A Pilot Study on Brain Plasticity of Functional Connectivity Modulated by Cognitive Training in Mild Alzheimer’s Disease and Mild Cognitive Impairment

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Abstract

Alzheimer’s disease (AD) alters the functional connectivity of the default mode network (DMN) but also the topological properties of the functional connectome. Cognitive training (CT) is a tool to slow down AD progression and is likely to impact on functional connectivity. In this pilot study, we aimed at investigating brain functional changes after a period of CT and active control (AC) in a group of 26 subjects with mild AD (mAD), 26 with amnestic mild cognitive impairment (aMCI), and a control group of 29 healthy elderly (HE) people. They all underwent a CT and AC in a counterbalanced order following a crossover design. Resting-state functional MRI and neuropsychological testing were acquired before and after each period. We tested post-CT and post-AC changes of cognitive abilities, of the functional connectivity of the DMN, and of topological network properties derived from graph theory and network-based statistics. Only CT produced functional changes, increasing the functional connectivity of the posterior DMN in all three groups. mAD also showed functional changes in the medial temporal lobe and topological changes in the anterior cingulum, whereas aMCI showed more widespread topological changes involving the frontal lobes, the cerebellum and the thalamus. Our results suggest specific functional connectivity changes after CT for aMCI and mAD.

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Network Analysis of Intrinsic Functional Brain Connectivity in Alzheimer's Disease

Kaustubh Supekar, Vinod Menon, Daniel Rubin … (2008)

