Communicability disruption in Alzheimer’s disease connectivity networks

Communicability disruption in Alzheimer’s disease connectivity networks Abstract In real-world networks, information from source to destination does not only flow along the shortest path connecting them, but can flow along any alternative route. Communicability is a network metric that accounts for this issue and, especially in diffusion-like processes, provides a reliable measure of the ease of communication between node pairs. Accordingly, communicability appears to be promising for highlighting the disruption of connectivity among brain regions, caused by the white matter degeneration due to Alzheimer’s disease (AD). Such a degeneration can be captured by digital imaging techniques, in particular diffusion tensor imaging (DTI), which allow to build the brain connectivity network through tractography algorithms and studying its complexity through graph theory. In this study, a cohort of 122 DTI scans, composed by 52 healthy control (HC) subjects, 40 AD patients and 30 mild cognitive impairment (MCI) converter subjects, from Alzheimer’s Disease Neuroimaging Initiative (ADNI) database, has been employed to study the suitability of communicability to serve as discriminant factor for AD. We developed a two-fold investigation. On one hand, a statistical analysis has been carried out to ascertain the information content provided by communicability to detect the brain regions mostly affected by the disease: node pairs with statistical significant different communicability have been found, corresponding to some well-known AD-related brain regions. On the other hand, heterogeneous groups of network features (which include/not include communicability) were input to a support vector machine, to assess the impact of communicability on the classification performances in the HC/AD and the HC/AD/MCI discrimination. The best performances, i.e., AUC = 0.82 in the HC/AD case and multiclass AUC = 0.77 in the HC/AD/MCI task, were obtained by using the values of communicability, outperforming the performance obtained with the other network metrics. In summary, this article suggests that communicability can be promising for an automatized AD diagnosis. 1. Introduction Alzheimer’s disease (AD) is the most common type of neurodegenerative disorder and a growing health problem [1]. It is characterized by short-term memory loss in its early stages, followed by a progressive decline in other cognitive and behavioural functions as the disease advances. There is evidence supporting the biological hypothesis that this decline is related to a disrupted connectivity among brain regions, caused by white matter (WM) degeneration [2–4]. Because of their homogeneous chemical composition, conventional magnetic resonance imaging (MRI) is not able to highlight the structure of the WM fibres; therefore, it is not tailored to investigate the physical disconnections arising among them. Conversely, diffusion tensor imaging (DTI) has emerged as an helpful technique that measures the water diffusion along the WM fibres, and it can thus provide useful information regarding their integrity [5]. Fractional anisotropy (FA) and mean diffusivity (MD) are among the invariants derived from the diffusion tensor that are closely related to such integrity [6]: the water diffusion along a healthy axon is highly anisotropic, being constrained almost completely to one direction, so high values of FA and low values of MD are able to describe non-pathological scenarios. In this view, diffusion anisotropy effects point out micro-structural changes related to the disease, which can complement the information coming from conventional MRI in investigating human brain atrophy. When combined with tractography algorithms [7], DTI enables the reconstruction of the WM fibre tracts, providing a characterization of the physical connections of the brain that can be subsequently investigated through a graph theory-based approach [8]. Traditional network metrics tailored to describe topological properties of the brain include nodal degree and strength, shortest path length, and so on [9]. Mostly, the literature applies the complex network approach on DTI data for revealing significant differences between the values of the network’s measures observed in AD patients, also at early stages, against healthy control (HC) subjects by means of statistical analyses, e.g., [4, 10–12]. Very few studies, on the other hand, focused on applying DTI tractography, in combination with graph theory, to automatize the AD/HC discrimination through the use of machine learning algorithms [13]. Developing decision support systems can provide a quantitative, non-invasive and low-cost tool-support to the neuropsychological assessments performed by expert clinicians. More importantly, such an approach can be employed for the AD classification at a prodromal stage. To this end, a special attention is devoted to mild cognitive impairment (MCI) signs, as a person with MCI is at a high risk of developing dementia of the Alzheimer’s type. MCI is characterized as a non-disabling disorder that represents an early state of abnormal cognitive function [14]. Although not all MCI cases represent prodromal AD, an estimated 10–15% of MCI subjects enter the dementia spectrum every year. Discriminating AD at such an early stage is crucial in the perspective of future medical treatments and for improving the quality of life of the patient. The literature investigated these issues applying only traditional network metrics, but no conclusive results have been so far obtained. It would be of great interest investigating whether alternative, uncommon network metrics could serve as novel, potentially effective biomarkers for the AD diagnosis. In this article, we use connectivity networks obtained by DTI tractography in order to investigate the usefulness of the communicability metric as a novel discriminant factor for AD. Communicability is a more general measure of connectivity whose aim is to quantify the ease of communication between two nodes taking into account not only the shortest path but all the possible paths connecting them [15, 16]. This metric reflects the network property of information to flow under a diffusion model: for this reason, it could be particularly suited to study DTI networks; moreover, it may be particularly sensitive to the presence of brain lesions. In [16], communicability was successfully used for distinguishing local and global differences between stroke patients and controls, using DTI data. Similarly, communicability was used to detect subtle changes following stroke in the contralesional hemisphere [17]. Moreover, results obtained from the analysis of the human connectome showed advantages in using communicability over the conventional metrics in detecting highly connected nodes as well as subsets of nodes vulnerable to lesions [18]. Communicability has been also used to successfully differentiate the tolerance response to simulated network attacks in case of spread WM degeneration due to AD [19]. Therefore, communicability may provide an insight into the structural properties of the brain, which may be useful for emphasizing the topological differences between AD patients and HC subjects also at early stages. The contribution of this article is two-fold. On one hand, we investigate whether communicability is tailored to describe the disruption of communication between brain regions caused by AD. To this end, a statistical approach is followed. On the other hand, we evaluate if and to which extent the communicability metric positively impacts the performance of a classification algorithm for the AD classification. To this end, we report a comparative study, based on the Alzheimers Disease Neuroimaging Initiative (ADNI) publicly available dataset,2 between classification models trained with the traditional network metrics and models trained with communicability. To our best knowledge, this is the first time the communicability metric is proposed to study the alteration of brain networks in HC, AD and MCI. 2. Data Data used for this study were taken from the ADNI database. ADNI is a multisite, longitudinal study, which combines several biological markers and clinical and neuropsychological assessments to measure the progression of MCI and early AD. The overall goal of the study is to validate biological markers for use in AD clinical treatment trials. With established, standardized methods for imaging and biomarker collection and analysis, ADNI facilitates a way for researchers all over the world to conduct cohesive research and share compatible data. The images analysed for this study belong to 122 subjects, both male and female. In accordance with the diagnosis, the subjects were grouped into 52 HCs (age $$73 \pm 6$$), 40 AD patients (age $$73 \pm 8$$) and 30 MCI converter subjects (age $$75 \pm 6$$), i.e., MCI that converted to AD from 3 months to 5 years after the date of scan. Scans were randomly selected from baseline and follow-up study visits. HC subjects show no signs of depression, MCI or dementia; participants with AD are those who meet the NINCDS/ADRDA criteria for probable AD; MCI subjects have reported a subjective memory concern, but without any significant impairment in other cognitive domains: they substantially preserved everyday activities with no sign of dementia. The diffusion-weighted scans were acquired using a 3-T GE Medical Systems scanner; more precisely, 46 separate images were acquired for each scan: 5 with negligible diffusion effects ($$b_0$$ images) and 41 diffusion-weighted images ($$b$$ = 1000 s/mm$$^2$$). 3. Methods The main steps of our analysis are described in the following. Note that all data analysis here presented require a huge computational burden, with image preprocessing time, in particular, of about 1 h per subject. To this end, this study was carried out on the distributed infrastructure ReCaS-Bari computing farm.3 3.1 Image preprocessing For each subject, DICOM images were acquired from ADNI database. The dcm2nii software, within the MRIcron suite, was used to convert DICOM to NIFTI format. Then, the FMRIB Software Library (FSL) [20], and in particular its diffusion toolkit FDT, was employed for the subsequent processing pipeline. First, eddy current correction was performed to mitigate artefacts, such as enhanced background, image intensity loss and image blurring, caused by eddy currents and head motion. Second, Brain Extraction Tool (BET) was used in order to delete non-brain tissues from each subject scan. After these preliminary steps, an affine registration of all scans was employed in order to spatially normalize the whole data set to the MNI152 standard space. Then, a single diffusion tensor was fitted at each voxel in every image by using DTIfit. From the diffusion tensor, FA and MD can be calculated accordingly. Finally, probabilistic tractography was performed using ProbTrackX [21] in order to obtain the connectivity matrix of each subject. More specifically, the Harvard-Oxford cortical atlas [22] was used, resulting in a brain parcellation of 96 regions, 48 for each hemisphere. The final output consisted of a weighted connectivity matrix $$W$$ whose elements $$w_{ij}$$ corresponded to the strength of connectivity i.e., the number of fibres, between region $$i$$ and region $$j$$. The fundamental step of the whole image preprocessing was the fibre reconstruction. The FDT tool generates a probabilistic streamline or a sample of the distribution on the location of the true streamline. By taking many such samples, the histogram of the posterior distribution on the streamline location or the connectivity distribution is then built. Finally, the most probable traits connecting two regions are computed. It is worth noting that the intrinsic feature of the tractography algorithm to be probabilistic not always results in weighted symmetric connectivity matrices: to overcome this effect, we averaged the traits connecting region $$i$$ to $$j$$ and vice versa $$j$$ to $$i$$ to obtain a symmetric matrix for each subject. The overall preprocessing is depicted in Fig. 1. Fig. 1. View largeDownload slide The figure shows the processing pipeline underwent by the brain DTI scans. The dotted box includes the dedicated image processing steps: (a) eddy correction, (b) brain extraction and (c) affine registration. For each voxel, the diffusion tensor was estimated (d), thus allowing the probabilistic fibre reconstruction (e). Using the Harvard-Oxford cortical atlas, the connectivity matrix derived from tractography was computed for each subject. Fig. 1. View largeDownload slide The figure shows the processing pipeline underwent by the brain DTI scans. The dotted box includes the dedicated image processing steps: (a) eddy correction, (b) brain extraction and (c) affine registration. For each voxel, the diffusion tensor was estimated (d), thus allowing the probabilistic fibre reconstruction (e). Using the Harvard-Oxford cortical atlas, the connectivity matrix derived from tractography was computed for each subject. 