This page has definitions for measurements found in the General tab of the Measurements window. The Measurements window is accessed through the Measurement Tool icon in the Spreadsheet. The Object Classifier and some recipes automatically generate Advanced Measurements, and the equations for such measurements are shown in the Advanced tab of the Measurements window. Custom measurements can also be added, removed, and edited in the Advanced tab. Colocalization measurements can be added in the Colocal tab.
Outline
Outlines are 2D objects defined by closed sets of line segments.
Type: Morphology, Per Time Point Aspect Ratio is the ratio of the height of the object’s bounding box to the width of the object’s bounding box.   Type: Morphology, Per Time Point Bounding Height is the extent in Y of the object’s bounding box.
Type: Morphology, Per Time Point Bounding Width is the extent in X of the object’s bounding box.
Type: Morphology, Per Time Point Breadth is the length of the minor axis of a best-fit ellipse for the object.
 Type: Morphology, Per Time Point Circularity is a measure of how circular an object is and is defined by the equation below. The circularity of a circle is one (1).  Type: Intensity, Per Time Point Coefficient of Variation is the ratio of the standard deviation of the intensity of a given channel in the pixel-based area encompassed by the object to the mean intensity of the same channel and area. Outlines are pixelated using a custom algorithm that is derived from Bresenham’s line algorithm [1] as well as a filling algorithm. The image channel for the measurement is indicated in the measurement name; for example, the Coefficient of Variation for a channel named “GFP” is called “Coefficient of Variation (GFP)” or “Coefficient of Variation - GFP.”  Type: Morphology, Per Time Point Length is the length of the major axis of a best-fit ellipse for the object.
Type: Morphology, Per Time Point Length/Breadth Ratio is the ratio of the length of the major axis to the length of the minor axis of a best-fit ellipse for the object.
Type: Intensity, Per Time Point Mean Intensity is the mean intensity of a given channel in the area encompassed by the object. Sub-pixel estimation is used to calculate Mean Intensity. The image channel for the measurement is indicated in the measurement name; for example, the Mean Intensity for a channel named “GFP” is called “Mean Intensity (GFP)” or “Mean Intensity - GFP.”  Type: Morphology, Per Time Point Object Angle is the angle between the major axis of an ellipse that is fit to the object and the x-axis. In the example below, the Object Angle is dθ.
 Type: Intensity, Per Time Point Total Intensity is the sum of all intensities for a given channel in the area encompassed by the object with sub-pixel estimation. Sub-pixel estimation is done using a sample of intensities along the outer edge of the outline with the equations below, where nv is the number of vertices the outline has along its outer edge, I(x, y) is the intensity of the pixel at the uncalibrated location (x, y), and (xi, yi) is the uncalibrated location of vertex i. The image channel for the measurement is indicated in the measurement name; for example, the Total Intensity for a channel named “GFP” is called “Total Intensity (GFP)” or “Total Intensity - GFP.”   |
Whole image outline
Whole image outlines may be composed of separate, closed 2D shapes on multiple image frames that are grouped as one object in Aivia. Whole image outlines are generated by the Wound Healing recipe.
Type: Intensity, Per Time Point Outline Whole Image Mean Intensity is the mean intensity of a given channel in the area encompassed by all outlines making up the object on the current frame with sub-pixel accuracy. The image channel for the measurement is indicated in the measurement name; for example, the Outline Whole Image Mean Intensity for a channel named “GFP” is called “Outline Whole Image Mean Intensity (GFP)” or “Outline Whole Image Mean Intensity - GFP.”  Type: Morphology, Per Time Point Whole Image Circularity is a measure of how circular the object is and is defined by the equation below. The circularity of a circle is one (1).  Type: Intensity, Per Time Point Whole Image Coefficient of Variation is the ratio of the standard deviation of the intensity of a given channel in the pixel-based area encompassed by all outlines making up the object on the current frame to the mean intensity of the same channel and area. Outlines are pixelated using a custom algorithm that is derived from Bresenham’s line algorithm [1] as well as a filling algorithm. The image channel for the measurement is indicated in the measurement name; for example, the Whole Image Coefficient of Variation for a channel named “GFP” is called “Whole Image Coefficient of Variation (GFP)” or “Whole Image Coefficient of Variation - GFP.”  Type: Intensity, Per Time Point Whole Image Total Intensity is the total intensity of a given channel in the area encompassed by all outlines making up the object on the current frame with sub-pixel accuracy. The image channel for the measurement is indicated in the measurement name; for example, the Whole Image Total Intensity for a channel named “GFP” is called “Whole Image Total Intensity (GFP)” or “Whole Image Total Intensity - GFP.”  Type: Morphology, Per Time Point Wound Closure Speed is the rate at which the percentage of the image area that is not covered by the object is changing based on the areas covered on the current and previous frames according to the equation below, where Δt is the time between frames.  |
Mesh
Meshes are 3D objects defined by closed sets of triangles.
Type: Morphology, Per Time Point Bounding Depth is the depth (extent in Z) of the object’s bounding box.  Type: Morphology, Per Time Point Bounding Height is the height (extent in Y) of the object’s bounding box. Type: Morphology, Per Time Point Bounding Width is the width (extent in X) of the object’s bounding box. Type: Morphology, Per Time Point Equivalent Spherical Diameter is the diameter of a sphere that is fit to the mesh.  Type: Morphology, Per Time Point Sphericity is a measure of how round the mesh is based on the relationship between the Surface Area and Volume and is calculated using the equation below.  Type: Morphology, Per Time Point Surface Area to Volume Ratio is the ratio of the Surface Area to the Volume of the mesh.  |
Track
Track sets can either be made up of tracked outlines or tracked meshes; tracked outlines (2D tracks) can have all outline measurements in addition to track measurements, and tracked meshes (3D tracks) can have all mesh measurements in addition to track measurements. Tracks that have lineages (parent/child tracks) can also have lineage measurements.
Type: Morphology, Per Time Point Acceleration Angle is the planar angle between the acceleration vector and the x-axis in degrees. The acceleration vector for the object is estimated using the object’s current position, position at the two (2) previous time points, and the time between frames (Δt). This measurement is empty on the first two (2) time points of a track.   Type: Position, Per Time Point Acceleration Magnitude is the magnitude of the acceleration vector for the object, which is estimated using the object’s current position, position at the two (2) previous time points, and the time between frames (Δt) with the equations below. This measurement is empty on the first two (2) time points of a track but uses the position of the parent track(s) if there were any lineage splits between the current frame and two (2) frames prior.  
