Using the Optical Fractionator in non-uniform cell distributions

Question

Can the Optical Fractionator be used to obtain accurate results with non-uniform cell distribution? There seems to be concern among some people that the Optical Fractionator does not yield accurate results unless the cell distribution is uniform.
Can the Optical Fractionator be used to obtain accurate results with non-uniform cell distribution?

Discussion

By non-uniform distribution I assume you are referring to a distribution that is not uniformly random. It has been suggested in the literature that stereological procedures such as the Optical Fractionator provide inaccurate results unless the particles being counted are distributed in a uniformly random manner. It is important to differentiate the two parts of the problem. Part 1 is getting an unbiased value. This is very important since it means that the more data that is collected, the better the results. Part 2 is getting an estimate of how good the answer is. This is where the CE comes into play.

The estimated number is not affected by the distribution of the cells. The estimation of the number of cells is not dependent on any argument that the particles are distributed in any fashion. On the other hand, the CE estimations are affected. This is to be expected. This simply says that the distribution of the particles together with the manner in which the particles were sampled could lead to poor estimates. This is true for all estimation techniques. Estimation does not mean exact determination. There is always some random error in the results.

The CE estimations available for the Optical Fractionator are all model based. This means that they are not unbiased. It is always possible to construct a population that will cause the CE estimations to fail. This does not mean that the population estimate is biased. The Matheron technique (aka Gundersen CE) has a model that the number of particles per section changes slowly across sections. A graph of the number of particles vs sections is a plot of points. The model assumes that connecting the points is a rough approximation of the actual curve. A population that violates this is a population of thin bands of cells and the section are taken parallel to these thin bands. The actual curve plummets to zero between the points. Sectioning perpendicular to the bands does not have this sampling problem that leads to a poor CE estimation. In either case, the population estimate is unbiased.

In summary, the accuracy of the Optical Fractionator is estimated by the CE and that is why it an important value.

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