3.2 Metrics calculation The connectivity matrix represents the structural complexity of the brain network. Graph theory is usually considered the most appropriate framework for the mathematical treatment of such complex systems: a complex network is represented as a graph in which nodes are the elements of the system and edges represent the interactions between them [9]. If only the presence or absence of a connection between two brain regions is considered, the graph $$G(N,L)$$ consists of $$N$$ nodes connected by $$L$$ unweighted links. Then, a graph $$G$$ can be completely described by the adjacency matrix $$A$$, which is an $$N \times N$$ square matrix whose elements $$a_{ij}$$ are equal to 1 if the link $$l_{ij}$$ exists, or 0 if the link is absent. If the weight $$w_{ij}$$ of the link $$l_{ij}$$ is taken into account, the graph $$G(N,L,W)$$ is fully described by the weights matrix $$W$$, which is an $$N$$$$\times$$$$N$$ square matrix whose element $$w_{ij}$$ is the weight of the edge $$l_{ij}$$. In this study, we considered both the unweighted and the weighted graph of the brain connectivity network. Each weight $$w_{ij}$$ corresponds to the number of WM fibres connecting region $$i$$ to region $$j$$, resulting from the application of the probabilistic tractography algorithm to every brain scan. The weights have been normalized in the range between 0 and 1. Several graph metrics can be computed from the connectivity matrix in order to describe the topological properties of the brain. In this article, both traditional metrics and communicability, briefly described in the following sections, have been taken into account. 3.2.1 Traditional network metrics. Several traditional metrics used in graph theoretical analysis are based on the shortest path length $$d_{ij}$$, defined as the number of edges along the shortest path connecting node $$i$$ to $$j$$ [9]. For a weighted network, the length $$\lambda_{ij}$$ of the edge $$l_{ij}$$ is defined as $$\lambda_{ij}= 1/w_{ij}$$ and the weighted shortest path length $$d_{ij}$$ is the smallest sum of the edge lengths throughout all the possible paths in the graph from $$i$$ to $$j$$. The edge betweenness is defined as the number of shortest paths between pairs of nodes that run through that edge [23]: it gives information about how the relation between two nodes is important for the ‘communication’ between all nodes in the network. The concept of betweenness can also be extended to nodes, as a measure of node centrality, giving the importance of a node for the information flow across the network. More precisely, the betweenness $$b_i$$ of a node $$i$$, is defined as:   \begin{equation} b_{i}=\sum_{j,k\in N,j\neq k}\frac{n_{jk}(i)}{n_{jk}}, \end{equation} (1) where $$n_{jk}$$ is the number of shortest paths connecting $$j$$ and $$k$$, while $$n_{jk}(i)$$ is the number of shortest paths connecting $$j$$ and $$k$$ and passing through $$i$$. Other traditional network metrics are defined without the use of the shortest path length. The degree $$k_i$$ of a node $$i$$ in an unweighted network is the number of edges crossing $$i$$:   \begin{equation} k_{i}=\sum_{j\in N}a_{ij}. \end{equation} (2) For a weighted network, the concept of degree is replaced by the concept of node strength $$s_i$$, defined as:   \begin{equation} s_{i}=\sum_{j\in N}w_{ij}. \end{equation} (3) The clustering coefficient $$c_i$$ of node $$i$$, as introduced by Watts and Strogatz for an unweighted network [24], is defined as the ratio between the actual number of edges (denoted by $$e_i$$) in the subgraph $$G_i$$ of neighbours of $$i$$ and $$k_{i}(k_{i}-1)$$/$$2$$, the maximum possible number of edges in $$G_i$$:   \begin{equation} c_{i}=\frac{2 e_{i}}{k_{i}(k_{i} - 1)}=\frac{\sum_{j,m}a_{ij}a_{jm}a_{mi}}{k_{i}(k_{i} - 1)}. \end{equation} (4) For a weighted network, the clustering coefficient of a node $$i$$, $$C^{w}$$$$(i)$$, can be expressed as follows [25]:   \begin{equation} C^{w}(i)=\frac{2}{k_{i}(k_{i}-1)}\sum_{j,k}(\bar{w}_{ij}\bar{w}_{jk}\bar{w}_{ki})^{1/3}. \end{equation} (5) Finally, the eigenvector centrality $$e_i$$ of a node $$i$$ is given by the sum of the values within the principal eigenvector $$e$$ corresponding to direct neighbours, as defined by the adjacency matrix, then scaled by the proportionality factor $$1/m$$ where $$m$$ denotes the largest eigenvalue:   \begin{equation} e_i=\frac{1}{m}\sum_{j\in N}a_{ij}e_{j}. \end{equation} (6) The same definition holds for weighted graphs but the adjacency matrix is replaced by the weights matrix. 3.2.2 Communicability. Traditional network metrics assume that information between two nodes flows through the shortest path connecting them and the communication between the two nodes is usually considered as this shortest path. However, in many real-world networks, e.g. social and communication networks, information can also travel along paths alternative to the shortest one and information can flow back and forward several times before reaching its final destination [26, 27]. Indeed, especially in a network working in a diffusion-like process, information does not necessary flow through the shortest paths because the sender may not know the global structure of the network: (i) it may not know which of the many routes connecting it with the addressee is the shortest one and (ii) even if it knows the shortest path, it does not know whether there are damaged edges along this path. On the basis of this idea, Estrada and Hatano [15] proposed a new concept of communicability, initially only for binary complex networks, defining the communicability between two nodes in a network as a function of the total number of walks connecting them, giving more importance to the shorter than to the longer ones. If $$G$$ is a graph of $$N$$ nodes connected by edges and $$A$$ is the $$N \times N$$ adjacency matrix, then:   \begin{equation} (A^{k})_{pq}:=\sum_{r_1=1}^{N}\sum_{r_2=1}^{N}\cdots\sum_{r_{k-1}=1}^{N}a_{p,r_{1}}a_{r_{1},r_{2}}a_{r_{2},r_{3}}\cdots a_{r_{k-2},r_{k-1}}a_{r_{k-1},r_{q}} \end{equation} (7) counts the number of walks of length$$k$$ starting at node $$p$$ and ending at node $$q$$. The communicability between node $$p$$ and node $$q$$ is given by the total number of walks, weighted in decreasing order of their lengths, connecting the vertices $$p$$ and $$q$$ in a network $$G$$:   \begin{equation} G_{pq}=\sum_{k=0}^{\infty}\frac{(A^k)_{pq}}{k!}=(e^A)_{pq}. \end{equation} (8) Equation (8) can be also rewritten in terms of the graph spectrum as:   \begin{equation} G_{pq}=\sum_{j=1}^{n}\varphi_j(p)\varphi_j(q)e^{\lambda_j}, \end{equation} (9) where $$\varphi_j(p)$$ is the $$p$$-th element of the $$j$$-th orthonormal eigenvector of the adjacency matrix associated with the eigenvalue $$\lambda_j$$. The concept of communicability was then extended to the weighted case by Crofts and Higham in [16] in the context of DTI connectivity matrices. The definition in (7) is still valid but $$A$$ is the $$N \times N$$ weighted matrix and the terms $$a_{p,r_{1}}a_{r_{1},r_{2}}a_{r_{2},r_{3}}\cdots a_{r_{k-2},r_{k-1}}a_{r_{k-1},r_{q}}$$ represent the weights of the walks $$i\mapsto r_{1}$$, $$r_{1}\mapsto r_{2}$$, etc. In order to avoid the excessive influence of a node depending on its high weight, they introduced a normalization step dividing the weight $$a_{ij}$$ by the product $$\sqrt{s_{i}s_{j}}$$, where $$s_{i}$$ is the strength of node $$i$$. Therefore, the communicability between two nodes $$p$$ and $$q$$ in a weighted network is defined as:   \begin{equation} G_{pq}=(exp(D^{-1/2}AD^{-1/2}))_{pq}, \end{equation} (10) where $$D=diag(s_{i})$$ is the $$N \times N$$ diagonal strength matrix. 3.3 Statistical analysis on communicability The first goal of this study was to assess whether communicability is suitable to describe the disruption of communication between brain regions due to AD. In other words, we investigated the information content provided by communicability from a biological perspective. To this end, a non-parametric rank sum test was performed over the communicability values of all node pairs, between the HC and AD matrices. The false discovery rate multiple testing correction was used to calculate the adjusted $$P$$-values. The node pairs with statistically significant different communicability ($$P$$$$< 0.05$$) were detected and an analysis was conducted to find if the regions involved in these connections are related, according to the literature, to the neurodegenerative processes of AD. Moreover, a non-parametric Kruskal–Wallis test was performed to compare the distibutions of the communicability values for the three groups HC/AD/MCI in order to find the node pairs with statistically significant different communicability scores according to the adjusted $$P$$-values. 