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Determination of membrane thickness distribution from orthogonal intercepts
Author(s) -
Jensen E. B.,
Gundersen H. J. G.,
Østerby R.
Publication year - 1979
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.1365-2818.1979.tb00149.x
Subject(s) - distribution (mathematics) , membrane , perpendicular , mathematical analysis , parametric statistics , mathematics , probability density function , orthogonal functions , geometry , physics , chemistry , statistics , biochemistry
SUMMARY This report deals with the reconstruction of the distribution of membrane thickness T from that of orthogonal intercept length L 0 , measured in random section planes. In such planes the membrane appears as a band and the linear distance from one of its boundaries perpendicular to the opposite one is the length of the orthogonal intercept. Using a membrane model, an integral equation relating the probability density functions of orthogonal intercept length f ( l 0 ) and membrane thickness g (τ) is derived. Relations between moments are derived and the analytic solution to the problem of reconstructing g (τ) from f ( l 0 ) is given. The parametric approach by which it is assumed that g (τ) has some known analytic form with unknown parameters is considered, and the use of a suggested analytic form for describing the thickness distribution of the human glomerular basement membrane is discussed.