{"title": "Learning Brain Connectivity of Alzheimer's Disease from Neuroimaging Data", "book": "Advances in Neural Information Processing Systems", "page_first": 808, "page_last": 816, "abstract": "Recent advances in neuroimaging techniques provide great potentials for effective diagnosis of Alzheimer\u2019s disease (AD), the most common form of dementia. Previous studies have shown that AD is closely related to 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 \u201cmonotone property\u201d we established in this paper. Our experimental results on neuroimaging PET data of 42 AD, 116 MCI, and 67 NC subjects reveal several interesting connectivity patterns consistent with literature findings, and also some new patterns that can help the knowledge discovery of AD.", "full_text": " \n\n \n \n\nLearning Brain Connectivity of Alzheimer's \n\nDisease from Neuroimaging Data \n\nShuai Huang1, Jing Li1, Liang Sun2,3, Jun Liu2,3, Teresa Wu1, Kewei Chen4, \n\nAdam Fleisher4, Eric Reiman4, Jieping Ye2,3 \n\n1Industrial Engineering, 2Computer Science and Engineering, and 3Center for Evolutionary \n\nFunctional Genomics, The Biodesign Institute, Arizona State University, Tempe, USA \n\n{shuang31, jing.li.8, sun.liang, j.liu, teresa.wu, jieping.ye}@asu.edu \n\n 4Banner Alzheimer\u2019s Institute and Banner PET Center, Banner Good Samaritan Medical \n\n{kewei.chen, adam.fleisher, eric.reiman}@bannerhealth.com \n\nCenter, Phoenix, USA \n\n \n\nAbstract \n\nRecent advances in neuroimaging techniques provide great potentials for \neffective diagnosis of Alzheimer\u2019s disease (AD), the most common form of \ndementia. Previous studies have shown that AD is closely related to the \nalternation in the functional brain network, i.e., the functional connectivity \namong different brain regions. In this paper, we consider the problem of \nlearning functional brain connectivity from neuroimaging, which holds \ngreat promise for identifying image-based markers used to distinguish \nNormal Controls (NC), patients with Mild Cognitive Impairment (MCI), \nand patients with AD. \n More specifically, we study sparse inverse \ncovariance estimation (SICE), also known as exploratory Gaussian \ngraphical models, for brain connectivity modeling. In particular, we apply \nSICE to learn and analyze functional brain connectivity patterns from \ndifferent subject groups, based on a key property of SICE, called the \n\u201cmonotone property\u201d we established in this paper. Our experimental results \non neuroimaging PET data of 42 AD, 116 MCI, and 67 NC subjects reveal \nseveral interesting connectivity patterns consistent with literature findings, \nand also some new patterns that can help the knowledge discovery of AD. \n\n \n \n\n1 \n\nI n t ro d u c t i o n \n\nAlzheimer\u2019s disease (AD) is a fatal, neurodegenerative disorder characterized by progressive \nimpairment of memory and other cognitive functions. It is the most common form of \ndementia and currently affects over five million Americans; this number will grow to as \nmany as 14 million by year 2050. The current knowledge about the cause of AD is very \nlimited; clinical diagnosis is imprecise with definite diagnosis only possible by autopsy; \nalso, there is currently no cure for AD, while most drugs only alleviate the symptoms. \n\nTo tackle these challenging issues, the rapidly advancing neuroimaging techniques provide \ngreat potentials. These techniques, such as MRI, PET, and fMRI, produce data (images) of \nbrain structure and function, making it possible to identify the difference between AD and \nnormal brains. Recent studies have demonstrated that neuroimaging data provide more \nsensitive and consistent measures of AD onset and progression than conventional clinical \n\n\fassessment and neuropsychological tests [1]. \n\nRecent studies have found that AD is closely related to the alternation in the functional brain \nnetwork, i.e., the functional connectivity among different brain regions [ 2]-[3]. Specifically, \nit has been shown that functional connectivity substantially decreases between the \nhippocampus and