3.4 Classification procedure The second goal of the analysis we carried out was a comparative study, based on the same dataset, between classification models trained with traditional metrics and models trained with communicability. The learning and classification procedure was accomplished by using linear support vector machines (SVMs): the classification workflow is depicted in Fig. 2. Fig. 2. View largeDownload slide Classification workflow. For each cross-validation iteration, the whole dataset is split into a training and a test set. The training connectivity matrices are subjected to a two-stage feature selection. The first stage measures a mean HC matrix, to form a binary mask. The mask is binarized in accordance with a binomial test, which established to keep a link only if it occurs in more than 70% of the training HC matrices. Once all subjects’ matrices are projected onto the mask, they are subjected to a recursive feature elimination. The output features are used to train the SVM model. Fig. 2. View largeDownload slide Classification workflow. For each cross-validation iteration, the whole dataset is split into a training and a test set. The training connectivity matrices are subjected to a two-stage feature selection. The first stage measures a mean HC matrix, to form a binary mask. The mask is binarized in accordance with a binomial test, which established to keep a link only if it occurs in more than 70% of the training HC matrices. Once all subjects’ matrices are projected onto the mask, they are subjected to a recursive feature elimination. The output features are used to train the SVM model. The initial dataset consisted in the weighted and unweighted connectivity matrices obtained from the image preprocessing step described in Section 3.1. From these raw data the following features have been extracted, in accordance with the discussion provided in Section 3.2: edge betweenness; shortest path length; presence or absence of edge; communicability. In the rest of the article, they are referred to as ‘connectivity features’. The next step concerns the validation of the classification procedure through a proper splitting of the dataset into training and test sets. To this end, a 50-times repeated 10-fold cross-validation was performed. This procedure consists in dividing the entire set of examples into ten subsets, i.e. folds: one-fold was treated as test set, while the remaining folds formed the training set. This splitting was repeated until each fold was used as test set once. Note that the subjects were stratified by diagnosis, so that each fold contained roughly the same number of subjects from each diagnostic group. Moreover, we repeated the 10-fold cross-validation 50 times, using different permutations, in order to shuffle the subjects into the folds for a more general approximation of the performance. In order to reduce the dimensionality of the feature space and so to alleviate the problem of overfitting, a two-stage feature selection strategy was then applied. The first stage is an ad hoc selection of features, customized to connectivity matrices. It consisted in the calculation of an HC binary mean matrix, i.e. a mask, onto which the matrices of all subjects were later projected to reduce the number of connectivity metrics to be considered for classification. For each training set in every cross validation iteration, the mean matrix of only the HC connectivity matrices was calculated. The HC mean matrix is a weighted matrix whose entries $$e_{ij}$$ range from 0 to 1 and represent the frequency at which the corresponding edges occur among all HC matrices. The HC mean matrix was then thresholded in order to obtain the reference HC binary mean matrix to be used as mask. The threshold value was chosen at 0.7, using a binomial test (with $$\alpha=0.01$$): if we consider an a priori probability of 0.5 that a link is present or not in a connectivity matrix, the binomial test established that a link is considered to be a ‘real’ link if it occurs in more than 70% of all HC connectivity matrices. This feature selection strategy was motivated by the observation that, independently of the applied threshold, the HC mean matrix always shares more links than the unhealthy counterpart. In other words, HC matrices show a more stable topology; AD matrices, instead, show a greater intra-variability due to the disrupted connectivity. This procedure would evaluate a significant and robust reference model to select the important links, as sampling of subjects considered in each round makes the definition of the set of significant links (i.e., the mask) robust with respect to outliers. Additionally, weak connections that can introduce noisy effects are filtered out in accordance with an objective statistical test with a strict significance threshold of the mask. This nested procedure of significant link selection was preferred to other thresholding methods such as fixing the same mean degree across all groups. Indeed, the latter procedure could be particularly problematic in ‘disconnection syndromes’ or neurodegenerative diseases, where the assumption that node degree is the same between groups is likely to be invalid [28]. The second stage was a more conventional SVM recursive feature elimination (SVM-RFE) [29], embedded in the learning algorithm. The technique was applied to all the subjects’ matrices obtained by the former feature selection. SVM-RFE uses criteria derived from the coefficients in the SVM models to assess features, then iteratively removes features having small criteria. In each iteration, a linear SVM model is trained: the feature with the smallest ranking criterion is removed as it has the least effect on classification. The remaining features are kept for the next iteration. The process is iteratively computed until all the features have been removed. The final outcome of the algorithm is a ranked feature list: feature selection is achieved by choosing a group of top-ranked features. Depending on the output of SVM-RFE, subsets with an increasing number of features were evaluated, keeping only the one that obtained the best accuracy for the overall performance evaluation. Note that we used the implementation proposed in [30], which introduces a correlation bias reduction strategy that alleviates the problem of underestimating features that are highly correlated. It is worth emphasizing that, according to our previous work [31], we employed a nested feature selection strategy: for each cross-validation iteration, the two-stage feature selection was applied only on the training set blind to the test set. This methodological procedure avoids to introduce a feature selection bias, which necessarily leads to overoptimistic results. Once the dimensionality of data has been reduced, the SVM model can be fitted. The main intuition of SVMs is to find a separating hyperplane with the largest possible margin on either side, i.e. with the largest minimal distance from the closest data points. New examples are then predicted to belong to a class based on which side of the gap they fall [32]. SVMs are well known for their generalization ability and are particularly useful when the number of features, as in our case, is high [33]. 4. Results The results concerning both the statistical analysis and classification are described in the following subsections. 4.1 Statistics on communicability group differences Considering the HC and AD groups, 186 node pairs were found to have statistical significant different communicability (adjusted $$P$$$$< 0.05$$). Most of these pairs showed a reduced mean communicability in the AD subjects. Considering the HC and the AD distributions of the mean communicability values of the significant node pairs, the hypothesis of a decrease in the AD population median was tested performing a one-sided Wilcoxon rank sum test. A $$P$$-value of $$1.35\times 10^{-7}$$ was obtained: with enough evidence, it can be concluded that there is a negative shift in the median of the mean communicability values of the significant edges in AD compared with HC, at the 0.01 significance level, pointing out an overall communicability disruption due to AD. The differences between the HC and AD mean communicability values of the significant node pairs are shown in Fig. 3 by means of a glass brain: it is a 3D brain visualization in which nodes are localized exactly in the centroid position of the region of interest, in accordance with the Harvard-Oxford cortical atlas. For purposes of clarity, only the values in the 90th and 10th percentile of the communicability differences distribution are shown in the glass brain. The edges in the figure are a ‘nominal’ representation of the difference of mean communicability, between HC and AD, of the two nodes they link: the edge colour and the edge thickness are descriptive of the communicability difference of those brain region pairs between the two groups. Fig. 3. View largeDownload slide Glass brain visualization of the difference between the mean communicability values of the significant edges in HC and AD; the edge colour and the edge thickness are descriptive of these values. Only the values in the 90th and 10th percentile of the distribution of the communicability differences are shown. Fig. 3. View largeDownload slide Glass brain visualization of the difference between the mean communicability values of the significant edges in HC and AD; the edge colour and the edge thickness are descriptive of these values. Only the values in the 90th and 10th percentile of the distribution of the communicability differences are shown. The brain regions mostly involved in all the 186 significant edges were found to be: Supramarginal Gyrus posterior and anterior division, Lateral Occipital Cortex, Angular Gyrus, Insular Cortex, Inferior and Superior Frontal Gyrus, Superior Parietal Lobule, Postcentral Gyrus, Middle Temporal Gyrus Temporoccipital part left, Lateral Occipital Cortex inferior division left, Frontal Pole left, Precentral Gyrus and Precuneous Cortex. Considering the three groups HC, AD and MCI converter, 70 node pairs were found to be statistically significant different in communicability. Among these 70 pairs, 63 are in common with the 186 pairs previously found. The brain regions mostly involved in this case were found to be: Supramarginal Gyrus posterior and Supramarginal Gyrus anterior division, Angular Gyrus right, Insular Cortex, Precentral Gyrus, Postcentral Gyrus, Middle Frontal Gyrus, Superior Parietal Lobule right. Additionally, a permutation test was performed to test the significance of the overlapping between the node pairs with statistical significant different communicability in the 3-class analysis (HC/AD/MCI) and the 186 node pairs with statistical significant different communicability in the 2-class analysis (HC/AD). The estimated $$P$$-value was found to be $$<0.01$$, proving a significant percentage of overlapping links between the two tasks. 4.2 Classification performance evaluation 4.2.1 HC/AD classification. Classification performances, averaged all over the cross validation rounds, are expressed in terms of area under the ROC curve (AUC), accuracy, sensitivity and specificity. An overview of the best classification performance obtained by the network metrics individually is provided in Fig. 4. Note that each measure refers to the mean value obtained by averaging the performances achieved over all the cross-validation rounds. In the figure, each bar’s height indicates the mean value of the corresponding performance; the error bars indicate the standard errors. The best performances were obtained using the communicability values as features ($$0.75\pm 0.02$$ of accuracy; $$0.82\pm 0.02$$ of AUC; $$0.69\pm 0.02$$ of sensitivity; $$0.80\pm 0.02$$ of specificity). Note that they are higher than the best performances obtained using as features the traditional connectivity metrics ($$0.69\pm 0.02$$ of accuracy; $$0.74\pm 0.02$$ of AUC; $$0.65\pm 0.03$$ of sensitivity; $$0.78\pm 0.03$$ of specificity). It is worth remarking that the outperformance obtained when using communicability was tested by means of a non-parametric rank sum test. The performances achieved using communicability were found to be statistically significant different ($$P$$$$<$$ 0.0001) from those obtained using the traditional metrics, except for specificity in the case of binary Edge Betweenness. Fig. 4. View largeDownload slide Overview of the performances achieved by using, as features for the HC/AD classification, the individual metrics computed on the weighted and binary connectivity matrices. Fig. 4. View largeDownload slide Overview of the performances achieved by using, as features for the HC/AD classification, the individual metrics computed on the weighted and binary connectivity matrices. Figure 5 shows an overview of the best performance obtained using, as features for training the classification models, all the binary connectivity measures together with or without weighted communicability. All the weighted measures together with or without weighted communicability are also reported. The inclusion of communicability, among the features used, significantly improved classification performances ($$P$$$$<$$ 0.0001, except for specificity in the case of binary measures). Note that they are quite comparable to the performance achieved using only the communicability values as features. Fig. 5. View largeDownload slide Performance overview of all the connectivity metrics, with and without communicability, computed on the unweighted and weighted connectivity matrices (HC/AD classification). Fig. 5. View largeDownload slide Performance overview of all the connectivity metrics, with and without communicability, computed on the unweighted and weighted connectivity matrices (HC/AD classification). Figure 6 shows the same results of Fig. 5, adding the nodal measures degree, strength, clustering coefficient, betweenness and eigenvector centrality as features. The best performances ($$0.77\pm 0.02$$ of accuracy; $$0.81\pm 0.02$$ of AUC; $$0.72\pm 0.02$$ of sensitivity; $$0.81\pm 0.03$$ of specificity) have been obtained for the weighted matrices case. Also in this case the improvement of classification performances using communicability is statistically significant ($$P$$$$<$$ 0.0001, except for specificity in the case of binary measures). Fig. 6. View largeDownload slide Performance overview of all the connectivity and nodal metrics, with and without communicability, calculated on the unweighted and weighted connectivity matrices (HC/AD classification). Fig. 6. View largeDownload slide Performance overview of all the connectivity and nodal metrics, with and without communicability, calculated on the unweighted and weighted connectivity matrices (HC/AD classification). 