Type: Morphology, Per Time Point The Curvature of a track at a certain time point is the reciprocal of the radius of the best-fit circle/sphere at that time point. In Aivia, Curvature (Κ) is calculated using the equation below, where dθ is the change in the Velocity Angle between the current and previous time points in radians; dx, dy, and dz are the changes in the x-, y-, and z-coordinates respectively of the detected object between the current and previous time points; and dt is the time between frames.   Type: Morphology, Per Time Point The Diffusion Coefficient is a proportionality constant between the flux due to diffusion and the driving force for that diffusion, which is typically concentration. The Diffusion Coefficient (D) is calculated using the equation below, where t0 is the time when the track first appears. The Diffusion Coefficient is not calculated for the first time point in which the track is present.  Type: Morphology, Per Time Point Direct Line Length is the Euclidean distance between where the object was when the track first appeared and where the object is at the current time point. Direct Line Length is not calculated for the first time point in which the track is present. In the figure below, Direct Line Length at time t is the distance a.    Type: Position, Per Time Point Direct Line Velocity depends on the object’s current position, the object’s position at the time when its track first appears, and the amount of time that the track has existed up to the current time. Direct Line Velocity is calculated according to the equation below, where t0 is the time when the track first appears. As with Direct Line Length, Direct Line Velocity is not calculated for the first time point in which the track is present.  Type: Position, Per Time Point Direct Line Velocity Squared is the square of the velocity of the object based on the object’s current position, the object’s position at the time when its track first appears, and the amount of time that the track has existed up to the current time. Direct Line Velocity is calculated according to the equation below, where t0 is the time when the track first appears. Direct Line Velocity Squared is not calculated for the first time point in which the track is present.  Type: Morphology, Per Time Point Instantaneous Directedness is the cosine of the Velocity Angle (θ at time t in the figure below) and is calculated using the equation below. Velocity Angle is measured in degrees relative to the x-axis.   Type: Position, Per Time Point Mean Square Displacement is the mean of the squared displacements from the position of the track at its earliest time point to it position at each time point up to the current time point. In the equation below, n0 is equal to the First Frame of the track and nc is the current frame number.  Type: Position, Over All Time Mean Velocity is the Path Length (a+b+c+d+e for the example shown below) divided by the total time that the track exists.
Type: Morphology, Over All Time Overall Directedness is the cosine of the Straight Line Velocity Angle (θ in the figure below).   Type: Morphology, Over All Time Path Length is the distance traveled by the object along its trajectory over the entire duration of the track. Path Length is calculated as the sum of the Euclidean distances between the object’s positions at sequential time points, which is a+b+c+d+e for the example shown below.
Type: Morphology, Over All Time Straight Line Velocity Angle is the angle of the object’s velocity based on the object’s position on the first and last frames of its track. Straight Line Velocity Angle is the planar angle between the straight line velocity vector and the x-axis in degrees. In the example below, the Straight Line Velocity Angle is θ.
Type: Morphology, Over All Time Tortuosity is a measure of twist in the track calculated as the Path Length (a+b+c+d+e for the example below) divided by the Euclidean distance between the endpoints of the track (f for the example below).
Type: Position, Over All Time Track Straight Line Velocity is the object’s velocity based on the object’s position on the first and last frames of its track and the duration of its track. Track Straight Line Velocity is the Euclidean distance between the endpoints of the track (a in the example below) divided by the Total Time of the track.
   Type: Morphology, Per Time Point Velocity Angle is the planar angle between the velocity vector at the current time point, which is estimated using the object's position at the current and previous time points and the time between frames (Δt), and the x-axis in degrees. This measurement is empty on the first time point of a track. In the example below, the Velocity Angle at time t is θ.
 Type: Position, Per Time Point Velocity Magnitude is the magnitude of the velocity vector at the current time point, which is estimated using the object's position at the current and previous time points and the time between frames (Δt). This measurement is empty on the first time point of a track but uses the position of the parent track if there was a lineage split between the current and previous frames.  Type: Position, Over All Time Velocity Magnitude Variation is the variation in Velocity Magnitude over the duration of the track.  |
Lineage
Lineage measurements are for tracks that have parents and/or children and are not calculated for tracks that are not part of lineages.
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Neuron
Neurons are made up of up to four (4) basic components: somas, dendrite segments, spine heads, and spine necks.
Neuron
Neuron measurements are available for neuron objects with somas.
Type: Morphology, Per Time Point Fractal Dimension is the slope of the linear regression line for the log-log plot of Total Path Length vs. Straight Center Line Length (Euclidean distance between endpoints) for all dendrite segments making up the neuron.  Type: Position, Per Time Point Max Dendrite Branch Euclidean Distance To Root is the maximum of the dendrite-branch-Euclidean-distance-to-root measurements for all dendrite segments belonging to the neuron. The dendrite branch Euclidean distance to root for a dendrite segment is the Euclidean distance from the endpoint of the dendrite segment, which is either a terminal point or a bifurcation point, to the root point (dendrite point that is connected to the soma) of the dendrite tree to which the dendrite segment belongs. In the example below, the dendrite branch Euclidean distance to root for “Dendrite Segment 3” is a.
Type: Count, Per Time Point Max Dendrite Branch Generation is the highest number of generations in a lineage from a dendrite segment back to its or its ancestor’s connection to the soma for the entire neuron. A dendrite segment that is directly connected to the soma has a dendrite branch generation of zero (0). In the example below, dendrite segments are color-coded by their generation, which is given in the same color.
Type: Morphology, Per Time Point Max Dendrite Branch Local Bifurcation Angle is the maximum dendrite branch local bifurcation angle for all bifurcations in the neuron. Dendrite branch local bifurcation angle is the angle formed by the bifurcation point and the two dendrite points (one on each child dendrite segment) that are directly connected to the bifurcation point. This angle is given in degrees and is represented by θ in the figure below.