other regions of AD brains [3]-[4]. Also, some studies have found \nincreased connectivity between the regions in the frontal lobe [ 6]-[7]. \n\nLearning functional brain connectivity from neuroimaging data holds great promise for \nidentifying image-based markers used to distinguish among AD, MCI (Mild Cognitive \nImpairment), and normal aging. Note that MCI is a transition stage from normal aging to \nAD. Understanding and precise diagnosis of MCI have significant clinical value since it can \nserve as an early warning sign of AD. Despite all these, existing research in functional brain \nconnectivity modeling suffers from limitations. A large body of functional connectivity \nmodeling has been based on correlation analysis [2]-[3], [5]. However, correlation only \ncaptures pairwise information and fails to provide a complete account for the interaction of \nmany (more than two) brain regions. Other multivariate statistical methods have also been \nused, such as Principle Component Analysis (PCA) [8], PCA-based Scaled Subprofile Model \n[9], Independent Component Analysis [10]-[11], and Partial Least Squares [12]-[13], which \ngroup brain regions into latent components. The brain regions within each component are \nbelieved to have strong connectivity, while the connectivity between componen ts is weak. \nOne major drawback of these methods is that the latent components may not correspond to \nany biological entities, causing difficulty in interpretation. In addition, graphical models \nhave been used to study brain connectivity, such as structural equation models [14]-[15], \ndynamic causal models [16], and Granger causality. However, most of these approaches are \nconfirmative, rather than exploratory, in the sense that they require a prior model of brain \nconnectivity to begin with. This makes them inadequate for studying AD brain connectivity, \nbecause there is little prior knowledge about which regions should be involved and how they \nare connected. This makes exploratory models highly desirable. \n\nIn this paper, we study sparse inverse covariance estimation (SICE), also known as \nexploratory Gaussian graphical models, for brain connectivity modeling. Inverse covariance \nmatrix has a clear interpretation that the off-diagonal elements correspond to partial \ncorrelations, i.e., the correlation between each pair of brain regions given all other regions. \nThis provides a much better model for brain connectivity than simple correlation analysis \nwhich models each pair of regions without considering other regions. Also, imposing \nsparsity on the inverse covariance estimation ensures a reliable brain connectivity to be \nmodeled with limited sample size, which is usually the case in AD studies since clinical \nsamples are difficult to obtain. From a domain perspective, imposing sparsity is also valid \nbecause neurological findings have demonstrated that a brain region usually only directly \ninteracts with a few other brain regions in neurological processes [ 2]-[3]. Various algorithms \nfor achieving SICE have been developed in recent year [ 17]-[22]. In addition, SICE has been \nused in various applications [17], [21], [23]-[26]. \n\nIn this paper, we apply SICE to learn functional brain connectivity from neuroimaging and \nanalyze the difference among AD, MCI, and NC based on a key property of SICE, called the \n\u201cmonotone property\u201d we established in this paper. Unlike the previous study which is based \non a specific level of sparsity [26], the monotone property allows us to study the \nconnectivity pattern using different levels of sparsity and obtain an order for the strength of \nconnection between pairs of brain regions. In addition, we apply bootstrap hypothesis testing \nto assess the significance of the connection. Our experimental results on PET data of 42 AD, \n116 MCI, and 67 NC subjects enrolled in the Alzheimer\u2019s Disease Neuroimaging Initiative \nproject reveal several interesting connectivity patterns consistent with literature findings, \nand also some new patterns that can help the knowledge discovery of AD. \n\n \n2 \n\nS I C E : B a c k g ro u n d a n d t h e M o n o t o n e P ro p e r t y \n\nAn inverse covariance matrix can be represented graphically. If used to represent brain \nconnectivity, the nodes are activated brain regions; existence of an arc between two nodes \nmeans that the two brain regions are closely related in the brain's functiona l process. \n\n\f be all the brain regions under study. We assume that \n\n follows a \nLet \n be the \nmultivariate Gaussian distribution with mean \ninverse covariance matrix. Suppose we have \n subjects with AD) for these \nbrain regions. Note that we will only illustrate here the SICE for AD, whereas the SICE for \nMCI and NC can be achieved in a similar way. \n\n and covariance matrix \n samples (e.g., \n\n. Let \n\nWe can formulate the SICE into an optimization problem, i.e., \n\n \n\n (1) \n\n, \n\n, and \n\n is the sample covariance matrix; \n\n\u201d in (1) is the log-likelihood, whereas the part \u201c\n\n denote the \nwhere \ndeterminant, trace, and sum of the absolute values of all elements of a matrix, respectively. \nThe part \u201c\n\u201d \nrepresents the \u201csparsity\u201d of the inverse covariance matrix \n. (1) aims to achieve a tradeoff \nbetween the likelihood fit of the inverse covariance estimate and the sparsity. The tradeoff is \ncontrolled by \n will result in more sparse estimate \nfor \n-norm regularization, which has been \nintroduced into the least squares formulation to achieve model sparsity and the resulting model is \ncalled Lasso [27]. We employ the algorithm in [19] in this paper. Next, we show that with \n \ngoing from small to large, the resulting brain connectivity models have a monotone property. \nBefore introducing the monotone property, the following definitions are needed. \n\n. The formulation in (1) follows the same line of the \n\n, called the regularization parameter; larger \n\nDefinition: In the graphical representation of the inverse covariance, if node \nto \nchain of arcs, then \n\n is called a \u201cconnectivity component\u201d of \n\n is called a \u201cneighbor\u201d of \n\n by an arc, then \n\n is connected to \n\n. If \n\n. \n\n is connected \n though some \n\nIntuitively, being neighbors means that two nodes (i.e., brain regions) are directly connected, \nwhereas being connectivity components means that two brain regions are indirectly \nconnected, i.e., the connection is mediated through other regions. In other words, not being \nconnectivity components (i.e., two nodes completely separated in the graph) means that the \ntwo corresponding brain regions are completely independent of each other. Connectivity \ncomponents have the following monotone property: \n\nMonotone property of SICE: Let \ncomponents of \n\n with \n\n and \n\n and \n\n be the sets of all the connectivity \n\n, respectively. If \n\n, then \n\n. \n\n), they will be connected at all lower levels of sparseness (\n\nIntuitively, if two regions are connected (either directly or indirectly) at one level of \nsparseness (\n). Proof \nof the monotone property can be found in the supplementary file [29]. This monotone \nproperty can be used to identify how strongly connected each node (brain region) \n to its \nconnectivity components. For example, assuming that \n, \nthis means that \n from small \n than \nto large, we can obtain an order for the strength of connection between pairs of brain \nregions. As will be shown in Section 3, this order is different among AD, MCI, and NC. \n\n is more strongly connected to \n\n. Thus, by changing \n\n and \n\n \n3 \n \n3 . 1 \n\n A p p l i c a t i o n i n B r ai n C o n n e c t i v i t y M o d e l i n g o f A D \n\nD a t a a c q u i s i t i o n a n d p r e p r o c e s s i n g \n\nWe apply SICE on FDG-PET images for 49 AD, 116 MCI, and 67 NC subjects downloaded from \nthe ADNI website. We apply Automated Anatomical Labeling (AAL) [28] to extract data from \neach of the 116 anatomical volumes of interest (AVOI), and derived average of each AVOI for \nevery subject. The AVOIs represent different regions of the whole brain. \n\n \n3 . 