4.2.2 HC/AD/MCI classification. The three class HC/AD/MCI performances, averaged over all the cross-validation rounds, are expressed in terms of accuracy and AUC, considering first AD as positive class and then MCI as positive class. In Fig. 7, the performances obtained using the previous traditional connectivity metrics as features and those obtained using communicability are compared. The best accuracy, i.e. $$0.60\pm 0.02$$, was obtained using communicability, and it is higher than the best one obtained by the models fitted on the weighted shortest path length ($$0.49\pm 0.02$$). The best AUC was achieved using communicability ($$0.79\pm 0.02$$ when considering AD as positive class, and $$0.72\pm 0.02$$ when considering MCI as positive class), which was higher than the best performance reached with traditional metrics, considering the presence or absence of a link as features ($$0.70\pm 0.02$$ when considering AD as positive class, and $$0.64\pm 0.03$$ when considering MCI as positive class). In addition, according to [34], a multiclass AUC was calculated through a pairwise comparison of classifiers, i.e. by using a one-vs-one strategy. Again, communicability outperformed the other metrics, as a multiclass AUC of $$0.77\pm 0.02$$ was obtained against the best value of $$0.68\pm 0.02$$ achieved with the traditional metrics. Also in the three-class classification, in all cases the classification performances obtained using communicability were found to be statistically significant different from those obtained with traditional network metrics ($$P < 0.0001$$). Fig. 7. View largeDownload slide Performance overview of the individual metrics computed on the weighted and binary connectivity matrices (HC/AD/MCI classification). Fig. 7. View largeDownload slide Performance overview of the individual metrics computed on the weighted and binary connectivity matrices (HC/AD/MCI classification). 5. Discussion The aim of this study was to show the capability of the communicability metric of highlighting the connectivity changes among brain regions in patients with AD, also at the early stages. The advantage of using this metric has been evaluated from two points of view: (i) A statistical analysis pointed out pairs of brain regions with different communicability in AD and HC subjects and in AD, HC and MCI subjects; (ii) A classification framework with different groups of features showed how communicability positively affects classification performance both for the HC/AD and the HC/AD/MCI discrimination. First, 186 node pairs with statistical significant different communicability values between HC and AD subjects have been found, revealing a general communicability disruption among AD brains. For the three groups (HC, AD and MCI converter) statistical analysis, 70 node pairs were found to be statistically significant different in communicability, 63 in common with the 186 pairs previously found. The brain regions mostly involved in these pairs were found to be highly AD-related brain regions. It is well known the involvement of the Angular Gyrus in semantic processing, word reading and comprehension, number processing, default mode network, memory retrieval, attention and spatial cognition, reasoning and social cognition [35]. Also the language function impairment in AD patients is due to synaptic loss and dysfunction involving the Angular Gyrus [36]. The Supramarginal Gyrus is a cortical region of interest involved in impairments in verbal and semantic memory for AD [37], and an area of anatomical connectivity decrease related to the short-term memory dysfunction [38]. The Lateral Occipital Cortex, left worse than right, is a region of atrophy and hypo-metabolism in AD [39]. The regional atrophy of the Insular Cortex is associated with neuropsychiatric symptoms in AD patients [40] and pathologic changes within this area may play essential roles in AD symptoms like behavioural dyscontrol and visceral dysfunction related to autonomic instability and loss of the sense of self [41]. Moreover, left-Insula and left-Inferior Frontal Gyrus were recently found to be important regions to act on to protect memory performance against AD [42]. The Parietal Lobe, which is involved in many cognitive functions, including memory, is considered vulnerable to AD and a site of metabolic changes and loss of WM integrity [43]. In fact, it is an AD-related area in preclinical dementia [44]. Also Precentral Gyrus is considered an AD-related brain region [45, 46]. Similarly, the medial Occipitotemporal and middle Temporal Gyri are sites affected by AD and atrophy in these areas may herald the presence of future AD among non-demented individuals [47]. The Frontal Pole left and the Lateral Occipital Cortex were found to have altered WM networks’ properties in preclinical AD [11]. It is also well known the specific role of the Precuneous in self-processing during autobiographical memory retrieval [48]. Moreover the Middle Frontal Gyrus has been found to be a region of abnormal connectivity in MCI subjects [49]. Second, this study showed that communicability improves the overall classification performance compared with the traditional network metrics. This finding supports the idea that communicability is more apt than shortest path length to describe the efficiency of communication between brain regions when modelled as nodes of DTI networks. It is worth remarking that this study was the first using the communicability metric to classify HC, AD and MCI and select disease-relevant biomarkers through the use of machine learning algorithms. Several other works using machine learning algorithms in this context mainly focused on two approaches to train the classification models: voxel-based, e.g. [31, 50], and region of interest-based, e.g. [51]. In particular, we reported results comparable to those obtained in the present paper in previous studies on data coming from the same database [31, 52]. In those works, the discriminating information provided by direct DTI measures, i.e. FA and MD, was evaluated. An increase in prediction performance has not here been observed; however, our results are encouraging and may pave the way for developing network-based classification models attaining a gain in terms of predictive accuracy. Indeed, from the prediction point of view, the potentiality of the network-based approach in this classification problem, as well as its limitations, have yet to be investigated. Currently, very few works used complex networks on DTI data; in [13], for example, several traditional network metrics are used as features of classification algorithms applied on private DTI data, but no conclusive result has yet been obtained. Moreover, we believe that the complex network approach may provide a gain also in terms of inference, as novel insights and better understanding of the data may be revealed. The network approach, in fact, may complement the localized information provided by the voxelwise analysis, by capturing more global patterns of alternation in the WM connectivity structure due to AD. Indeed, in this work, the network approach enabled to uncover connectivity differences in specific brain regions and connections due to AD. 6. Conclusion In this study, for the first time, the communicability metric was exploited with successful results to the problem of discovering connectivity differences in DTI brain networks of AD and MCI subjects. Communicability can be considered an alternative metric to traditional ones, mostly based on shortest path length. At a first step, the importance of investigating a metric more suitable to describe diffusive processes was highlighted. Then, the application of communicability to DTI connectivity networks was firstly investigated with a statistical-descriptive aim: pairs of brain regions with statistical significant different communicability values in AD and HC subjects were found; also for the three class analysis between HC, AD and MCI subjects, pairs of brain regions, mostly overlapping with the previous case, were found to be statistical significant different in communicability. Second, the advantage of applying communicability was investigated from a quantitative point of view: it was demonstrated that, for both the two discrimination tasks HC/AD and HC/AD/MCI, using the communicability values as features for training classification models improves the performances achieved using traditional network measures instead. Although the final goal of this article was to introduce a novel methodology in the DTI analysis for the study of AD, the clinical validity of our founding was verified by means of a comparison with literature results. In fact, it was demonstrated that communicability is really able to detect the brain connections mostly affected by the disease and to find the differences of network’s communication in AD subjects also at early stages. The efficiency of this metric to uncover connectivity differences in AD brain networks brings to the conclusion that communicability could be a powerful discriminant factor for more accurate AD diagnosis. The introduction of the communicability metric in this context can represent a starting point to develop new classification strategies and for proposing new measures based on this metric that could further improve classification performance. The advantage of using communicability for this purpose is not limited to the HC/AD classification, but can contribute to the early diagnosis of AD, which is one of the major challenges in current medical research. It is worth remarking that an important issue concerns the dependence of the adopted method on the network size. In this study, coarse anatomical connectivities have been considered for the estimated brain networks. Connectivities obtained between relatively large regions patterns are more robust and reproducible; however, they could overlook detailed patterns of connectivity, which may play a role in neurological diseases investigation. Future work should address this issue from a clinical perspective, taking into account different parcellation schemes and different reconstructions of the brain connectivity network to study more detailed patterns of connectivity and to develop more accurate classification models. Footnotes 1 Data used in preparation of this article were obtained from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in analysis or writing of this report. A complete listing of ADNI investigators can be found at: http://adni.loni.usc.edu/wp-content/uploads/how_to_apply/ADNI_Acknowledgement_List.pdf. (last accessed 6 February 2018). 2http://adni.loni.usc.edu (last accessed 6 February 2018). 3https://www.recas-bari.it (last accessed 6 February 2018). References 1. 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Abstract

