SNT › Metrics

Metrics

Branch contraction

A measure of straightness. The ratio between the Euclidean distance of a branch (i.e., Euclidean distance between the first and last node of the branch) and its path length. Range of values: ]0–1] (unitless). L-measure metric¹
See also: Path contraction

Branch extension angle XY

The absolute extension angle of a branch in the XY plane

Branch extension angle XZ

The absolute extension angle of a branch in the XZ plane

Branch extension angle ZY

The absolute extension angle of a branch in the ZY plane

Branch fractal dimension

Also known has Hausdorff dimension. Defined as the slope obtained from the log-log plot of Path distance vs Euclidean distance, as implemented by L-measure following the definition of Marks & Burke (2007). It is only computed for branches defined by at least five nodes. L-measure metric¹ described in: doi:10.1002/cne.21418

Branch length

The path length of a branch (i.e., the sum of all its internode distances)
See also: Path length

Branch mean radius

The average of the radii of the nodes defining a branch

Branch surface area

Estimated surface area² of a branch computed from treating each internode segment as a conical frustum and summing the surface area of all frusta

Branch volume

Estimated volume² of a branch computed from treating each internode segment as a conical frustum and summing the volume of all frusta

Cable length

The total path length of a structure, i.e., the sum of all internode distances of its paths

Complexity Indices

Complexity Indices are ratios of anatomical properties that summarize branching patterns. Typically, this type of descriptors have been created to summarize (early) neural development in vitro

Complexity index: ACI

Also known as “Axonal Complexity Index”. An index based on path orders, defined as \(\frac{\sum_{n=1}^{N} {Path\,order - 1}}{N}\), with \(N\) being the total number of paths in the reconstruction. Described in:

doi:10.1523/JNEUROSCI.4434-06.2007

Complexity index: DCI

Also known as “Dendritic Complexity Index”. An index based on the number of primary neurites, total arbor length, and the number and Strahler-order of terminal branches. Described in:

doi:10.1523/JNEUROSCI.19-22-09928.1999

Convex hull

Defined as the polygon (2D) or the polyhedron (3D) enclosing a reconstruction

Convex hull: Boundary size

The perimeter of the 2D polygon or the surface area of the 3D polyhedron of the convex hull

Convex hull: Boxivity

The extent to which the convex hull approaches a rectangle (2D) or a cuboid (3D). Range of values: 0–1 (unitless)

Convex hull: Centroid-root distance

The distance between the root of a neuronal arbor and the centroid of its convex hull

Convex hull: Elongation

The caliper (also known as Feret) diameter of the convex hull

Convex hull: Roundness

The extent to which the convex hull approaches a circle (2D) or a sphere (3D). Range of values: 0–1 (unitless)

Convex hull: Size

Either the area of the 2D polygon, or the volume of the 3D polyhedron defining the convex hull

Depth

The depth of the bounding box embedding the structure being measured

Extension angle

The overall outgrowth direction of a branch or path with at least two nodes. It is obtained from the slope of a linear regression performed across allcoordinates on either the XY, XZ, or ZY plane. Extension angles absolute or relative (rel.):

• Absolute angles are measured with respect to a fixed reference and range from [0°-360°[ under a West-clockwise convention (W: 0°; N: 90°; E: 180°; S: 270°)

• Relative (rel.) angles are measured as the acute intersection angle between the extension angle of a branch/path and the extension angle of its parent, and range between [0°-180°[. When no parent exists the relative extension angle is NaN

Height

The height of the bounding box embedding the structure being measured

Horton-Strahler bifurcation ratio

The average bifurcation ratio of Strahler bifurcation ratios

Horton-Strahler root number

The highest Horton-Strahler number of a tree, i.e., the Horton-Strahler number of its root node

Inner branches

Defined as the branches of highest Strahler order. Typically, these correspond to the most ‘internal’ branches of an arbor, in direct sequence from the root. Note that Primary branches are inner branches starting at the tree’s root
See also: Primary branches, Terminal branches

Inner branches: Extension angle XY

The absolute extension angle of inner branches in the XY plane

Inner branches: Extension angle XZ

The absolute extension angle of inner branches in the XZ plane

Inner branches: Extension angle ZY

The absolute extension angle of inner branches in the ZY plane

Inner branches: Length

The length of inner branches

Internode angle

The angle (in degrees, 0-360 range) between a node and its immediate neighbors. I.e., if node B is preceeded by node A and followed by node C, the internode angle at position B is defined as the angle between vecors AB and BC: \(\angle (\overrightarrow{AB}, \overrightarrow{BC})\)

Internode distance

The distance between nodes defining a branch or a Path. Can be retrieved as squared internode distance when faster computations are required

Longest shortest path

The longest graph geodesic. Considering a graph-theory tree, the longest shortest path corresponds to its graph diameter (also known as maximum geodesic, or longest graph geodesic). Can only be computed for structures that are valid mathematical trees.