2 \n\nB r a i n c o n n e c t i v i t y m o d e l i n g b y S I C E \n\n42 AVOIs are selected for brain connectivity modeling, as they are considered to be potentially \nrelated to AD. These regions distribute in the frontal, parietal, occipital, and temporal lobes. Table \n1 list of the names of the AVOIs with their corresponding lobes. The number before each AVOI is \nused to index the node in the connectivity models. \n\n\fWe apply the SICE algorithm to learn one connectivity model for AD, one for MCI, and one for \nNC, for a given \n. With different \u2019s, the resulting connectivity models hold a monotone property, \nwhich can help obtain an order for the strength of connection between brain regions. To show the \norder clearly, we develop a tree-like plot in Fig. 1, which is for the AD group. To generate this \nplot, we start \n at a very small value (i.e., the right-most of the horizontal axis), which results in a \nfully-connected connectivity model. A fully-connected connectivity model is one that contains no \nregion disconnected with the rest of the brain. Then, we decrease \n by small steps and record the \norder of the regions disconnected with the rest of the brain regions. \n\nTable 1: Names of the AVOIs for connectivity modeling (\u201cL\u201d means that the brain region \n\nis located at the left hemisphere; \u201cR\u201d means right hemisphere.) \n\n \n\n decreases below \n\n (but still above \n\n), region \u201cTempora_Sup_L\u201d is \nFor example, in Fig. 1, as \n decreases below \n (but still \nthe first one becoming disconnected from the rest of the brain. As \nabove \n), the rest of the brain further divides into three disconnected clusters, including the \ncluster of \u201cCingulum_Post_R\u201d and \u201cCingulum_Post_L\u201d, the cluster of \u201cFusiform_R\u201d up to \n\u201cHippocampus_L\u201d, and the cluster of the other regions. As \n continuously decreases, each current \ncluster will split into smaller clusters; eventually, when \n reaches a very large value, there will be \nno arc in the IC model, i.e., each region is now a cluster of itself and the split will stop. The \nsequence of the splitting gives an order for the strength of connection between brain regions. \nSpecifically, the earlier (i.e., smaller ) a region or a cluster of regions becomes disconnected from \nthe rest of the brain, the weaker it is connected with the rest of the brain. For example, in Fig. 1, it \ncan be known that \u201cTempora_Sup_L\u201d may be the weakest region in the brain network of AD; the \nsecond weakest ones are the cluster of \u201cCingulum_Post_R\u201d and \u201cCingulum_Post_L\u201d, and the \ncluster of \u201cFusiform_R\u201d up to \u201cHippocampus_L\u201d. It is very interesting to see that the weakest and \nsecond weakest brain regions \ninclude \u201cCingulum_Post_R\u201d and \n\u201cCingulum_Post_L\u201d as well as regions all in the temporal lobe, all of which have been found to be \naffected by AD early and severely [3]-[5]. \n\nthe brain network \n\nin \n\nNext, to facilitate the comparison between AD and NC, a tree-like plot is also constructed for NC, \nas shown in Fig. 2. By comparing the plots for AD and NC, we can observe the following two \ndistinct phenomena: First, in AD, between-lobe connectivity tends to be weaker than within-lobe \nconnectivity. This can be seen from Fig. 1 which shows a clear pattern that the lobes become \ndisconnected with each other before the regions within each lobe become disconnected with each \nother, as \n goes from small to large. This pattern does not show in Fig. 2 for NC. Second, the \nsame brain regions in the left and right hemisphere are connected much weaker in AD than in NC. \nThis can be seen from Fig. 2 for NC, in which the same brain regions in the left and right \nhemisphere are still connected even at a very large \n for NC. However, this pattern does not show \nin Fig. 1 for AD. \n\nFurthermore, a tree-like plot is also constructed for MCI (Fig. 3), and compared with the plots for \nAD and NC. In terms of the two phenomena discussed previously, MCI shows similar patterns to \nAD, but these