Abstract In real-world networks, information from source to destination does not only flow along the shortest path connecting them, but can flow along any alternative route. Communicability is a network metric that accounts for this issue and, especially in diffusion-like processes, provides a reliable measure of the ease of communication between node pairs. Accordingly, communicability appears to be promising for highlighting the disruption of connectivity among brain regions, caused by the white matter degeneration due to Alzheimer’s disease (AD). Such a degeneration can be captured by digital imaging techniques, in particular diffusion tensor imaging (DTI), which allow to build the brain connectivity network through tractography algorithms and studying its complexity through graph theory. In this study, a cohort of 122 DTI scans, composed by 52 healthy control (HC) subjects, 40 AD patients and 30 mild cognitive impairment (MCI) converter subjects, from Alzheimer’s Disease Neuroimaging Initiative (ADNI) database, has been employed to study the suitability of communicability to serve as discriminant factor for AD. We developed a two-fold investigation. On one hand, a statistical analysis has been carried out to ascertain the information content provided by communicability to detect the brain regions mostly affected by the disease: node pairs with statistical significant different communicability have been found, corresponding to some well-known AD-related brain regions. On the other hand, heterogeneous groups of network features (which include/not include communicability) were input to a support vector machine, to assess the impact of communicability on the classification performances in the HC/AD and the HC/AD/MCI discrimination. The best performances, i.e., AUC = 0.82 in the HC/AD case and multiclass AUC = 0.77 in the HC/AD/MCI task, were obtained by using the values of communicability, outperforming the performance obtained with the other network metrics. In summary, this article suggests that communicability can be promising for an automatized AD diagnosis. 1. Introduction Alzheimer’s disease (AD) is the most common type of neurodegenerative disorder and a growing health problem [1]. It is characterized by short-term memory loss in its early stages, followed by a progressive decline in other cognitive and behavioural functions as the disease advances. There is evidence supporting the biological hypothesis that this decline is related to a disrupted connectivity among brain regions, caused by white matter (WM) degeneration [2–4]. Because of their homogeneous chemical composition, conventional magnetic resonance imaging (MRI) is not able to highlight the structure of the WM fibres; therefore, it is not tailored to investigate the physical disconnections arising among them. Conversely, diffusion tensor imaging (DTI) has emerged as an helpful technique that measures the water diffusion along the WM fibres, and it can thus provide useful information regarding their integrity [5]. Fractional anisotropy (FA) and mean diffusivity (MD) are among the invariants derived from the diffusion tensor that are closely related to such integrity [6]: the water diffusion along a healthy axon is highly anisotropic, being constrained almost completely to one direction, so high values of FA and low values of MD are able to describe non-pathological scenarios. In this view, diffusion anisotropy effects point out micro-structural changes related to the disease, which can complement the information coming from conventional MRI in investigating human brain atrophy. When combined with tractography algorithms [7], DTI enables the reconstruction of the WM fibre tracts, providing a characterization of the physical connections of the brain that can be subsequently investigated through a graph theory-based approach [8]. Traditional network metrics tailored to describe topological properties of the brain include nodal degree and strength, shortest path length, and so on [9]. Mostly, the literature applies the complex network approach on DTI data for revealing significant differences between the values of the network’s measures observed in AD patients, also at early stages, against healthy control (HC) subjects by means of statistical analyses, e.g., [4, 10–12]. Very few studies, on the other hand, focused on applying DTI tractography, in combination with graph theory, to automatize the AD/HC discrimination through the use of machine learning algorithms [13]. Developing decision support systems can provide a quantitative, non-invasive and low-cost tool-support to the neuropsychological assessments performed by expert clinicians. More importantly, such an approach can be employed for the AD classification at a prodromal stage. To this end, a special attention is devoted to mild cognitive impairment (MCI) signs, as a person with MCI is at a high risk of developing dementia of the Alzheimer’s type. MCI is characterized as a non-disabling disorder that represents an early state of abnormal cognitive function [14]. Although not all MCI cases represent prodromal AD, an estimated 10–15% of MCI subjects enter the dementia spectrum every year. Discriminating AD at such an early stage is crucial in the perspective of future medical treatments and for improving the quality of life of the patient. The literature investigated these issues applying only traditional network metrics, but no conclusive results have been so far obtained. It would be of great interest investigating whether alternative, uncommon network metrics could serve as novel, potentially effective biomarkers for the AD diagnosis. In this article, we use connectivity networks obtained by DTI tractography in order to investigate the usefulness of the communicability metric as a novel discriminant factor for AD. Communicability is a more general measure of connectivity whose aim is to quantify the ease of communication between two nodes taking into account not only the shortest path but all the possible paths connecting them [15, 16]. This metric reflects the network property of information to flow under a diffusion model: for this reason, it could be particularly suited to study DTI networks; moreover, it may be particularly sensitive to the presence of brain lesions. In [16], communicability was successfully used for distinguishing local and global differences between stroke patients and controls, using DTI data. Similarly, communicability was used to detect subtle changes following stroke in the contralesional hemisphere [17]. Moreover, results obtained from the analysis of the human connectome showed advantages in using communicability over the conventional metrics in detecting highly connected nodes as well as subsets of nodes vulnerable to lesions [18]. Communicability has been also used to successfully differentiate the tolerance response to simulated network attacks in case of spread WM degeneration due to AD [19]. Therefore, communicability may provide an insight into the structural properties of the brain, which may be useful for emphasizing the topological differences between AD patients and HC subjects also at early stages. The contribution of this article is two-fold. On one hand, we investigate whether communicability is tailored to describe the disruption of communication between brain regions caused by AD. To this end, a statistical approach is followed. On the other hand, we evaluate if and to which extent the communicability metric positively impacts the performance of a classification algorithm for the AD classification. To this end, we report a comparative study, based on the Alzheimers Disease Neuroimaging Initiative (ADNI) publicly available dataset,2 between classification models trained with the traditional network metrics and models trained with communicability. To our best knowledge, this is the first time the communicability metric is proposed to study the alteration of brain networks in HC, AD and MCI. 2. Data Data used for this study were taken from the ADNI database. ADNI is a multisite, longitudinal study, which combines several biological markers and clinical and neuropsychological assessments to measure the progression of MCI and early AD. The overall goal of the study is to validate biological markers for use in AD clinical treatment trials. With established, standardized methods for imaging and biomarker collection and analysis, ADNI facilitates a way for researchers all over the world to conduct cohesive research and share compatible data. The images analysed for this study belong to 122 subjects, both male and female. In accordance with the diagnosis, the subjects were grouped into 52 HCs (age $$73 \pm 6$$), 40 AD patients (age $$73 \pm 8$$) and 30 MCI converter subjects (age $$75 \pm 6$$), i.e., MCI that converted to AD from 3 months to 5 years after the date of scan. Scans were randomly selected from baseline and follow-up study visits. HC subjects show no signs of depression, MCI or dementia; participants with AD are those who meet the NINCDS/ADRDA criteria for probable AD; MCI subjects have reported a subjective memory concern, but without any significant impairment in other cognitive domains: they substantially preserved everyday activities with no sign of dementia. The diffusion-weighted scans were acquired using a 3-T GE Medical Systems scanner; more precisely, 46 separate images were acquired for each scan: 5 with negligible diffusion effects ($$b_0$$ images) and 41 diffusion-weighted images ($$b$$ = 1000 s/mm$$^2$$). 3. Methods The main steps of our analysis are described in the following. Note that all data analysis here presented require a huge computational burden, with image preprocessing time, in particular, of about 1 h per subject. To this end, this study was carried out on the distributed infrastructure ReCaS-Bari computing farm.3 3.1 Image preprocessing For each subject, DICOM images were acquired from ADNI database. The dcm2nii software, within the MRIcron suite, was used to convert DICOM to NIFTI format. Then, the FMRIB Software Library (FSL) [20], and in particular its diffusion toolkit FDT, was employed for the subsequent processing pipeline. First, eddy current correction was performed to mitigate artefacts, such as enhanced background, image intensity loss and image blurring, caused by eddy currents and head motion. Second, Brain Extraction Tool (BET) was used in order to delete non-brain tissues from each subject scan. After these preliminary steps, an affine registration of all scans was employed in order to spatially normalize the whole data set to the MNI152 standard space. Then, a single diffusion tensor was fitted at each voxel in every image by using DTIfit. From the diffusion tensor, FA and MD can be calculated accordingly. Finally, probabilistic tractography was performed using ProbTrackX [21] in order to obtain the connectivity matrix of each subject. More specifically, the Harvard-Oxford cortical atlas [22] was used, resulting in a brain parcellation of 96 regions, 48 for each hemisphere. The final output consisted of a weighted connectivity matrix $$W$$ whose elements $$w_{ij}$$ corresponded to the strength of connectivity i.e., the number of fibres, between region $$i$$ and region $$j$$. The fundamental step of the whole image preprocessing was the fibre reconstruction. The FDT tool generates a probabilistic streamline or a sample of the distribution on the location of the true streamline. By taking many such samples, the histogram of the posterior distribution on the streamline location or the connectivity distribution is then built. Finally, the most probable traits connecting two regions are computed. It is worth noting that the intrinsic feature of the tractography algorithm to be probabilistic not always results in weighted symmetric connectivity matrices: to overcome this effect, we averaged the traits connecting region $$i$$ to $$j$$ and vice versa $$j$$ to $$i$$ to obtain a symmetric matrix for each subject. The overall preprocessing is depicted in Fig. 1. Fig. 1. View largeDownload slide The figure shows the processing pipeline underwent by the brain DTI scans. The dotted box includes the dedicated image processing steps: (a) eddy correction, (b) brain extraction and (c) affine registration. For each voxel, the diffusion tensor was estimated (d), thus allowing the probabilistic fibre reconstruction (e). Using the Harvard-Oxford cortical atlas, the connectivity matrix derived from tractography was computed for each subject. Fig. 1. View largeDownload slide The figure shows the processing pipeline underwent by the brain DTI scans. The dotted box includes the dedicated image processing steps: (a) eddy correction, (b) brain extraction and (c) affine registration. For each voxel, the diffusion tensor was estimated (d), thus allowing the probabilistic fibre reconstruction (e). Using the Harvard-Oxford cortical atlas, the connectivity matrix derived from tractography was computed for each subject. 