In the graph theoretical analysis of anatomical brain connectivity, the white matter connections between regions of the brain are identified and serve as basis for the assessment of regional connectivity profiles, for example, to locate the hubs of the brain. But regions of the brain can be characterised further with respect to their gray matter volume or resting state perfusion. Local anatomical connectivity, gray matter volume and perfusion are traits of each brain region that are likely to be interdependent, however, particular patterns of systematic covariation have not yet been identified.We quantified the covariation of these traits by conducting an integrative MRI study on 23 subjects, utilising a combination of Diffusion Tensor Imaging, Arterial Spin Labeling and anatomical imaging. Based on our hypothesis that local connectivity, gray matter volume and perfusion are linked, we correlated these measures and particularly isolated the covariation of connectivity and perfusion by statistically controlling for gray matter volume. We found significant levels of covariation on the group- and regionwise level, particularly in regions of the Default Brain Mode Network.Connectivity and perfusion are systematically linked throughout a number of brain regions, thus we discuss these results as a starting point for further research on the role of homology in the formation of functional connectivity networks and on how structure/function relationships can manifest in the form of such trait interdependency. Recent findings are beginning to shed light on the organisational principles behind the structure of the brain Such principles are identified by studying the parts (e.g. brain regions) and analysing the global properties of the entire system that emerge from links between the parts (e.g. white matter connections). The network of white matter connections in the brain seems to adhere to a small-world organisation principle, defined by short path lengths for reaching any part from any other part, while providing high clustering and highly efficient wiring.Once such a property is established, relations to properties of other systems can be analysed.The shared small-world properties of interregional gray matter structural similarity As some of these traits, such as number of synapses, cell body population, perfusion and type and quantity of neural fiber bundles have proven to be examinable using advanced imaging methods of spectroscopy, perfusion, structural or diffusion MRI, brain regions can now be characterised regarding multiple traits at once. In certain cases the relationship between different structural properties is formed in a systematic way, e.g. larger brain regions tend to have more connections than smaller brain regions. In other cases, structural and functional traits are also systematically coupled, e.g. the neural computations that take place in a particular brain region are partially shaped by the quantity, quality and usage of the in- and outgoing connections of that region. In turn the principle of functional  segregation - as reflected in the typology of unimodal motor and sensory or heteromodal association areas of the cortex - is known to be mirrored both in the macroscopic white matter network topology Mounting evidence suggests If local white matter connectivity shapes neurocomputational processes, and these processes influence local function and therefore metabolic demand, one could hypothesise that local white matter connectivity and local perfusion might be coupled throughout the brain as well. If this were the case, such coupling would constitute the manifestation of a supply-and-demand-principle - the metabolic demand being shaped by connectivity - in the formation of a previously undocumented structure/function relationship.In order to quantify the outlined traits of perfusion and white matter connectivity we conducted an integrative MRI study on 23 healthy subjects (divided into two groups of 11 and 12 participants), utilising a combination of Diffusion Tensor Imaging (DTI), Arterial Spin Labeling (ASL) and anatomical imaging.DTI and ASL are methods to non-invasively characterise white matter structure and gray matter function of the brain, respectively DTI based tractography can be used to characterise the amount and integrity of white matter tracks between two regions and allows for an estimation of connection probability. For this purpose, probability density maps can be formed from the repeated propagation of curves through the DTI-based tensor field, which is representing local white matter orientation. Currently, DTI data are integrated into graph representations This approach allows for the quantification of node specific traits , edge specific traits  and general graph properties .ASL So far, only limited attention has been paid to possible synergies from the combined use of these two imaging modalities. As a result, the link between white matter network connectivity and rCBF has not yet been systematically addressed. Currently, there are a few studies focusing on rCBF alterations and changes in white matter integrity  as markers of Alzheimer's disease (AD) and mild cognitive impairment Following our hypothesis that local metabolic demands are largely determined by the connectivity profile of a brain region, we assumed that local perfusion and local connectivity measures of gray matter regions are to be correlated. In order to take into account the properties of the gray matter regions themselves (e.g. a region with larger volume might show higher perfusion and higher degree), we integrated a Voxel-based Morphometry (VBM) analysis into our design. VBM is an established method Our approach allows for the analysis of the entire trait triplet of gray matter volume (GMV), white matter connectivity and perfusion at once.Using this multi-facetted data we analysed the connectivity/perfusion-covariation profiles for regions of the Automated Anatomical Labeling (AAL) atlas, while controlling for GMV see .For the further analysis we divided the regions into the region classes cortical, subcortical and regions of the Default Brain Mode Network (DMN). The rationale for this division are manifold, on the one hand the graph theoretical and perfusion specific characterisation of subcortical regions is a novelty of this study, on the other hand it stands to reason that vasculature and connectivity systematically differ between cortical and subcortical regions and thus should be considered separately. Because we were particularly interested in the covariation profiles of regions with documented high resting state activity, we subdivided the class of cortical regions further into a DMN regions class. These region classes were comprehensively analysed on the individual-, group- and regionwise levels while controlling for local GMV. Furthermore we report on the correlation between perfusion with GMV, as well as GMV and perfusion with graph theoretical properties of white matter connectivity, respectively.We employed a probabilistic tractography approach for the estimation of our white matter connectivity graphs and provide results from not one, but many plausible white matter networks (connectomes). Whereas the state of the art does currently not serve with unambiguous properties of a commonly accepted connectome standard, we provide results from a sweep over plausible edge probability thresholds and resulting cortico-cortical sparsity values in Adjacency graphs such as connectomes can be described regarding their small-world properties using path length, clustering and the ratio of both. Relative path length is calculated as the current path length in a given adjacency graph relative to the path length in an equal random graph and expressed in the coefficient Lambda. The coefficient Gamma is calculated analogously for clustering and the coefficient Sigma is defined as Gamma/Lambda ratio, respectively.The estimated connectomes of all subjects showed small-world characteristics  as described by The different DTI scanning parameters  for both groups resulted in Group 2 showing higher Sigma values for the sweep range than Group 1 for comparable sparsity values. Further it is to note that thresholding with equal edge probability values in both groups consistently lead to a higher number of accepted edges for the connectomes of Group 2.Small-world property analyses for interregional GMV and perfusion correlations are provided in To address relation between the total rCBF in non-cerebellar regions of the brain and whole-brain graph theoretical metrics, we tested for such correlations in each group. For this analysis, whole-brain connection density, Lambda, Gamma, average degree, clustering coefficient and global efficiency values for the brain of each subject were paired with the same individual's average rCBF values (ASL measured in resting state), derived from of all non-cerebellar brain regions. These variables were tested for potential correlations (Spearman's rho) with graph metrics resulting from each step of the sweep over plausible edge probability thresholds. For each group p-values for all thresholding steps were False Discovery Rate  corrected. No significant results were obtained.