﬁve subjects across all experiments. [sent-118, score-0.313]

49 In all cases, semi-supervision from resting state activity (Exp C) improves over regression using only fully labeled data (Exp A). [sent-120, score-1.168]

50 15 Table 2: Mean holdout correlations for human body in the ﬁve subjects across all experiments. [sent-171, score-0.372]

51 In all cases, semi-supervision from resting state activity (Exp C) improves over regression using only fully labeled data (Exp A). [sent-173, score-1.168]

52 • C: We introduce semi-supervision from resting state activity. [sent-226, score-0.779]

53 • E: Finally, we combine the unlabeled data from both resting state activity and from the unlabeled movie. [sent-229, score-1.355]

54 Table 1 shows the test correlations for all subjects and experiments for the motion output variable, while Table 2 shows results for the human body variable, and Table 3 for the language variable. [sent-233, score-0.408]

55 Wilcoxon signed-rank tests have shown signiﬁcant Table 3: Mean holdout correlations for language in the ﬁve subjects across all experiments. [sent-234, score-0.266]

56 In all cases, semi-supervision from resting state activity (Exp C) improves over regression using only fully labeled data (Exp A). [sent-236, score-1.168]

57 Figure 1: Illustration of weight maps obtained for the visual motion feature in experiments A, B, and D. [sent-290, score-0.182]

58 Transverse slices are shown through a single subjects T1-weighted structural image with superimposed weight-maps, colored in red for positive weights (left column), and colored in blue for negative weights (right column). [sent-291, score-0.194]

59 The positive weight maps (left column) reveal the motion processing area V5/MT+, as well as posterior in the midline a part of peripheral early visual area V1 (not labelled). [sent-292, score-0.333]

60 The negative weight maps reveal a reduction of BOLD signal in the occipital poles (the foveal representation of early visual areas V1-V3). [sent-293, score-0.277]

61 Figure 2: Illustration of weight maps for the human body feature. [sent-298, score-0.182]

62 Weight maps (in red) are show on transverse (left) and sagittal (right) brain sections of a single subject. [sent-299, score-0.356]

63 Activity involves the objectresponsive lateral occipital cortex (LOC) extending dorsally into region responsive to human bodies, dubbed extrastriate body area (EBA) [13]. [sent-300, score-0.34]

64 Figure 1 shows the weights for the motion variable, Figure 2 for the human body variable, and Figure 3 for the language variable. [sent-304, score-0.243]

65 This supports the primary hypothesis of this work – that the marginal distribution of resting state activity in combination of that from the visual 6 (a) Regression without Laplacian regularization. [sent-313, score-1.098]

66 (c) Semi-supervised Laplacian regularized solution using resting state data. [sent-315, score-0.823]

67 Weight maps (in red) are superimposed on sagittal, coronal and transverse sections of a single subjects brain. [sent-317, score-0.207]

68 As the unlabeled data for experiment D were generated speciﬁcally to match the distribution of the labeled data, we conclude that resting state activity gives a similar increase in performance to semi-supervised learning with i. [sent-321, score-1.261]

69 We conclude that the two sources of unlabeled data may not hold complimentary data, indicating that a wholesale replacement of one source by another is an effective strategy. [sent-326, score-0.234]

70 Here we asked whether using semi-supervised learning methods can improve a feature-driven analysis when adding data obtained in the resting state. [sent-329, score-0.661]

71 The motivation for this stems from prior studies that suggest a functionally relevant involvement of cortical regions during rest. [sent-330, score-0.166]

72 Data-driven analyses of resting state activity reveals a similar functional architecture that can also be observed during stimulus-driven activity, and which can be reproducibly found across subjects [12, 35]. [sent-331, score-1.287]

73 In addition, also the functional connectivity between distinct regions appears to be physiologically plausible at rest [21, 8, 20], and in fact is very similar to the functional connectivity observed during viewing of movies [3]. [sent-332, score-0.676]

74 Taken together, these ﬁndings would suggest that resting state activity may in theory be able to augment in a non-biased way datasets obtained in a functional setting. [sent-333, score-1.209]

75 At the same time, if resting state data were indeed found to augment results of feature-driven analyses, this would form an important ﬁnding, as it would directly indicate that resting state activity indeed is similar in its nature to that induced by stimulus-driven settings. [sent-334, score-1.883]

76 For example, the activation of visual motion responsive cortex V5+/MT+ clearly increased in experiments A-C. [sent-336, score-0.319]

77 Since the resting state is not well-deﬁned, it may also be that particular internal states, sleepiness, etc. [sent-340, score-0.779]

78 All in all however our results show that adding resting state data can indeed augment ﬁndings obtained in stimulus-inducing settings. [sent-342, score-0.844]

79 This method may therefore be useful for the increasing number of imaging centres acquiring resting state data for completely different purposes, which may then be used to augment functional data, entirely free of cost in terms of scan time. [sent-343, score-1.004]

80 Our approach is therefore an extension of prior attempts to characterize the complex, rich, yet difﬁcult to characterize brain activation during the absence of externally driven stimulation. [sent-347, score-0.385]

81 8 Conclusions In this work, we have proposed the use of resting state data as a source for the unlabeled component of semi-supervised learning for fMRI studies. [sent-348, score-1.013]

82 As data acquisition and the manual labeling of stimulus data are expensive components of brain imaging, the beneﬁts of exploiting additional unlabeled data are clear. [sent-352, score-0.431]

83 Resting state data is a promising source as there are no task speciﬁc biases introduced. [sent-353, score-0.194]

84 In future work we intend to further study the properties of the distribution of resting state activity. [sent-354, score-0.779]

85 If brain activity is consistent across subjects for the speciﬁc task measured by a study, a large cross subject sample of resting state data may be employed to improve results. [sent-356, score-1.411]

86 The chronoarchitecture of the human brain–natural viewing conditions reveal a time-based anatomy of the brain. [sent-362, score-0.235]

87 Functional brain mapping during free viewing of natural scenes. [sent-367, score-0.338]

88 Brain dynamics during natural viewing conditions–a new guide for mapping connectivity in vivo. [sent-372, score-0.222]

89 Natural vision reveals regional specialization to local motion and to contrast-invariant, global ﬂow in the human brain. [sent-379, score-0.167]

90 Modulation of spontaneous fMRI activity in human visual cortex by behavioral state. [sent-403, score-0.549]

91 Functional connectivity in the motor cortex of resting human brain using echo-planar mri. [sent-413, score-1.153]

92 Simultaneous assessment of ﬂow and bold signals in restingstate functional connectivity maps. [sent-421, score-0.218]

93 Coherent spontaneous activity accounts for trial-to-trial variability in human evoked brain responses. [sent-477, score-0.659]

94 Sex differences in regional cerebral glucose metabolism during a resting state. [sent-536, score-0.661]

95 Detection of functional connectivity using temporal correlations in mr images. [sent-547, score-0.33]

96 A default mode of brain function: A brief history of an evolving idea. [sent-640, score-0.265]

97 Semi-supervised subspace analysis of human functional magnetic resonance imaging data. [sent-646, score-0.316]

98 Measuring brain connectivity: Diffusion tensor imaging validates resting state temporal correlations. [sent-657, score-1.12]

99 Functional connectivity as revealed by spatial independent component analysis of fmri measurements during rest. [sent-677, score-0.291]

100 Learning from labeled and unlabeled data with label propagation. [sent-691, score-0.222]

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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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