Type: Morphology, Per Time Point Max Dendrite Branch Partition Asymmetry is the maximum dendrite branch partition asymmetry of all dendrite segments belonging to the neuron. Dendrite branch partition asymmetry is a measure of dendrite tree asymmetry that is based on the number of terminal points in each sub-tree extending from a bifurcation point. Dendrite branch partition asymmetry is calculated for each dendrite segment using the equation below, where T1 is the number of terminal points in the first sub-tree and T2 is the number of terminal points in the second sub-tree. For the example below the equation, the left sub-tree extending from “Dendrite Segment 2” has two (2) terminal points (circled in blue), while the right sub-tree has three (3) terminal points (circled in red); letting the left sub-tree be considered the first sub-tree and the right sub-tree be considered the second sub-tree, T1 is 2 and T2 is 3 for “Dendrite Segment 2.”   Type: Morphology, Per Time Point Max Dendrite Branch Path Length is the longest Total Path Length of a dendrite segment in the neuron. Total Path Length for a dendrite segment is the sum of all Euclidean distances between adjacent dendrite points (nodes) making up the dendrite segment.  Type: Morphology, Per Time Point Max Dendrite Branch Path Length To Root is the maximum dendrite branch path length to root for all dendrite segments belonging to the neuron and is equal to the maximum Longest Path Length of all dendrite trees belonging to the neuron. Dendrite branch path length to root for a dendrite segment is the path length from the endpoint of the dendrite segment back to its or its ancestor’s connection to the soma: it is the sum of the Total Path Lengths of the dendrite segment, its parent dendrite segment, its grandparent dendrite segment, and so on back to the root (ancestor that is directly connected to the soma). In the figure below, the dendrite branch path length to root for “Dendrite Segment 3” is represented by the length a.
 Type: Morphology, Per Time Point Max Dendrite Branch Ralls' Ratio is the maximum of the Ralls' ratios at each bifurcation in the neuron. Ralls' ratio at a bifurcation is calculated according to the equation below, where da is the diameter of the dendrite point that is connected to the bifurcation point on one of the child segments, db is the diameter of the dendrite point that is connected to the bifurcation point on the other child segment, and dp is the diameter of the bifurcation point on the parent segment.  Type: Morphology, Per Time Point Max Dendrite Branch Remote Bifurcation Angle is the maximum of the dendrite branch remote bifurcation angles for all bifurcations belonging to the neuron. Dendrite branch remote bifurcation angle is the angle formed by the bifurcation point and the endpoints of the two (2) child dendrite segments extending from the bifurcation point. This angle is given in degrees and is represented by θ in the example below.
 Type: Position, Per Time Point Mean Dendrite Branch Euclidean Distance To Root is the mean of the dendrite-branch-Euclidean-distance-to-root measurements for all dendrite segments belonging to the neuron. The dendrite branch Euclidean distance to root for a dendrite segment is the Euclidean distance from the endpoint of the dendrite segment, which is either a terminal point or a bifurcation point, to the root point (dendrite point that is connected to the soma) of the dendrite tree to which the dendrite segment belongs. In the example below, the dendrite branch Euclidean distance to root for “Dendrite Segment 3” is a.
Type: Count, Per Time Point Mean Dendrite Branch Generation is the mean dendrite branch generation of all dendrite segments belonging to the neuron. A dendrite segment that is directly connected to the soma has a dendrite branch generation of zero (0). In the example below, dendrite segments are color-coded by their generation, which is given in the same color.
Type: Morphology, Per Time Point Mean Dendrite Branch Local Bifurcation Angle is the mean dendrite branch local bifurcation angle for all bifurcations in the neuron. Dendrite branch local bifurcation angle is the angle formed by the bifurcation point and the two dendrite points (one on each child dendrite segment) that are directly connected to the bifurcation point. This angle is given in degrees and is represented by θ in the figure below.
Type: Morphology, Per Time Point Mean Dendrite Branch Partition Asymmetry is the mean of the dendrite branch partition asymmetries of all dendrite segments belonging to the neuron. Dendrite branch partition asymmetry is a measure of dendrite tree asymmetry that is based on the number of terminal points in each sub-tree extending from a bifurcation point. Dendrite branch partition asymmetry is calculated for each dendrite segment using the equation below, where T1 is the number of terminal points in the first sub-tree and T2 is the number of terminal points in the second sub-tree. For the example below the equation, the left sub-tree extending from “Dendrite Segment 2” has two (2) terminal points (circled in blue), while the right sub-tree has three (3) terminal points (circled in red); letting the left sub-tree be considered the first sub-tree and the right sub-tree be considered the second sub-tree, T1 is 2 and T2 is 3 for “Dendrite Segment 2.” Type: Morphology, Per Time Point Mean Dendrite Branch Path Length is the mean of the Total Path Lengths of all dendrite segments belonging to the neuron. Total Path Length for a dendrite segment is the sum of all Euclidean distances between adjacent dendrite points (nodes) making up the dendrite segment. Type: Morphology, Per Time Point Mean Dendrite Branch Path Length To Root is the mean dendrite branch path length to root for all dendrite segments belonging to the neuron. Dendrite branch path length to root for a dendrite segment is the path length from the endpoint of the dendrite segment back to its or its ancestor’s connection to the soma: it is the sum of the Total Path Lengths of the dendrite segment, its parent dendrite segment, its grandparent dendrite segment, and so on back to the root (ancestor that is directly connected to the soma). In the figure below, the dendrite branch path length to root for “Dendrite Segment 3” is represented by the length a.
Type: Morphology, Per Time Point Mean Dendrite Branch Ralls' Ratio is the mean of the Ralls' ratios at each bifurcation in the neuron. Ralls' ratio at a bifurcation is calculated according to the equation below, where da is the diameter of the dendrite point that is connected to the bifurcation point on one of the child segments, db is the diameter of the dendrite point that is connected to the bifurcation point on the other child segment, and dp is the diameter of the bifurcation point on the parent segment. Type: Morphology, Per Time Point Mean Dendrite Branch Remote Bifurcation Angle is the mean of the dendrite branch remote bifurcation angles for all bifurcations in the neuron. Dendrite branch remote bifurcation angle is the angle formed by the bifurcation point and the endpoints of the two (2) child dendrite segments extending from the bifurcation point. This angle is given in degrees and is represented by θ in the example below.