−8).With respect to regional properties, as expected relative perfusion  was found to be higher in DMN regions than in other regions of the cortex , in accordance with our hypothesis. The difference between total perfusion  in regions of the DMN and the rest of the cortex showed a tendency towards significance . Regions of the DMN had significantly higher relative GMV than other regions of the cortex  are reported for a whole-sample analysis  in Both GMV and perfusion are systematically correlated with graph metrics, hence we repeated our analysis using GMV as a control variable.For the 78 cortical nodes the partial correlations (PCs) of perfusion and the graph theoretical metrics local clustering coefficient, local efficiency, local vulnerability, degree and betweenness  fail to reach significance  in both groups for all connectome estimations from the cortico-cortical sparsity range 11–17%. Significant PCs are found for Group 1 in the form of a negative covariation of the clustering coefficient  and a positive covariation of vulnerability , degree  and betweenness  with perfusion, but are minor in magnitude. Group 2 only shows a minor covariation of perfusion and degree .For the 10 subcortical nodes the PCs of perfusion and the graph theoretical metrics namely local clustering coefficient and betweenness  fail to reach significance  in both groups for all connectome estimations from the cortico-cortical sparsity range 11–17%.Significant PCs are found for both groups in the sparsity range of 13–16% in the form of a negative covariation of local efficiency with perfusion , and a positive covariation of vulnerability and perfusion .When groups are analysed separately, significant PCs are found for Group 2 in the form of a negative covariation of degree  with perfusion, but are not supported by results from Group 1.In order to specifically characterise regions  which are associated with the Default Brain Mode For these 12 cortical nodes the PCs of perfusion and the graph theoretical metrics local clustering coefficient, local efficiency, vulnerability, degree and betweenness  reached significance  in both groups for all connectome estimations from the cortico-cortical sparsity range 11–17%. The results are summarised in For each group, double FDR correction (p<0.05) was applied separately for the PC analyses carried out for each single subject and each single edge threshold (for the plausible sparsity range). On the individual level only five subjects showed any significant covariation (four from Group 1).The significant correlations on the individual level were all positive and minor to medium in magnitude, found only for the graph metrics degree, betweenness and vulnerability and only for nodes from the DMN and cortical regions.The perfusion, GMV and five graph theoretical metric trait measures of each non-cerebellar brain region of the AAL atlas were collected from each subject into two groupwise tables, one seven-value vector per person for each edge probability threshold. As a result each region can be characterised with respect to the covariation profile of perfusion and graph theoretical anatomical connectivity metrics while controlling for local GMV. For each group, double FDR correction (p<0.05) was applied separately for the PC analyses carried out for each single region and each single edge threshold. Only covariation profiles of regions are reported that passed the double FDR correction in both groups for more than half of the edge thresholds in the plausible cortico-cortical sparsity range. The statistically significant regional covariation profiles of the five graph theoretical metrics with local perfusion are provided in the supporting information files  with a vTo the best of our knowledge, this study represents the first attempt to quantify the relation of local perfusion and local anatomical connectivity, using the described MR sequences in combination with a probabilistic estimation of the connectivity graph. Our results on the robust small-world properties of the white matter connectomes are in accordance with previous findings.When conducting a sweep over the range of plausible edge probability thresholds, the properties of the white matter networks from both groups of participants show marked differences. For identical edge probability thresholds the sparsity of the resulting connectomes from Group 2  is higher than the sparsity of connectomes in Group 1. On the other hand small-world property (Sigma) values are numerically higher for the same sparsity levels in Group 2.It can be assumed that more edges of the white matter network are reliably identified with the superior DTI measurement parameters used in Group 2, and that the entirety of these reliably identifiable edges tend to display small-world properties. The numerically higher path length ratio values (Lambda) in Group 1 might indicate that long-distance white matter connections are measured more reliably with the superior DTI measurement parameters, thus facilitating their probabilistic tracking and acceptance as edge in the subsequent edge probability thresholding process. The acceptance of only a few more long-distance edges can decrease path length drastically, while influencing the sparsity value only minimally.The deviating Sigma values for equal cortico-cortical sparsity in the two groups might indicate that two qualitatively different white matter networks are compared with one another. But as we presently provide whole-connectome Sigma over cortico-cortical sparsity the deviation in small-world properties may as well be attributable to superior reliability in measuring non-cortico-cortical edges for the DTI sequences applied to Group 2.As can be seen in The lack of any significant relation of whole-brain graph metrics and average perfusion values indicates that there is no relation of overall absolute perfusion and overall connectivity in our healthy sample.Both local GMV and local perfusion show a pattern of significant covariation with local graph theoretical metrics in both groups and for all three described region classes. This pattern of covariation indicates that higher perfusion and higher GMV are more likely to be found in hub-like regions of the brain, with high degree, betweenness and vulnerability, thus with low clustering coefficient and local efficiency.GMV and perfusion show a marked covariation profile on the whole-sample level, with the strongest correlation for subcortical regions, followed by regions of the DMN and finally non-cerebellar regions in general and cortical regions. The marked correlations of perfusion and GMV could theoretically be a confound due the fact that relatively larger regions contain more large vessels and have a superior ASL Signal-to-Noise ratio (SNR) when compared with smaller regions. Alternatively the correlations could indicate a genuine association of average perfusion and relative GMV.Cortical and subcortical nodes were characterised with respect to their graph theoretical properties, which were further correlated with measures of perfusion, while controlling for local GMV.The covariations found on a group level, analysing the trait correlations of all cortical nodes, were only minor (<0.25) in magnitude and inconclusive in terms of cross-group stability. The covariation profile of traits from subcortical nodes on the other hand shows a negative covariation of local efficiency and a positive covariation of vulnerability with perfusion in a minor to medium (<0.6) range of magnitude.For regions associated with the DMN we observe similar patterns of covariation, but complemented by a positive covariation of degree and betweenness and a negative covariation of the clustering coefficient with perfusion, in a range of minor to medium magnitude.For all three classes of nodes, the magnitude of covariation observed in Group 1 exceeds the magnitude of covariations in Group 2.On the individual level correlations for all cortical, subcortical and DMN regions largely fail to reach significance in a stable pattern.On a regionwise level, frontal, cingular and hippocampal regions show a negative covariation of perfusion with the clustering coefficient and local efficiency, while mainly posterior portions of the brain show a positive covariation particularly with vulnerability. All covariations remain minor to medium in magnitude and have the same sign in both groups, except for the Frontal Inferior Cortex , the Frontal Superior Medial Gyrus, the Supplementary Motor Area, the Olfactory Cortex and the Rolandic Operculum, where the signs of covariation are contradictory.The present results do not allow for a clear and global falsification of a perfusion/connectivity-covariation in the brain. Rather the results on group- and regionwise levels point towards a positive covariation of rCBF with degree, betweenness and vulnerability and a negative covariation of rCBF with the clustering coefficient and efficiency for some particular regions of the brain.The correlation results for the covariation of GMV, perfusion and connectivity  point into the same direction, thus could be influenced by the issues indicated in the methods section.This might indicate that for some areas of the brain an increased rCBF is more likely to be found in regions, which have a central position in the white matter network and possess hub-like properties, but have poor local clustering and number of parallel pathways to any other node . This might be the manifestation of a structural organisation principle, which strives to minimise the potential of metabolic deficiencies in central nodes, which are part of a rather sequential connection architecture.The failure of the correlations to reach significance on the individual level could be attributed to the low statistical power, since for the DMN twelve and for the subcortical regions merely ten pairs of values are correlated for each participant, further decreasing the degrees of freedom by using PC and using conservative multiple comparison correction. The same holds for results on the regionwise level , which might offer one explanation for the contradictory findings in some regions.The most stable results are obtained for regions of the DMN on a group- and regionwise level. Regions of the DMN are known to possess hub-like properties in terms of both anatomical and functional connectivity These results might have implications on our understanding of resting state networks in general, not only those exclusively involving nodes of the DMN network The finding that DMN regions (e.g. Posterior Cingulate) might play a role as bottlenecks in a potentially task-negative default mode of macroscopic neural traffic might be underlined by past It is possible that the common traits  and the strong covariation of these traits contribute either causally to the formation, or confoundingly to our awareness of resting state networks. Similar Blood Oxygen Level Dependent (BOLD) activity profiles might in principle be caused by node interactivity in a functionally relevant information processing network or alternatively by mere similarity of isolated neural processes in individual nodes Understanding the link between local function and local connectivity better, might help understand the apparent link between functional and anatomical connectivity networks It is a further open question of interest, whether there is any causal