There is probably more controversy about the CE than any other aspect of stereology. This controversy has its origins by claims in early papers (for example Gundersen, 1986; Gundersen 1988) that it was necessary to count as few as 100 cells to accurately estimate a cell population. However, numerous papers and comprehensive computer simulations (for example Glaser, 1998; Schmitz, 2000) point to the need for caution in performing a minimum of work based on optimistic predictions of some theoretical CE methods. As mentioned earlier, all of the CE estimation methods are based on models and each method has conditions where the model is not met. The different CE methods and their associated formulas have been developed, based upon different assumptions and with different considerations taken into account, such as the shape of the region of interest, the distribution of objects within the region of interest, and the sampling criteria applied to the examination.

So, the question for the biologist is in light of the theoretical controversy over the CE is what to do? When counting cells using the Optical Fractionator or quantifying volume using the Cavalieri estimator, it is recommended to use either the ‘oversampling-subsampling’ approach or the ‘oversampling’ approach described on the page Study Design. The only arguments against using one of these approaches are that these may not be the most efficient approaches and may result in performing more work than necessary. Yet, many researchers believe that performing a little more work to ensure the accuracy of their experimental finds is a sacrifice well worth making. The amount of additional effort to use one of these approaches is small considering the time and energy to perform a complete experiment. Those researchers who consider the validity of their experimental findings paramount have little concern in justifying their thorough means.

For counting cells, it is recommended to use the Optical Fractionator method rather than the Nv Vref method whenever possible since computer simulations have also shown that the methods to predict the CE of estimated total numbers of cells obtained with the NV Vref method do not result in adequate predictions of CE.

For quantifying volume with the Cavalieri estimator, various methods have been developed to predict the CE. In a pilot computer simulation, Schmitz and colleagues obtained CE values with the method given in Equation 4 in Roberts et al. (Roberts 1994), which were precise predictions of the actual coefficient of variation when investigating regular, “quasi-ellipsoidal” objects (C. Schmitz, personal communication). In addition, the method described in García-Fiñana et al. is a refinement of Equation 4 of Roberts et al., taking irregular objects into consideration. Therefore, this method is likely a good choice for predicting the CV of any estimates of volumes obtained with the Cavalieri estimator, provided the area estimates are based on point counting.

### REFERENCES

- Gundersen HJ, J Microsc 1986;143:3.
- Gundersen HJ, Bagger P, Bendtsen TF, Evans SM, Korbo L, Marcussen N, Moller A, Nielsen K, Nyengaard JR, Pakkenberg B, et al., Acta Pathol Microbiol Immunol Scand 96:857.
- Glaser EM, Wilson PD., J Microsc 1998;192:163.
- Schmitz C, Hof PR., J Chem Neuroanat 2000;20:93.
- Roberts N, Garden AS, Cruz-Orive LM, Whitehouse GH, Edwards RH., Br J Radiol 1994;67:1067.
- Garcia-Finana M, Cruz-Orive LM, Mackay CE, Pakkenberg B, Roberts N., Neuroimage 2003;18:505.

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*developers of Stereo Investigator, the world’s most cited stereology system *