Longest shortest path: Extension angle XY

Absolute Extension angle of longest shortest path in the XY plane

Longest shortest path: Extension angle XZ

Absolute Extension angle of longest shortest path in the XZ plane

Longest shortest path: Extension angle ZY

Absolute Extension angle of longest shortest path in the ZY plane

Longest shortest path: Length

Length of longest shortest path

Maximum geodesic

Same as Length of longest shortest path

No. of branch nodes (branch fragmentation)

The total number of nodes (and thus compartments) in a branch

No. of branch points

The total number (count) of branch points (also known as fork points)

No. of branches

The total number (count) of branches

No. of fitted paths

The total number (count) of fitted paths

No. of inner branches

The number of branches of highest Strahler order. Typically, these correspond to the most ‘internal’ branches of an arbor, in direct sequence from the root

No. of path nodes (path fragmentation)

The total number of nodes (and thus compartments) in a path

No. of paths

The total number (count) of paths defining a structure

No. of primary branches

The total number (count) of primary (or root-associated) branches. Primary branches have origin in a tree’s root, extending to the closest branch point or end-point, i.e., they are inner branches starting at the root. Note that a primary branch can also be terminal.

No. of spines/varicosities

Sum of all spine/varicosity markers in a structure

No. of spines/varicosities per path

Number of spines/varicosities associated with a path

No. of terminal branches

The total number (count) of branches ending at terminal endpoints (tips)

No. of tips

The total number (count) of terminal endpoints in a structure

No. of total nodes

The total number (count) of nodes in a structure

Node intensity values

The pixel intensity at each node location

Node radius

The radius at each node, typically obtained from fitting procedures

Partition asymmetry

L-measure metric¹. Computed at each bifurcation point of the structure being measured. Note that branch points with more than 2 children are ignored. Given \(n1, n2\) the number of tips on each side of a bifurcation point, Partition asymmetry is defined as: \(\frac{abs(n1-n2)}{(n1+n2-2)}\).

Path channel

The color channel associated with a path (multidimensional images)

Path contraction

A measure of straightness of a path. See Branch contraction for definition

Path extension angle XY

Absolute Extension angle of a path in the XY plane

Path extension angle XY (Rel.)

Relative Extension angle of a path in the XY plane

Path extension angle XZ

Absolute Extension angle of a path in the XZ plane

Path extension angle XZ (Rel.)

Relative Extension angle of a path in the XZ plane

Path extension angle ZY

Absolute Extension angle of a path in the ZY plane

Path extension angle ZY (Rel.)

Relative Extension angle of a path in the ZY plane

Path frame

The time-point associated with a path (multidimensional images)

Path length

The sum of all internode distances in a path
See also: Branch length

Path mean radius

The average of the radii of the nodes defining a traced path

Path order

See Path Order Analysis

Path spine/varicosity density

The number (count) of spine/varicosity markers associated with a path, divided by its path length

Path surface area

Estimated surface area² of a path computed from treating each internode segment as a conical frustum and summing the surface area of all frusta

Path volume

Estimated volume² of a path computed from treating each internode segment as a conical frustum and summing the volume of all frusta

Persistence diagram

See persistence homology

Persistence landscapes

See persistence homology

Primary branches

Primary branches that have origin in a tree’s root, extending to the closest branch point or end-point, i.e., inner branches starting at the root. Also known as root-associated branches. Note that a primary branch can also be terminal
See also: Inner branches, Terminal branches

Primary branches: Extension angle XY

Absolute Extension angle of primary branches in the XY plane

Primary branches: Extension angle XZ

Absolute Extension angle of primary branches in the XZ plane

Primary branches: Extension angle ZY

Absolute Extension angle of primary branches in the ZY plane

Primary branches: Length

The length of primary branches
See also: Inner branches length, Terminal branches length

Remote bif. angles

The angle between each bifurcation point and its children in the simplified graph, which comprise either branch points or terminal nodes. Note that branch points with more than 2 children are ignored. L-measure metric¹

Sholl: Decay

The Sholl regression coefficient

Sholl: Degree of Polynomial fit

The polynomial degree used to fit the Sholl profile. See Sholl › Fitting functions

Sholl: Kurtosis

See Kurtosis in Sholl › Metrics based on sampled data

Sholl: Max

See Max inters. in Sholl › Metrics based on sampled data

Sholl: Max (fitted)