Introduction Alzheimer's disease (AD) is a neurodegenerative disorder characterized by progressive impairment of episodic memory and other cognitive domains resulting in dementia and, ultimately, death. Imaging studies in AD have begun a shift from studies of brain structure [1],[2] to more recent studies highlighting focal regions of abnormal brain function [3]–[6]. Most recently, fMRI studies have moved beyond focal activation abnormalities to dysfunctional brain connectivity. Functional connectivity is defined as temporal correlations between spatially distinct brain regions [7]. PET studies, restricted to across-subject connectivity measures, have shown that AD patients have decreased hippocampus connectivity with prefrontal cortex [8] and posterior cingulate cortex [9] during memory tasks. Using fMRI, we demonstrated that AD patients performing a simple motor task had reduced intra-subject functional connectivity within a network of brain regions—termed the default-mode network—that includes posterior cingulate cortex, temporoparietal junction, and hippocampus [10]. Bokde et al. reported abnormalities in fusiform gyrus connectivity during a face-matching task in subjects with mild cognitive impairment—frequently a precursor to AD [11]. Three recent studies have reported reduced default-mode network deactivation in MCI and/or AD patients during encoding tasks [12],[13] and during a semantic classification task [14]. Celone et al also reported increased default-mode network deactivation in a subset of “less impaired” MCI patients. In addition to analyzing functional connectivity during task performance, functional connectivity has also been investigated during task-free (“resting-state”) conditions. Task-free functional connectivity MRI detects interregional correlations in spontaneous blood oxygen level-dependent (BOLD) signal fluctuations [15]. Using this approach, Wang et al. found disrupted functional connectivity between hippocampus and several neocortical regions in AD [16]. Similarly, Li et al. reported reduced intrahippocampal connectivity during task-free conditions [17]. Most recently Sorg et al. [18] reported reduced resting-state functional connectivity in the default-mode network of MCI patients. Although evidence is accumulating that AD disrupts functional connections between brain regions [19], it is not clear whether AD disrupts global functional brain organization. Graph metrics–the clustering coefficient and the characteristic path length—are useful measures of global organization of large-scale networks [20]. Graphs are data structures which have nodes and edges between the nodes. The clustering coefficient is a measure of local network connectivity. A network with a high average clustering coefficient is characterized by densely connected local clusters. The characteristic path length is a measure of how well connected a network is. A network with a low characteristic path length is characterized by short distances between any two nodes. Small-world network is characterized by a high clustering coefficient and a low characteristic path length [20],[21]. In a graphical representation of a brain network, a node corresponds to a brain region while an edge corresponds to the functional interaction between two brain regions. Functional connectivity networks of the human brain derived from electroencephalograms (EEGs), magnetoencephalograms and task-free fMRI data exhibit small-world characteristics [22]–[24]. In a recent EEG study, Stam et al. reported that small-world architecture in functional networks in the brain is disrupted in AD [25]. Here we examined the global functional organization of the brain in AD by (1) creating whole-brain functional connectivity networks from task-free fMRI data, (2) characterizing the organization of these networks using small-world metrics, and (3) comparing these characteristics between AD patients and age-matched controls. We hypothesized that global functional brain organization would be abnormal in AD. Further, given the need for a reliable, non-invasive clinical test for AD [26], we sought to determine whether a small-world metric obtained from task-free fMRI data might provide a sensitive and specific biomarker in AD. Results Subjects Demographic data is shown in Table 1. Subject groups did not differ significantly in age (p = 0.73), gender distribution (p = 0.62), or years of education (p = 0.58). The mean MMSE was significantly lower (p 1) showed a linear increase in small-worldness as the threshold increased (degree decreased). σ values for higher correlation thresholds are difficult to interpret, as at higher threshold values, graphs of functional brain networks have fewer edges (smaller degree) and tend to split into isolated sub-graphs. Graph metrics such as clustering coefficient, characteristic path length, and small-world property do not meaningfully characterize network structures that are not composed of a single, large group of interconnected nodes [20]. 10.1371/journal.pcbi.1000100.g001 Figure 1 Graph metrics–degree, λ (L/Lran), γ (C/Cran), σ (γ/λ), for the AD group (Δ) and the control group (○) at three frequency intervals–0.01 to 005 Hz (green), 0.06 to 0.12 Hz (blue), and 0.13 to 0.25 Hz (red). (A) For both groups, the mean degree–a measure of network connectivity is highest at Scale 3 for a wide range of correlation thresholds (0.01 1) showed a linear increase in small-worldness as the threshold increased (degree decreased). σ values for higher correlation thresholds are hard to interpret as at higher threshold values graphs of functional brain networks have fewer edges (smaller degree) and tend to split into isolated sub-graphs. Since functional connectivity and small-world properties were salient at lower-frequencies (0.01 to 0.05 Hz) for the AD group and the control group, we only report results for this frequency interval in subsequent analyses. Comparison of small-world metrics in the AD and control groups In the frequency interval between 0.01 to 0.05 Hz, we examined λ and γ values in the two groups. For group comparison, we controlled for the average correlation value (r). r is different across groups. Thus, for a given correlation threshold, the number of edges in the graph are likely to be less in AD, resulting in high λ and low γ values. To ensure that graphs in both groups had the same number of edges, individual correlation matrices were thresholded such that the resultant graph had exactly K′ edges. K′ is the average number of edges in the graph obtained by thresholding individual correlation matrices with R = ri (ri is the average correlation value for subject i, i = 1 to 39). The value of K′ selected according to this procedure was 40 for both the groups. Mean λ, mean γ, and mean σ values for the networks of the AD group and control group were derived by thresholding the correlation matrices such that the network has K′ ( = 40) edges (shown in Figure 2). Results were: (i) No significant differences in the mean λ values were observed, Mean γ values in the AD group were significantly lower than in the control group (p 0.6, mainly due to the large variance observed at higher threshold values. This analysis was extended to the remaining 86 regions of the whole brain functional network (see Table S1 to find regions that showed significant differences in clustering coefficient values between the two subject groups). 10.1371/journal.pcbi.1000100.g005 Figure 5 Small-world property γ (C/Cran), the normalized clustering coefficient, for four regions of interest–left hippocampus (Hippocampus - Left), right hippocampus (Hippocampus - Right), left precentral gyrus (Precentral Gyrus - Left), right precentral gyrus (Precentral Gyrus - Right)–for the AD group (red) and the control group (blue) as a function of the correlation threshold. In the left and the right hippocampus, for threshold values from 0.1 to 0.6, the clustering coefficient values in the AD group were significantly lower (p 172) was assumed to be a symmetric reflection of itself. At each of the three scales, wavelet correlations between signals in the 90 anatomical regions were determined by computing the correlation coefficient between the transformed signals at that scale. For each subject, a 90-node, scale-specific, undirected graph of the functional connectivity network was constructed by thresholding the wavelet correlation matrix computed at that scale. If the wavelet correlation value between two anatomical regions represented by nodes i and j in the network exceeded a threshold then an edge was drawn between node i and node j. There is currently no formal consensus regarding threshold selection, so we computed networks for threshold values from 0.01 to 0.99 with an increment of 0.01. Once a whole-brain functional connectivity network was constructed from the correlation matrix, we characterized this network in terms of its small-world properties. Small-world analysis of the whole-brain functional connectivity network Small-World properties of a network are described by the clustering coefficient and the characteristic path length of the network. The clustering coefficient and characteristic path length of functional brain networks generated from the task-free fMRI data obtained from 21 AD subjects and 18 age-matched controls were computed. The clustering coefficient of every node was computed as the ratio of the number of connections between its neighbors divided by the maximum possible connections between its neighbors. The clustering coefficient (C) of the network was calculated as the mean of the clustering coefficients of all the nodes in the network. The mean minimum path length of a node was computed as the average of minimum distances from that node to all the remaining nodes in the network. The characteristic path length (L) of the network was the average of the mean minimum path lengths of all the nodes in the network. The clustering coefficient and path length of nodes completely disconnected with the network were set as 0 and Inf respectively, and these nodes were excluded while computing C and L. To evaluate the network for small-world properties, we compared the clustering coefficient and the characteristic path length of the network with corresponding values (Cran, Lran) obtained and averaged across 1000 random networks with the same number of nodes and degree distribution [48]. Degree of a network is a measure of its connectivity. The degree of every node was computed by counting the number of edges incident on that node. Small world networks are characterized by high normalized clustering coefficient γ (C/Cran)>1 and low normalized characteristic path length λ (L/Lran)∼1 compared to random networks [24]. A cumulative metric σ–the ratio of normalized clustering coefficient (γ) to the characteristic path length (λ), a measure of small-worldness–is thus greater than 1 for small world networks. Analysis of global efficiency of whole-brain functional connectivity network Small-world networks are characterized by high clustering coefficient and low characteristic path length. These small-world metrics, particularly the path length, are not meaningful when the graph contains disconnected nodes. To address this issue, we ensured that only small-world metrics computed on connected graphs were considered in our analysis. Specifically, the algorithm used to choose the correlation threshold (R) guaranteed that disconnected graphs were excluded from the analysis. Also, in the node-wise clustering coefficient comparison analysis, we only considered thresholds from 0.1 to 0.6. We chose these thresholds because beyond 0.6 the network gets divided into disconnected subset of nodes. To determine if our characteristic path length findings were robust and reliable, we computed efficiency of functional brain networks. It has been previously reported that efficiency as a graph metric (1) is not susceptible to disconnected nodes, (2) is applicable to unweighted as well as weighted graphs, and (3) is a more meaningful measure of parallel information processing than path length [49]. Efficiency of a graph (Eglobal-net) [50] is inverse of the harmonic mean of the minimum path length between each pair of nodes, Lij, and was computed as, (1) To evaluate the network for its global efficiency of parallel information processing, we compared the global efficiency of the network (Eglobal-net) with corresponding values (Eglobal-ran) obtained and averaged across 1000 random networks with the same number of nodes and degree distribution. A network with small-world properties is characterized by global efficiency value that is lower than the random network–Eglobal (Eglobal-net/Eglobal-ran)<1. Regional profile of clustering coefficient In the frequency interval 0.01 to 0.05 Hz, we next examined small world metric values of four anatomical regions of interest in the two groups. These four regions included the left hippocampus, the right hippocampus, the left precentral gyrus, and the right precentral gyrus. These were chosen because we hypothesized significant differences in the hippocampus (a region targeted early in AD), but not in the precentral gyrus (which is typically spared even in the advanced stages of AD) [51]. This regional profiling analysis was performed on the clustering coefficient (and not the path length) because only the former differed significantly between the AD and control groups. Growth curve modeling, with an intercept (baseline), linear and quadratic terms, was used to compare the clustering coefficient values for threshold values from 0.1 to 0.6 in the two subject groups. We chose these thresholds because beyond 0.6 the network divides into disconnected subsets of nodes and small-world metrics are then no longer meaningful [20]. This analysis was performed using the Mplus software (http://www.statmodel.com). Growth curve models describe change (growth) with respect to a control variable. They are well-suited for analyzing group-level differences in biomedical data, particularly in cases where capturing and analyzing individual growth trajectories is important. In our study, the growth trajectories of clustering coefficient of a subject carry important information about the variance within the group and needs to be incorporated in the model. The coefficients of growth curve models capture the baseline performance, instantaneous growth rate, and the acceleration of the variable of interest–γ. Regional connectivity We then examined regional correlation values (connectivity) in the two groups. Wavelet correlation values of 4005 pairs of anatomical regions were first z-normalized and then compared between the two subject groups. T-test with a false discovery rate of 0.01 was used to test if the difference was significant. For the frequency range 0.01 to 0.05 Hz, the correlation values of 108 pairs of anatomical regions out of a total 4005 pairs were significantly lower in the AD group as compared to the control group while only 42 correlation values showed a significant increase in the AD group (p<0.01, corrected for multiple comparisons). To get an idea of average differences in the global functional organization in the two groups, we investigated the regional connectivity at a coarser level of granularity. Ninety anatomical regions of our network were grouped into eight higher-level anatomical regions using the grouping defined by Tzourio-Mazoyer et al. [45]. The prefrontal lobe region consists of the superior frontal gyrus (dorsolateral, orbital, medial, medial orbital), the middle frontal gyrus, the middle frontal gyrus (orbital), the inferior frontal gyrus (opercular, triangular, orbital), the olfactory gyrus, the gyrus rectus, and the anterior cingulate. The other parts of frontal lobe region consists of the precentral gyrus, the supplementary motor area, the median cingulate, and the rolandic operculum. The occipital lobe region consists of the calcarine fissure, the cuneus, the lingual gyrus, the superior occipital gyrus, the middle occipital gyrus, and the inferior occipital gyrus. The temporal lobe and the medial temporal region consists of the superior temporal gyrus, the temporal pole (superior, middle), the middle temporal gyrus, the inferior temporal gyrus, the heschl gyrus, the fusiform gyrus, the hippocampus, the parahippocampal gyrus, and the amygdala. The parietal lobe region consists of the postcentral gyrus, the superior parietal lobule, the inferior parietal lobule, the supramarginal gyrus, the angular gyrus, the precuneus, the paracentral lobule, and the posterior cingulate gyrus. The corpus striatum region consists of the caudate nucleus, the putamen, and the pallidum. Each higher level anatomical region consists of regions from both the hemispheres. Differences in mean correlation coefficients for 4005 pairs were aggregated into 32 pairs and the resulting differences were then normalized. (see also [52]). In the aggregation step, the number of decreased (−1) or increased connectivities (+1) for each of the 32 pairs ( = (8×8)/2) was counted. For example, to identify differential connectivity between the prefrontal lobe region and the occipital lobe region the number of decreased or increased connectivities between all pairs of sub-regions belonging to the prefrontal lobe region and occipital lobe region was counted. Since each brain region has a different number of sub-regions, the aggregated differential connectivity count was normalized by the number of possible connections between pairs of sub regions belonging to the two brain regions under investigation. Supporting Information Table S1 Regions of whole brain functional network ranked in ascending order of the p-value (computed using growth curve modeling) and then descending order of absolute difference between the clustering coefficient values of the AD group and the control group. (0.18 MB DOC) Click here for additional data file.

