The superior efficiency of systematic sampling at all levels in stereological studies is emphasized and various commonly used ways of implementing it are briefly described. Summarizing recent theoretical and experimental studies a set of very simple estimators of efficiency are presented and illustrated with a variety of biological examples. In particular, a nomogram for predicting the necessary number of points when performing point counting is provided. The very efficient and simple unbiased estimator of the volume of an arbitrary object based on Cavalieri's principle is dealt with in some detail. The efficiency of the systematic fractionating of an object is also illustrated.

The efficiency of systematic sampling in stereology and its prediction

A stereological method for obtaining estimates of the total number of neurons in five major subdivisions of the rat hippocampus is described. The new method, the optical fractionator, combines two recent developments in stereology: a three-dimensional probe for counting neuronal nuclei, the optical disector, and a systematic uniform sampling scheme, the fractionator. The optical disector results in unbiased estimates of neuron number, i.e., estimates that are free of assumptions about neuron size and shape, are unaffected by lost caps and over-projection, and approach the true number of neurons in an unlimited manner as the number of samples is increased. The fractionator involves sampling a known fraction of a structural component. In the case of neuron number, a zero dimensional quantity, it provides estimates that are unaffected by shrinkage before, during, and after processing of the tissue. Because the fractionator involves systematic sampling, it also results in highly efficient estimates. Typically only 100–200 neurons must be counted in an animal to obtain a precision that is compatible with experimental studies. The methodology is compared with those used in earlier works involving estimates of neuron number in the rat hippocampus and a number of new stereological methods that have particular relevance to the quantitative study of the structure of the nervous system are briefly described in an appendix.

Unbiased stereological estimation of the total number of neurons in the subdivisions of the rat hippocampus using the optical fractionator

The new stereological methods for correct and efficient sampling and sizing of cells and other particles are reviewed. There is a hierarchy of methods starting from the simplest where even the microscopic magnification may be unknown to the most complex where typically both section thickness and the magnification must be known. Optical sections in suitably modified microscopes can be used to improve the ease and speed with which even the most demanding of these methods are performed. The methods are illustrated by practical examples of applications to a wide range of histological entities including synapses, neurons and cancer cells, glomerular corpuscles and ovarian follicles.

The new stereological tools: disector, fractionator, nucleator and point-sampled intercepts and their use in pathological research and diagnosis

This paper deals with isolated, countable items, often termed particles, in three-dimensional space. Its substance is the unbiased stereological estimation of the number, height, surface and volume of such particles without any assumptions about their shape. The full range of estimators is described, some of them for the first time, some in an improved form, several in more than one version, and all of them under the single, absolute requirement that one can in fact identify what one is quantifying on sections. In terms of the minimal number of sections for the analysis, the estimators may be classified as follows: On a single section it is possible to estimate vV, the mean volume of particles in the volume-weighted or 'sieving'-distribution. On two parallel sections, separated by a known distance, estimators exist of particle number and of all mean sizes (height, surface and volume) in the ordinary number distribution, as well as of SDN(v), the standard deviation in the number distribution of particle volumes. If the containing space is relatively transparent the sections may be two optical sections within one thick physical section. On a stack of parallel sections, at least as high as the largest particle, and separated by known distances, one can get twelve mean sizes and twelve distributions of individual sizes: all combinations of three sizes: height, surface and volume in four different types of distributions: number, height, surface and volume. Fulfilling the sampling requirements of the above two estimation principles it has been shown very recently that by combining them one may even estimate mean sizes and number of arbitrary particles in a stack of sections with constant but unknown separation. Finally, a unique, unbiased estimator of the total number of items in a specimen is described for the use of which one need not measure the distance between sections, nor their thickness, nor the volume of the specimen, nor assume anything about shrinkage/swelling, sectioning compression or lost caps. It is the fractionator.

Stereology of arbitrary particles. A review of unbiased number and size estimators and the presentation of some new ones, in memory of William R. Thompson

Neurodegenerative disorders are characterized by extensive neuron death that leads to functional decline, but the neurobiological correlates of functional decline in normal aging are less well defined. For decades, it has been a commonly held notion that widespread neuron death in the neocortex and hippocampus is an inevitable concomitant of brain aging, but recent quantitative studies suggest that neuron death is restricted in normal aging and unlikely to account for age-related impairment of neocortical and hippocampal functions. In this article, the qualitative and quantitative differences between aging and Alzheimer's disease with respect to neuron loss are discussed, and age-related changes in functional and biochemical attributes of hippocampal circuits that might mediate functional decline in the absence of neuron death are explored. When these data are viewed comprehensively, it appears that the primary neurobiological substrates for functional impairment in aging differ in important ways from those in neurodegenerative disorders such as Alzheimer's disease.

https://science.sciencemag.org/content/sci/278/5337/412.full.pdf

Life and Death of Neurons in the Aging Brain

A three-dimensional counting rule and its integral test system, the disector, for obtaining unbiased estimates of the number of arbitrary particles in a specimen is presented. Used in combination with ordinary and recently developed stereological methods unbiased estimates of various mean particle sizes and the variance of particle volume are obtainable on sets of two parallel sections with a known separation. The same principle allows the unbiased estimation of the distribution of individual particle volumes in sets of serial sections.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1365-2818.1984.tb02501.x

D. C. Sterio

Papers

The unbiased estimation of number and sizes of arbitrary particles using the disector