Type: Position, Per Time Point Min Dendrite Branch Euclidean Distance To Root is the minimum of the dendrite-branch-Euclidean-distance-to-root measurements for all dendrite segments belonging to the neuron. The dendrite branch Euclidean distance to root for a dendrite segment is the Euclidean distance from the endpoint of the dendrite segment, which is either a terminal point or a bifurcation point, to the root point (dendrite point that is connected to the soma) of the dendrite tree to which the dendrite segment belongs. In the example below, the dendrite branch Euclidean distance to root for “Dendrite Segment 3” is a.
Type: Count, Per Time Point Min Dendrite Branch Generation is the smallest number of generations in a lineage from a dendrite segment back to its or its ancestor’s connection to the soma for the entire neuron. A dendrite segment that is directly connected to the soma has a dendrite branch generation of zero (0). In the example below, dendrite segments are color-coded by their generation, which is given in the same color.
Type: Morphology, Per Time Point Min Dendrite Branch Local Bifurcation Angle is the minimum dendrite branch local bifurcation angle for all bifurcations in the neuron. Dendrite branch local bifurcation angle is the angle formed by the bifurcation point and the two dendrite points (one on each child dendrite segment) that are directly connected to the bifurcation point. This angle is given in degrees and is represented by θ in the figure below.
Type: Morphology, Per Time Point Min Dendrite Branch Partition Asymmetry is the minimum of the dendrite branch partition asymmetries of all dendrite segments belonging to the neuron. Dendrite branch partition asymmetry is a measure of dendrite tree asymmetry that is based on the number of terminal points in each sub-tree extending from a bifurcation point. Dendrite branch partition asymmetry is calculated for each dendrite segment using the equation below, where T1 is the number of terminal points in the first sub-tree and T2 is the number of terminal points in the second sub-tree. For the example below the equation, the left sub-tree extending from “Dendrite Segment 2” has two (2) terminal points (circled in blue), while the right sub-tree has three (3) terminal points (circled in red); letting the left sub-tree be considered the first sub-tree and the right sub-tree be considered the second sub-tree, T1 is 2 and T2 is 3 for “Dendrite Segment 2.” Type: Morphology, Per Time Point Min Dendrite Branch Path Length is the Total Path Length of the dendrite segment that has the shortest Total Path Length for the whole neuron. Total Path Length for a dendrite segment is the sum of all Euclidean distances between adjacent dendrite points (nodes) making up the dendrite segment. Type: Morphology, Per Time Point Min Dendrite Branch Path Length To Root is the minimum dendrite branch path length to root for all dendrite segments belonging to the neuron and is equal to the minimum Shortest Path Length of all dendrite trees belonging to the neuron. Dendrite branch path length to root for a dendrite segment is the path length from the endpoint of the dendrite segment back to its or its ancestor’s connection to the soma: it is the sum of the Total Path Lengths of the dendrite segment, its parent dendrite segment, its grandparent dendrite segment, and so on back to the root (ancestor that is directly connected to the soma). In the figure below, the dendrite branch path length to root for “Dendrite Segment 3” is represented by the length a.
Type: Morphology, Per Time Point Min Dendrite Branch Ralls' Ratio is the minimum of the Ralls' ratios at each bifurcation in the neuron. Ralls' ratio at a bifurcation is calculated according to the equation below, where da is the diameter of the dendrite point that is connected to the bifurcation point on one of the child segments, db is the diameter of the dendrite point that is connected to the bifurcation point on the other child segment, and dp is the diameter of the bifurcation point on the parent segment. Type: Morphology, Per Time Point Min Dendrite Branch Remote Bifurcation Angle is the minimum of the dendrite branch remote bifurcation angles for all bifurcations in the neuron. Dendrite branch remote bifurcation angle is the angle formed by the bifurcation point and the endpoints of the two (2) child dendrite segments extending from the bifurcation point. This angle is given in degrees and is represented by θ in the example below.
Type: Position, Per Time Point Soma Skewness Euclidean Distance is the Euclidean distance between the Centroid of the soma and the Centroid of the entire neuron.     Type: Position, Per Time Point Soma Skewness X is the difference between the x-coordinate of the Centroid of the soma and the x-coordinate of the Centroid of the entire neuron. Type: Position, Per Time Point Soma Skewness Y is the difference between the y-coordinate of the Centroid of the soma and the y-coordinate of the Centroid of the entire neuron. Type: Position, Per Time Point Soma Skewness Z is the difference between the z-coordinate of the Centroid of the soma and the z-coordinate of the Centroid of the entire neuron. Type: Position, Per Time Point Std Dev Dendrite Branch Euclidean Distance To Root is the standard deviation of the dendrite-branch-Euclidean-distance-to-root measurements for all dendrite segments belonging to the neuron. The dendrite branch Euclidean distance to root for a dendrite segment is the Euclidean distance from the endpoint of the dendrite segment, which is either a terminal point or a bifurcation point, to the root point (dendrite point that is connected to the soma) of the dendrite tree to which the dendrite segment belongs. In the example below, the dendrite branch Euclidean distance to root for “Dendrite Segment 3” is a.
Type: Count, Per Time Point Std Dev Dendrite Branch Generation is the standard deviation of the dendrite branch generations of all dendrite segments belonging to the neuron. A dendrite segment that is directly connected to the soma has a dendrite branch generation of zero (0). In the example below, dendrite segments are color-coded by their generation, which is given in the same color.
Type: Morphology, Per Time Point Std Dev Dendrite Branch Local Bifurcation Angle is the standard deviation of the dendrite branch local bifurcation angles for all bifurcations in the neuron. Dendrite branch local bifurcation angle is the angle formed by the bifurcation point and the two dendrite points (one on each child dendrite segment) that are directly connected to the bifurcation point. This angle is given in degrees and is represented by θ in the figure below.
