Elsevier

Neuroscience

Volume 136, Issue 3, 2005, Pages 757-767
Neuroscience

Estimators of the precision of stereological estimates: An example based on the CA1 pyramidal cell layer of rats

https://doi.org/10.1016/j.neuroscience.2005.06.086Get rights and content

Abstract

Because of the complex and dynamic structure of the brain, there is perhaps no other organ system in which the application of stereological methods can contribute so much with regard to understanding normal and pathological processes. In order to design the studies in an optimal manner, with regard to the number of individuals, sections, probes, and to be able to critically evaluate the stereological studies made by others, it is important for neuroscientists to have an understanding of the precision or reproducibility of a stereological estimation procedure. This precision or reproducibility is often referred to as the coefficient of error of the estimate, which is a statistical expression for the size of the standard error of the mean of repeated estimates, relative to the mean of the estimates. Like the ‘margin of error’ associated with public opinion polls, it indicates how much the estimate would vary if it were repeated numerous times.

It is difficult and time consuming to empirically derive the coefficient of error of estimates made of features observed in histological preparations. To overcome this obstacle, it is common practice to try to get a feeling for the precision of an estimate by estimating the coefficient of error itself. In this paper, we will compare and discuss the coefficient of error of estimates of volume and cell number made with different numbers of sections and probes in the CA1 pyramidal cell layer of the rat hippocampus. The conclusions drawn from this analysis indicate that, using practically feasible and anatomically sensible sampling schemes, the Gundersen–Jensen coefficient of error estimator or the ‘Split-Sample’ coefficient of error estimator can provide useful information about the precision of stereological estimates even in highly irregular brain regions and requires little work.

Section snippets

Animals and tissue processing

Two male Wistar rats (305 and 315g) were deeply anesthetized with sodium pentobarbital and perfused transcardially with ∼500ml of a solution of 2% paraformaldehyde and 1% glutaraldehyde in 0.15M phosphate buffer (pH 7.4). The brains were removed immediately after perfusion and postfixed for 6 h. Subsequently, the brains were divided into left and right hemispheres and non-telencephalic structures were removed. The dorsal cortex was removed by a cut in the horizontal plane above the hippocampal

Volume distribution

The volume distributions of the CA1 pyramidal cell layer in a horizontal and a coronal series of sections, are illustrated in Fig. 1a and b respectively. In Fig. 1a, several sharp peaks are observed in the first one-third of the horizontal series. These peaks correspond to sections that cut the CA1 pyramidal cell layer in a plane that is close to the plane of the layer itself, i.e. in a plane that is close to being tangential to the CA1 pyramidal cell layer. These include sections in which the

Discussion

The main focus of this study has been to describe the issues that should be addressed when making a proper decision about the precision of a stereological estimation procedure, the CE, needed for a specific study. This has been done by collecting data from relatively large numbers of sections and sample sites (i.e. over-sampling) in an irregularly shaped brain structure, CA1 of the rat hippocampus. We then calculated the precision of the estimates for the different combinations of subsets of

Acknowledgments

We gratefully acknowledge the technical assistance of Irmgard Amrein. We also want to thank the participants of several NeuroStereology Workshops for the inspiration that prompted us to examine the CE in more detail. This work was supported by Swiss National Foundation (SNF) and NCCR ‘Neural Plasticity & Repair,’ and The Danish Health Sciences Research Council.

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