Moreover, the results of pilot analyses may be used to balance precision of estimation against the natural differences between animals (biological variation). high precision per unit cost) estimates of structural quantities. By using systematic probes (see Gundersen & Jensen, 1987), sampling can also produce very efficient (i. A design-based approach to sampling satisfies the conditions necessary for maintaining the validity of relationships, giving the methods general applicability. The great strength and value of stereology resides in the two properties of unbiasedness and efficiency (Gundersen et al., 1988b). Though developed in the context of physical slicing for histology and electron microscopy, stereology is applicable wherever random slices can be generated and ingredients within those slices can be recognized unequivocally. on a transparent test overlay or on an eyepiece graticule) or volumes (represented by the space between parallel sectionģ14 planes). The probes may be points, lines or areas arranged in regular arrays (e.g. Its efficiency depends on generating chance encounters between randomly sampled sectional images and test probes superimposed on them. Therefore, it is ideal for making unbiased estimates of 3-D structural quantities from counts performed on 2-D images (Weibel, 1979 Gundersen et aI., 1988a,b Cruz-Orive & Weibel, 1990 Mayhew, 1991a). Earlier methods relied heavily on the use of simplistic models of real objects and on assumptions about object shape, size and orientation. In order to convert measurements made on 2-D slices into 3-D structural quantities, stereological methods must be exploited. deliberately choosing 'typical' or 'interesting' sections) will introduce bias, a source of error which cannot be eliminated merely by sampling more items, and which will serve only to frustrate the successful interpretation of apparent changes in structure. Selected, will provide an unbiased sample. Only rigorously defined and executed random sampling, giving every item in the population the same chance of being 0300-4864/92 $03.00 +.12 9 1992 Chapman and Hall Ltd This is particularly important given the wide range and accessibility of quantitative image analysis devices of the black-box variety.
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Regardless of their provenance and whether they are needed for qualitative or quantitative investigations, such images should always be collected by random sampling procedures, or their credentials will be suspect. cells growing on a matrix in a culture dish or contained within a thick tissue slice). The 2-D images may be (a) physical slices cut using a knife or microtome, (b) optical slices generated by focusing at different depths within a thick physical slice using a conventional optical microscope or (if the objects exhibit reflectance or fluorescence) a confocal microscope, (c) slices obtained by medical imaging such as CT, MRI and PET or (d) projected images of 3-D objects observed on a plane (e. Often this must be gleaned from essentially flat (2-D) images of real (3-D) objects. Introduction Much of modern neuroscience is concerned with abstracting information about the spatial content, arrangement and connectivity of organs, tissues, cells and cellular components. These include the counting and sizing of synapses, neurites, cells and whole brains. This review provides an account of major developments and the state of the art, emphasizes the importance of properly randomized sampling and identifies some applications to neural structure at different levels of organization. All the recent developments in stereology are applicable to problems in neuromorphometry. physical or optical sections, MRI slices, CT scans) but they must be sampled so as to be random in orientation and/or position if valid estimates are to be made.
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Stereology is ideal for extrapolating 3-D structural quantities (real volumes, surface areas, lengths and numbers) from simple counts made on 2-D slice images. No other morphometric approach currently offers these twin benefits.
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Summary The science of stereology has undergone a revolution over the past decade with the introduction of design-based (assumption- or model-free) methods which are highly efficient and generally unbiased. M A Y H E Wĭepartment of Human Morphology, Queen's Medical Centre, University of Nottingham, Nottingham NG7 2 UH, UK Received 13 August 1991 revised 3 December 1991 accepted 17 December 1991 Journal of Neurocytology 21, 313-328 (1992)Ī review of recent advances in stereology for quantifying neural structure T.