patterns are not as distinct from NC as AD. Specifically, in terms of the first \n\n1Frontal_Sup_L13Parietal_Sup_L21Occipital_Sup_L 27Temporal_Sup_L 2Frontal_Sup_R14Parietal_Sup_R22Occipital_Sup_R 28Temporal_Sup_R 3Frontal_Mid_L15Parietal_Inf_L23Occipital_Mid_L 29Temporal_Pole_Sup_L 4Frontal_Mid_R16Parietal_Inf_R24Occipital_Mid_R 30Temporal_Pole_Sup_R 5Frontal_Sup_Medial_L 17Precuneus_L25Occipital_Inf_L 31Temporal_Mid_L6Frontal_Sup_Medial_R 18Precuneus_R 26Occipital_Inf_R 32Temporal_Mid_R 7Frontal_Mid_Orb_L 19Cingulum_Post_L 33Temporal_Pole_Mid_L 8Frontal_Mid_Orb_R 20Cingulum_Post_R 34Temporal_Pole_Mid_R9Rectus_L35Temporal_Inf_L 830110Rectus_R36Temporal_Inf_R 830211Cingulum_Ant_L 37Fusiform_L 12Cingulum_Ant_R 38Fusiform_R 39Hippocampus_L 40Hippocampus_R 41ParaHippocampal_L 42ParaHippocampal_R Temporal lobeFrontal lobeParietal lobeOccipital lobe\fphenomenon, MCI also shows weaker between-lobe connectivity than within-lobe connectivity, \nwhich is similar to AD. However, the degree of weakerness is not as distinctive as AD. For \nexample, a few regions in the temporal lobe of MCI, including \u201cTemporal_Mid_R\u201d and \n\u201cTemporal_Sup_R\u201d, appear to be more strongly connected with the occipital lobe than with other \nregions in the temporal lobe. In terms of the second phenomenon, MCI also shows weaker \nbetween-hemisphere connectivity in the same brain region than NC. However, the degree of \nweakerness is not as distinctive as AD. For example, several left-right pairs of the same brain \nregions are still connected even at a very large \n, such as \u201cRectus_R\u201d and \u201cRectus_L\u201d, \n\u201cFrontal_Mid_Orb_R\u201d and \u201cFrontal_Mid_Orb _L\u201d, \u201cParietal_Sup_R\u201d and \u201cParietal_Sup_L\u201d, as \nwell as \u201cPrecuneus_R\u201d and \u201cPrecuneus_L\u201d. All above findings are consistent with the knowledge \nthat MCI is a transition stage between normal aging and AD. \n\n \n\n \n\nFig 1: Order for the strength of connection between brain regions of AD \n\n Fig 2: Order for the strength of connection between brain regions of NC \n\n \n\nSmall \u03bbLarge \u03bb\u03bb3\u03bb2\u03bb1Small \u03bbLarge \u03bb\f \n\n \n\nFig 3: Order for the strength of connection between brain regions of MCI \n\nFurthermore, we would like to compare how within-lobe and between-lobe connectivity is \ndifferent across AD, MCI, and NC. To achieve this, we first learn one connectivity model for AD, \none for MCI, and one for NC. We adjust the \n in the learning of each model such that the three \nmodels, corresponding to AD, MCI, and NC, respectively, will have the same total number of \narcs. This is to \u201cnormalize\u201d the models, so that the comparison will be more focused on how the \narcs distribute differently across different models. By selecting different values for the total \nnumber of arcs, we can obtain models representing the brain connectivity at different levels of \nstrength. Specifically, given a small value for the total number of arcs, only strong arcs will show \nup in the resulting connectivity model, so the model is a model of strong brain connectivity; when \nincreasing the total number of arcs, mild arcs will also show up in the resulting connectivity \nmodel, so the model is a model of mild and strong brain connectivity. \n\nFor example, Fig. 4 shows the connectivity models for AD, MCI, and NC with the total number of \narcs equal to 50 (Fig. 4(a)), 120 (Fig. 4(b)), and 180 (Fig. 4(c)). In this paper, we use a \u201cmatrix\u201d \nrepresentation for the SICE of a connectivity model. In the matrix, each row represents one node \nand each column also represents one node. Please see Table 1 for the correspondence between the \nnumbering of the nodes and the brain region each number represents. The matrix contains black \nand white cells: a black cell at the -th row, -th column of the matrix represents existence of an \narc between nodes \n in the SICE-based connectivity model, whereas a white cell \nrepresents absence of an arc. According to this definition, the total number of black cells in the \nmatrix is equal