neurobiological link between a regional perfusion profile and the emergence of hub characteristics or vice versa.The method described might hold potential for the diagnosis of various diseases, as the identified dependency of perfusion and connectivity might reflect the balance resulting from organisational principles inherent to the structural architecture of the healthy brain. Although the identified coefficients from the present healthy sample are only minor to medium in magnitude, it is to note that two traits might be only rudimentarily related in the healthy brain, but might show stronger links in the pathologically altered brain (e.g. hypoperfusion preceding gray matter atrophy).However, to better understand the relevance of the identified relationships and to explore changes of the derived coefficients due to ageing or disease future studies have to be performed on the respective populations.It can be assumed that during our resting state ASL measurement, the regions of the DMN showed their - by definition - heightened resting state activity and metabolic demand and it is possible that our measurements were therefore systematically biased. If the metabolic profile of a region is best assessed when this region shows a stable amount of activity over time, the metabolic demand of the resting state active brain regions (the DMN) was eventually captured more clearly by our resting state experiment, than the metabolic demand profile of a less resting state involved region such as e.g. the Fusiform Gyrus. This issue touches on the general question whether stimulus-free measurements constitute a reliable baseline measurement for the whole brain, or only for regions active under stimulus-free conditions.Thus it can not be excluded that covariations of the present form could be identified more conclusively for others regions of the brain as well. For such experiments, these regions would need to be consistently activated for a prolonged amount of time (e.g. by presentation of a series of faces for characterisation of the Fusiform Gyrus), what might allow us to assess their metabolic demand during activity better.It might be argued that the prospect of such studies might be limited, as brain regions do not merely show a straightforward type of homogeneous functional specialisation, but are rather able to perform heterogenous functions that depend on the task-specific network(s) they are integrated in at a point of time. Nevertheless it should be possible to capture the range of metabolic demand spanned by the conditions of activity and rest for each region of the brain, as any computational process is likely to influence metabolic demand in a specific way.Studies on the relation of functional and anatomical connectivity networks in general might be influenced by a similar aspect. The definition of functional connectivity is always limited to the state of the brain the connectivity is observed in, therefore the definition of network nodes is not state-independent (the stable association of the nodes with a network is one but not the only defining trait of the nodes) and thus probably not one-by-one mappable onto other data, e.g. to adequately assess the underlying anatomical connectivity network.It stands to reason that both the range of metabolic demand states, local connectivity and GMV, and the probability ranking of affiliations to functional connectivity networks of a brain region might be related in some manner to the shape of the Hemodynamic Response Function in that region.Alternatively to a direct causal interpretation, the co-variation of perfusion and connectivity could as well be caused by a confounding third, presently unregarded variable other than GMV. Our initial hypothesis on the link between local connectivity and local neural computations, neural computations and neural activity, and neural activity and metabolic demand involves a series of dependencies, making the influence of intermediary variables highly likely.A more comprehensive model, including more potentially intermediate variables beyond merely GMV, could be used in future studies to investigate the relations of local computational processes , neural circuitry , neurotransmitter concentrations (e.g. by using Magnetic Resonance Spectroscopy), metabolism and connectivity at once. With such a larger and more comprehensive dataset it is likely that the particular perfusion/connectivity balance profile of each region could be resolved further.Several methodological issues need to be addressed. Although we employed a probabilistic tracking approach with a high number of random walks and conservative thresholding, presently it is not possible to ensure the validity of one singular estimated connectome with complete certainty due to the methodological difficulty of proper edge falsification and the strong dependency of the results upon the chosen brain parcellation scheme (the AAL atlas in this case). For a more precise estimation, the methodology has to be refined by extending it to more sophisticated graph estimation methods e.g. based on Q-ball imaging data The combination of multiple methods  allows for quantifying and describing brain regions with a high number of measures, both on a global as well as on a regional scale. The proper interpretation of this multifaceted data, with respect to the multiple comparisons problem and open questions on the combination of non-gaussian measures with classical statistical approaches, needs to be advanced in an integrative manner.Further as the present findings are based on cross-sectional data from small samples, the results could be influenced by potential cohort or small sample size effects. A longitudinal study design with a higher number of subjects is necessary to broaden our understanding of the link of these structural and functional brain properties.It is to note that many different methods with their individual assumptions and errors are combined in an integrative study, and that any of the modules  could clearly be improved on their own. Our approach is merely intended as a starting point for the combination of the provided measures.Therefore the present findings are of a preliminary nature, as for the integration of information about local perfusion, connectivity and gray matter properties, the issues of natural variability versus the distribution of measurement error have to be further resolved. Other quantification approaches for measuring integrity or impairment of gray matter such as spectroscopy of synaptic density or recently introduced Positron Emission Tomography methods Eleven participants  were recruited for Group 1 from a student sample . After an update of scanner software twelve further participants  were recruited, referred to as Group 2 . Participants of both groups gave written informed consent. All participants were right handed (as confirmed by the Edinburgh Handedness Questionnaire) and both physically  and mentally healthy (confirmed by the german ICD-10-Symptomrating questionnaire). The experiments were approved by the local ethics committee. All MR data were acquired on a 3T Siemens MAGNETOM Trio TIM  scanner using a 12-channel head coil. The head of each subject was bedded in a deflatable pillow so as to minimise head motion artefacts.http://www.fmrib.ox.ac.uk/fsl).Anatomical images were acquired using a T1 weighted sequence using a 3D MP-RAGE (magnetisation prepared - rapid acquisition gradient echo) sequence . The brain was extracted from the raw image using the robust iterative estimation function  of the Brain Extraction Tool and subsequently segmented into gray and white matter (2) with the field of view (FoV) comprising the full cerebrum and parts of the rostral cerebellum like the Uvula and Tuber of Vermis, Flocculus and Crus Cerebelli .Each subject in Group 1 participated in a DTI measurement  with the FoV comprising the full cerebrum and parts of the rostral cerebellum. The DTI data were processed using the DTI and Fibertools Software Package Each subject in Group 2 participated in a DTI measurement  image and then normalised to the Montreal Neurological Institute (MNI) space. The resulting transformation was inverted to warp the AAL template from MNI space to the DTI space. The discrete labeling values were preserved by using a nearest neighbour interpolation method. Normalisation and inverse transformation were implemented using the SPM8 package.All available subcortical  and cerebellar areas, which were within the individual DTI FoV were included as nodes in order to round out the validity of the individual connectivity graph estimation.Using in-house code, the white matter voxels, which were neighbouring the gray matter of each network node, were defined as seed voxels of that area.Only voxels with a Fractional Anisotropy (FA) value above 0.3  derived from the literature, we provide our results in the form of a sweep over a range of plausible thresholds - in order to avoid false conclusions originating in the limitations of only one threshold-specific white matter network see .