Archive for the ‘Counting frames’ Category

Early and Late Recognition

July 23, 2010

Each observer is different when it comes to doing stereological research. The reason for this is the way that the researchers interpret what they see. One of the basic issues in recognition is deciding whether or not something is a part of the population being counted. A cell or structure seen in the microscope is something to count or something not to count. After a decision is reached about whether or not something should be counted, comes the issue about the intersection of the probes and the item of interest.

The easiest decision is whether or not an object is intersected by a line. A counting frame is composed of 2 types of lines. The green or dashed lines are the inclusion lines and the red or solid lines are the exclusion lines. Touching a line seems to be a simple rule. In fact, there are many cases that becomes gray issues. Whatever decision is made in one place has to be used at all times. The decision that a certain fuzzy condition is a touch or not needs to be used in all similar conditions. The same conditions need to be used for both the inclusion and exclusion lines. If the rules are not applied in a consistent manner then a bias is introduced. This bias may be quite small if the counting frame is small. The bias becomes more pronounced as the counting frame decreases in size.

The most difficult decision is the decision about the z-position of an object. Some observers tend to be early recognizers. The tendency is to see something in focus before others. The idea is that the researcher is focusing through the material and decides that something is in focus before other people. A late recognizer is someone that decides later than other people that an object is in focus. Near the top of the optical disector an early recognizer might say that a cell is not counted, while a later recognizer might decide that the cell is indeed counted. Problems occur when late and early recognition are used consistently across the height of the disector.

If someone uses early recognition at the top of an optical disector and late recognition near the bottom of the optical disector it is as if the optical disector is smaller than it is. The result is that fewer counts are made and the population is underestimated. The opposite can happen as well if someone uses late recognition at the top and early recognition at the bottom, then the result is that more cells are accepted and an over projection occurs.

It does not matter if a person is an early or late recognizer. What matters is being consistent in the application of counting rules regardless of the position where counts are made.


Who needs to use the Proportionator

April 2, 2010

Anyone doing stereology and counting cells needs the proportionator.

  • If you use your stereological equipment more than once a year you need the proportionator.
  • If you have tens or hundreds or more tissue samples to process  you need the proportionator.
  • If you find the the CE is often too large then  you need the proportionator
  • If you have plans to increase your research you need the proportionator
  • If you are moving to a larger experiment with more lab animals you need the proportionator

The proportionator is the stereological tool that makes more effort easier to handle. It is the only tool today that makes it possible to obtain the best results with the least effort. Weibel is quoted as saying “Do more, less well.” The fractionator makes it possible to “Do better, less effort.”

The quadrat

March 25, 2010

The quadrat is sampling shape. It is often thought of as a square or rectangular frame used in the field to sample an area. This is the way the quadrat appears in geographical, ecological, or forestry studies. But the fact is that the quadrat is not necessarily a 2-dimensional sampling shape.

Before looking into the more general definition of a quadrat lets consider the 2-dimensional quadrat. That an area. Typically, an area is a square or rectangle. There’s a simple reason for that. It’s easy to make a quadrat of that shape. A few boards and fasteners and the quadrat is done.  Early on it was realized that there existed a problem with quadrats. The problem was realized as early as probably the late 1890s when Clements and Pounds published there article on the quadrat. One of the early solutions was the proposal to use disc shaped quadrats. This meant that the quadrat minimized the edge effect. In fact, it didn’t. The problem was that the sampling rules associated with curved quadrats were too complex to use effectively.

You’d think that the square quadrat would have been the choice. It enclosed a large area for the perimeter. That didn’t happen. It was learned that the long thin quadrats such as the belt or strip quadrats were more effective sampling methods.

The shapes of quadrats was a hot topic in a number of disciplines from range management, to forestry, to ecology, to grassland studies. In all of this of course the assumption was that a quadrat was a 2-dimensional shape.

A quadrat is geometric sampling shape. It can be any dimension from 0 to 3 dimensions. These are points, lines, areas, and volumes. Even though you might think of a quadrat as a square frame, a quadrat can be any sampling geometric shape that is needed to get the work done and done efficiently.

Measures of abundance

March 8, 2010

One of the basic concerns of field work is to develop a sense of how much is out there. In a recent presentation I encountered a fascinating study in which the researchers were studying a shore bird called the Wilson’s plover. This bird is a beach nester that is not too common, but not endangered.

One of the foods of choice for the bird is the hermit crabs. The food source lives in burrows along the shore in muddy zones. The crabs dig burrows. A knowledge of the number of crabs in the nesting are used by the Wilson’s plover provides information about the available food supply. The measure of abundance in this case is the number of crabs and not the weight of the crabs.

The present sampling strategy is to toss a quadrat, a wooden square in this case, onto the mud flat where the crabs live and to count the number of crabs in the frame. Crab counting is hard. They move. They hide. The strategy used today is count multiple times and use the average number of crabs as the estimate for the selected quadrat.

A short discussion with the researchers demonstrated their knowledge of sampling and its issues, but they were not aware of 2 things.

  1. They were not aware of counting frames
  2. They were not aware of the efficiency of SRS

This isn’t surprising since stereology is a relatively unknown science.

The researchers will be doing more studies next year. They know that it is better to count burrows than it is to count crabs that run and hide. They are likely to use the counting frame and SRS in next year’s study.