to twice the total number of arcs in the SICE-based connectivity model. Moreover, \non each matrix, four red cubes are used to highlight the brain regions in each of the four lobes; that \nis, from top-left to bottom-right, the red cubes highlight the frontal, parietal, occipital, and \ntemporal lobes, respectively. The black cells inside each red cube reflect within-lobe connectivity, \nwhereas the black cells outside the cubes reflect between-lobe connectivity. \n\n and \n\nWhile the connectivity models in Fig. 4 clearly show some connectivity difference between AD, \nMCI, and NC, it is highly desirable to test if the observed difference is statistically significant. \nTherefore, we further perform a hypothesis testing and the results are summarized in Table 2. \nSpecifically, a P-value is recorded in the sub-table if it is smaller than 0.1, such a P-value is further \nhighlighted if it is even smaller than 0.05; a \u201c---\u201d indicates that the corresponding test is not \nsignificant (P-value>0.1). We can observe from Fig. 4 and Table 2: \n\n\fWithin-lobe connectivity: The temporal lobe of AD has significantly less connectivity than NC. \nThis is true across different strength levels (e.g., strong, mild, and weak) of the connectivity; in \nother words, even the connectivity between some strongly-connected brain regions in the temporal \nlobe may be disrupted by AD. In particular, it is clearly from Fig. 4(b) that the regions \n\u201cHippocampus\u201d and \u201cParaHippocampal\u201d (numbered by 39-42, located at the right-bottom corner \nof Fig. 4(b)) are much more separated from other regions in AD than in NC. The decrease in \nconnectivity in the temporal lobe of AD, especially between the Hippocampus and other regions, \nhas been extensively reported in the literature [3]-[5]. Furthermore, the temporal lobe of MCI does \nnot show a significant decrease in connectivity, compared with NC. This may be because MCI \ndoes not disrupt the temporal lobe as badly as AD. \n\n AD MCI NC \n\nFig 4(a): SICE-based brain connectivity models (total number of arcs equal to 50) \n\n AD MCI NC \n\nFig 4(b): SICE-based brain connectivity models (total number of arcs equal to 120) \n\n \n\n \n\n \n\n AD MCI NC \n\nFig 4(c): SICE-based brain connectivity models (total number of arcs equal to 180) \n\n \nThe frontal lobe of AD has significantly more connectivity than NC, which is true across different \nstrength levels of the connectivity. This has been interpreted as compensatory reallocation or \nrecruitment of cognitive resources [6]-[7]. Because the regions in the frontal lobe are typically \naffected later in the course of AD (our data are early AD), the increased connectivity in the frontal \nlobe may help preserve some cognitive functions in AD patients. Furthermore, the frontal lobe of \nMCI does not show a significant increase in connectivity, compared with NC. This indicates that \nthe compensatory effect in MCI brain may not be as strong as that in AD brains. \n\n\fTable 2: P-values from the statistical significance test of connectivity difference among \n\nAD, MCI, and NC \n\n(a) Total number of arcs = 50 (b) Total number of arcs = 120 (c) Total number of arcs = 180 \n\n \n\n \n\n \n\nThere is no significant difference among AD, MCI, and NC in terms of the connectivity within the \nparietal lobe and within the occipital lobe. Another interesting finding is that all the P-values in the \nthird sub-table of Table 2(a) are insignificant. This implies that distribution of the strong \nconnectivity within and between lobes for MCI is very similar to NC; in other words, MCI has not \nbeen able to disrupt the strong connectivity among brain regions (it disrupts some mild and weak \nconnectivity though). \n\nBetween-lobe connectivity: In general, human brains tend to have less between-lobe connectivity \nthan within-lobe connectivity. A majority of the strong connectivity occurs within lobes, but rarely \nbetween lobes. These can be clearly seen from Fig. 4 (especially Fig. 4(a)) in which there are \nmuch more black cells along the diagonal direction than the