Should I use m=0 or m=1?

The sampling process has two considerations. The first is the value of interest, be it cell counts or any other geometric quantity. The second issue is to get an idea of how good the estimate is. The latter is done by estimating the CE. Basically, you guess what the value is and then guess how good the first guess was.

All CE estimates are model based and the CE method published by Gundersen is no exception. The m=0 and m=1 results differ in some arcane mathematical descriptions that relate the collected samples to a model of the object from which the samples were obtained. The authors decided that most biological tissue has characteristics that are described by the m=1 results. This is not always true. If there are any sharp cutoffs in the data, then the m=0 results are the appropriate results to use. Notice that the decision to use m=0 or m=1 is made outside of the obtained samples.

The easiest way to understand the difference is to consider an example of sampling in which the m=0 result is appropriate. Suppose that the samples come from something that has a triangular graph. A triangular graph is 0 until it ramps up in a straight line segment and suddenly plummets back to 0. (Please excuse my lack of knowledge of proper biological terms.) The volume of the chambers of a heart can approximate a triangular graph when the heart is sectioned perpendicular to its long axis. Near the tip of the heart the chambers are small and so is the cross sectional area. Sections closer to the top of the heart show increasing area until the end of the chambers is reached. Suddenly the area drops to 0.

Sudden cutoffs are uncommon in biological tissues. That is why m=1 is recommended and usually used today. The SI software computes both, because it is not possible to know from the samples which method is appropriate.

Kieu et. al. have published a paper in which they examine the samples, assuming that there are enough, to see which method is appropriate. The general idea is to see how smooth the samples appear to be.

Stereo Investigator calculates the CE estimates with both smoothness class equations: m=0 and m=1. m=1 is the newer method, and is recommended.

In short, the m=0 CE equation was the original CE estimate developed for use with the optical fractionator (see Gundersen and Jensen, 1987).

In 1999, Gundersen et. al. published a new paper referenced below, which reconsiders the CE issue and recommended estimating the CE with the m=1 smoothness class. The authors determined that biological tissues are best described by the m=1 class.

If you want to compare your results with older papers published using the pre-1999 CE estimate, you may want to use the m=0 smoothness class for a more direct comparison.

For a full explanation, please refer to the paper “The efficiency of systematic sampling in stereology – reconsidered” by H.J.G. Gundersen, E.B.V. Jensen, K. Kieu & J. Nielsen, Journal of Microscopy Vol. 193, Pt 3, March 1999, pp. 199-211.

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