See Critical value in Sholl › Metrics based on fitted data

Sholl: Max (fitted) radius

See Critical radius in Sholl › Metrics based on fitted data

Sholl: Mean

See Mean inters. in Sholl › Metrics based on sampled data

Sholl: No. maxima

The number of times Max inters. occurs in a Sholl profile. See Max inters. in Sholl › Metrics based on sampled data

Sholl: No. secondary maxima

The number of times a secondary peak occurs in a Sholl profile. See Max inters. in Sholl › Metrics based on sampled data

Sholl: Ramification index

See Schoenen Ramification index in Sholl › Metrics based on sampled data

Sholl: Skewness

See Skewness in Sholl › Metrics based on sampled data

Sholl: Sum

See Sum inters. in Sholl › Metrics based on sampled data

Surface area

Treating each internode segment as a conical frustum, the sum of the surface areas² of all frusta

Terminal branches

Branches ending at terminal endpoints (tips)
See also: Inner branches, Primary branches

Terminal branches: Extension angle XY

Absolute Extension angle of terminal branches in the XY plane

Terminal branches: Extension angle XZ

Absolute Extension angle of terminal branches in the XZ plane

Terminal branches: Extension angle ZY

Absolute Extension angle of terminal branches in the ZY plane

Terminal branches: Length

The sum of branch lengths of branches ending at terminal endpoints (tips)
See also: Inner branches length, Primary branches length

TMD

Topological Morphology Descriptor. See persistence homology analysis

Volume

Treating each internode segment as a conical frustum, the sum of the volume² of all frusta

Width

The width of the bounding box embedding the structure being measured

X,Y,Z coordinates

Cartesian coordinates in the three-dimensional space

Notes

• This list does not include all of the specialized metrics provided by dedicated modules, such as Strahler, Sholl, Persistence diagrams/landscapes, or Graph-based analysis

• Some combinations of metrics/statistics may not be meaningful: e.g., when measuring a single cell, pairing cable length to SD will not be useful, since only one cable length value can be computed. In such cases, the Measurements table appends ‘[Single metric]’ to such data

• Each of the 90+ metrics is represented by five statistical properties: minimum, maximum, mean, standard deviation and sum, resulting in a total of at least \(90\times 5\) features. Note that there is an intrinsic redundancy between these features: E.g., for a given cell, retrieving Branch length’s N is effectively the same as retrieving No. of branches

• NaN values for a reported metric typically reflect undefined operations (e.g., division by zero), or the fact that the reconstruction being parsed is not a valid mathematical tree

• Currently, volume-related metrics do not take into account path fillings

Group Statistics

SNT assembles comparison reports and simple statistical reports (two-sample t-test/one-way ANOVA) for up to six groups of cells. This is described in Comparing Reconstructions. Descriptive statistics of measurements can be obtained by running Summarize Existing Results in the Measurements dialog or by running Frequency/Distribution Analysis commands.

Glossary

Mesh

A polygon mesh defines the shape of a three-dimensional polyhedral object. In neuronal anatomy, meshes define neuropil annotations, typically compartments of a reference brain atlas (e.g., the hippocampal formation in mammals, or mushroom bodies in insects)

Multi-dimensional image

An image with more than 3 dimensions (3D). Examples include fluorescent images associated with multiple fluorophores (multichannel) and images with a time-dimension (time-lapse videos). A 3D multichannel timelapse has 5 dimensions

Neurite

Same as neuronal process. Either an axon or a dendrite

Path

Can be defined as a sequence of branches, starting from soma or a branch point until a termination. In manual and assisted (semi-automated) tracing, neuronal arbors are traced using paths, not branches. Fitting algorithms that take into account voxel intensities can be used to refine the center-line coordinates of a path, typically to obtain more accurate curvatures. Fitting procedures can also be used to estimate the volume of the neurite(s) associated with a path

(Neuronal) morphometry

Quantification of neuronal morphology

Neuropil

Any area in the nervous system. The cellular tissue around neuronal processes

Out-of-core

Software with out-of-core capabilities is able to process data that is too large to fit into a computer’s main memory. SNT supports out-of-core tracing via scripting.

Reconstruction

See Tracing

ROI

Region of Interest. Define specific parts of an image to be processed in image processing routines

Skeleton

A thinned version of a digitize shape (such as a neuronal reconstruction) or of a binary image

Tracing

A digital reconstruction of a neuron or neurite. The term predates computational neuroscience and reflects the manual ‘tracing’ on paper performed with camera lucida devices by early neuroanatomists

Volume rendering

A visualization technique for displaying image volumes (3D images) directly as 3D objects