3.2 Metrics calculation The connectivity matrix represents the structural complexity of the brain network. Graph theory is usually considered the most appropriate framework for the mathematical treatment of such complex systems: a complex network is represented as a graph in which nodes are the elements of the system and edges represent the interactions between them [9]. If only the presence or absence of a connection between two brain regions is considered, the graph $$G(N,L)$$ consists of $$N$$ nodes connected by $$L$$ unweighted links. Then, a graph $$G$$ can be completely described by the adjacency matrix $$A$$, which is an $$N \times N$$ square matrix whose elements $$a_{ij}$$ are equal to 1 if the link $$l_{ij}$$ exists, or 0 if the link is absent. If the weight $$w_{ij}$$ of the link $$l_{ij}$$ is taken into account, the graph $$G(N,L,W)$$ is fully described by the weights matrix $$W$$, which is an $$N$$$$\times$$$$N$$ square matrix whose element $$w_{ij}$$ is the weight of the edge $$l_{ij}$$. In this study, we considered both the unweighted and the weighted graph of the brain connectivity network. Each weight $$w_{ij}$$ corresponds to the number of WM fibres connecting region $$i$$ to region $$j$$, resulting from the application of the probabilistic tractography algorithm to every brain scan. The weights have been normalized in the range between 0 and 1. Several graph metrics can be computed from the connectivity matrix in order to describe the topological properties of the brain. In this article, both traditional metrics and communicability, briefly described in the following sections, have been taken into account. 3.2.1 Traditional network metrics. Several traditional metrics used in graph theoretical analysis are based on the shortest path length $$d_{ij}$$, defined as the number of edges along the shortest path connecting node $$i$$ to $$j$$ [9]. For a weighted network, the length $$\lambda_{ij}$$ of the edge $$l_{ij}$$ is defined as $$\lambda_{ij}= 1/w_{ij}$$ and the weighted shortest path length $$d_{ij}$$ is the smallest sum of the edge lengths throughout all the possible paths in the graph from $$i$$ to $$j$$. The edge betweenness is defined as the number of shortest paths between pairs of nodes that run through that edge [23]: it gives information about how the relation between two nodes is important for the ‘communication’ between all nodes in the network. The concept of betweenness can also be extended to nodes, as a measure of node centrality, giving the importance of a node for the information flow across the network. More precisely, the betweenness $$b_i$$ of a node $$i$$, is defined as:   \begin{equation} b_{i}=\sum_{j,k\in N,j\neq k}\frac{n_{jk}(i)}{n_{jk}}, \end{equation} (1) where $$n_{jk}$$ is the number of shortest paths connecting $$j$$ and $$k$$, while $$n_{jk}(i)$$ is the number of shortest paths connecting $$j$$ and $$k$$ and passing through $$i$$. Other traditional network metrics are defined without the use of the shortest path length. The degree $$k_i$$ of a node $$i$$ in an unweighted network is the number of edges crossing $$i$$:   \begin{equation} k_{i}=\sum_{j\in N}a_{ij}. \end{equation} (2) For a weighted network, the concept of degree is replaced by the concept of node strength $$s_i$$, defined as:   \begin{equation} s_{i}=\sum_{j\in N}w_{ij}. \end{equation} (3) The clustering coefficient $$c_i$$ of node $$i$$, as introduced by Watts and Strogatz for an unweighted network [24], is defined as the ratio between the actual number of edges (denoted by $$e_i$$) in the subgraph $$G_i$$ of neighbours of $$i$$ and $$k_{i}(k_{i}-1)$$/$$2$$, the maximum possible number of edges in $$G_i$$:   \begin{equation} c_{i}=\frac{2 e_{i}}{k_{i}(k_{i} - 1)}=\frac{\sum_{j,m}a_{ij}a_{jm}a_{mi}}{k_{i}(k_{i} - 1)}. \end{equation} (4) For a weighted network, the clustering coefficient of a node $$i$$, $$C^{w}$$$$(i)$$, can be expressed as follows [25]:   \begin{equation} C^{w}(i)=\frac{2}{k_{i}(k_{i}-1)}\sum_{j,k}(\bar{w}_{ij}\bar{w}_{jk}\bar{w}_{ki})^{1/3}. \end{equation} (5) Finally, the eigenvector centrality $$e_i$$ of a node $$i$$ is given by the sum of the values within the principal eigenvector $$e$$ corresponding to direct neighbours, as defined by the adjacency matrix, then scaled by the proportionality factor $$1/m$$ where $$m$$ denotes the largest eigenvalue:   \begin{equation} e_i=\frac{1}{m}\sum_{j\in N}a_{ij}e_{j}. \end{equation} (6) The same definition holds for weighted graphs but the adjacency matrix is replaced by the weights matrix. 3.2.2 Communicability. Traditional network metrics assume that information between two nodes flows through the shortest path connecting them and the communication between the two nodes is usually considered as this shortest path. However, in many real-world networks, e.g. social and communication networks, information can also travel along paths alternative to the shortest one and information can flow back and forward several times before reaching its final destination [26, 27]. Indeed, especially in a network working in a diffusion-like process, information does not necessary flow through the shortest paths because the sender may not know the global structure of the network: (i) it may not know which of the many routes connecting it with the addressee is the shortest one and (ii) even if it knows the shortest path, it does not know whether there are damaged edges along this path. On the basis of this idea, Estrada and Hatano [15] proposed a new concept of communicability, initially only for binary complex networks, defining the communicability between two nodes in a network as a function of the total number of walks connecting them, giving more importance to the shorter than to the longer ones. If $$G$$ is a graph of $$N$$ nodes connected by edges and $$A$$ is the $$N \times N$$ adjacency matrix, then:   \begin{equation} (A^{k})_{pq}:=\sum_{r_1=1}^{N}\sum_{r_2=1}^{N}\cdots\sum_{r_{k-1}=1}^{N}a_{p,r_{1}}a_{r_{1},r_{2}}a_{r_{2},r_{3}}\cdots a_{r_{k-2},r_{k-1}}a_{r_{k-1},r_{q}} \end{equation} (7) counts the number of walks of length$$k$$ starting at node $$p$$ and ending at node $$q$$. The communicability between node $$p$$ and node $$q$$ is given by the total number of walks, weighted in decreasing order of their lengths, connecting the vertices $$p$$ and $$q$$ in a network $$G$$:   \begin{equation} G_{pq}=\sum_{k=0}^{\infty}\frac{(A^k)_{pq}}{k!}=(e^A)_{pq}. \end{equation} (8) Equation (8) can be also rewritten in terms of the graph spectrum as:   \begin{equation} G_{pq}=\sum_{j=1}^{n}\varphi_j(p)\varphi_j(q)e^{\lambda_j}, \end{equation} (9) where $$\varphi_j(p)$$ is the $$p$$-th element of the $$j$$-th orthonormal eigenvector of the adjacency matrix associated with the eigenvalue $$\lambda_j$$. The concept of communicability was then extended to the weighted case by Crofts and Higham in [16] in the context of DTI connectivity matrices. The definition in (7) is still valid but $$A$$ is the $$N \times N$$ weighted matrix and the terms $$a_{p,r_{1}}a_{r_{1},r_{2}}a_{r_{2},r_{3}}\cdots a_{r_{k-2},r_{k-1}}a_{r_{k-1},r_{q}}$$ represent the weights of the walks $$i\mapsto r_{1}$$, $$r_{1}\mapsto r_{2}$$, etc. In order to avoid the excessive influence of a node depending on its high weight, they introduced a normalization step dividing the weight $$a_{ij}$$ by the product $$\sqrt{s_{i}s_{j}}$$, where $$s_{i}$$ is the strength of node $$i$$. Therefore, the communicability between two nodes $$p$$ and $$q$$ in a weighted network is defined as:   \begin{equation} G_{pq}=(exp(D^{-1/2}AD^{-1/2}))_{pq}, \end{equation} (10) where $$D=diag(s_{i})$$ is the $$N \times N$$ diagonal strength matrix. 3.3 Statistical analysis on communicability The first goal of this study was to assess whether communicability is suitable to describe the disruption of communication between brain regions due to AD. In other words, we investigated the information content provided by communicability from a biological perspective. To this end, a non-parametric rank sum test was performed over the communicability values of all node pairs, between the HC and AD matrices. The false discovery rate multiple testing correction was used to calculate the adjusted $$P$$-values. The node pairs with statistically significant different communicability ($$P$$$$< 0.05$$) were detected and an analysis was conducted to find if the regions involved in these connections are related, according to the literature, to the neurodegenerative processes of AD. Moreover, a non-parametric Kruskal–Wallis test was performed to compare the distibutions of the communicability values for the three groups HC/AD/MCI in order to find the node pairs with statistically significant different communicability scores according to the adjusted $$P$$-values. 