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2015 Alzheimer's disease facts and figures.

(2015)

This report discusses the public health impact of Alzheimer’s disease (AD), including incidence and prevalence, mortality rates, costs of care and the overall effect on caregivers and society. It also examines the challenges encountered by health care providers when disclosing an AD diagnosis to patients and caregivers. An estimated 5.3 million Americans have AD; 5.1 million are age 65 years, and approximately 200,000 are age <65 years and have younger onset AD. By mid-century, the number of people living with AD in the United States is projected to grow by nearly 10 million, fueled in large part by the aging baby boom generation. Today, someone in the country develops AD every 67 seconds. By 2050, one new case of AD is expected to develop every 33 seconds, resulting in nearly 1 million new cases per year, and the estimated prevalence is expected to range from 11 million to 16 million. In 2013, official death certificates recorded 84,767 deaths from AD, making AD the sixth leading cause of death in the United States and the fifth leading cause of death in Americans age 65 years. Between 2000 and 2013, deaths resulting from heart disease, stroke and prostate cancer decreased 14%, 23% and 11%, respectively, whereas deaths from AD increased 71%. The actual number of deaths to which AD contributes (or deaths with AD) is likely much larger than the number of deaths from AD recorded on death certificates. In 2015, an estimated 700,000 Americans age 65 years will die with AD, and many of them will die from complications caused by AD. In 2014, more than 15 million family members and other unpaid caregivers provided an estimated 17.9 billion hours of care to people with AD and other dementias, a contribution valued at more than $217 billion. Average per-person Medicare payments for services to beneficiaries age 65 years with AD and other dementias are more than two and a half times as great as payments for all beneficiaries without these conditions, and Medicaid payments are 19 times as great. Total payments in 2015 for health care, long-term care and hospice services for people age 65 years with dementia are expected to be $226 billion. Among people with a diagnosis of AD or another dementia, fewer than half report having been told of the diagnosis by their health care provider. Though the benefits of a prompt, clear and accurate disclosure of an AD diagnosis are recognized by the medical profession, improvements to the disclosure process are needed. These improvements may require stronger support systems for health care providers and their patients.

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Abnormal Cortical Networks in Mild Cognitive Impairment and Alzheimer's Disease

Zhijun Yao, Yuanchao Zhang, Lei Lin … (2010)

