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)

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. Described in: doi:10.1002/cne.21418

Branch length

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

Branch mean radius

The average of the radii of the nodes defining a branch

Branch surface area

Estimated surface area¹ of a branch computed from treating each internode segment as a conical frustum and summing the surface area of all frusta

Branch volume

Estimated volume¹ 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 index

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: 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

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 number

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

Internode distance

The distance between nodes defining a branch or a Path

Internode distance (squared)

The squared distance between nodes defining a branch or a Path. Alternative to Internode distance when faster computations are required.

Length of inner branches

The sum of branch lengths of 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.

Length of longest shortest path

Considering a graph-theory tree, the Length of longest shortest path corresponds to the graph diameter. Note that this metric can only be computed for structures that are valid mathematical trees.

Length of primary branches

The sum of branch lengths 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.

Length of terminal branches

The sum of branch lengths of branches ending at terminal endpoints (tips)

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 metric. 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 image)

Path contraction

The ratio between the Euclidean distance of a path (i.e., Euclidean distance between the first and last node of the path) and its path length. Range of values: ]0–1[ (unitless)

Path frame

The time-lapse frane associated with a path (multidimensional image)

Path length

The sum of all internode distances in a path

Path mean radius

The average of the radii of the nodes defining a 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 area¹ of a path computed from treating each internode segment as a conical frustum and summing the surface area of all frusta

Path volume

Estimated volume¹ of a path computed from treating each internode segment as a conical frustum and summing the volume of all frusta

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.

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: Skeweness

See Skeweness 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 areas¹ of all frusta

Volume

Treating each internode segment as a conical frustum, the sum of the volume¹ 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 specialized metrics provided by dedicated SNT plugins, such as Strahler or Sholl
• Some combinations of metrics/statistics may not be meaningful: e.g., if you are only measuring a single cell, pairing cable length to SD will not be useful, since only one value has been computed. In this case, the Measurements table will append ‘[Single metric]’ to such data
• Each of the 60+ metrics is represented by five statistical properties: minimum, maximum, mean, standard deviation and sum, resulting in a total of at least \(60\times 5\) 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 (multi-channel) and images with a time-dimension (time-lapse videos). A 3D multi-channel 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

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