I will use this space to flesh out the details of the methods paper I will be writing with Dr. Khan

I am thinking of titling the paper Methods to estimate the density of Fibers and Cell–Bodies Mapped onto Rat Brain Atlases. I'm going with Rat Brain Atlases since it's a larger scope, but we can change it to Brain Maps 4.0.

The purpose of this paper is to establish the validity of the proposed density estimation methods under a Brain Maps 4.0 framework. These methods will be included in the data analysis portions of Navarro et. al. & Peru et. al.'s 2021 papers as well as Pinales's dissertation. Then, the long–term goal is to implement these methods directly on the Community Brain Maps 5.0 currently being developed, possibly in the form of a plugin for the NewArtII system.

Data

What kind of data do we have?

• Fibers

  • paths

  • pixels (best)

• Cell Bodies

  • coordinates (best)

  • pixels

Methods

Choropleths

• Counts (coordinates or pixels) per brain region

• Ratios

  • number of coordinates or pixels in one brain region to the total area of that brain region

Isopleths

• Density Estimation (isodense)

  • Kernel Density Estimation for continuous data (coordinates)

  • Density by Gaussian Blurring or other low-pass filters for raster data (pixels)

Validation..?

I feel that we would need a lot of experimental datasets to validate the methods. But then again, I'm not sure how we would validate them in the first place. Not even sure what I mean by "validate".

Discussion with Dr. Khan (5/21/2021)

Maybe the method is self-validated by overlaying the mapped data and the contours.

Another way would be to manually generate contours over the mapped fibers and compare metrics such as the area of contours. Similarly, we could have experts determine the most dense areas in a file

Intro: Density methods

Narrative: 2-3 goals. 1 goal was to capture spatial patterns for multiple animals and represent them statistically; 2 make sure we can do it in a way that generates a graphical representation in vector format to overlay in AI template; 3 accurately measure density areas that can be flexibly useful for experimenters targeting dense areas (e.g. different probe sizes)

Script:

Refs: Saper 2009 JC Neuro Editor

At the end of the conversation, we agreed the density work was not enough for a stand-alone paper.

5/29/21 – Following up with the meeting on 5/21/2021 👆, I sought a way to visualize potential regions of poor consensus in our averaged density maps.

The question we had was, how can we tell if the density (fiber or cell) in one animal differs drastically from the other animals in the study, and similarly, what are the regions of consensus.

We originally thought we could obtain the consensus by taking the average density across cases. But with a small n, say 3 cases, the average map may be more sensitive to outliers.

An idea was to use the median since it could be robust against outliers.

I took all aMSH cases at level 27 (a total of 9) and plotted the averaged and median distributions bellow

The main point of the figure section above is to somehow quantify where multiple cases show consensus. I think we are already doing that. Here is why.

If we are using a sigma value of 14 µm, it means we can obtain a cross-section with a diameter of 28 µm from the first standard deviation of the gaussian curve. Now, if a cell is approximately 28 µm in diameter, this means that a region with a diameter of 28µm can physically only contain information about one cell's position. The only time a region of 28µm can contain information about more than one cell is if there is an overlap of cell positions in the multiple cases. We can find the probability value or the height of the curve at the first standard deviation and use multiples of that height as thresholds to draw contours. This would effectively give us a contour for regions of agreement.