3.4 Classification procedure The second goal of the analysis we carried out was a comparative study, based on the same dataset, between classification models trained with traditional metrics and models trained with communicability. The learning and classification procedure was accomplished by using linear support vector machines (SVMs): the classification workflow is depicted in Fig. 2. Fig. 2. View largeDownload slide Classification workflow. For each cross-validation iteration, the whole dataset is split into a training and a test set. The training connectivity matrices are subjected to a two-stage feature selection. The first stage measures a mean HC matrix, to form a binary mask. The mask is binarized in accordance with a binomial test, which established to keep a link only if it occurs in more than 70% of the training HC matrices. Once all subjects’ matrices are projected onto the mask, they are subjected to a recursive feature elimination. The output features are used to train the SVM model. Fig. 2. View largeDownload slide Classification workflow. For each cross-validation iteration, the whole dataset is split into a training and a test set. The training connectivity matrices are subjected to a two-stage feature selection. The first stage measures a mean HC matrix, to form a binary mask. The mask is binarized in accordance with a binomial test, which established to keep a link only if it occurs in more than 70% of the training HC matrices. Once all subjects’ matrices are projected onto the mask, they are subjected to a recursive feature elimination. The output features are used to train the SVM model. The initial dataset consisted in the weighted and unweighted connectivity matrices obtained from the image preprocessing step described in Section 3.1. From these raw data the following features have been extracted, in accordance with the discussion provided in Section 3.2: edge betweenness; shortest path length; presence or absence of edge; communicability. In the rest of the article, they are referred to as ‘connectivity features’. The next step concerns the validation of the classification procedure through a proper splitting of the dataset into training and test sets. To this end, a 50-times repeated 10-fold cross-validation was performed. This procedure consists in dividing the entire set of examples into ten subsets, i.e. folds: one-fold was treated as test set, while the remaining folds formed the training set. This splitting was repeated until each fold was used as test set once. Note that the subjects were stratified by diagnosis, so that each fold contained roughly the same number of subjects from each diagnostic group. Moreover, we repeated the 10-fold cross-validation 50 times, using different permutations, in order to shuffle the subjects into the folds for a more general approximation of the performance. In order to reduce the dimensionality of the feature space and so to alleviate the problem of overfitting, a two-stage feature selection strategy was then applied. The first stage is an ad hoc selection of features, customized to connectivity matrices. It consisted in the calculation of an HC binary mean matrix, i.e. a mask, onto which the matrices of all subjects were later projected to reduce the number of connectivity metrics to be considered for classification. For each training set in every cross validation iteration, the mean matrix of only the HC connectivity matrices was calculated. The HC mean matrix is a weighted matrix whose entries $$e_{ij}$$ range from 0 to 1 and represent the frequency at which the corresponding edges occur among all HC matrices. The HC mean matrix was then thresholded in order to obtain the reference HC binary mean matrix to be used as mask. The threshold value was chosen at 0.7, using a binomial test (with $$\alpha=0.01$$): if we consider an a priori probability of 0.5 that a link is present or not in a connectivity matrix, the binomial test established that a link is considered to be a ‘real’ link if it occurs in more than 70% of all HC connectivity matrices. This feature selection strategy was motivated by the observation that, independently of the applied threshold, the HC mean matrix always shares more links than the unhealthy counterpart. In other words, HC matrices show a more stable topology; AD matrices, instead, show a greater intra-variability due to the disrupted connectivity. This procedure would evaluate a significant and robust reference model to select the important links, as sampling of subjects considered in each round makes the definition of the set of significant links (i.e., the mask) robust with respect to outliers. Additionally, weak connections that can introduce noisy effects are filtered out in accordance with an objective statistical test with a strict significance threshold of the mask. This nested procedure of significant link selection was preferred to other thresholding methods such as fixing the same mean degree across all groups. Indeed, the latter procedure could be particularly problematic in ‘disconnection syndromes’ or neurodegenerative diseases, where the assumption that node degree is the same between groups is likely to be invalid [28]. The second stage was a more conventional SVM recursive feature elimination (SVM-RFE) [29], embedded in the learning algorithm. The technique was applied to all the subjects’ matrices obtained by the former feature selection. SVM-RFE uses criteria derived from the coefficients in the SVM models to assess features, then iteratively removes features having small criteria. In each iteration, a linear SVM model is trained: the feature with the smallest ranking criterion is removed as it has the least effect on classification. The remaining features are kept for the next iteration. The process is iteratively computed until all the features have been removed. The final outcome of the algorithm is a ranked feature list: feature selection is achieved by choosing a group of top-ranked features. Depending on the output of SVM-RFE, subsets with an increasing number of features were evaluated, keeping only the one that obtained the best accuracy for the overall performance evaluation. Note that we used the implementation proposed in [30], which introduces a correlation bias reduction strategy that alleviates the problem of underestimating features that are highly correlated. It is worth emphasizing that, according to our previous work [31], we employed a nested feature selection strategy: for each cross-validation iteration, the two-stage feature selection was applied only on the training set blind to the test set. This methodological procedure avoids to introduce a feature selection bias, which necessarily leads to overoptimistic results. Once the dimensionality of data has been reduced, the SVM model can be fitted. The main intuition of SVMs is to find a separating hyperplane with the largest possible margin on either side, i.e. with the largest minimal distance from the closest data points. New examples are then predicted to belong to a class based on which side of the gap they fall [32]. SVMs are well known for their generalization ability and are particularly useful when the number of features, as in our case, is high [33]. 4. Results The results concerning both the statistical analysis and classification are described in the following subsections. 4.1 Statistics on communicability group differences Considering the HC and AD groups, 186 node pairs were found to have statistical significant different communicability (adjusted $$P$$$$< 0.05$$). Most of these pairs showed a reduced mean communicability in the AD subjects. Considering the HC and the AD distributions of the mean communicability values of the significant node pairs, the hypothesis of a decrease in the AD population median was tested performing a one-sided Wilcoxon rank sum test. A $$P$$-value of $$1.35\times 10^{-7}$$ was obtained: with enough evidence, it can be concluded that there is a negative shift in the median of the mean communicability values of the significant edges in AD compared with HC, at the 0.01 significance level, pointing out an overall communicability disruption due to AD. The differences between the HC and AD mean communicability values of the significant node pairs are shown in Fig. 3 by means of a glass brain: it is a 3D brain visualization in which nodes are localized exactly in the centroid position of the region of interest, in accordance with the Harvard-Oxford cortical atlas. For purposes of clarity, only the values in the 90th and 10th percentile of the communicability differences distribution are shown in the glass brain. The edges in the figure are a ‘nominal’ representation of the difference of mean communicability, between HC and AD, of the two nodes they link: the edge colour and the edge thickness are descriptive of the communicability difference of those brain region pairs between the two groups. Fig. 3. View largeDownload slide Glass brain visualization of the difference between the mean communicability values of the significant edges in HC and AD; the edge colour and the edge thickness are descriptive of these values. Only the values in the 90th and 10th percentile of the distribution of the communicability differences are shown. Fig. 3. View largeDownload slide Glass brain visualization of the difference between the mean communicability values of the significant edges in HC and AD; the edge colour and the edge thickness are descriptive of these values. Only the values in the 90th and 10th percentile of the distribution of the communicability differences are shown. The brain regions mostly involved in all the 186 significant edges were found to be: Supramarginal Gyrus posterior and anterior division, Lateral Occipital Cortex, Angular Gyrus, Insular Cortex, Inferior and Superior Frontal Gyrus, Superior Parietal Lobule, Postcentral Gyrus, Middle Temporal Gyrus Temporoccipital part left, Lateral Occipital Cortex inferior division left, Frontal Pole left, Precentral Gyrus and Precuneous Cortex. Considering the three groups HC, AD and MCI converter, 70 node pairs were found to be statistically significant different in communicability. Among these 70 pairs, 63 are in common with the 186 pairs previously found. The brain regions mostly involved in this case were found to be: Supramarginal Gyrus posterior and Supramarginal Gyrus anterior division, Angular Gyrus right, Insular Cortex, Precentral Gyrus, Postcentral Gyrus, Middle Frontal Gyrus, Superior Parietal Lobule right. Additionally, a permutation test was performed to test the significance of the overlapping between the node pairs with statistical significant different communicability in the 3-class analysis (HC/AD/MCI) and the 186 node pairs with statistical significant different communicability in the 2-class analysis (HC/AD). The estimated $$P$$-value was found to be $$<0.01$$, proving a significant percentage of overlapping links between the two tasks. 4.2 Classification performance evaluation 4.2.1 HC/AD classification. Classification performances, averaged all over the cross validation rounds, are expressed in terms of area under the ROC curve (AUC), accuracy, sensitivity and specificity. An overview of the best classification performance obtained by the network metrics individually is provided in Fig. 4. Note that each measure refers to the mean value obtained by averaging the performances achieved over all the cross-validation rounds. In the figure, each bar’s height indicates the mean value of the corresponding performance; the error bars indicate the standard errors. The best performances were obtained using the communicability values as features ($$0.75\pm 0.02$$ of accuracy; $$0.82\pm 0.02$$ of AUC; $$0.69\pm 0.02$$ of sensitivity; $$0.80\pm 0.02$$ of specificity). Note that they are higher than the best performances obtained using as features the traditional connectivity metrics ($$0.69\pm 0.02$$ of accuracy; $$0.74\pm 0.02$$ of AUC; $$0.65\pm 0.03$$ of sensitivity; $$0.78\pm 0.03$$ of specificity). It is worth remarking that the outperformance obtained when using communicability was tested by means of a non-parametric rank sum test. The performances achieved using communicability were found to be statistically significant different ($$P$$$$<$$ 0.0001) from those obtained using the traditional metrics, except for specificity in the case of binary Edge Betweenness. Fig. 4. View largeDownload slide Overview of the performances achieved by using, as features for the HC/AD classification, the individual metrics computed on the weighted and binary connectivity matrices. Fig. 4. View largeDownload slide Overview of the performances achieved by using, as features for the HC/AD classification, the individual metrics computed on the weighted and binary connectivity matrices. Figure 5 shows an overview of the best performance obtained using, as features for training the classification models, all the binary connectivity measures together with or without weighted communicability. All the weighted measures together with or without weighted communicability are also reported. The inclusion of communicability, among the features used, significantly improved classification performances ($$P$$$$<$$ 0.0001, except for specificity in the case of binary measures). Note that they are quite comparable to the performance achieved using only the communicability values as features. Fig. 5. View largeDownload slide Performance overview of all the connectivity metrics, with and without communicability, computed on the unweighted and weighted connectivity matrices (HC/AD classification). Fig. 5. View largeDownload slide Performance overview of all the connectivity metrics, with and without communicability, computed on the unweighted and weighted connectivity matrices (HC/AD classification). Figure 6 shows the same results of Fig. 5, adding the nodal measures degree, strength, clustering coefficient, betweenness and eigenvector centrality as features. The best performances ($$0.77\pm 0.02$$ of accuracy; $$0.81\pm 0.02$$ of AUC; $$0.72\pm 0.02$$ of sensitivity; $$0.81\pm 0.03$$ of specificity) have been obtained for the weighted matrices case. Also in this case the improvement of classification performances using communicability is statistically significant ($$P$$$$<$$ 0.0001, except for specificity in the case of binary measures). Fig. 6. View largeDownload slide Performance overview of all the connectivity and nodal metrics, with and without communicability, calculated on the unweighted and weighted connectivity matrices (HC/AD classification). Fig. 6. View largeDownload slide Performance overview of all the connectivity and nodal metrics, with and without communicability, calculated on the unweighted and weighted connectivity matrices (HC/AD classification). 