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Some Stereological Principles in Morphometric Cytology

Franklin, Joel N. (1977) Some Stereological Principles in Morphometric Cytology. SIAM Journal of Applied Mathematics, 33 (2). pp. 267-278. ISSN 0036-1399. http://resolver.caltech.edu/CaltechAUTHORS:FRAsiamjam77

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Abstract

In this paper several statistical methods are developed that are of use in morphometric cytology, for the purpose of obtaining three-dimensional information from two-dimensional measurements made on cell sections. An estimator is described for counting $N_V $, the number of organelles (e.g., mitochondria) per unit of cellular volume. Unlike those currently employed, this estimator for $N_V $ does not depend on the sizes of the organelle bodies. The remainder of the paper discusses the axis ratios, $t$, of elliptical cross sections that are the intersections of an ellipsoid with random planes. For prolate spheroids, an explicit formula is developed for the probability density. For general ellipsoids, a numerical method is presented for calculating the distribution function. As one approach toward deriving information about organelle shape, frequency distributions of $t$ derived by these techniques may be compared with experimental frequency distributions of the axis ratios of organelle cross sections.


Item Type:Article
Additional Information:©1977 Society for Industrial and Applied Mathematics Received by the editors June 4, 1976, and in revised form October 29, 1976.
Record Number:CaltechAUTHORS:FRAsiamjam77
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:FRAsiamjam77
Alternative URL:http://dx.doi.org/10.1137/0133016
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4870
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:11 Sep 2006
Last Modified:26 Dec 2012 09:02

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