Introduction Alzheimer's disease, the most common form of dementia, is associated with plaques and tangles in the brain which would lead to a loss of neurons and synapses [1]–[2]. In the early stages, Alzheimer's disease is characterized by a decline in cognitive and memory functions. Clinical symptoms of Alzheimer's disease include confusion, aggression, language breakdown, and the loss of cognitive functions [3]–[4]. Mild Cognitive Impairment (MCI), characterized by memory impairment, is considered to be the clinical transition stage between normal aging and dementia [5]–[6]. Studies suggest that subjects with MCI tend to progress to probable Alzheimer's disease at a rate of approximately 10% to 15% per year [7]. Facing these serious facts, many research groups have studied AD and MCI from various perspectives, attempting to understand the pathogenesis with a goal of discovering effective therapies [8]–[9]. Voxel based morphometry (VBM), proposed by Friston and Ashburner [10], allows a fully automated whole-brain analysis of structural MRI scans [11]. Using the VBM method, previous studies showed atrophy of the parahippocampal gyrus, medial temporal lobe [12], entorhinal cortex, cingulum [13], insula and thalamus [14] in subjects with MCI and atrophy of the entire hippocampus and some localized regions in the temporal lobe, cingulum, precuneus, insular cortex, caudate nucleus, and frontal cortex [14]–[16] in patients with AD. Recently, studies of functional and structural brain networks in AD patients have indicated that cognitive function deficits could be due to abnormalities in the connectivity between different brain areas. These brain areas include the bilateral parietal regions, middle temporal gyrus, cingulum, medial frontal gyrus, precentral gyrus, fusiform, etc. [17]–[19]. Small-worldness, which was characterized by a high degree of clustering and short path lengths, has been found to exist in social networks, the connectivity of the internet, and in gene networks [20]–[21]. Previous studies have reported that the human cortical network also has small-world properties [22]–[25], and a loss of small-world characteristics has been detected in patients with AD [18]–[19]. Reports on the characteristics of the structural cortical network in MCI have been rare [26]. In the present study, we constructed structural cortical networks using average gray matter volumes of each AAL area to investigate the characteristics of the cortical networks in NCs, MCI subjects and AD patients. In addition, we also inspected the pattern of structural connections and hub regions. This type of research may contribute to understanding the pathogenesis of MCI and AD. Since MCI is considered to be an intermediate stage between normal aging and AD, we hypothesized that the measurements of the cortical network properties (for example clustering coefficient and absolute path length) in MCI would lie between those of NC and AD subjects. Results The interregional correlation coefficients of the cortical networks were calculated to construct correlation matrices (90×90) for the NC, MCI and AD groups (see Materials and Methods). The images of the interregional correlation matrices are shown in Figure 1. We revealed one feature in common among the three groups that strong interregional correlations exist between most homotopic regions (the same areas in opposite hemispheres). This finding is consistent with earlier studies using cortex thickness [24] and gray matter volume [27]. 10.1371/journal.pcbi.1001006.g001 Figure 1 The interregional correlations matrix in the AD, MCI and NC groups. The color bar indicates the value of the correlation coefficient r (ranging from −0.8 to 1). A. The correlations matrices obtained by calculating the correlations between pairs of AAL areas within each group (left - the AD group, middle - the MCI group and right - the NC group). B. The binarized matrices obtained by thresholding the above correlations matrices of A with a sparsity threshold (15%). The sparsity threshold sets the same number of nodes and edges in each of the three cortical networks. Small-world properties of cortical networks Some recent studies demonstrated that small-world properties are exhibited in functional brain networks [23], [28] and structural brain networks [24], [29]. Compared with random networks, small-world networks have higher clustering coefficients and similar shortest absolute path length. Over a wide range of sparsity values ( ), clustering coefficients and absolute path lengths were calculated for the three networks. The small-world attributes of three cortical networks are shown in Figure 2. Compared with matched random networks which have the same number of nodes and degree distribution, the three cortical networks had similarly identical absolute path lengths ( ) and larger clustering coefficients ( ) (see Materials and Methods). A precise quantitative analysis suggests that small-world networks with a high global efficiency and an optimal organization can support distributed information processing and high dynamic complexity [25]. Similar to previous studies, the cortical networks of the groups with MCI and AD showed varying degrees of loss of small-world characteristics [18]–[19]. As shown in Figure 3, the clustering coefficient was the greatest for the AD group and the absolute path length was shortest for the normal controls. Additionally, the corresponding measurements were intermediate for the MCI group among the three cortical networks. A permutation test was used to detect the statistical significance of the between-group differences of the attributes (see Materials and Methods). In Figure 4, the arrows indicated the significant differences between NCs and ADs in the cluster coefficients (p 0.05). Our findings provided additional support for the hypothesis that the cortical networks had a further loss in the small-world characteristics in the progression from MCI to AD [18]–[19]. 10.1371/journal.pcbi.1001006.g002 Figure 2 Small-world properties of the structural cortical networks. The graphs show the absolute path lengths (Gamma γ = Cp real/Cp rand) and clustering coefficients (Lambda λ = Lp real/Lp rand) over a wide range of sparsity values ( ) and the error bars were obtained using bootstrap method. All the networks have γ>1 (the blue lines) and λ≈1 (the black lines), which imply small-world properties. As the values of the sparsity thresholds increase, the γ values decrease rapidly and the λ values change only slightly. A – The values of Gamma and Lambda in NC. B – The values of Gamma and Lambda in MCI. C – The values of Gamma and Lambda in AD. 10.1371/journal.pcbi.1001006.g003 Figure 3 Mean clustering coefficients and mean absolute path lengths of the cortical networks in the three subject groups. Mean clustering coefficient (Cp) and mean absolute path length (Lp) over a wide range of sparsity values ( ) and the error bars were obtained using bootstrap method. A - The red stars represent the mean clustering coefficient in the AD group. The blue circles represent the mean clustering coefficient in the MCI group. The black squares represent the mean clustering coefficient in the NC group. B - The red stars represent the mean absolute path length in the AD group. The blue circles represent the mean absolute path length in the MCI group. The black squares represent the mean absolute path length in the NC group. The mean clustering coefficient was the greatest for the AD group and the absolute path length was shortest for the NC group. The measurements of the MCI group were intermediate between the NCs and ADs. 10.1371/journal.pcbi.1001006.g004 Figure 4 Between-group differences in the clustering coefficient (Cp) and the absolute path length (Lp) over a range of sparsity values. The left shows the between-group differences in clustering coefficients (ΔCp) and the right shows the between-group differences in absolute path lengths (ΔLp) over a wide range of sparsity values ( ). The black open circles represent the mean values and the black lines represent the 95% confidence intervals of the between-group differences obtained from 1000 permutation tests at each sparsity value. A - Differences between the NC and AD groups (ΔCp = CpNC−CpAD, ΔLp = LpNC−LpAD). B - Differences between the NC and MCI groups (ΔCp = CpNC−CpMCI, ΔLp = LpNC−LpMCI). C - Differences between the MCI and AD groups (ΔCp = CpMCI−CpAD, ΔLp = LpMCI−LpAD). The arrows indicate the significant (p<0.05) between-group differences in the clustering coefficients and absolute path lengths. Measurements of the cortical networks In order to detect the specific between-group differences among the three cortical networks, a fixed sparsity threshold value (sp = 15%) was used. This sparsity value can ensure that the cortical networks are fully connected while minimizing the number of false-positive paths [19], [23]. Hub regions of the three cortical networks To ascertain the hub regions of the cortical networks, the normalized betweenness centrality ( ) of each node was evaluated (see Materials and Methods). Hub nodes were defined as those whose betweenness values were more than twice the average betweenness of the network ( ). Based on our results, some regions were identified as hub regions in the cortical networks of each of the three populations. Details of the hub regions in the three cortical networks are shown in Table 1. 