−9). The applied thresholds ranged from implausibly low thresholds (average edge probability in non-zero voxels min. 10−10) allowing for a very high number of accepted edges to overly conservative high thresholds (average non-zero edge probability min. 8*10−7) making the adjacency matrix very sparse respectively. The selection of the threshold for calculation of the graph metrics employed in the present work was based on both empirical and theoretical considerations and reproduces values for cortico-cortical sparsity, clustering, average path length and resulting small-world coefficients, which are comparable with the results described by In order to substantiate this sweep, to ensure the validity of the present findings and to avoid false conclusions due to erroneous selection of the edge probability threshold, we performed a number of connectome estimations based on a large range of thresholds  with perfusion for both cortical and subcortical network nodes. This might indicate that the real relation is even stronger than depicted in this context, since there is no other overt reason why the consideration of implausible edges with lower connection probability (which appear only when the threshold is decreased) should systematically increase the PCs. Instead the presented results of our sweep over possible thresholds show that reforming the white matter network topology by adding more edges systematically strengthens statistical relations of perfusion and connectivity.Further, as for the same threshold more edges are identified for the superior DTI measurement scheme , indicating that for a low number of edges probability values are very high, while for a very large number of possible edges probability values are very low. How this is related to the observed power-law distribution of hubs for certain edge probability thresholds could be subject of further numerical simulations.For each node, edge and resulting overall graph the available metrics were calculated using the scripts provided within the Brain Connectivity Toolbox It is to be noted, that graph analysis of white matter connectivity has the advantage that connectivity is not restricted to concepts of direct links only, which is often the case in classical Region-of-Interest to Region-of-Interest deterministic tractography, but incorporates notions of indirect (path length >1) connectivity in all utilised graph metrics but degree.Degree is the number of edges connecting one node by a path length of one with other nodes (e.g. a hub has a high degree vs. an isolated node with only one connection to the rest of the network has a low degree). In order to normalise local degree values to make them comparable across graphs, the values are divided by the sum of all node degree values.betweenness is at a central position of the network, meaning that many of the paths connecting any node A and any node B traverse that node . Betweenness is calculated as the fraction of all shortest paths in the network, which traverse a given edge/node. In order to normalise local betweenness values to make them comparable across graphs, the values are divided by the sum of all node betweenness values within the graph.A node with high clustering coefficient quantifies the number of connections that exist between the nearest neighbours of a node as a proportion of the maximum number of possible connections amongst them. This normalisation allows comparing the clustering coefficient of two nodes directly, irrespective of their individual degree.If the nearest neighbours (path length  =  1) of a node are also directly connected to each other they form a cluster . The Efficiency is inversely related to minimum path length (shortest) and quantifies how easily one node can be reached from any other node. Nodes with a high efficiency have many interconnected neighbours and are thus more easily reachable via a number of  direct paths from any other node. Local efficiency of a node is therefore calculated as the harmonic mean for neighbour-neighbour distances.vulnerability metric describes how strongly the average shortest path lengths (the mean distance to get from any node A to any node B) in a network grow if a node is removed. If a node with high betweenness, high degree, low efficiency and low clustering coefficient is removed, a central hub is eliminated leading to insufficient cost-effective (short) detours for reconnecting severed nodes and high node vulnerability. If a network is fully connected  degree, efficiency and clustering coefficient might be high for all nodes, but vulnerability might be low, as the removal of one node would not affect the average distance of any pair of nodes significantly, due to the high number of parallel connecting paths/cost-effective detours.The http://www.fmrib.ox.ac.uk/fsl), self-written MATLAB  and Linux shell script routines were used. Time courses of all voxels were motion-corrected utilising the MCFLIRT module of FSL using the mean volume of the corresponding run as reference. CBF time series were created by calculating control-tag difference images using surround subtraction , thereby reducing BOLD signal contamination of the CBF time course ASL data were acquired with a FAIR-QUIPSSII PASL encoding scheme with echo-planar imaging (EPI) readout. A total of 201 alternating tag and control images were obtained in each run . For ASL measurements of Group 2 the number of slices was increased from ten to eleven (TI2 was changed to 1400 respectively). In order to determine the equilibrium magnetisation for absolute CBF quantification, the same parameters as above were used except that the TR and TI2 were 10000 ms and 4000 ms, respectively For the ASL resting state data acquisition subjects were instructed to relax with closed eyes while staying awake. The ASL values for the nodes were extracted by averaging the absolute CBF (in ml/100 g-min) from the voxels within each network node Volume of interest (VOI) for each subject.Regional absolute and within-subject normalised rCBF values are provided for all non-cerebellar regions of the AAL atlas in the In order to address the relation between gray matter characteristics, graph theoretical measures and resting state perfusion, we performed a VBM Analysis of the T1 weighted anatomical scans so as to derive descriptives regarding the relative volume of each AAL region. As described in the section Network Node Definition, each anatomical image was skull stripped and the Voxel-based Morphometry Toolbox  was used subsequently for estimation of the individual modulated and unmodulated segmentation outputs. As the modulated outputs can be corrected for non-linear warping only and therefore make any further correction for different brain size redundant, these images can be used directly for volume estimations.For the unified segmentation approach  revealed that the VBM results of the images were all within a tolerable range.So as to optimise the validity of our GMV estimation, we performed a voxel-wise multiplication of each modulated gray matter image with the coregistered corresponding perfusion image (containing absolute CBF information). Although perfusion imaging of white matter regions of the brain is possible in principle Regional GMV values are provided for all non-cerebellar regions of the AAL atlas in As a univariate factor analysis revealed significant interindividual variability of rCBF values and an effect of gender, the analysis was performed using within-subject z-scored rCBF values. Following this approach, graph metrics and the GMV of nodes were all normalised (z-scored) on a within-subject level. The normalisation was performed separately for cortical and subcortical nodes.Cortical or subcortical regions for which no connections could be found (due to a tracking failure) or for which no perfusion data could be obtained  were excluded pairwise from the analysis . Cerebellar regions were not considered for correlation analysis, as for 30.94% of cerebellar regions rCBF could not be measured.VOI specific artefacts in the estimation of rCBF can not be fully eliminated, due to the generally increased SNR ratio of the ASL signal and the higher chance of intravascular artefacts in larger VOIs, which naturally contain more large arteries and veins that distort rCBF estimations. Also imperfect slice profiles, remaining magnetisation transfer effects and blood tissue water exchange time are factors, which cause artefacts on rCBF estimation. In order to decrease the impact of VOI size on the estimation of relations, we included GMV estimations from VBM as a control variable into our analysis and restricted the presented results to the significant PCs calculated with Spearman's rho.The data derived from the entirety of these measures constitute for each member of the sample a subjectwise region-by-trait table, with the columns representing local perfusion, local GMV and five graph theoretical metrics of local white matter connectivity, and with 116 rows - one for each region of the AAL atlas.In order to interpret such multifaceted data one can take various perspectives. The data can be sorted and the trait measurements can be correlated on an individual subjectwise level, to answer the question, whether there is a significant PC - controlling for local GMV - between local perfusion and local connectivity for all the 116 regions of the AAL atlas in the brain of a given subject. Alternatively the data can be normalised on a within-subject level and integrated with data from all other subjects into a group table, to answer the question whether the previously outlined PC is significant in an analysis of pooled data as well. As a second alternative approach, the data can be sorted by region, so as to answer the question whether in pooled group data local perfusion and local connectivity of some regions shows stronger correlation than others . Figures of dataflow and analaysis schemes are depicted in Results are presented for white matter connectomes that show plausible cortico-cortical sparsity (between 11 and 17%).Figure S1Dataflow of each participant is illustrated; please see (10.24 MB TIF)Click here for additional data file.Figure S2Illustration for the group, individual and regionwise analysis schemes. C indicates the control variable GMV in the PC approach.(10.24 MB TIF)Click here for additional data file.Figure S3Upper: Distribution of cortico-cortical sparsity over identical edge probability thresholds for both groups. Lower: Distribution of whole-brain sparsity over identical edge probability thresholds for both groups; edge probability thresholds (x-axis) become more conservative towards the right end of the x-axis (higher threshold) leading to lower resulting sparsity due to less accepted edges.(1.82 MB TIF)Click here for additional data file.Figure S4Upper: Regional total perfusion in all 23 subjects . Lower: Regional within-subject normalised perfusion in all 23 subjects for cortical regions .(12.04 MB TIF)Click here for additional data file.Figure S5Relative GMV of non-cerebellar Regions for all 23 subjects .(10.24 MB TIF)Click here for additional data file.Table S1Results of the regionwise PC analysis , presented for statistically significant  regions only provided with minima and maxima of correlation magnitudes for Group 1 and Group 2.(0.04 MB XLS)Click here for additional data file.Text S1Notes on the small-world characteristics of binary adjacency graphs defined by the significant correlations of cortical perfusion and GMV values.(0.04 MB PDF)Click here for additional data file.