Type: Morphology, Per Time Point Std Dev Dendrite Branch Partition Asymmetry is the standard deviation of the dendrite branch partition asymmetries of all dendrite segments belonging to the neuron. Dendrite branch partition asymmetry is a measure of dendrite tree asymmetry that is based on the number of terminal points in each sub-tree extending from a bifurcation point. Dendrite branch partition asymmetry is calculated for each dendrite segment using the equation below, where T1 is the number of terminal points in the first sub-tree and T2 is the number of terminal points in the second sub-tree. For the example below the equation, the left sub-tree extending from “Dendrite Segment 2” has two (2) terminal points (circled in blue), while the right sub-tree has three (3) terminal points (circled in red); letting the left sub-tree be considered the first sub-tree and the right sub-tree be considered the second sub-tree, T1 is 2 and T2 is 3 for “Dendrite Segment 2.” Type: Morphology, Per Time Point Std Dev Dendrite Branch Path Length is the standard deviation of the Total Path Lengths of all dendrite segments belonging to the neuron. Total Path Length for a dendrite segment is the sum of all Euclidean distances between adjacent dendrite points (nodes) making up the dendrite segment. Type: Morphology, Per Time Point Std Dev Dendrite Branch Path Length To Root is the standard deviation of the dendrite-branch-path-length-to-root measurements for all dendrite segments belonging to the neuron. Dendrite branch path length to root for a dendrite segment is the path length from the endpoint of the dendrite segment back to its or its ancestor’s connection to the soma: it is the sum of the Total Path Lengths of the dendrite segment, its parent dendrite segment, its grandparent dendrite segment, and so on back to the root (ancestor that is directly connected to the soma). In the figure below, the dendrite branch path length to root for “Dendrite Segment 3” is represented by the length a.
Type: Morphology, Per Time Point Std Dev Dendrite Branch Ralls' Ratio is the standard deviation of the Ralls' ratios at each bifurcation in the neuron. Ralls' ratio at a bifurcation is calculated according to the equation below, where da is the diameter of the dendrite point that is connected to the bifurcation point on one of the child segments, db is the diameter of the dendrite point that is connected to the bifurcation point on the other child segment, and dp is the diameter of the bifurcation point on the parent segment. Type: Morphology, Per Time Point Std Dev Dendrite Branch Remote Bifurcation Angle is the standard deviation of the dendrite branch remote bifurcation angles for all bifurcations in the neuron. Dendrite branch remote bifurcation angle is the angle formed by the bifurcation point and the endpoints of the two (2) child dendrite segments extending from the bifurcation point. This angle is given in degrees and is represented by θ in the example below.
Type: Position, Per Time Point Total Dendrite Branch Euclidean Distance To Root is the sum of the dendrite-branch-Euclidean-distance-to-root measurements for all dendrite segments belonging to the neuron. The dendrite branch Euclidean distance to root for a dendrite segment is the Euclidean distance from the endpoint of the dendrite segment, which is either a terminal point or a bifurcation point, to the root point (dendrite point that is connected to the soma) of the dendrite tree to which the dendrite segment belongs. In the example below, the dendrite branch Euclidean distance to root for “Dendrite Segment 3” is a.
Type: Count, Per Time Point Total Dendrite Branch Generation is the sum of the dendrite branch generations of all dendrite segments belonging to the neuron. A dendrite segment that is directly connected to the soma has a dendrite branch generation of zero (0). In the example below, dendrite segments are color-coded by their generation, which is given in the same color.
Type: Morphology, Per Time Point Total Dendrite Branch Local Bifurcation Angle is the sum of the dendrite branch local bifurcation angles for all bifurcations in the neuron. Dendrite branch local bifurcation angle is the angle formed by the bifurcation point and the two dendrite points (one on each child dendrite segment) that are directly connected to the bifurcation point. This angle is given in degrees and is represented by θ in the figure below.
Type: Morphology, Per Time Point Total Dendrite Branch Partition Asymmetry is the sum of the dendrite branch partition asymmetries of all dendrite segments belonging to the neuron. Dendrite branch partition asymmetry is a measure of dendrite tree asymmetry that is based on the number of terminal points in each sub-tree extending from a bifurcation point. Dendrite branch partition asymmetry is calculated for each dendrite segment using the equation below, where T1 is the number of terminal points in the first sub-tree and T2 is the number of terminal points in the second sub-tree. For the example below the equation, the left sub-tree extending from “Dendrite Segment 2” has two (2) terminal points (circled in blue), while the right sub-tree has three (3) terminal points (circled in red); letting the left sub-tree be considered the first sub-tree and the right sub-tree be considered the second sub-tree, T1 is 2 and T2 is 3 for “Dendrite Segment 2.” Type: Morphology, Per Time Point Total Dendrite Branch Path Length is the sum of the Total Path Lengths of all dendrite segments belonging to the neuron. Total Path Length for a dendrite segment is the sum of all Euclidean distances between adjacent dendrite points (nodes) making up the dendrite segment. Type: Morphology, Per Time Point Total Dendrite Branch Path Length To Root is the sum of the dendrite-branch-path-length-to-root measurements for all dendrite segments belonging to the neuron. Dendrite branch path length to root for a dendrite segment is the path length from the endpoint of the dendrite segment back to its or its ancestor’s connection to the soma: it is the sum of the Total Path Lengths of the dendrite segment, its parent dendrite segment, its grandparent dendrite segment, and so on back to the root (ancestor that is directly connected to the soma). In the figure below, the dendrite branch path length to root for “Dendrite Segment 3” is represented by the length a.
Type: Morphology, Per Time Point Total Dendrite Branch Ralls' Ratio is the sum of the Ralls' ratios at each bifurcation in the neuron. Ralls' ratio at a bifurcation is calculated according to the equation below, where da is the diameter of the dendrite point that is connected to the bifurcation point on one of the child segments, db is the diameter of the dendrite point that is connected to the bifurcation point on the other child segment, and dp is the diameter of the bifurcation point on the parent segment. Type: Morphology, Per Time Point Total Dendrite Branch Remote Bifurcation Angle is the sum of the dendrite branch remote bifurcation angles for all bifurcations in the neuron. Dendrite branch remote bifurcation angle is the angle formed by the bifurcation point and the endpoints of the two (2) child dendrite segments extending from the bifurcation point. This angle is given in degrees and is represented by θ in the example below.
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Dendrite
Dendrites inherit all mesh measurements and have a few additional measurements, which are listed in the expandable panel below. Dendrite measurements are available for whole dendrites trees in the Dendrite Trees tab of the Spreadsheet and for individual dendrite segments in the Dendrite Segments tab of the Spreadsheet. Dendrite segments are composed of sets of dendrite points (nodes), which are defined in 3D space by their location and diameter.