10.1371/journal.pcbi.1001006.t001 Table 1 Hub regions in cortical networks of the three populations listed in descending order of their normalized betweenness in the NCs. AAL areas Betweenness NC MCI AD Temporal_Mid_R 4.660 1.297 0.106 Lingual_R 3.474 2.793 0 Frontal_Med_Orb_R 2.898 7.341 1.116 Lingual_L 2.825 0.133 0 Paracentral_Lobule_R 2.641 1.830 3.806 Frontal_Mid_Orb_L 2.601 0.284 0 Frontal_Med_Orb_L 2.575 1.382 2.253 Occipital_Mid_L 2.462 3.819 2.194 Temporal_Pole_Sup_L 2.287 0.629 0.332 Parietal_Sup_R 2.256 0.623 0.522 Paracentral_Lobule_L 2.253 2.935 3.069 Frontal_Inf_Orb_L 2.237 1.579 1.697 ParaHippocampal_R 2.084 0.984 1.649 Insula_L 2.049 0.240 1.038 Parietal_Sup_L 1.782 3.095 2.544 Caudate_R 1.632 3.8108 0.036 Putamen_R 1.207 0 3.189 Precuneus_L 1.034 3.612 5.974 Temporal_Sup_R 1.025 2.176 1.428 Frontal_Inf_Orb_R 1.022 2.713 4.494 Frontal_Inf_Tri_R 0.975 2.159 2.442 Postcentral_R 0.963 2.026 0.964 Cingulum_Ant_R 0.652 0.178 2.367 Cuneus_L 0.639 2.534 5.534 Precentral_R 0.547 2.827 2.612 Insula_R 0.529 1.741 3.321 Supp_Motor_Area_R 0.358 2.489 0.958 Rolandic_Oper_R 0.329 1.094 6.464 Pallidum_R 0.165 4.122 0 Calcarine_L 0.125 0.761 3.864 10.1371/journal.pcbi.1001006.t002 Table 2 The abbreviations of AAL regions except the cerebellum. Region ID AAL Regions Abbreviation 1 Precentral PreCG 2 Frontal_Sup SFGdor 3 Frontal_Sup_Orb ORBsup 4 Frontal_Mid MFG 5 Frontal_Mid_Orb ORBmid 6 Frontal_Inf_Oper IFGoperc 7 Frontal_Inf_Tri IFGtriang 8 Frontal_Inf_Orb ORBinf 9 Rolandic_Oper ROL 10 Supp_Motor_Area SMA 11 Olfactory OLF 12 Frontal_Sup_Medial SFGmed 13 Frontal_Med_Orb ORBsupmed 14 Rectus REC 15 Insula INS 16 Cingulum_Ant ACG 17 Cingulum_Mid DCG 18 Cingulum_Post PCG 19 Hippocampus HIP 20 ParaHippocampal PHG 21 Amygdala AMYG 22 Calcarine CAL 23 Cuneus CUN 24 Lingual LING 25 Occipital_Sup SOG 26 Occipital_Mid MOG 27 Occipital_Inf IOG 28 Fusiform FFG 29 Postcentral PoCG 30 Parietal_Sup SPG 31 Parietal_Inf IPL 32 SupraMarginal SMG 33 Angular ANG 34 Precuneus PCUN 35 Paracentral_Lobule PCL 36 Caudate CAU 37 Putamen PUT 38 Pallidum PAL 39 Thalamus THA 40 Heschl HES 41 Temporal_Sup STG 42 Temporal_Pole_Sup TPOsup 43 Temporal_Mid MTG 44 Temporal_Pole_Mid TPOmid 45 Temporal_Inf ITG In our work, the identified hub regions involved the middle temporal gyrus, temporal pole, lingual gyrus, orbital frontal gyrus, and superior parietal gyrus in the NC group and the orbital frontal gyrus, inferior frontal gyrus, cingulum, and medial orbital frontal gyrus in the AD group. The findings for these two groups were compatible with previous studies [19], [23]–[24]. In subjects with MCI, some hub regions, such as the medial orbital frontal gyrus, lingual gyrus, and paracentral lobule, were the same as those in the normal controls and in the AD group. These identical hub regions were predominately located in regions of the association cortex, which has been regarded as a pivotal region for receiving convergent information in human cortical networks. The primary location of the hub regions in the association cortex also supports the perspective that it plays a critical role in combining signals from the primary sensory and motor modalities to create emergent psychological properties [30]. Changes in nodal centrality 1000 nonparametric permutation tests were used (see Materials and Methods) to inspect the between-group differences. The regions with significant abnormal changes in nodal centrality in MCI and AD groups are shown in Figure 5. Compared with the NC group, the nodal centrality of the MCI and AD groups significantly decreased in the left lingual gyrus, middle temporal gyrus, middle orbital frontal gyrus and significantly increased in the precuneus. Moreover, compared with the NC and MCI groups, the nodal centrality in AD population showed significant decreases in the right lingual gyrus and significant increases in the right rolandic operculum, anterior cingulum and left calcarine. Additionally, compared with NC and AD groups, no brain areas showed significant changes in nodal centrality in the MCI population. 10.1371/journal.pcbi.1001006.g005 Figure 5 Abnormal changes in between-group nodal centrality in the MCI and AD groups. Each of the eight regions belongs to the hub regions in at least one of the three cortical networks and showed a significant difference (p<0.05). The blue spheres indicate significant decreases in between-group nodal centrality. The red spheres indicate significant increases in between-group nodal centrality. A - Abnormal changes shared by the MCI and AD groups. B - Abnormal changes only in the AD group. Note that no abnormal changes occurred only in the MCI group. For the abbreviations of the regions, see Table 2. Changes in the correlation coefficients Fisher's Z transformation was used to investigate the differences in the between-group interregional correlations (see Materials and Methods). The abnormal interregional correlations that were detected in groups with MCI and AD (p<0.01) are shown in Figure 6. Regions that showed significant changes in the interregional correlations between the NC and AD populations primarily included the parahippocampus gyrus, temporal pole, fusiform, cingulum, superior parietal region and orbital frontal gyrus. The regions that showed significant changes in the interregional correlations between the NC and MCI populations included the parahippocampus gyrus, cingulum, fusiform, orbital frontal gyrus, olfactory, paracentral lobule, inferior temporal gyrus, and rolandic operculum. The regions that showed significant changes in the interregional correlations between the MCI and AD populations included the middle frontal gyrus, superior motor area, paracentral lobule, parahippocampus, temporal pole, orbital frontal gyrus, and middle cingulum. As we can see from Figure 6, our results were consistent with previous studies, which reported progressively increased short distance connectivity and progressively decreased long distance connectivity from MCI to AD [17], [19], [31]. 10.1371/journal.pcbi.1001006.g006 Figure 6 Abnormal interregional correlations in the MCI and AD subjects. The red and blue lines indicate significant between-group differences in interregional correlations between pairs of regions (p<0.01, FDR-corrected); the yellow dots represent those AAL regions with significantly abnormal correlations. The red and blue lines indicate the significantly increased and decreased interregional correlations between the corresponding regions, respectively. A - Significant changes in interregional correlations between the NC and AD groups. B - Significant changes in interregional correlations between the NC and MCI groups. C - Significant changes in interregional correlations between the MCI and AD groups. For the abbreviations of the regions, see Table 2. Discussion In this study, we constructed cortical networks of NC, MCI and AD groups by calculating correlation coefficients between pairs of gray matter regions. Gray matter, which primarily consists of neuronal cell bodies, is a major component of the central nervous system and can directly reflect the function in the brain. Gray matter volume has been widely adopted as an important measurement by many studies [10], [12], [16], [23], [27], [32]–[34]. Covariation of gray matter volume might provide additional insight into the topographical organization of multiple cortical regions, as indicated by a previous study which reported that related components of the visual system covaried in volume across individuals [22], [27], [34]. Mechelli et al. analyzed the level of covariation in gray matter density in cortical regions to investigate brain symmetry [27]. They suggested that covariation might be the result of mutually trophic influences or common experience-related plasticity and that the level of covariation might be disrupted in some patient populations. Raz et al. examined hemisphere-related differences in the cerebral cortex using the gray matter volume [34]. Bassett et al. constructed a whole-brain anatomical network by compiling a matrix of correlations in gray matter volumes between all pairs of regions [22]. In the present work, we took into account the cortical networks of NC, MCI and AD populations to investigate synthetically the abnormal structure of cortical networks in MCI and AD. For the first time, we investigated the characteristics of cortical networks as an aid in understanding the abnormal structural brain network in subjects with MCI. The main finding of this study was that the characteristics of the cortical network in the MCI populations displayed an intermediate position between those of NC and AD subjects. The relevant detailed attributes of the three cortical networks were: 1. The cortical networks in the NC, MCI and AD groups all showed small-world properties. 2. Abnormal nodal centrality changes were detected in the cortical network in the MCI and AD groups. 3. Significant changes in the interregional correlations were found in populations with MCI and AD. These results may indicate that a loss of small-world characteristics was shown in the cortical network of MCI subjects, as has previously been identified in AD populations. These hub regions and the interregional correlations of the cortical network in MCI provided additional structural evidence to support the opinion that MCI is the transitional stage between normal aging and AD. Small-world properties of the three cortical networks Small-world properties, which are frequently found to be properties of complex networks, seem to be common to a wide variety of information systems. Since gray matter volume has played an important role in brain research in recent years [14], [35]–[36], we constructed cortical networks using gray matter volumes to investigate small-world properties in subjects with MCI and AD. Previous studies have showed abnormal cerebral structures accompanied by atrophy of the gray matter in groups with MCI and AD. Therefore we hypothesized that the small-world characteristics of the cortical network in an MCI population might be the similar to that in AD patients, which was characterized by a higher clustering coefficient and a longer absolute path length [18]. We observed that the clustering coefficient and the absolute path length of the cortical network in subjects with MCI exhibited median values between those of the normal controls and those with AD over a wide range of sparsity threshold values. Using permutation tests, we detected statistically significant differences in the clustering coefficients and absolute path lengths between the normal controls and patients with AD (p<0.05). However, we found no significant difference in the two measurements between the NC and the MCI population and between the MCI and AD populations over the entire range of sparsity