off-diagonal direction, regardless of \nAD, MCI, and NC. \n\nThe connectivity between the parietal and occipital lobes of AD is significantly more than NC \nwhich is true especially for mild and weak connectivity. The increased connectivity between the \nparietal and occipital lobes of AD has been previously reported in [3]. It is also interpreted as a \ncompensatory effect in [6]-[7]. Furthermore, MCI also shows increased connectivity between the \nparietal and occipital lobes, compared with NC, but the increase is not as significant as AD. \n\nWhile the connectivity between the frontal and occipital lobes shows little difference between AD \nand NC, such connectivity for MCI shows a significant decrease especially for mild and weak \nconnectivity. Also, AD may have less temporal-occipital connectivity, less frontal-parietal \nconnectivity, but more parietal-temporal connectivity than NC. \n\nBetween-hemisphere connectivity: Recall that we have observed from the tree-like plots in Figs. 3 \nand 4 that the same brain regions in the left and right hemisphere are connected much weaker in \nAD than in NC. It is desirable to test if this observed difference is statistically significant. To \nachieve this, we test the statistical significance of the difference among AD, MCI, and NC, in term \nof the number of connected same-region left-right pairs. Results show that when the total number \nof arcs in the connectivity models is equal to 120 or 90, none of the tests is significant. However, \nwhen the total number of arcs is equal to 50, the P-values of the tests for \u201cAD vs. NC\u201d, \u201cAD vs. \nMCI\u201d, and \u201cMCI vs. NC\u201d are 0.009, 0.004, and 0.315, respectively. We further perform tests for \nthe total number of arcs equal to 30 and find the P-values to be 0. 0055, 0.053, and 0.158, \nrespectively. These results indicate that AD disrupts the strong connectivity between the same \nregions of the left and right hemispheres, whereas this disruption is not significant in MCI. \n\n \n4 \n\n C o n c l u s i o n \n\nIn the paper, we applied SICE to model functional brain connectivity of AD, MCI, and NC based \non PET neuroimaging data, and analyze the patterns based on the monotone property of SICE. Our \nfindings were consistent with the previous literature and also showed some new aspects that may \nsuggest further investigation in brain connectivity research in the future. \n\n\fR e f e r e n c e s \n\n[1] S. Molchan. (2005) The Alzheimer's disease neuroimaging initiative. Business Briefing: US \nNeurology Review, pp.30-32, 2005. \n[2] C.J. Stam, B.F. Jones, G. Nolte, M. Breakspear, and P. Scheltens. (2007) Small-world networks and \nfunctional connectivity in Alzheimer\u2019s disease. Cerebral Corter 17:92-99. \n[3] K. Supekar, V. Menon, D. Rubin, M. Musen, M.D. Greicius. (2008) Network Analysis of Intrinsic \nFunctional Brain Connectivity in Alzheimer's Disease. PLoS Comput Biol 4(6) 1-11. \n[4] K. Wang, M. Liang, L. Wang, L. Tian, X. Zhang, K. Li and T. Jiang. (2007) Altered Functional \nConnectivity in Early Alzheimer\u2019s Disease: A Resting-State fMRI Study, Human Brain Mapping 28, 967-\n978. \n[5] N.P. Azari, S.I. Rapoport, C.L. Grady, M.B. Schapiro, J.A. Salerno, A. Gonzales-Aviles. (1992) Patterns \nof interregional correlations of cerebral glucose metabolic rates in patients with dementia of the Alzheimer \ntype. Neurodegeneration 1: 101\u2013111. \n[6] R.L. Gould, B.Arroyo, R,G. Brown, A.M. Owen, E.T. Bullmore and R.J. Howard. (2006) Brain \nMechanisms of Successful Compensation during Learning in Alzheimer Disease, Neurology 67, 1011-1017. \n[7] Y. Stern. (2006) Cognitive Reserve and Alzheimer Disease, Alzheimer Disease Associated Disorder 20, \n69-74. \n[8] K.J. Friston. (1994) Functional and effective connectivity: A synthesis. Human Brain Mapping 2, 56-78. \n[9] G. Alexander, J. Moeller. (1994) Application of the Scaled Subprofile model: a statistical approach to the \nanalysis of functional patterns in neuropsychiatric disorders: A principal component approach to modeling \nregional patterns of brain function in disease. Human Brain Mapping, 79-94. \n[10] V.D. Calhoun, T. Adali, G.D. Pearlson, J.J. Pekar. (2001) Spatial and temporal independent component \nanalysis of functional MRI data containing a pair of task-related waveforms. Hum.Brain Mapp. 13, 43-53. \n[11] V.D. Calhoun, T. Adali, J.J. Pekar, G.D. Pearlson. (2003) Latency (in)sensitive ICA. Group independent \ncomponent analysis of fMRI data in the temporal frequency domain. Neuroimage. 