Type: Count, Per Time Point For dendrite trees, Bifurcation Count is the number of bifurcations, or branch points, in the dendrite tree. For dendrite segments, Bifurcation Count is the number of bifurcations in the dendrite segment’s sub-trees plus 0.5 for the bifurcation at the end the dendrite segment; if the dendrite segment has no children, the Bifurcation Count is zero (0). In the example below, the Bifurcation Count for “Dendrite Segment 2” is 3.5 since “Dendrite Segment 2” has three (3) bifurcations in its sub-trees (circled in red) and a bifurcation at its end (circled in orange). The dendrite tree in the example below has a Bifurcation Count of five (5).
 Type: Morphology, Per Time Point Branch Angle is the local bifurcation angle for the dendrite segment, which is the smallest planar angle between vectors extending from the bifurcation point to dendrite points on each child segment that are directly connected to the bifurcation point. This angle is given in degrees and is represented by θ for “Dendrite Segment 1” in the figure below. This measurement is empty for dendrite segments that do not have children as well as for dendrite trees.
 Type: Count, Per Time Point For a dendrite segment, Branch Order is the generation of the segment: the Branch Order of the root segment is zero (0), the Branch Order of the root segment’s children is one (1), the Branch Order of the root segment’s grandchildren is two (2), and so on. In the example below, dendrite segments are color-coded by their Branch Order, which is given in the same color. Branch Order is always zero (0) for dendrite trees.
Type: Morphology, Per Time Point Longest Path Length for a dendrite tree is the longest path length from the root node to the end of a terminal branch. For dendrite segments, Longest Path Length is equal to Shortest Path Length, and both are equal to the sum of the Total Path Length of the dendrite segment and the Total Path Lengths of each of its ancestors back to the root segment.
 Type: Count, Per Time Point For dendrite trees, Max Child Branch Order is the highest Branch Order, or generation, of a dendrite segment in the dendrite tree. For dendrite segments, Max Child Branch Order is the highest Branch Order of a dendrite segment in either of the segment’s sub-trees; if a dendrite segment has no children, its Max Child Branch Order is blank. In the example below, dendrite segments are color-coded by their Branch Order, which is given in the same color. The Max Child Branch Order for “Dendrite Segment 3” is three (3) because “Dendrite Segment 3” has only two (2) child segments, both of which are third (3rd) generation. The Max Child Branch Order for the dendrite tree is four (4).
 Type: Morphology, Per Time Point Shortest Path Length for a dendrite tree is the shortest path length from the root node to the end of a terminal branch. For dendrite segments, Shortest Path Length is equal to Longest Path Length, and both are equal to the sum of the Total Path Length of the dendrite segment and the Total Path Lengths of each of its ancestors back to the root segment.
 Type: Morphology, Per Time Point Total Path Length for a dendrite segment is the sum of all Euclidean distances between adjacent dendrite points (nodes) making up the dendrite segment. For a dendrite tree, Total Path Length is the sum of the Total Path Lengths of all dendrite segments making up the dendrite tree.  |
Spine
Spine measurements are separated into three (3) tabs in the Spreadsheet section of Aivia: the “Spines” tab for whole-spine measurements that include both the spine heads and necks, the “Spine Heads” tab for spine-head measurements, and the “Spine Necks” tab for spine-neck measurements. Spine heads and necks each inherit all mesh measurements. Additional spine measurements, which can be found in the “Spines” tab, are listed in the expandable panel below.
Type: Morphology, Per Time Point Branch Angle for a spine is the planar angle (in degrees) between the vector that extends from the first to last points of the parent dendrite segment and the vector that extends from the first to last points of the center line of the spine neck. Branch Angle is represented by θ for one of the spines in the example below.
 Type: Morphology, Per Time Point Head Neck Length Ratio is the ratio of the Center Line Length of the spine head to the Center Line Length of the spine neck.  Type: Morphology, Per Time Point Head Neck Volume Ratio is the ratio of the Volume of the spine head to the Volume of the spine neck.  Type: Morphology, Per Time Point Length To Head Diameter Ratio is the ratio of the Total Spine Length to the Spine Head Diameter.  Type: Morphology, Per Time Point Spine Convex Hull Volume Ratio is the ratio of the Convex Hull Volume of the spine head to the Convex Hull Volume of the spine neck. Convex Hull Volume of a mesh is the volume of the smallest convex set shape that contains the mesh.  Type: Morphology, Per Time Point Spine Diameter Ratio is the ratio of the Spine Head Diameter to an estimation of the spine neck diameter that depends on the Volume of the spine neck and the Center Line Length of the spine neck.  Type: Morphology, Per Time Point Spine Head Diameter is estimated as the longest axis of a cross-section of the spine head that is perpendicular to the center line. If estimation by the previous method fails, Spine Head Diameter is calculated with the equation below.  Type: Morphology, Per Time Point Spine Surface Area Ratio is the ratio of the Surface Area of the spine head to the Surface Area of the spine neck.  |
Cell membrane
2D cell membranes inherit all outline measurements and can also have the measurements listed in the expandable panel below. A cell-membrane outline includes the entire area of what is considered the cell in Aivia.
Type: Morphology, Per Time Point Area to Contained Vesicle Area Ratio is the ratio of the Area of the membrane to the sum of the Areas of all vesicles on the membrane.  |
3D cell membranes inherit all mesh measurements and can also have the measurements listed in the expandable panel below. A cell-membrane mesh includes the entire volume of what is considered the cell in Aivia.
Type: Morphology, Per Time Point Volume to Contained Vesicle Volume Ratio is the ratio of the Volume of the membrane to the sum of the Volumes of all vesicles on the membrane.  |
Vesicle
Vesicle outlines inherit all outline measurements and can also have the measurements listed in the expandable panel below.