threshold values. A previous study indicated that the global gray matter volume in their MCI population was intermediate between that of the normal controls and patients with AD but was not significantly different from either group [14]. Our result suggests that MCI forms a boundary between normal aging and AD. We also found that MCI was not statistically significantly different from either group in the characteristic measurements of cortical networks. Altered interregional correlations in MCI and AD Details of the abnormal interregional correlations in groups with MCI and AD are shown in Figure 6. Compared with the normal controls, the AD patients were found to show a significant increase in their interregional correlations, mainly in the parahippocampal gyrus, temporal pole, fusiform gyrus and cingulum. We also observed that the locations of these involved regions were distributed within a limited area of the whole brain. Our results support recent resting-state fMRI studies which reported increased interregional functional connectivity within each brain lobe and decreased interregional functional connectivity between brain lobes in AD [31]. Decreased interregional correlations in patients with AD, that is, the disappearance of positive correlations between the right parahippocampal gyrus and the posterior cingulum, might suggest impairment of learning and memory [37].The disrupted connectivity between the hippocampus and the posterior cingulum may account for the posterior cingulum hypometabolism that has commonly been detected in positron emission tomography (PET) studies of early AD [38]. Compared with the normal control and AD groups, fewer regions showed significant changes in the interregional correlations in MCI group. Consistent with the concept that MCI is a transition stage in the evolution of AD, subjects with MCI showed the same status as those with AD, that is, increased short distance interregional correlations and decreased long distance interregional correlations. Compared with MCI population, we also observed increased short distance interregional correlations, but no decreased interregional correlation was significant in patients with AD. The abnormal increased interregional correlations may explain the higher clustering coefficients of cortical networks in groups with MCI and AD. Our results suggest that the cortical network structure is seriously abnormal and show a progressive loss of small-world characteristics in subjects with MCI [39]. Abnormal changes in nodal centrality in MCI and AD The hub regions of the cortical network that we identified in the normal controls were compatible with those found in previous studies of functional and structural cortical networks [24], [40]–[41]. These hub regions, which are thought to be the substrates for human cognition and consciousness, are in the association cortex that receives convergent inputs from multiple other cortical regions. Previous studies have found that subjects with MCI had a significant reduction in the amount of gray matter in the medial temporal lobe, hippocampus, inferior parietal areas, posterior cingulum, and the lingual and fusiform gyri [13], [33], [42]. In addition, a significant reduction in the gray matter in the frontal cortex has been found in patients with AD [15]–[16]. We expected to find that the structure of the cortical network in groups with MCI and AD changed in these regions along with the atrophy in their gray matter. Our result showed that the middle temporal gyrus, superior temporal pole, lingual gyrus, and parahippocampal gyrus were no longer hubs in groups with MCI and AD. A portion in the these abnormal changes of hub regions in MCI and AD belong to the default mode network, which has been hypothesized as being profoundly relevant to cognitive processing [43]. The abnormal hub regions in the default mode network could result from a decrease in brain metabolism that may occur in the course of the development of AD [38]. Figure 5 shows the regions with abnormal changes in nodal centrality. In fact, these results are to some extent consistent with previous studies. Abnormal changes in the middle temporal gyrus in subjects with MCI and AD were reported as being related to a decline in verbal memory performance [44]. Less activation, as measured using fMRI was detected in the lingual gyrus and cingulate in subjects with MCI and AD [45]. In the present study, the nodal centrality in the precuneus showed a significant difference between the NCs and MCIs and ADs and no significant difference between the MCIs and the ADs. This finding supports a previous study which indicated that differences in the activity in the precuneus were only distinguishable between ADs and NCs, not between the MCI and AD groups [5]. The calcarine and anterior cingulate areas of the cortex seem to be notably spared until the late stages. This sparing of some cortical areas might explain why the nodal centrality of the two areas is abnormal only in patients with AD [32]. From Figure 5, we can see that almost all the brain areas with abnormal changes in nodal centrality showed gradual changes along the transition from NCs to ADs and that no area with abnormal changes was only detected in MCI group. This result also implicates MCI as an intermediate stage between normal aging and AD. The longer absolute path length in subjects with MCI and AD may indicate that the disappearance of these hub regions disrupted the large-scale connections between pairs of brain regions [19], [46]. Meanwhile, we also observed that some regions which had a higher nodal centrality in MCI and AD became new hub regions. Previous studies have reported that increased functional connectivity occurred widely in MCI and AD in various brain regions [17], [47]–[48]. Such increased connectivity may effectively serve as a compensatory system. This compensatory mechanism may play an important role in MCI and AD by enabling patients to use additional cognitive resources to approach a normal level [49]–[51]. The abnormal characteristics of the cortical networks which we observed in MCI and AD may reflect anatomical structural abnormalities. Such a relationship may contribute to an understanding of the cerebral organization in MCI and AD. Methodological limitations and perspectives Our study also has some limitations. Firstly, only small amounts of 3T MRI data are available from the ADNI database. To ascertain the real cortical networks as accurately as possible, this study included as many subjects as were available from each group of the ADNI database, which made the sample size of each group inconsistent. Furthermore, we might have been able to demonstrate this transition from normal aging to MCI to Alzheimer's disease if we had had a larger sample size. As it was, our MCI population could not be separated from the normal controls or from the Alzheimer's group, but the combined groups could clearly be separated from each other. Secondly, Pearson correlation was adopted instead of partial correlation analysis. In fact, after a linear regression of the age, gender and total gray matter volumes of each subject, the matrices of gray matter volumes were not full rank. Thus, a partial correlation analysis could not be performed because the sample size was not large enough. That is why the Pearson correlation was adopted in this work. Finally, compared with the anatomical connectivity obtained by diffusion-based imaging, the method we used in the present study only measures the anatomical connectivity indirectly. However, it is more practical for revealing the anatomical connectivity patterns of the human brain because of its relatively low computational load and simple definition of the neuronal elements (regions) and connections. Future studies should be done to further investigate this issue and replicate our findings using diffusion-based imaging. In this paper, we only studied the global network manifestation of brain malfunction in MCI and AD based on gray matter volume correlations, an indirect anatomical connectivity. In order to understand the pathophysiological mechanism of MCI and AD, it is necessary to integrate the multi-level network features obtained with various functional and anatomical brain imaging technologies on different scales. On macroscale, such features can be obtained from networks based on illness special region of interest, networks related to special cognitive function, and whole brain networks. Here we would like to propose a concept of brainnetome to represent such integration framework. We define the essential components of brainnetome as network topological structure, performance, dynamics, manifestation of functions and malfunctions of brain on different scales. In fact, a big project (973 program) has been approved in China to conduct studies of brainnetome for four different diseases with focal lesion (stoke and glioma) and diffusion lesions (schizophrenia and AD). For AD, the goal is to find biomarkers on network level which can predict whom of MCIs will develop into AD. We envision that brainnetome will become an emerging co-frontier of brain science, information technology, neurology and psychiatry. Some long-standing issues in neuropsychiatry may be solved by combining brainnetome with genome. Materials and Methods Subjects All the subjects used in this study were selected from the Alzheimer's disease Neuroimaging Initiative (ADNI) database (http://www.loni.ucla.edu/ADNI/). This project is the most comprehensive effort to date to identify neuroimaging and other biomarkers of the cognitive changes associated with MCI and AD. The primary goal of this project is to measure the progression of MCI and early AD, in order to develop improved methods for clinical trials in this area. This study included 98 NCs who ranged in age from 70.02 to 90.74 (M = 77.27; SD = 4.66) (female/male, 49∶49), 113 MCI subjects who ranged in age from 56.28 to 89.40 (M = 75.12; SD = 7.60) (female/male, 34∶79), and 91 AD subjects who ranged in age from 55.73 to 90.20 (M = 76.16; SD = 7.81) (female/male 41∶50). Image acquisition