School of Anatomy and Human Biology - The University of Western Australia

     Blue Histology - Exercise: Volume Estimation

Volume estimation using the Cavalieri estimator

The images available in this exercise are an exhaustive series (all 84 sections are available) of horizontal sections of the mouse lateral septum. In this exercise you will determine the volume of the lateral septum.
If anyone with a deep love of the lateral septum accidentally should find this page I apologize for my poor definitions of the ventral lateral septum (hopefully, the image series will be upgraded some day).

Browse through the series to get a feel for the appearance of the septum. In some sections I have outlined the border of the lateral septum - if no border is outlined, it follows natural boundaries visible in the section.

For each estimate you will have to

  1. choose a uniform (sections selected at equal intervals, e.g. every third, fourth etc.) random (random position of the first section in the fist interval) systematic sample (urs sample) of sections containing the lateral septum,
  2. choose a point-grid to count with, and
  3. count the number of points which fall within the borders of the lateral septum.
  4. calculate the volume of the septum based on the point-to-point distance of the grid and the distance between the sections of your sample.
  5. repeat 1-4 until you have an idea of how much work is required to produce a reliable estimate of the volume of the lateral septum.

"In" or "out"?

Unfortunately, real 0-dimensional points cannot be counted because they have no size and therefore are invisible. In counting grids a point is often represented by the intersection of two short lines, i.e. a small cross. The intersection of the lines is not the smallest point that we can define with the cross. Its area is actually quite large (A), and it may obscure the border of the structure we want to measure. In case A, we would have to guess if the point was "in" or "out" if we use the intersection as our probe. The good thing about a cross is that it provides four much smaller points which can be used for the measurement: the corners formed at the intersection. One of these four "cornerpoints" should be used for the counts, and the same one should be used throughout each estimation procedure. In B, we can unequivocally decide if a point we choose needs to be counted: corners 1 and 4 are "out", corners 2 and 3 are "in".

Here is your job ....

The first estimation should be rather precise - choose an urs sample of sections and a grid that you think would give a good estimate.

Thereafter, do a few estimations which require less and less effort. Use fewer sections or coarser grids or both. Try to do two or three estimates of the volume with the same spacing of the sections and the same grid but different starting points of the sample of sections.

Compare the estimates and give some thought to which number of sections and which grid size would be sufficient to give a reasonably precise estimate. "Reasonable" will depend on the nature of the study - let's just say that in this exercise reasonable is something within 10-20% of you first labour-intensive estimate.

Think about which factors determine the number of sections and number of points needed to give good estimate in structures of different shapes.

You will need the following numbers to calculate the volume of this part of the brain:

The nominal section thickness, i.e. the thickness set on the microtome, was 20 µm.

Point to point distances
Grid 1: 100 µm
Grid 2: 150 µm
Grid 3: 200 µm

Start the Volume Estimation simulation.

page content and construction: Lutz Slomianka
last updated: 5/08/09