In some large-scale face recognition task, such as driver license identification and law enforcement, the training set only contains one image per person. This situation is referred to as one sample problem. Because many face recognition techniques implicitly assume that several (at least two) images per person are available for training, they cannot deal with the one sample problem. This paper investigates principal component analysis (PCA), Fisher linear discriminant analysis (LDA), and locality preserving projections (LPP) and shows why they cannot perform well in one sample problem. After that, this paper presents four reasons that make one sample problem itself difficult: the small sample size problem; the lack of representative samples; the underestimated intra-class variation; and the overestimated inter-class variation. Based on the analysis, this paper proposes to enlarge the training set based on the inter-class relationship. This paper also extends LDA and LPP to extract features from the enlarged training set. The experimental results show the effectiveness of the proposed method. Face recognition has attracted much attention in the last two decades. However, it is still an unsolved problem that needs further investigation. Several factors challenge the current face recognition techniques, including the variations of pose, illumination, expression, age, and the occlusion. Face recognition from one image per person  is another important sub-area, which recently attracts increasing attention The most popular face recognition methods are subspace-based methods, including principal component analysis (PCA) Researchers have proposed methods to deal with one sample problem. The extensions of PCA In this paper, we analyze why face recognition is difficult from two different viewpoints. The first viewpoint is the principal of the popular feature extraction methods. We study the principals of PCA, LDA, and LPP and show why they cannot perform well or applicable to one sample problem. We also present our analysis from the second viewpoint: why is one sample problem itself difficult? For the first time, we ascribe the difficulty of one sample problem to four reasons: 1. the training set is small; 2. one sample is not representative; 3. the intra-class variation is unknown or underestimated; and 4. the inter-class variation is overestimated.Our analysis leads us to solve the one sample problem by enlarging the training set based on the inter-class relationship. By synthesizing many samples, our method not only turns the one sample problem into a multiple samples problem, but also can rectify the underestimated intra-class variation and the overestimated inter-class variation. In the enlarged training set, the synthesized images for one individual are independent from each other. This enhances the representative of the training set. We propose extensions of both LDA and LPP for feature extraction from the enlarged training set. These two extensions treat the real images and the synthesized images differently, and suitable for use on the enlarged training set. The experimental results show that the feature extraction methods achieve higher classification accuracy on the enlarged training set.PCA, LDA, and LPP are three popular methods proposed for feature extraction in the task of face recognition. These three methods and their extensions are developed based on an implicit assumption that several images (at least two) from each individual are available in the training stage. As this implicit assumption does not hold in the one sample problem, these methods cannot achieve high classification accuracy. In the following, we analyze why one sample problem degrades the performances of PCA, LDA, and LPP in face recognition.As one of the most popular methods, PCA  problem, and one sample problem is the extreme situation. The face images are normally of tens of thousands of dimensional. By contrast, the number of available face images for each individual is normally much smaller, and decreases to its minimum value in one sample problem. It is proved that if the samples are of Secondly, one image is not representative enough in the task of face recognition. It is widely recognized that the variations of pose, illumination, expression can induce large variations on the face images. Face images of the same individual are different from each other if they are captured under different conditions. As the capture environment changes, the difference among face images from the same individual is not avoidable. One image is far from enough to represent the face images of one individual. Researchers have studied the relationship among face images captured under different conditions and found ways to predict on from the others Thirdly, as the intra-class variation is unknown, one samples problem deprives the opportunity of feature extraction methods to minimize the intra-class distance, and provides far from enough inputs for classifiers in the training stage. To achieve high classification accuracy, most feature extraction methods in pattern recognition try to minimize the intra-class distance in the feature space. However, the intra-class variation is unavailable in one sample problem. This deprives our chance to minimize the intra-class variation in the feature extraction procedure. Thus, the intra-class variation is large with high probability in the feature space and unfavorably affects the following classification procedure. We need the inter-class and intra-class variation to train classifiers Fourthly, the inter-class variation is overestimated in one sample problem. The inter-class variations measure the differences between images that have different class labels. As there is only one image per person in one sample problem, all the variations are inter-class variations. The following analysis shows how the inter-class variation is overestimated.We suppose the face images of two individuals respectively form a cluster, as shown in From the above analysis, we conclude that the difference between the one sample problem and multiple samples problem is beyond the number of training samples. It is the above four reasons that make one sample problem more difficult.In this section, we will propose a novel method to enlarge the training set based on the inter-class relationship.We consider the face images as points in the high dimensional face space. Due to the variations of pose, illumination, and expression, face images of the same individual are different from each other and represented by different points. However, as they associate with the same individual, these images have some similarity to each other and the corresponding points form a cluster. This is especially true when the capture environment does not change significantly. Based on this observation, we assume that the images of one individual cluster together in this paper, as shown in Regarding the image Note that, it is not necessarily that all of these points are real images. The points in the middle of this line segment are far from both of the real images and they are not real images in most cases. However, having small differences to one of the real images, the ones near to the end points can be considered as variations of the real images.To synthesize images using (3) based on two images Proof.Suppose two images The distance between them can be computeda). If b). If Based on a) and b), we know that all the intra-class variations are smaller than In the above, we talk about the image synthesis based on two images. In a multi-class problem, however, we must take more into consideration to obtain small intra-class variations and large inter-class variation. We design the following algorithm for face image synthesis in a multi-class problem:Algorithm 1.For each real image Step 1: among all the real images, find Step 2: synthesize images using Using the above algorithm, we can synthesize many images to enlarge the training set. This training set has two properties.Firstly, a image Proof:Suppose Thus,Suppose Based on (9) and (10), we know that the synthesized image Secondly, if Proof:Based on the triangle inequality theorem, we know thatBased on (9), we haveThus,So,We can use algorithm 1 to synthesize variations for each real face image and obtain an enlarged training set. This enlarged training set has four properties.Firstly, this set of images has a reduced intra-class variation and increased inter-class variation. As mentioned above, the intra-class variation is underestimated and the inter-class variation is overestimated in one sample problem. We can easily prove that, compared to shown in . Though Secondly, the local structure is useful for classification in the enlarged training set. It is proved that the synthesized samples are nearer to the real face images belonging to the same individual than the real face images of the others. In other words, each image must have a neighbor that share the same class label with it. Because of this, the feature extraction method that keeps the local structure will generate a small intra-class variation in the feature space. Thus, the local structure is useful for classification.Thirdly, the enlarged training dataset makes it possible to learn a robust model for feature extraction. If we synthesize Fourthly, the synthesized images captured the variations along different directions. Step 2 synthesizes images based on an image and its several neighbors, which are normally along different directions. This enriches the variations of the training set and enhances its representation. Also, the synthesized images are independent if they are synthesized based on different pairs of real images.In this section, the LDA aims to maximize the inter-class variation and simultaneously minimize the intra-class variation. The projection vectors are obtained by maximizing the following Fisher criterionwhere In this one sample problem, we take the real image as the mean of the Though the synthesized images are neighbors of the real images, it is possible that they do not accurately model the variations of the real image. The mean computed based these synthesized images may vary from the real mean value. It is reasonable to take the real image as the mean value. Through this way, we not only save the time to compute the mean value, but also alleviate the adversely effect (if any) of the synthesized images. Even if the synthesized images do not accurately model the variations of the real image, we still can get the valid mean value of the We can rewrite the inter-class scatter matrix as followsThis inter-class scatter matrix is derived based on the differences between the synthesized images. Based on our discussion, such differences model the inter-class variations more accurately.To summary, we seek LDA-based projection vectors by maximizing the following Fisher criterionThe feature extractors that maximize the above Fisher criterion are the eigenvectors of the following generalized eigen-equation problem corresponding to the maximum eigenvaluesLPP tries to learn a subspace that preserves the local structure of the image space. In this paper, we propose the following extension of LPP for one sample problemWe define To solve the optimization problem (22), we have the following stepswhere We introduce a constraint as followsThe minimization problem (24) reduces toBased on (29), the projection vectors are the eigenvectors