The datasets included standard T1-weighted MR images acquired sagittally using volumetric 3D MPRAGE with 1.25×1.25 mm in-plane spatial resolution and 1.2 mm thick sagittal slices. All the high-resolution magnetic resonance images were obtained using 1.5 T scanners. Images using 3T scanners were excluded to remove the discrimination that might be introduced by using different magnetic field strengths. All scans were downloaded in the DICOM format and finally converted to the NIFTI format. Detailed information about the MR acquisition procedures is available at the ADNI website. Measure of gray matter volume All the structural images were preprocessed using voxel based morphometry (VBM) implemented with Statistical Parametric Mapping software (SPM5) running under Matlab 7.0 on the Ubuntu operating system. VBM is a whole-brain, unbiased, semiautomatic, neuroimaging analysis technique that allows the investigation of regional differences in brain volume. In brief, the average gray matter volumes of each brain area were obtained for each subject using the following steps. First, all the structural images were corrected for non-uniformity artifacts. Then, the corrected images were registered to an asymmetric T1-weighted template using nonlinear normalization. Next, the corrected and normalized images were segmented into gray matter, white matter, cerebrospinal fluid and other background classes. Fourth, the resulting gray matter images were smoothed by a 4 mm isotropic Gaussian kernel to compensate for the inexact nature of the spatial normalization. Finally, from these smoothed gray matter images, we calculated the average gray matter volumes for each of n = 90 brain areas, which were comprised of 45 cortical regions in each hemisphere (excluding the cerebellum) in each participant. Construction of the structural cortical network Before obtaining the structural cortical networks, the anatomical connection matrix was calculated. In this study, the structural connections of the cortical network are defined as statistical correlations between pairs of average gray matter volumes from the corresponding AAL areas. We considered that a structural connection existed if the correlation coefficient for a pair of brain areas was statistically significant. Subsequently, an interregional correlation matrix ( ) was obtained for each group by calculating the Pearson correlation coefficients across individuals between the average gray matter volumes for each pair of brain areas. We tested the difference in age between the three groups and found a significant difference between the NC and MCI groups (p = 0.016). We found no significant difference for the NC and AD as well as for the AD and MCI in age (p = 0.23 and p = 0.34 respectively). Prior to the correlation analysis, a linear regression was performed to remove the effects of age, gender and total gray matter volume on the full set of individual measurements in each region. The residuals of this regression represented the regional volumes corrected for age, gender and total gray matter volume and provided the substrate for additional analysis. Finally, the matrices for the interregional correlations were obtained with diagonal elements equal to one and the number of total probable connections 90×89/2 = 4005. Graph theoretical approaches Structural cortical networks for each group were represented by binarized matrices Pij with N nodes and K edges. In each case the nodes and the edges corresponded to the AAL areas and the undirected connections between the pairs of AAL areas, respectively. If the same correlations threshold had been applied to the interregional correlation matrices of all the three groups, the topology of the three cortical networks would have differed markedly from each other. In that situation, the resulting graphs would have been comprised of different numbers of edges, even though they were based on the same threshold. Thus, the between-group differences in the three groups would not have done a good job of reflecting alterations in the cortical network topology. To accommodate for this difficulty, sparsity (S) was applied to threshold the interregional correlations matrices of the three cortical networks into binarized matrices. Sparsity is defined as the total number of edges, K, in a graph divided by the maximum possible number of edges. In our case, the maximum possible number of edges equals 90×89/2 = 4005. Since no definitive way for selecting a single threshold value exists, we thresholded each interregional correlations matrix repeatedly over a range of sparsities ( ) [19]. Utilizing a lower sparsity would not allow for the creation of a fully connected network with 90 nodes, but using a higher sparsity would introduce a lot of spurious edges into each network. Therefore this range of sparsities was chosen because it allows for the creation of fully connected undirected graphs that permit a reasonable estimation of the properties of the graphs. Furthermore, to investigate the abnormal connectivity and hub regions in groups with MCI and AD, a fixed sparsity ( ), which can minimize the number of spurious edges, was used to construct the cortical networks of the three groups [18], [52]. Using this method the three resulting graphs had the same numbers of nodes and edges. Small-world properties analysis Small-worldness is a ubiquitous property of complex real-life networks that supports both modular and distributed dynamic processing as a principle of brain topology [23]. Certain measurements are usually used to describe small-world properties, such as: mean network clustering coefficient (Cp) and mean network shortest absolute path length (Lp). A shorter absolute path length and a higher global efficient may indicate a higher speed of information dissemination and more efficient information processing [29]. In brief, the Cp is the average of the clustering coefficient over all the nodes in a network, where the clustering coefficient Ci of node i is defined as the number of existing connections among the immediately connected neighbors of the node divided by all their possible connections. Cp measures the extent of local cliquishness or local efficiency of information transfer of a network. Lp is the average of the mean shortest absolute path length over all nodes in the network, where the mean shortest absolute path length of node i is defined as the total shortest absolute path length between node i and all the others divided by . A real network has been found to exhibit small-word characteristics if it meets the following criteria: and , where and are the mean network clustering coefficient and the mean network absolute shortest path length of matched random networks that have the same number of nodes, edges, and degrees distribution (the degree Ki of a node i is the number of connections to the node) as the real network [21]. Nodal centrality We investigated the nodal characteristics of the cortical network among the NC, MCI and AD groups. To do this, we introduced the betweenness centrality of the nodes in the networks. Betweenness is a measure of the centrality of a node in a graph. The betweenness, B, of node i is defined as the the number of absolute shortest paths that are between any two other nodes and that run through node i. For further comparison, the betweenness Bi would be normalized as , where B is the average betweenness of the network. Based on this concept, the hub nodes that occur on many shortest paths between other nodes have higher betweenness than those that have fewer paths between them. In this study, a node i in which was defined as a hub of the network. Statistical analysis Interregional correlation differences. In order to test whether the interregional correlations of the cortical networks were significantly different among the NC, MCI and AD groups, Fisher's z transformation was applied to convert the correlation coefficients to z values which were approximately normally distributed [53]. A z statistic was used to compare these transformed z values to determine the significance of the between-group differences in the interregional correlations. To correct for multiple comparison, a false discovery rate (FDR) test was performed using a q value of 0.01 [54]. Differences in network topology. We used a nonparametric permutation test to test the statistical significance of the between-group differences in the two characteristics of the cortical networks, Cp and Lp. In this permutation test, we obtained a reference distribution on which we calculated possible values of the test statistic after repeatedly rearranging the observed data from the NC, MCI and AD groups. First, we calculated the Cps and Lps of the real cortical networks at a given sparsity for each of the three groups separately. To test whether these measurements were significantly different between the three groups, we pooled the data from ADs with the data from the NCs. From this pooled group, we randomly choose some of the subjects to be considered as NCs and the rest to be considered as AD patients. The number of supposed AD patients was equal to the number of actual patients in the original group. We then calculated the differences between the new groups and repeated this process 1000 times. In each of the 1000 cases, we used the same sparsity threshold to generate corresponding binarized matrices and computed the Cp and Lp characteristics of the two cortical networks for each randomized groups, obtaining the between-group differences. We sorted the 1000 recorded differences and observed whether the between-group differences in the real cortical networks were contained within 95% (two-tailed) of the supposed between-group differences. If they were, we accepted the null hypothesis that the two groups had identical probability distributions at the 5% significance level; otherwise we rejected the null hypothesis. This permutation test procedure was repeated over the range of sparsity threshold values from . This same procedure was repeated comparing the MCI with the AD groups and comparing the NC with the MCI groups.

