Branched structure analysis Segment Any portion of microglial branched structure with endings that are either nodes or terminations with no intermediate nodes Segments/mm Number of segments/total length of the segments expressed in millimeters No of trees Number of trees in the astrocytes Total no of segments Refer to the total number of segments in the tree Branch length Total length of the line segments used to trace the branch of interest. Total branch length Total length for all branches in the tree Mean = [length]/[number of branches] Tortuosity =[Actual length of the segment]/[distance between the endpoints of the segment]. The smallest value is 1; this represents a straight segment. Tortuosity allows segments of different lengths to be compared in terms of the complexity of the paths they take Surface area Computed by modeling each branch as a frustum (truncated right circular cone) Tree surface area Branch volume Computed by modeling each piece of each branch as a frustum. Total branch volume Total volume for all branches in the tree Base diameter of primary branch Diameter at the start of the 1st segment Planar Angle Computed based on the endpoints of the segments. It refers to the change in direction of a segment relative to the previous segment Fractal dimension The “k-dim” of the fractal analysis, describes how the structure of interest fills space. Significant statistical differences in k-dim suggest morphological dissimilarities Convex hull-perimeter Convex hull measures the size of the branching field by interpreting a branched structure as a solid object controlling a given amount of physical space. The amount of physical space is defined in terms of convex-hull volume, surface area, area, and or perimeter Vertex analysis Describes the overall structure of a branched object based on topological and metrical properties. Root (or origin) point: For neurons, microglia or astrocytes, the origin is the point at which the structure is attached to the soma. Main types of vertices: Vd (bifurcation) or Vt (trifurcation): Nodal (or branching) points. Vp: Terminal (or pendant) vertices. Va: primary vertices connecting 2 pendant vertices; Vb: secondary vertices connecting 1 pendant vertex (Vp) to 1 bifurcation (Vd) or 1 trifurcation (Vt); Vc: tertiary vertices connecting either 2 bifurcations (Vd), 2 trifurcations (Vt), or 1 bifurcation (Vd) and 1 trifurcation (Vt). In the present report we measure the number of vertices Va, Vb and Vc Complexity Complexity = [sum of the terminal orders + number of terminals] × [total branch length/number of primary branches] Cell body Area Refers to the 2-dimensional cross-sectional area contained within the boundary of the cell body Perimeter Length of the contour representing the cell body Feret max/min Largest and smallest dimensions of the cell body as if a caliper was used to measure across the contour. The two measurements are independent of one another and not necessarily at right angles to each other Aspect ratio Aspect ratio = [min diameter]/[max diameter] Indicates the degree of flatness of the cell body Range of values is 0–1 A circle has an aspect ratio of 1 Compactness Compactness = $$\frac{{\sqrt {\left( {\frac{4}{\pi }} \right)} \times Area}}{Max Diam}$$ The range of values is 0–1 A circle is the most compact shape (compactness = 1) Convexity Convexity = [convex perimeter]/[perimeter] A completely convex object does not have indentations, and has a convexity value of 1 (e.g., circles, ellipses, and squares) Concave objects have convexity values less than 1 Contours with low convexity have a large boundary between inside and outside areas Form factor $$Form factor = 4\pi \times \frac{Area}{{perimeter^{2} }}$$ As the contour shape approaches that of a perfect circle, this value approaches a maximum of 1.0 As the contour shape flattens out, this value approaches 0 Roundness Roundness = [compactness]2 Use to differentiate objects that have small compactness values Solidity Solidity = [area]/[convex Area] The area enclosed by a ‘rubber band’ stretched around a contour is called the convex area Circles, squares, and ellipses have a solidity of 1 Indentations in the contour take area away from the convex area, decreasing the actual area within the contour