Type: Position, Per Time Point Relative Center of Mass X Position is the difference between the x-coordinate of the vesicle’s Center of Mass and the x-coordinate of its parent’s Center of Mass. The vesicle’s parent (if it exists) is a cell membrane, cytoplasm, nuclear membrane, or nucleus.  Type: Position, Per Time Point Relative Center of Mass Y Position is the difference between the y-coordinate of the vesicle’s Center of Mass and the y-coordinate of its parent’s Center of Mass. The vesicle’s parent (if it exists) is a cell membrane, cytoplasm, nuclear membrane, or nucleus.  Type: Position, Per Time Point Relative Center of Mass Z Position is the difference between the z-coordinate of the vesicle’s Center of Mass and the z-coordinate of its parent’s Center of Mass. The vesicle’s parent (if it exists) is a cell membrane, cytoplasm, nuclear membrane, or nucleus.  Type: Position, Per Time Point Relative X Position is the difference between the x-coordinate of the vesicle’s Centroid and the x-coordinate of its parent’s Centroid. The vesicle’s parent (if it exists) is a cell membrane, cytoplasm, nuclear membrane, or nucleus.  Type: Position, Per Time Point Relative Y Position is the difference between the y-coordinate of the vesicle’s Centroid and the y-coordinate of its parent’s Centroid. The vesicle’s parent (if it exists) is a cell membrane, cytoplasm, nuclear membrane, or nucleus.  |
Vesicle meshes and spots can have all measurements listed in the expandable panel below. Vesicle meshes can additionally have all mesh measurements. Vesicle spots can have select mesh measurements: Bounding Depth, Bounding Height, Bounding Width, Centroid X, Centroid Y, Centroid Z, Max Intensity, Mean Intensity, Min Intensity, Std. Dev. Intensity, and Total Intensity.
Type: Position, Per Time Point Relative Center of Mass X Position is the difference between the x-coordinate of the vesicle’s Center of Mass and the x-coordinate of its parent’s Center of Mass. The vesicle’s parent (if it exists) is a cell membrane, cytoplasm, nuclear membrane, or nucleus. Type: Position, Per Time Point Relative Center of Mass Y Position is the difference between the y-coordinate of the vesicle’s Center of Mass and the y-coordinate of its parent’s Center of Mass. The vesicle’s parent (if it exists) is a cell membrane, cytoplasm, nuclear membrane, or nucleus. Type: Position, Per Time Point Relative Center of Mass Z Position is the difference between the z-coordinate of the vesicle’s Center of Mass and the z-coordinate of its parent’s Center of Mass. The vesicle’s parent (if it exists) is a cell membrane, cytoplasm, nuclear membrane, or nucleus. Type: Position, Per Time Point Relative X Position is the difference between the x-coordinate of the vesicle’s Centroid and the x-coordinate of its parent’s Centroid. The vesicle’s parent (if it exists) is a cell membrane, cytoplasm, nuclear membrane, or nucleus. Type: Position, Per Time Point Relative Y Position is the difference between the y-coordinate of the vesicle’s Centroid and the y-coordinate of its parent’s Centroid. The vesicle’s parent (if it exists) is a cell membrane, cytoplasm, nuclear membrane, or nucleus. Type: Position, Per Time Point Relative Z Position is the difference between the z-coordinate of the vesicle’s Centroid and the z-coordinate of its parent’s Centroid. The vesicle’s parent (if it exists) is a cell membrane, cytoplasm, nuclear membrane, or nucleus.  |
Cell
Type: Morphology, Per Time Point Area to Contained Vesicle Area Ratio is the ratio of the Area of the cell to the sum of the Areas of all vesicles belonging to the cell.  Type: Morphology, Per Time Point Cell/Cytoplasm Area Ratio is the ratio of the Area of the cell to the Area of the cytoplasm.  Type: Morphology, Per Time Point Cell/Nucleus Area Ratio is the ratio of the Area of the cell to the Area of its nucleus.  Type: Morphology, Per Time Point Cell/Organelle Area Ratio is the ratio of the Area of the cell to the sum of the Areas of all its vesicles and its nucleus.  Type: Position, Per Time Point Cytoplasm to Nucleus Vesicle Ratio is the ratio of the number of vesicles contained by the cell membrane or cytoplasm to the number of vesicles contained by the nuclear membrane or nucleus.  |
Type: Morphology, Per Time Point Cell/Cytoplasm Volume Ratio is the ratio of the Volume of the cell to the Volume of the cytoplasm.  Type: Morphology, Per Time Point Cell/Nucleus Volume Ratio is the ratio of the Volume of the cell to the Volume of its nucleus.  Type: Morphology, Per Time Point Cell/Organelle Volume Ratio is the ratio of the Volume of the cell to the sum of the Volumes of all its vesicles and its nucleus.  Type: Position, Per Time Point Cytoplasm to Nucleus Vesicle Ratio is the ratio of the number of vesicles contained by the cell membrane or cytoplasm to the number of vesicles contained by the nuclear membrane or nucleus. Type: Morphology, Per Time Point Volume to Contained Vesicle Volume Ratio is the ratio of the Volume of the cell to the sum of the Volumes of all vesicles belonging to the cell.  |
Cytoplasm
In Aivia, the cytoplasm is the space inside of the cell membrane and outside of the nuclear membrane, if it exists.
Type: Morphology, Per Time Point Area to Contained Vesicle Area Ratio is the ratio of the Area of the cytoplasm to the sum of the Areas of all vesicles contained by the cytoplasm.  |
Type: Morphology, Per Time Point Volume to Contained Vesicle Volume Ratio is the ratio of the Volume of the cytoplasm to the sum of the Volumes of all vesicles contained by the cytoplasm.  |
Nucleus
In Aivia, the nucleus is the space inside of the nuclear membrane.
Type: Morphology, Per Time Point Area to Contained Vesicle Area Ratio is the ratio of the Area of the nucleus to the sum of the Areas of all vesicles contained by the nucleus.  Type: Position, Per Time Point Relative Center of Mass X Position is the difference between the x-coordinate of the nucleus' Center of Mass and the x-coordinate of its parent cell’s Center of Mass.  Type: Position, Per Time Point Relative Center of Mass Y Position is the difference between the y-coordinate of the nucleus' Center of Mass and the y-coordinate of its parent cell’s Center of Mass.  Type: Position, Per Time Point Relative Center of Mass Z Position is the difference between the z-coordinate of the nucleus' Center of Mass and the z-coordinate of its parent cell’s Center of Mass.  Type: Position, Per Time Point Relative X Position is the difference between the x-coordinate of the nucleus' Centroid and the x-coordinate of its parent cell’s Centroid.  Type: Position, Per Time Point Relative Y Position is the difference between the y-coordinate of the nucleus' Centroid and the y-coordinate of its parent cell’s Centroid.  |
Type: Position, Per Time Point Relative Center of Mass X Position is the difference between the x-coordinate of the nucleus' Center of Mass and the x-coordinate of its parent cell’s Center of Mass. Type: Position, Per Time Point Relative Center of Mass Y Position is the difference between the y-coordinate of the nucleus' Center of Mass and the y-coordinate of its parent cell’s Center of Mass. Type: Position, Per Time Point Relative Center of Mass Z Position is the difference between the z-coordinate of the nucleus' Center of Mass and the z-coordinate of its parent cell’s Center of Mass. Type: Position, Per Time Point Relative X Position is the difference between the x-coordinate of the nucleus' Centroid and the x-coordinate of its parent cell’s Centroid. Type: Position, Per Time Point Relative Y Position is the difference between the y-coordinate of the nucleus' Centroid and the y-coordinate of its parent cell’s Centroid. Type: Position, Per Time Point Relative Z Position is the difference between the z-coordinate of the nucleus' Centroid and the z-coordinate of its parent cell’s Centroid.  Type: Morphology, Per Time Point Volume to Contained Vesicle Volume Ratio is the ratio of the Volume of the nucleus to the sum of the Volumes of all vesicles contained by the nucleus.  |
Relation
Relations between object sets can be defined using the Object Relation Tool in the Spreadsheet.