of the following generalized eigenvalue problem corresponding to the minimum eigenvalueThe ORL The Yale database We use a subset of the FERET database In the experiments on ORL and Yale databases, we use the first image of each individual for training and the rest images for testing. The training sets consist of 40 and 15 images in these two experiments, and their corresponding testing sets consist of 360 and 150 images. In the FERET database, we use the 200 fa images for training and the 200 fb images for testing.2A Besides the conventional PCA, LDA, and LPP, we compare our methods with other three methods To extract discriminative features, we first enlarge the training set using Algorithm 1 and perform feature extraction on the enlarged training set. These methods are referred to as PCA on the enlarged training set (PCAoE), LDA on the enlarged training set (LDAoE), and LPP on the enlarged training set (LPPoE). The extracted features are classified using K-nearest neighbor (KNN) classifier.Two important parameters in algorithm are: the number of neighbors 2A; the classification accuracy of LDAoE is 9.5% and 8.3% higher than those of the methods in 2A; the classification accuracy of LDAoE is 3.5% and 5.3% higher than those of the methods in 2A; the classification accuracy of LDAoE is 8.6% and 4.2% higher than those of the methods in The In our experiments, the original training sets of the ORL, Yale, and FERET databases consist of 40, 15, and 200 images, respectively. The training sets enlarged using algorithm 1 are much larger, and they consist of 400, 120, and 4400 images, respectively. Let real training image Recently, the sparse representation based classification (SRC) is widely studied recently and achieve high recognition accuracy with multiple training images from each person Most face recognition techniques require multiple images from each individual for training. The one sample problem either degrades the performance of these techniques or makes them fail to work. In this paper, we analyze the principal of three popular feature extraction methods  and show why they cannot perform well on one sample problem. Moreover, we present analyses from a new viewpoint: why is one sample problem itself difficult? We ascribe the difficulty to four reasons: the SSS problem; the lack of representative samples; the underestimated intra-class variation; and the overestimated inter-class variation.Based on our analysis, we propose a method to synthesize images and enlarge the training set for face recognition from one image per person. The synthesized images are weighted combinations of the pairs of real images. Two properties of the enlarged training set proclaim that the enlarged training set can replace the original training set. The enlarged training set overcomes the previously mentioned four difficulties of the one sample problem and improves the classification accuracy in our experiments.


Complex networks can often be decomposed into less complex sub-networks whose structures can give hints about the functional organization of the network as a whole. However, these structural motifs can only tell one part of the functional story because in this analysis each node and edge is treated on an equal footing. In real networks, two motifs that are topologically identical but whose nodes perform very different functions will play very different roles in the network.C. elegans with information about the biological function of these nodes, thus coloring nodes by function. We discover that particular colorations of motifs are significantly more abundant in the worm brain than expected by chance, and have particular computational functions that emphasize the feed-forward structure of information processing in the network, while evading feedback loops. Interneurons are strongly over-represented among the common motifs, supporting the notion that these motifs process and transduce the information from the sensor neurons towards the muscles. Some of the most common motifs identified in the search for significant colored motifs play a crucial role in the system of neurons controlling the worm's locomotion.Here, we combine structural information derived from the topology of the neuronal network of the nematode The analysis of complex networks in terms of colored motifs combines two independent data sets to generate insight about these networks that cannot be obtained with either data set alone. The method is general and should allow a decomposition of any complex networks into its functional  motifs as long as both wiring and functional information is available. Over the last decades, systems biology and network theory have contributed tremendously to our understanding of complex systems Complex networks like electronic circuits are frequently represented in terms of modules such as operational amplifiers, logical gates and memory, and it is often suggested that biological networks can similarly decomposed into functional modules that have stereotypical functions C. elegans. This network controls one of the most well-understood complex biological systems to date, and most of the network architecture of the 302 neurons of the hermaphrodite worm is known from experimental work We analyze motifs in the network of synaptic and gap-junction connections of the neuronal network of the nematode C. elegans neuronal network: the feedforward loop, and the bi-fan motif An analysis of topological motifs in this network has revealed that two major building blocks are significantly overrepresented in the how these motifs are used, or how they contribute to the worm's behavior. A simple example can illustrate this point: in Indeed, the identification of the feedforward and bifan motifs does not allow us to determine and functional motifs in the C. elegans brain: the connection graph and the functional characterization of each neuron C. elegans neuronal network becomes a colored graph where nodes represent neurons, edges are connections between neurons, and the color of the node tags the cell-type of the node. It is clear that the choice of the cell-type set (the colors) is crucial for the success of this method, and different choices will produce different results. At the same time, the classification into the three cell types is in itself ambiguous, because there are differences of annotation in the literature, and some cells are sometimes annotated as belonging to two classes. Other classifications exist  has adaptive significance, we should see a bias in the colored motif distribution with respect to control networks whose color assignments have been scrambled. We extract colored motif abundances from the colored networks by counting all distinct color combinations for each of the structural motifs of size 2, 3, and 4. Of the 279 neurons, 86 are classified as sensor neurons (and colored green in the following), 80 are classified as interneurons (red), and the remainder of 114 neurons are classified as motorneurons (blue) If the C. elegans is biased, we produce random colored control networks by shuffling the color assignments in the C. elegans network while maintaining the relative abundance of each kind. The mean abundance C. elegans are significantly different from the random control: all of the 2-node colored motif counts are significant, and all but one of the three-node motifs  and 3,667 motifs of size 4  were absent by chance in any of the 1,000 randomizations.We find a tendency of colored motifs in In previous work that analyzed structural motifs only These distributions show that the observed functional constraints make intuitive sense. For example, we find the motor-to-sensor-neuron motif to be significantly suppressed: we do not expect muscles to relay information to sensory neurons in a functioning worm (even though some of these connections do indeed exist). On the other hand, the sensor-to-inter- as well as inter-to-inter-neuron motifs appear significantly more often than expected by chance, as appropriate for information-processing motifs.C. elegans brain, as well as is gene regulatory networks C. elegans network, 40 motifs of size 3 .The larger the motif, the more specific its computational function. At the same time, the number of possible motifs also increases greatly with motif-size. Of the 13,770 possible colored motifs with four nodes and directed edges, only 8,310 actually appear in the functional classes of motifs using chemical synapses (directed edges) only, shown in For four nodes with directed edges, there are 199 possible motifs that are structurally different, but many of those topologies are not prominent among the 505 colored motifs that are most significantly over-represented shown in . Among tThe most common motif-class is the nested feed-forward motif , of whicFunctional motifs that we do not discuss (about 5% of the motifs in the set of 505) either do not show up among the 505 prominent motifs or else are under-represented. An example is the “nested rings” motif, an instance of which is shown in C. elegans sub-network used for forward locomotion , while motor neurons are most often the end of the signal chain. Interneurons represent a much larger fraction of nodes in computational motifs than their overall abundance in the network would imply, suggesting that they relay the bulk of the forward-processing information. Notably absent among the common motifs are feedback loops, and relay chains longer than three neurons, underscoring the need for immediate reaction and the integration of signals. While these observations cannot take into account whether the connections between neurons are excitatory or inhibitory (as this data is not available for the majority of the connections), the comparison with the core forward-locomotion network of C. elegans (where this inference has been made) suggests that an analysis of colored motif utilization captures the computational processes underlying that behavior well.Combining two sets of data that make the neuronal network of In the future, we imagine that an analysis of the utilization spectrum of colored motifs can be extended to any network where nodes can be assigned tags that differentiate their biological  function, but care must be taken to limit the number of functional classes as the predictive power of this approach is quickly overwhelmed when too many motifs are possible.C. elegans motif as C. elegans network, C. elegans colored graph is performed by repeatedly switching the colors of two randomly chosen nodes, thus preserving the color distribution and the underlying graph topology. The color switch is repeated sufficiently often to guarantee a random color distribution.The wiring diagram as well as the functional classification of neurons into sensor- inter- and motor-neurons, was obtained from C. elegans neuronal networks is significantly over-represented, compared to the same motif in a color-randomized network. Because many hypotheses are tested simultaneously, the probability of rejecting the null hypothesis for any motif by chance at least once increases with the number of hypotheses tested. To correct for this, we adapted the single-step min-P procedure for multiple-hypothesis adjustment C. elegans network Click here for additional data file.Figure S2C. elegans network than in any of the 100,000 randomized networks. But because there are 5,560 entries in Rank and s a  see , which i(PDF)Click here for additional data file.


