Measure Radial Distribution Explanation

Hello,
I apologize for the length of this post as I try to understand just how the MeasureRadialDistribution module works and I appreciate any help that can be provided! I am a research technician trying to determine whether a stain for EGFR spreads out farther throughout the interior of cells before and after treatment. I believe it aggregates more without treatment (thus less dispersion) and spreads out more after treatment and would like to quantitatively demonstrate that.

  1. FracAtD value is the sum of the intensity values for ONE circular bin divided by the sum of the intensity values for ALL the bins. In addition, the MeanPixelFraction is the average intensity per pixel within a given circular bin calculated by dividing the FracAtD value by the fraction of total object pixels within the bin. Is my understanding correct?

  2. For the MeanPixelFrac, if the above is true, are the “object pixels” used for the calculation simply the pixels within the image/cells with a non-zero intensity? Or are these object pixels (aka EGFR puncta) supposed to have been identified using the IdentifyPrimaryObjects module and then analyzed with MeasureRadDist? I believe its the former but I am unsure.

  3. Is it possible to get the fraction of total number pixels (not total intensity) for each bin by dividing FracAtD by MeanPixelFrac? What would I have to do to get the actual pixel number? I am not sure if you could answer this, but would there really be an advantage or disadvantage measuring the fraction of total stain pixels per bin versus the fraction of the total intensity per bin?

  4. Lastly, how is the distance of the largest bin determined? Is it simply the point on the edge farthest from the indicated center?

If it helps, this is a brief explanation of what I’m doing. I load three images; a mask for the cells, a mask for the centers of mass of the signal within each cell, and the original image itself with my stain of interest. I run the IdentifyPrimaryObjects for the cell mask and the center of mass. I then apply a threshold to the image with the stain to remove any background. For MeasureRadDist, I set the mask for the center of mass as my center (NewCenters.tif) and the object to be analyzed as the cell mask (Cells.tif). The image loaded is the thresholded image with my stain (B.ome.tif). I assume that the module analyzes the intensity values for the thresholded image within the perimeter of the cell mask.

I have attached the pipeline, and the relevant images. I ran this pipeline already and would upload the data but the site will not let me
I hope I was able to explain it well enough and I appreciate any help you could offer!

Treatment Images:
Image with stain

Cell Masks

Centers of Mass

Control Images
Image with Stain

Cell Masks

Centers of Mass

Pipeline: Dispersion Analysis Pipeline.cp (16.6 KB)

-Alex

Hello,

I apologize if the post may have been too confusing and long. If nothing else, could I just get an answer to how the MeanPixelFrac is calculated? Is it calculated by dividing the FracAtDistance value by the total area (in pixels) of each bin or is it divided by the total number of pixels with stain (in other words, pixels with intensity=0 are not counted)? I’ve looked through other posts but I haven’t found an explanation for which value is used.

Thanks for any help you can provide. If you need any clarification, please ask me and I will try my best to explain.

Hi Alex,

Sorry for the delay on this response.

[quote=“luna727”]
If nothing else, could I just get an answer to how the MeanPixelFrac is calculated? Is it calculated by dividing the FracAtDistance value by the total area (in pixels) of each bin or is it divided by the total number of pixels with stain (in other words, pixels with intensity=0 are not counted)? I’ve looked through other posts but I haven’t found an explanation for which value is used. [/quote]

The mean fractional intensity (MeanFrac) is calculated as: [fraction of the total stain intensity at a given radial bin to that of the total stain intensity for the object (i.e., FracAtDistance)] divided by [fraction of radial bin area to the total area of the object]. In other words:MeanFrac* = FracAtD*/(Area*/TotalArea) where * indicates the value at bin i***. So I think your first definition is the correct one.

All pixel intensities are included in this calculation, including those that are zero, since 0 is a valid intensity value. The intensities are measured from within the input objects, as specified by the user in the module. The objects are typically created using one of the identification modules beforehand.

If you want pixels with a value of 0 not to be counted, you would need to mask the zero pixels out using MaskImage or MaskObjects. Masked pixels are not considered in most measurement modules.

The distance of the largest bin is the point farthest from the indicated center, as you say. But keep in mind that since the bins are essentially concentric contours encircling the object center, they follow the object boundary at the furthest extent. That means the radial distance for the farthest bin varies as you follow the contour perimeter, i.e, it is shorter for radii where the object edge is close to the center, and longer where the boundary is father away, such long processes.

To get the fractional area at each bin, you could calculate this using the above formula by re-arranging the terms as: Area* = FracAtD**TotalArea/MeanFrac* Since TotalArea is not given to you by MeasureRadialDistribution as an output measurement, you would need to calculate it separately, using MeasureObjectSizeShape. You can then use CalculateMath to compute the formula for each bin, or do it offline in Excel or a similar program.

Regards,
-Mark****

Thank you very much Mark! I greatly appreciate your response. I only have one other question. Is there any advantage (in general) to using FracAtDistance vs MeanPixelFrac or does it simply depend on the experiment? I’ve looked at a paper that measured the radial distribution but the experimenters used only the MeanPixelFrac data and I haven’t heard a response after I asked them so i was wondering if there might be some inherent advantage to one vs the other.

-Alex

It strictly depends on your experiment, and what’s appropriate for your assay. :smile: If your cells vary widely in size, you can imagine cases where normalizing by cell area fractions would be important.

Regards,
-Mark