20, 1661-1669. \n[12] A.R. McIntosh, F.L. Bookstein, J.V. Haxby, C.L. Grady. (1996) Spatial pattern analysis of functional \nbrain images using partial least squares. Neuroimage. 3, 143-157. \n[13] K.J. Worsley, J.B. Poline, K.J. Friston, A.C. Evans. (1997) Characterizing the response of PET and \nfMRI data using multivariate linear models. Neuroimage. 6, 305-319. \n[14] E. Bullmore, B. Horwitz, G. Honey, M. Brammer, S. Williams, T. Sharma. (2000) How good is good \nenough in path analysis of fMRI data? NeuroImage 11, 289\u2013301. \n[15] A.R. McIntosh, C.L. Grady, L.G. Ungerieider, J.V. Haxby, S.I. Rapoport, B. Horwitz. (1994) Network \nanalysis of cortical visual pathways mapped with PET. J. Neurosci. 14 (2), 655\u2013666. \n[16] K.J. Friston, L. Harrison, W. Penny. (2003) Dynamic causal modelling. Neuroimage 19, 1273-1302. \n[17] O. Banerjee, L. El Ghaoui, and A. d\u2019Aspremont. (2008) Model selection through sparse maximum \nlikelihood estimation for multivariate gaussian or binary data. Journal of Machine Learning Research 9:485-\n516. \n[18] J. Dahl, L. Vandenberghe, and V. Roycowdhury. (2008) Covariance selection for nonchordal graphs via \nchordal embedding. Optimization Methods Software 23(4):501-520. \n[19] J. Friedman, T.astie, and R. Tibsirani. (2007) Spares inverse covariance estimation with the graphical \nlasso, Biostatistics 8(1):1-10. \n[20] J.Z. Huang, N. Liu, M. Pourahmadi, and L. Liu. (2006) Covariance matrix selection and estimation via \npenalized normal likelihood. Biometrika, 93(1):85-98. \n[21] H. Li and J. Gui. (2005) Gradient directed regularization for sparse Gaussian concentration graphs, with \napplications to inference of genetic networks. Biostatistics 7(2):302-317. \n[22] Y. Lin. (2007) Model selection and estimation in the gaussian graphical model. Biometrika 94(1)19-35, \n2007. \n[23] A. Dobra, C. Hans, B. Jones, J.R. Nevins, G. Yao, and M. West. (2004) Sparse graphical models for \nexploring gene expression data. Journal of Multivariate Analysis 90(1):196-212. \n[24] A. Berge, A.C. Jensen, and A.H.S. Solberg. (2007) Sparse inverse covariance estimates for hyperspectral \nimage classification, Geoscience and Remote Sensing, IEEE Transactions on, 45(5):1399-1407. \n[25] J.A. Bilmes. (2000) Factored sparse inverse covariance matrices. In ICASSP:1009-1012. \n[26] L. Sun and et al. (2009) Mining Brain Region Connectivity for Alzheimer's Disease Study via Sparse \nInverse Covariance Estimation. In KDD: 1335-1344. \n[27] R. Tibshirani. (1996) Regression shrinkage and selection via the lasso. Journal of the Royal Statistical \nSociety Series B 58(1):267-288. \n[28] N. Tzourio-Mazoyer and et al. (2002) Automated anatomical labeling of activations in SPM using a \nmacroscopic anatomical parcellation of the MNI MRI single subject brain. Neuroimage 15:273-289. \n[29] Supplemental information for \u201cLearning Brain Connectivity of Alzheimer's Disease from Neuroimaging \nData\u201d. http://www.public.asu.edu/~jye02/Publications/AD-supplemental-NIPS09.pdf \n\n\f", "award": [], "sourceid": 802, "authors": [{"given_name": "Shuai", "family_name": "Huang", "institution": null}, {"given_name": "Jing", "family_name": "Li", "institution": null}, {"given_name": "Liang", "family_name": "Sun", "institution": null}, {"given_name": "Jun", "family_name": "Liu", "institution": null}, {"given_name": "Teresa", "family_name": "Wu", "institution": null}, {"given_name": "Kewei", "family_name": "Chen", "institution": null}, {"given_name": "Adam", "family_name": "Fleisher", "institution": null}, {"given_name": "Eric", "family_name": "Reiman", "institution": null}, {"given_name": "Jieping", "family_name": "Ye", "institution": null}]}