The diagnosis of neuromuscular diseases is strongly based on the histological characterization of muscle biopsies. However, this morphological analysis is mostly a subjective process and difficult to quantify. We have tested if network science can provide a novel framework to extract useful information from muscle biopsies, developing a novel method that analyzes muscle samples in an objective, automated, fast and precise manner.Our database consisted of 102 muscle biopsy images from 70 individuals . We used this to develop a new method, Neuromuscular DIseases Computerized Image Analysis (NDICIA), that uses network science analysis to capture the defining signature of muscle biopsy images. NDICIA characterizes muscle tissues by representing each image as a network, with fibers serving as nodes and fiber contacts as links.P <0.00001). Importantly, our approach can be used to quantify new images without the need for prior ‘training’. Therefore, we show that network science analysis captures the useful information contained in muscle biopsies, helping the diagnosis of muscular dystrophies and neurogenic atrophies.After a ‘training’ phase with control and pathological biopsies, NDICIA was able to quantify the degree of pathology of each sample. We validated our method by comparing NDICIA quantification of the severity of muscular dystrophies with a pathologist’s evaluation of the degree of pathology, resulting in a strong correlation (R = 0.900, Our novel network analysis approach will serve as a valuable tool for assessing the etiology of muscular dystrophies or neurogenic atrophies, and has the potential to quantify treatment outcomes in preclinical and clinical trials. Neuromuscular diseases (NMD) comprise a large and heterogeneous group of disorders affecting the motor unit -3. NMD cSkeletal muscle fibers are bundled together in fascicles that are separated by the perimysium, a connective tissue sheath that conveys innervation and vascular irrigation. Each muscle fiber is in turn enclosed by a very thin band of connective tissue, the endomysium. Skeletal muscles fibers can be classified into type I (slow) or type II (fast) fibers, which are distributed in a mosaic pattern along the fascicles ,7. A traNetwork science involves the study of the generally asymmetric relationships that exist between elements that form complex systems. This approach has been used successfully to capture information from systems ranging from the Internet to social networks -20. AlthFor the retrospective analysis of human muscle tissue, we obtained images from processed biopsies stored in tissue banks at the Virgen del Rocío University Hospital (Seville), the Santa Creu i Sant Pau Hospital (Barcelona) and the Doce de Octubre Hospital (Madrid). Our database consisted of 102 images from 70 individuals. Fifty images were considered controls and came from patients who were referred to the Neuromuscular Unit of Virgen del Rocío University Hospital because of minor symptoms, such as unspecific fatigue or pain, in whom the physical examination and complete routine biopsy analysis were completely normal. Seventeen images came from adults with diverse NA and 20 images were from the quadriceps of children with either Duchenne or Becker MD  of the MD samples by following routine and specific protocols  image was used because of the high contrast that exists between muscle fibers and collagen. Considering that fibers are darker than the surrounding collagen, we searched the image for intensity valleys. Accordingly, the h-minima transform  was applℎ = ed transform may be applied to an original image as given. However, if the gradient of the original image is used, the minima in the gradient image will correspond to sites within homogeneous regions in the original image. Thus, the watershed transform is usually applied to the gradient image. The watershed algorithm yields results with substantial over-segmentation; that is, the number of segmented regions could be much larger than desired, with clearly identifiable objects or regions being broken into multiple smaller regions. This undesirable result is because the gradient image used in the process is sensitive to noise. The problem of over-segmentation can be overcome with the use of markers that identify objects. The objects’ contours in the gradient image can be seen as the highest crest-lines around the object marker. In our case, the image gradient was calculated in the G component and the internal and external markers were derived from the first step. The block diagram of Additional file For a structural analysis of the biopsy images, we formed a muscle network, where each fiber is represented as a node and two nodes are connected if two fibers are adjacent. This network was formed from the external markers, that is, from the watershed transformation directly to the binary image considered as internal markers, resulting in the first step of the segmentation process. The resulting image was a mosaic where each fiber contour reached the adjacent fiber contour.The next step concerned feature extraction. Geometric features such as the fiber area or the length of the major and minor axes of the fiber were extracted from the detected contours. Other parameters that took into account the neighboring vicinity of each fiber, such as the ratio between the fiber area and adjacent fiber areas, or the ratio between the fiber area and the area resulting from the expansion of its contour (computed in the previous step), were calculated from the muscle network. Finally, graph theory was applied to the muscle network to compute additional features.A total of 82 characteristics were computed, including 16 geometric features, 22 features derived from the muscle network, and 44 from graph theory   and the SFS is a bottom-up search procedure where one feature at a time is added to the current feature set. At each stage, the feature to be included in the feature set is selected from among the remaining available features, which have not been added to the feature set. The new enlarged feature set yields a minimum classification error compared to adding any other single feature. The algorithm stops when the addition of a new feature yields an increase of the classification error. The SBS is the top-down counterpart of the SFS method. It starts from the complete set of features and, at each stage, the feature that shows the least discriminatory power is discarded. The algorithm stops when removing another feature results in an increase of the classification error.The selection performance was evaluated by five-fold cross-validation . In thiset al.[The classifier used was the Fuzzy-ARTMAP neural network architecture developed by Carpenter et al., which iOnce the feature vector with the most discriminatory power to distinguish between the classes analyzed had been selected, it was possible to classify new biopsy images and to estimate the degree of pathology with respect to control images.The Fuzzy-ARTMAP neural network classifies new biopsies based on the selected features. Also, principal component analysis (PCA)  allows tPCA was applied to the selected feature vector. To check the vector’s performance as an indicator of the degree of pathology, the Pearson correlation coefficient was computed. This parameter provides a measure of the strength of linear dependence between two variables X and Y, giving a value between +1 and -1 inclusive. In this case, the variable X is the degree of pathology evident in the biopsies used in the training stage, which have previously been analyzed by the pathologist. The variable Y is the Euclidean distance between the pathological images and the centroid of the controls in the PCA graph.Immunohistochemical staining of the collagen network surrounding the muscle fibers (endomysium and perimysium) with anti-collagen VI antibody enabled quantification of the amount of collagen in the tissue and, at the same time, provided an outline of the muscle fibers. The muscle fiber type was identified using anti-myosin slow (type I) or anti-myosin fast (type II) specific antibodies Figure a. By appThe network and segmented images were used to extract 82 characteristics from muscle biopsies  between the degree of pathology diagnosed by the pathologist and the Euclidean distance between the MD image and the centroid of the controls in the PCA graph . First, we performed a new feature selection step using more control images to cover a wider range of age and muscle types . To the best of our knowledge, this is the largest and most comprehensive dataset of images analyzed in a neuromuscular study. Previous reports have been published of attempts to facilitate the automated extraction of geometric characteristics from muscle biopsies -16. ThesWe have shown that the characteristics chosen in the feature selection step were different for MD and NA. Using 24 characteristics, NDICIA selected one geometrical (‘A1/A2 relation’) and two network (‘average degree of neighbors’ and ‘standard deviation of the degree of neighbors’) characteristics