Type: Position, Per Time Point Relative Center of Mass Distance is the Euclidean distance between the Center of Mass of the object and the Center of Mass of the related, primary object. Relative Center of Mass Distance is calculated for objects in the secondary/associate sets of relations.  Type: Position, Per Time Point Relative Center of Mass X Position is the x-coordinate of the Center of Mass of the object when the origin is considered to be the Center of Mass of the related, primary object. Relative Center of Mass X Position is calculated for objects in the secondary/associate sets of relations.  Type: Position, Per Time Point Relative Center of Mass Y Position is the y-coordinate of the Center of Mass of the object when the origin is considered to be the Center of Mass of the related, primary object. Relative Center of Mass Y Position is calculated for objects in the secondary/associate sets of relations.  Type: Position, Per Time Point Relative Center of Mass Z Position is the z-coordinate of the Center of Mass of the object when the origin is considered to be the Center of Mass of the related, primary object. Relative Center of Mass Z Position is calculated for objects in the secondary/associate sets of relations.  Type: Position, Per Time Point Relative Distance is the Euclidean distance between the Centroid of the object and the Centroid of the related, primary object. Relative Distance is calculated for objects in the secondary/associate sets of relations.  Type: Position, Per Time Point Relative X Position is the x-coordinate of the Centroid of the object when the origin is considered to be the Centroid of the related, primary object. Relative X Position is calculated for objects in the secondary/associate sets of relations.  Type: Position, Per Time Point Relative Y Position is the y-coordinate of the Centroid of the object when the origin is considered to be the Centroid of the related, primary object. Relative Y Position is calculated for objects in the secondary/associate sets of relations.  |
Type: Position, Per Time Point Relative Center of Mass Distance is the Euclidean distance between the Center of Mass of the object and the Center of Mass of the related, primary object. Relative Center of Mass Distance is calculated for objects in the secondary/associate sets of relations. Type: Position, Per Time Point Relative Center of Mass X Position is the x-coordinate of the Center of Mass of the object when the origin is considered to be the Center of Mass of the related, primary object. Relative Center of Mass X Position is calculated for objects in the secondary/associate sets of relations. Type: Position, Per Time Point Relative Center of Mass Y Position is the y-coordinate of the Center of Mass of the object when the origin is considered to be the Center of Mass of the related, primary object. Relative Center of Mass Y Position is calculated for objects in the secondary/associate sets of relations. Type: Position, Per Time Point Relative Center of Mass Z Position is the z-coordinate of the Center of Mass of the object when the origin is considered to be the Center of Mass of the related, primary object. Relative Center of Mass Z Position is calculated for objects in the secondary/associate sets of relations. Type: Position, Per Time Point Relative Distance is the Euclidean distance between the Centroid of the object and the Centroid of the related, primary object. Relative Distance is calculated for objects in the secondary/associate sets of relations. Type: Position, Per Time Point Relative X Position is the x-coordinate of the Centroid of the object when the origin is considered to be the Centroid of the related, primary object. Relative X Position is calculated for objects in the secondary/associate sets of relations. Type: Position, Per Time Point Relative Y Position is the y-coordinate of the Centroid of the object when the origin is considered to be the Centroid of the related, primary object. Relative Y Position is calculated for objects in the secondary/associate sets of relations. Type: Position, Per Time Point Relative Z Position is the z-coordinate of the Centroid of the object when the origin is considered to be the Centroid of the related, primary object. Relative Z Position is calculated for objects in the secondary/associate sets of relations.  |
Track relation
Type: Position, Per Time Point Relative Acceleration is the acceleration of the secondary/associate object relative to its related, primary object and is calculated using the equation below, where Δt is the time between frames. Relative Acceleration is not calculated on the first two (2) frames in a set of consecutive frames over which objects are related, and the positions of parent objects are used if the there are any lineage splits for the objects of interest between the current frame and two (2) frames prior. Relative Acceleration is given for objects in the secondary/associate sets of relations.   Type: Position, Per Time Point Relative Straight Line Velocity is the velocity of the secondary/associate object relative to its related, primary object based on the positions of both objects on the current frame and the earliest frame on which they are related. Relative Straight Line Velocity is not calculated on the first frame in a set of consecutive frames over which objects are related, and the positions of parent objects are used if the there are any lineage splits for the objects of interest between the current and previous frames. Relative Straight Line Velocity is given for secondary/associate objects.   Type: Position, Per Time Point Relative Straight Line Velocity Squared is the square of the velocity of the secondary/associate object relative to its related, primary object based on the positions of both objects on the current frame and the earliest frame on which they are related. Relative Straight Line Velocity Squared is not calculated on the first frame in a set of consecutive frames over which objects are related, and the positions of parent objects are used if the there are any lineage splits for the objects of interest between the current and previous frames. Relative Straight Line Velocity Squared is given for secondary/associate objects. 
Type: Position, Per Time Point Relative Velocity is the velocity of the secondary/associate object relative to its related, primary object and is calculated using the equation below, where Δt is the time between frames. Relative Velocity is not calculated on the first frame in a set of consecutive frames over which objects are related, and the positions of parent objects are used if the there are any lineage splits for the objects of interest between the current and previous frames. Relative Velocity is given for objects in the secondary/associate sets of relations. 
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