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School of Anatomy and Human Biology - The University of Western Australia
     Blue Histology - Exercise: Cell Density and Cell Number

Cell density and cell number estimation using the Optical Disector

One way to estimate the number of objects in a structure is to estimate their average number in small samples of the volume of the structure, i.e. to estimate the numerical density of the objects (NV). If we have a good estimate of the density, we can estimate the total number of objects by dividing the volume of the structure (Vref) by the volume of our sample and multiply the result with the density of our objects - the NV × Vref method

In this exercise we will estimate the density and number of neurones in the lateral septum of the mouse. You already have estimated the volume of the lateral septum in the "Volume Estimation" exercise.

Probing for the Neurons

Neurones are not points in space. They have, like the points we used in the "Volume Estimation" exercise, a size. To count them as points we need to know which unique "point" we can associate with a neuron. In a series of real histological sections, the "appearance" and the "disappearance" are two unique events associated with an object present in the section series. It will appear for the first time in one section and it will have disappeared for the first time in one section. We can only find out if the object has appeared or disappeared by comparing two sections of our series. The name of the method derives from this fact. It is called the Disector ("di" for two and "sector" for sections).

In a series of optical sections, the points at which an object for the first time appears in focus and the point at which it for the first time appears out of focus are again two unique "points". We can use either one to count the number of objects. In practice it is rarely the cell which is counted. Their often irregular outlines and fine processes make it very difficult to define the "focus" - "no focus" points reliably. The more regularly shaped nucleus is the "usual" unit which is counted. This approach is called the Optical Disector because we use two optical sections rather than two physical sections to determine the "in focus" and "out of focus" events.

In practice it is next to impossible to determine the thickness of an optical section and then move to the next one. Instead, the optical plane is continuously moved for a certain distance through the tissue, and every object that comes into focus is counted. We do not need to know how many optical sections are contained in this distance. However many there are, together they span the distance and in all of them together will be the number of objects we counted. It is the distance between the first and the last optical section, the depth of our probe, that defines the volume of the probe.

How to Probe for Neurons Using the Optical Disector

For each estimation you will have to follow this sequence of steps:

  1. Go to the first sample location (sample 1).
  2. Select a counting frame. You will use this frame at all subsequent sample locations (1-15).
  3. Decide on a depth for your probe (5-15 µm are feasible). This depth and the area of your frame define the volume of your probe. Use this depth at all sample locations (1-15).
  4. Move the focus down to the section until an object appears in focus anywhere in the section - not the first object in the frame unless it is the first to appear anywhere. Note the depth of this focal plane.
  5. The surfaces of histological sections are never completely smooth. To avoid sectioning artefacts, move 2-3 µm deeper into the section.
  6. Count the number of neuron nuclei which come into focus as you gradually move the frame down into the section by the number of microns you chose under 3. Note the number of nuclei you counted with your probe. "Come into focus" means that you do not count the nuclei which are already in focus before you start moving the frame into the section.
  7. Move to the last plane in which objects appear in focus anywhere in the section and note the depth of the plane. This measurement and the measurement made at step 2 allow you to estimate the thickness of the section.
  8. Go to the next sampling location and repeat steps 4 to 7 until you have used all samples.
  9. Calculate the average neuron density (sum of all counts divided by the number of samples) and then calculate the total number of neurons based on average neuron density and the volume you estimated in the "Volume Estimation" exercise.

Neuron or Glia?

If we want to count neurones we need to be able to identify neurones. Neurones (N) are typically (but not always) large cells, with large nuclei. The nucleus contains one or more well defined nucleoli. The nuclear membrane should be visible in at least a few of the focal planes which pass through the nucleus. The nucleus is surrounded by a rim of cytoplasm and the initial segments of the primary dendrites are sometimes visible. Glial cells (G) are usually much smaller than neurons. Their nuclei are also much smaller, sometimes quite dark and/or sometimes quite "granular". Often it is not possible to see the cytoplasm surrounding the nucleus. Use the image as an initial guide, and ask if you are in doubt.

To count or not to count ?

In theory we could place our frames side by side and count under the entire area of the section. However, some nuclei would fall right onto the border of two adjacent frames, and we do not want to count them twice. To avoid oversampling, we only count nuclei which are located in the frame or touch or cross the green inclusion lines. Nuclei touching or crossing the red exclusion lines are not counted. It is up to you to decide if you use "touch" or "cross" as the criterion, but you will have to use the same criterion for the inclusion and exclusion lines and in all samples.

Here is your job ....

There are rather few sampling locations available for this exercise. Subsampling locations is probably not a good idea. Instead we can vary the area of the frame (frame 1-3) and the depth of the probe. Try the different frames with different depths at one sampling location until you have a feel for how they work and how much work is involved to obtain a single estimate.

  1. Do one density estimates in which you think will give a rather precise estimate of the average cell density.
  2. Thereafter, do two more estimates in which you either use a smaller frame or a shallower probe or both.
  3. Compare the nominal section thickness we used in the volume estimation exercise with the average thickness of your measurements. Correct your volume estimates if necessary!
  4. Calculate total number of neurones in the lateral septum and compare the estimates.

A couple of questions to think about:

Try to estimate the number of cells in the lateral septum using the Optical Fractionator

The available samples are an urs sample of all possible locations. They were selected in every 10th section. In the sections they were selected at every 6th point of grid 2 of the volume estimation exercise that fell onto the lateral septum.

Compare the estimates you obtained using the Nv × VRef and Optical Fractionator methods. If they are different think about why that may be the case.

The sizes of the frames are
Frame 1: 75 x 75 µm
Frame 2: 50 x 50 µm
Frame 3: 30 x 30 µm

Start the Disector simulation

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