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Sholl Analysis

1 byte added, 13:18, 1 April 2016
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== Parameters ==
Input values take into account the scale information of the image that can be set using the <span style="border-bottom:1px dotted #ccc;">Analyze▷ Set Scale...</span> or <span style="border-bottom:1px dotted #ccc;">Image▷ Properties...</span> (<span style="display:inline-block;">{{key press|Shift|P}} </span>). The prompt is organized into 5 sections:
[[File:BitmapSholl-CA1Compartment.png|frame|right|Linear plot for CA1 cell [[#CA1CellMask|described above]]. Using the soma as center, image was sampled twice using the [[#Restrict|Restrict analysis to hemicircle/hemisphere]] option in order to segregate apical from basal dendrites. For convenience, distances for basal branches were assigned negative values. For clarity, the binary image of the arbor was rotated, scaled and overlaid (in green) over the plot canvas. Note that it is also possible to restrict [[#MethodsTable|curve fitting]] to a sub-range of distances once [[#Importing|data is collected]].]]
==== Definition of Shells ====
* <span id="StartRadius"></span>'''Starting radius''' <sup>&nbsp;</sup>The radius of the smallest sampling circle/sphere, i.e., the first distance to be sampled.
* <span id="EndRadius"></span>'''Ending radius''' <sup>&nbsp;</sup>The radius of the largest (last) sampling circle/sphere. It is automatically calculated if a [[#Usage|line ROI is used]]. Note that the specified distance may not be actually sampled, if ''Radius step size'' is not a divisor of ''Ending radius''-''Starting radius''. In this case, the program will choose the largest possible distance smaller than the specified value.<span id="CA1CellPlot"></span>
'''N.B.''' You can clear ''Ending radius'' or set it to ''NaN'' ("Not a Number") to sample the entire image. This is particularly useful when [[#Batch_Processing|batch processing]] images with different dimensions.[[File:BitmapSholl-CA1Compartment.png|frame|right|Linear plot for CA1 cell [[#CA1CellMask|described above]]. Using the soma as center, image was sampled twice using the [[#Restrict|Restrict analysis to hemicircle/hemisphere]] option in order to segregate apical from basal dendrites. For convenience, distances for basal branches were assigned negative values. For clarity, the binary image of the arbor was rotated, scaled and overlaid (in green) over the plot canvas. Note that it is also possible to restrict [[#MethodsTable|curve fitting]] to a sub-range of distances once [[#Importing|data is collected]].]]
* <span id="StepSize"></span>'''Radius step size''' <sup>&nbsp;</sup>The sampling interval between radii of consecutive sampling circles/spheres. This value may be set to zero for continuous (1-voxel increment) measurements.
'''N.B.''' For stacks with anisotropic voxel size, setting ''Radius step size'' to zero, sets the step length to the dimension of the matching isotropic voxel, i.e., the cube root of the product of the voxel dimensions (3D images) or the square root of the product of the pixel dimensions (2D images).
* <span id="Restrict"></span>'''Restrict analysis to hemicircle/hemisphere''' <sup>&nbsp;</sup>This option is only available when an orthogonal radius has been created (by holding {{key|Shift}} while using the <span style="border-bottom:1px dotted #ccc;">Straight Line Selection Tool</span>). It can be used to limit the analysis to sub-compartments of the arbor.
'''N.B.''' For horizontal lines, this option instructs the algorithm to measure intersections at sites equidistant from the center that have y-coordinates above/below the drawn line. For vertical lines, it instructs the plugin to measure intersections at sites equidistant from the center that have x-coordinates to the left/right of the drawn line.
[[ File:BitmapSholl-Prompt_v3.png|320px|right |Main prompt (version 3.4.1)]]
==== Multiple Samples and Noise Reduction ====
* '''Samples per radius ''(2D images only)''''' <sup>&nbsp;</sup>Defines the number of measurements to be performed at each sampling circumference. These measurements are then combined into a single value according to the chosen [[#SamplesIntegration|integration method]]. This strategy, a break from previous approaches, increases the accuracy of non-continuos profiles by diluting out the effect of processes extending tangent to the sampling circumference.
:Visually, this option can be imagined as the "thickness" of the sampling circumference: e.g., for a radius of 100 pixels and a value of 3 ''Samples per radius'', the final number of intersections would integrate the measurements sampled at distances 99, 100 and 101. [[ File:BitmapSholl-Prompt_v3.png|320px|right |Main prompt (version 3.4.1)]]
:Note that it would not make sense to increase the number of samples beyond the length (in pixels) of ''Radius step size''. For this reason, this option is limited to a draconian (and arbitrary) maximum of 10 samples.
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