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Estimating length density and quantifying anisotropy in skeletal muscle capillaries
Author(s) -
Mathieu Odile,
CruzOrive LuisM.,
Hoppeler Hans,
Weibel Ewald R.
Publication year - 1983
Publication title -
journal of microscopy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.569
H-Index - 111
eISSN - 1365-2818
pISSN - 0022-2720
DOI - 10.1111/j.1365-2818.1983.tb04240.x
Subject(s) - anisotropy , parameter space , distribution (mathematics) , mathematics , biological system , mathematical analysis , physics , statistics , biology , optics
SUMMARY The accurate estimation of stereological parameters defined on anisotropic structures is a long‐standing problem. In this paper we seek to estimate the capillary length density J v in skeletal muscle tissue. A well‐known model for directional anisotropy in space, namely the ‘spherical normal’ or ‘Fisher axial distribution’ model, is found to fit the relevant data satisfactorily. Based on this model, a short‐cut estimation method is proposed and illustrated with a numerical example. This method essentially consists in taking the ratio of mean capillary profile counts, as obtained from transversal and longitudinal sections of the muscle tissue, and making use of a table or a graph given in the paper to estimate J v . The conditions under which the methods are applicable and practicable are discussed in detail. Apart from an accurate estimation of J v , an important feature of our method is the possibility of quantifying the degree of anisotropy by a coefficient K (called the concentration parameter of the Fisher axial distribution), which enjoys both a biological significance and a sound statistical basis.