Spatial correlation analysis of isotropic microvessels: methodology and application to thyroid capillaries

The study of relations between structural organization and functions of microcirculatory networks is a major aim of modern microangiology. Such a structural aspect of microvessels (MVs) as their spatial arrangement has substantial influence on their transport and other functional properties. This paper describes a methodology of spatial correlation analysis for isotropic blood and lymphatic MVs which is based on a stereological estimator of the pair correlation function [g3D(r)] created recently by the authors for systems of elongated objects. The following main features of the methodology are presented: (i) interpretation of the shape of g3D(r) curves, (ii) their quantitative description by numerical parameters, and (iii) limitations of the method arising from statistical requirements to MVs under investigation. The methodology is considered in the light of multilevel sampling designs, which are typical for biomedical morphology. The estimator with its methodological framework is applied to perifollicular blood capillaries in the adult rat thyroid. Related methods for studying the spatial arrangement of MVs are thoroughly discussed in the paper.