4.2.2 HC/AD/MCI classification. The three class HC/AD/MCI performances, averaged over all the cross-validation rounds, are expressed in terms of accuracy and AUC, considering first AD as positive class and then MCI as positive class. In Fig. 7, the performances obtained using the previous traditional connectivity metrics as features and those obtained using communicability are compared. The best accuracy, i.e. $$0.60\pm 0.02$$, was obtained using communicability, and it is higher than the best one obtained by the models fitted on the weighted shortest path length ($$0.49\pm 0.02$$). The best AUC was achieved using communicability ($$0.79\pm 0.02$$ when considering AD as positive class, and $$0.72\pm 0.02$$ when considering MCI as positive class), which was higher than the best performance reached with traditional metrics, considering the presence or absence of a link as features ($$0.70\pm 0.02$$ when considering AD as positive class, and $$0.64\pm 0.03$$ when considering MCI as positive class). In addition, according to [34], a multiclass AUC was calculated through a pairwise comparison of classifiers, i.e. by using a one-vs-one strategy. Again, communicability outperformed the other metrics, as a multiclass AUC of $$0.77\pm 0.02$$ was obtained against the best value of $$0.68\pm 0.02$$ achieved with the traditional metrics. Also in the three-class classification, in all cases the classification performances obtained using communicability were found to be statistically significant different from those obtained with traditional network metrics ($$P < 0.0001$$). Fig. 7. View largeDownload slide Performance overview of the individual metrics computed on the weighted and binary connectivity matrices (HC/AD/MCI classification). Fig. 7. View largeDownload slide Performance overview of the individual metrics computed on the weighted and binary connectivity matrices (HC/AD/MCI classification). 5. Discussion The aim of this study was to show the capability of the communicability metric of highlighting the connectivity changes among brain regions in patients with AD, also at the early stages. The advantage of using this metric has been evaluated from two points of view: (i) A statistical analysis pointed out pairs of brain regions with different communicability in AD and HC subjects and in AD, HC and MCI subjects; (ii) A classification framework with different groups of features showed how communicability positively affects classification performance both for the HC/AD and the HC/AD/MCI discrimination. First, 186 node pairs with statistical significant different communicability values between HC and AD subjects have been found, revealing a general communicability disruption among AD brains. For the three groups (HC, AD and MCI converter) statistical analysis, 70 node pairs were found to be statistically significant different in communicability, 63 in common with the 186 pairs previously found. The brain regions mostly involved in these pairs were found to be highly AD-related brain regions. It is well known the involvement of the Angular Gyrus in semantic processing, word reading and comprehension, number processing, default mode network, memory retrieval, attention and spatial cognition, reasoning and social cognition [35]. Also the language function impairment in AD patients is due to synaptic loss and dysfunction involving the Angular Gyrus [36]. The Supramarginal Gyrus is a cortical region of interest involved in impairments in verbal and semantic memory for AD [37], and an area of anatomical connectivity decrease related to the short-term memory dysfunction [38]. The Lateral Occipital Cortex, left worse than right, is a region of atrophy and hypo-metabolism in AD [39]. The regional atrophy of the Insular Cortex is associated with neuropsychiatric symptoms in AD patients [40] and pathologic changes within this area may play essential roles in AD symptoms like behavioural dyscontrol and visceral dysfunction related to autonomic instability and loss of the sense of self [41]. Moreover, left-Insula and left-Inferior Frontal Gyrus were recently found to be important regions to act on to protect memory performance against AD [42]. The Parietal Lobe, which is involved in many cognitive functions, including memory, is considered vulnerable to AD and a site of metabolic changes and loss of WM integrity [43]. In fact, it is an AD-related area in preclinical dementia [44]. Also Precentral Gyrus is considered an AD-related brain region [45, 46]. Similarly, the medial Occipitotemporal and middle Temporal Gyri are sites affected by AD and atrophy in these areas may herald the presence of future AD among non-demented individuals [47]. The Frontal Pole left and the Lateral Occipital Cortex were found to have altered WM networks’ properties in preclinical AD [11]. It is also well known the specific role of the Precuneous in self-processing during autobiographical memory retrieval [48]. Moreover the Middle Frontal Gyrus has been found to be a region of abnormal connectivity in MCI subjects [49]. Second, this study showed that communicability improves the overall classification performance compared with the traditional network metrics. This finding supports the idea that communicability is more apt than shortest path length to describe the efficiency of communication between brain regions when modelled as nodes of DTI networks. It is worth remarking that this study was the first using the communicability metric to classify HC, AD and MCI and select disease-relevant biomarkers through the use of machine learning algorithms. Several other works using machine learning algorithms in this context mainly focused on two approaches to train the classification models: voxel-based, e.g. [31, 50], and region of interest-based, e.g. [51]. In particular, we reported results comparable to those obtained in the present paper in previous studies on data coming from the same database [31, 52]. In those works, the discriminating information provided by direct DTI measures, i.e. FA and MD, was evaluated. An increase in prediction performance has not here been observed; however, our results are encouraging and may pave the way for developing network-based classification models attaining a gain in terms of predictive accuracy. Indeed, from the prediction point of view, the potentiality of the network-based approach in this classification problem, as well as its limitations, have yet to be investigated. Currently, very few works used complex networks on DTI data; in [13], for example, several traditional network metrics are used as features of classification algorithms applied on private DTI data, but no conclusive result has yet been obtained. Moreover, we believe that the complex network approach may provide a gain also in terms of inference, as novel insights and better understanding of the data may be revealed. The network approach, in fact, may complement the localized information provided by the voxelwise analysis, by capturing more global patterns of alternation in the WM connectivity structure due to AD. Indeed, in this work, the network approach enabled to uncover connectivity differences in specific brain regions and connections due to AD. 6. Conclusion In this study, for the first time, the communicability metric was exploited with successful results to the problem of discovering connectivity differences in DTI brain networks of AD and MCI subjects. Communicability can be considered an alternative metric to traditional ones, mostly based on shortest path length. At a first step, the importance of investigating a metric more suitable to describe diffusive processes was highlighted. Then, the application of communicability to DTI connectivity networks was firstly investigated with a statistical-descriptive aim: pairs of brain regions with statistical significant different communicability values in AD and HC subjects were found; also for the three class analysis between HC, AD and MCI subjects, pairs of brain regions, mostly overlapping with the previous case, were found to be statistical significant different in communicability. Second, the advantage of applying communicability was investigated from a quantitative point of view: it was demonstrated that, for both the two discrimination tasks HC/AD and HC/AD/MCI, using the communicability values as features for training classification models improves the performances achieved using traditional network measures instead. Although the final goal of this article was to introduce a novel methodology in the DTI analysis for the study of AD, the clinical validity of our founding was verified by means of a comparison with literature results. In fact, it was demonstrated that communicability is really able to detect the brain connections mostly affected by the disease and to find the differences of network’s communication in AD subjects also at early stages. The efficiency of this metric to uncover connectivity differences in AD brain networks brings to the conclusion that communicability could be a powerful discriminant factor for more accurate AD diagnosis. The introduction of the communicability metric in this context can represent a starting point to develop new classification strategies and for proposing new measures based on this metric that could further improve classification performance. The advantage of using communicability for this purpose is not limited to the HC/AD classification, but can contribute to the early diagnosis of AD, which is one of the major challenges in current medical research. It is worth remarking that an important issue concerns the dependence of the adopted method on the network size. In this study, coarse anatomical connectivities have been considered for the estimated brain networks. Connectivities obtained between relatively large regions patterns are more robust and reproducible; however, they could overlook detailed patterns of connectivity, which may play a role in neurological diseases investigation. 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Journal of Complex NetworksOxford University Press

Published: May 30, 2018

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