Quantifiable diagnosis of muscular dystrophies and neurogenic atrophies through network analysis
1 Escuela Técnica Superior Ingeniería, Universidad de Sevilla, Seville, Spain
2 Department of Pathology, Hospital Universitario Virgen del Rocío, Seville, Spain
3 Instituto de Biomedicina de Sevilla, Hospital Universitario Virgen del Rocío/CSIC/Universidad de Sevilla, Seville, Spain
4 Neuromuscular Disease Unit, Neurology Department, Hospital Universitario Virgen del Rocío, Seville, Spain
5 Centro de Investigación Biomédica en Red de Enfermedades Neurodegenerativas (CIBERNED), Madrid, Spain
BMC Medicine 2013, 11:77 doi:10.1186/1741-7015-11-77Published: 20 March 2013
Additional file 1: Figure S1:
Procedure 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 (histochemical and histoenzymatic techniques). 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.
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Additional file 2: Table S1:
Muscle 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 (quadriceps, biceps or gastrocnemius muscle) and age (child or adult).
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Additional file 3: Figure S2:
Block diagram of the steps followed in the segmentation process. The diagram includes images showing the output of the different steps.
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Additional file 4: Table S2:
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. Area: 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 (horizontal to the image) 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 (A2, in pixels). 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 (equivalent to the fraction of a node’s neighbors that are neighbors of each other). 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 (Laplacian: degree matrix minus the adjacency. Adjacency matrix: matrix with rows and columns labeled by graph nodes, with a 1 or 0 in position (vi, vj) 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 (an alternative version of the clustering coefficient). Modularity: A statistic that quantifies the degree to which the network may be subdivided into such clearly delineated groups.
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Additional file 5: Figure S3:
Scheme 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.
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