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Journal ID (nlm-ta): Brain Sci

Journal ID (iso-abbrev): Brain Sci

Journal ID (publisher-id): brainsci

Title: Brain Sciences

Publisher: MDPI

ISSN (Electronic): 2076-3425

Publication date (Electronic): 29 April 2017

Publication date Collection: May 2017

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[2 ]Neuroimaging Laboratory, IRCCS Santa Lucia Foundation, Rome 00179, Italy; l.serra@ 123456hsantalucia.it (L.S.); g.giulietti@ 123456hsantalucia.it (G.G.); m.bozzali@ 123456hsantalucia.it (M.B.)

[3 ]Humboldt-Universität zu Berlin, Berlin School of Mind and Brain, Berlin 10117, Germany

[4 ]Department of Engineering, University of Rome “Roma Tre”, Rome 00146, Italy; ingmatteomancini@ 123456gmail.com

[5 ]Clinical Imaging Sciences Centre, Brighton and Sussex and Medical School, Brighton BN1 9RR, UK; m.cercignani@ 123456bsms.ac.uk

[6 ]Department of Systemic Medicine, University of Tor Vergata, Rome 00173, Italy

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[* ]Correspondence: francesco.barban@ 123456gmail.com ; Tel.: +39-06-5150-1547; Fax: +39-06-5150-1213

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Publisher ID: brainsci-07-00050

DOI: 10.3390/brainsci7050050

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A Pilot Study on Brain Plasticity of Functional Connectivity Modulated by Cognitive Training in Mild Alzheimer’s Disease and Mild Cognitive Impairment

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