title: Probability density functions for axial ratios of sectioning profiles of anisotropically arranged elliptical microvessels.
abstract: The article theoretically regards probability density functions (PDFs) for axial ratio (X/Y) of sectioning profiles of elliptical microvessels (MVs) arranged with anisotropy in a biological tissue volume. A technique for the PDF(X/Y) calculations in anisotropy of the elliptical MVs is described. The essence of this technique is introducing anisotropy in PDF(alpha,phi), i.e. the function of the joint distribution of the polar and planar angles alpha and phi, which define mutual orientation of the elliptical MVs and sectioning planes. With the aid of this technique, the anisotropy cases are studied with PDF(alpha,phi) given by pair combinations of the following distributions: (i) a uniform distribution of the angles alpha and/or phi, (ii) the angle alpha distribution with PDF(alpha)=sin alpha(alpha in [0,pi/2]), and (iii) Gaussian distributions of the alpha or phi values. Specifically, PDF(X/Y) curves are obtained for MVs with the true, or three-dimensional, axial ratio X(0)/Y(0)=2.0, and the anisotropy effects on the X/Y expected frequencies are analysed. Conclusions of this analysis, the PDF(X/Y) calculation technique, and the PDF(X/Y) curves obtained are useful for stereological reconstruction of anisotropically organised microcirculatory networks, with an ellipticity of their MVs being taken into consideration.
authors.affiliation: Proxima Technology Ltd., 5-2-64, General Karbyshev Blvd., Moscow 123154, Russia. info@proxima-t.com
authors.forename: R A
authors.initials: RA
authors.lastname: Krasnoperov
authors.forename: A N
authors.initials: AN
authors.lastname: Gerasimov