for the identification of dystrophies. The selection of ‘A1/A2 relation’ is logical because it reflects the level of fibrosis in the biopsy, this being an important biomarker for dystrophies. However, it was surprising that the ‘degree of neighbors’ was more important than features related to the shape of the fibers. Interestingly, none of the previous characteristics  were selected when control and NA  were compared. The three network characteristics selected are related to the organization of the fiber types and were able to capture the characteristic fiber-type grouping due to secondary reinnervation events. We also obtained different selected features from the analysis of the 82 characteristics . Therefore, NDICIA selects different features that capture the specific changes that occur within a particular NMD. This modular nature of NDICIA establishes an ideal framework to be adapted to the study of any NMD. In some cases, the selection of characteristics from among the 82 that we presented here will be sufficient, whereas in others the addition of new markers to a similar underlying method will be required.The potential of NCIDIA resides also in the quantification of severity of pathologic pattern. Whereas the first 24 characteristics were designed to ‘imitate’ the parameters that the pathologist typically analyses in a biopsy, the remaining 58 network features are extremely difficult (or even impossible) to evaluate by visual inspection. Our results demonstrated that the inclusion of these network parameters first improves the quantification of the degree of pathology by dystrophies (from R = 0.865 to R = 0.900) and, second, uncovered unexpected network traits that defined the differences between control and MD patterns. These results convincingly point to the average relation neighbors major axis (27) and average strength of fast cells (41) as two new parameters important for the evaluation of MD. The first reflects the homogeneity of fiber shapes and sizes along the image, and the second is an index of fiber packing. We conclude that network characteristics could serve as a valuable tool for assessing the etiology and/or progression of a disease, and may help to further our understanding of the pathological processes that accompany NMD.We have shown here that NDICIA (at least for MD and NA) was able to quantify the differences between control and pathological samples that were not used in the feature selection step. Remarkably, the results maintained a high degree of correlation with the evaluation of the pathologist Figure c. AlthouNDICIA´s major achievement is its potential clinical application. The combination of the precise quantification and the incorporation of new samples could allow fine-tuning of the diagnosis of the pathologies analyzed here. This enables the identification of the first signs of pathology, bringing forward the onset of potential treatment. In the neuromuscular field, objectivity in the quantification of outcome measurements is a clear, fundamental demand ,32. In aART: adaptive resonance theory; MD: muscular dystrophies; NA: neurogenic atrophies; NMD: neuromuscular diseases; NDICIA: Neuromuscular DIseases Computerized Image Analysis; PCA: principal component analysis; SBS: sequential backward selection; SFS: sequential forward selectionThe authors declare that they have already registered a patent with the content of the method. We declare no further competing interest.LME conceived the study with help from AP. ER evaluated and selected the muscle biopsies with help from CP. LME and AM obtained the images. AS processed the images, wrote the software, generated the network and performed all the comparisons and statistical analyses under the supervision and help of BA and CS. All authors participated in the interpretation of results, discussion and the development of the project at all stages. ER, CP, AP, AS and LME wrote the manuscript with input from all authors. All authors read and approved the final manuscript.The pre-publication history for this paper can be accessed here:http://www.biomedcentral.com/1741-7015/11/77/prepubProcedure for analysis of muscle biopsies in the neuropathology laboratory. Muscle biopsies are processed by cryostat. A large number of slides are necessary for the different stainings, and a series of routine techniques are performed for the initial evaluation . Depending of the results of the routine panel, other more specific protocols can be applied to obtain additional information. HE, hematoxylin-eosin, PAS, periodic acid-Schiff, MG Trichrome, modified Gomori trichrome.Click here for fileMuscle biopsies and images used in this study. Information about the age and type of muscle is provided. Control muscles have been grouped according to their location  and age (child or adult).Click here for fileBlock diagram of the steps followed in the segmentation process. The diagram includes images showing the output of the different steps.Click here for fileArea: Size (in pixels) of the fiber (A2). Major Axis: Length (in pixels) of the major axis of the ellipse that has the same normalized second central moments as the fiber. Minor Axis: Length (in pixels) of the minor axis of the ellipse that has the same normalized second central moments as the fiber. Relation Axis: Ratio between the major and minor axes of each fiber. Convex Hull: Proportion of the pixels in the convex hull that are also in the fiber. Computed as area of fiber/area of the convex hull. The convex hull is the smallest convex polygon that can contain the fiber. Angles: Angle (in degrees) between the x-axis  and the major axis of the ellipse that has the same second-moments as the fiber. Relation A1/A2: Ratio between the size (in pixels) of the ‘expanded fiber’ (A1) and the size of the fiber . Neighbors: Number of neighbor fibers of a fiber. Characteristics 25 to 38 are related to the value for a geometric characteristic of a node and the average value of its neighbors. A short description is given for characteristics 39 to 82: Strength: Node strength is the sum of weights of links connected to the node, where the weight of links, in our case, is the distance in pixels between two fibers. Clustering coefficient: The fraction of triangles around a node . Eccentricity: The shortest path length between a node and any other node. Betweenness centrality: The fraction of all shortest paths in the network that contain a given node. Nodes with high values of betweenness centrality participate in a large number of shortest paths. Shortest path lengths: The distance matrix containing lengths of shortest paths between all pairs of nodes. Radius: The minimum eccentricity. Diameter: The maximum eccentricity. Efficiency: The average inverse shortest path length in a network. Pearson: The Pearson correlation reflects the degree of linear relationship between two variables (nodes and weight of links). Algebraic_connectivity: The second smallest eigenvalue of the Laplacian  according to whether vi and vj are adjacent or not). S_metric: The sum of products of degrees across all edges. Assortativity: A positive assortativity coefficient indicates that nodes tend to link to other nodes to the same or a similar degree. Density: The fraction of present connections to possible connections. Connection weights are ignored in calculations. Transitivity: The ratio of 'triangles to triplets' in the network . Modularity: A statistic that quantifies the degree to which the network may be subdivided into such clearly delineated groups.List of 82 characteristics analyzed and their values for each image. Values for the 82 characteristics of the 87 images used for the training step and the 15 other images tested. Av. = Average, s. d. = standard deviation. Characteristics 1 to 24 mimic features that the pathologist evaluates when analyzing a biopsy. The 24 characteristics can be classified into four groups: geometrically related to the size of fibers (1 to 6), geometrically related to the shape and orientation of fibers (7 to 14), geometrically related to the collagen content (15 and 16), and network characteristics (17 to 24). The network features capture information about the organization of the fibers. Click here for fileScheme showing the approach proposed in this study. We present an example for the feature selection step using the artificial neuronal network (ANN) from the characteristics (yellow circle) and two categories (A and B) of images. Green and red squares represent two groups of images. The feature selection step provides the most discriminating characteristics for this comparison (orange circle) and the classification of the images into categories A and B. The blue squares represent new images. ANN classifies them into categories A and B using the selected characteristics. Principal component analysis (PCA) allows quantification of the degree of affection of the images used for the feature selection step, and also for the new images. This quantification is performed using the same selected characteristics.Click here for file