From: Age, environment, object recognition and morphological diversity of GFAP-immunolabeled astrocytes
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: V_{d} (bifurcation) or V_{t} (trifurcation): Nodal (or branching) points. V_{p}: Terminal (or pendant) vertices. V_{a}: primary vertices connecting 2 pendant vertices; V_{b}: secondary vertices connecting 1 pendant vertex (V_{p}) to 1 bifurcation (V_{d}) or 1 trifurcation (V_{t}); V_{c}: tertiary vertices connecting either 2 bifurcations (V_{d}), 2 trifurcations (V_{t}), or 1 bifurcation (V_{d}) and 1 trifurcation (V_{t}). 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 |