Abstract
The microvascular pattern in the histological section, i.e. the point-pattern composed of capillaries perpendicular to the plane of section, contains information about the three-dimensional structure of the capillary network. Histological processing is followed by the shrinkage of tissue of uncertain magnitude. In order to obtain relevant information, the scale-independent analysis is necessary. We used an approach based on the Minkowski cover of measured set. The true fractal dimension of the point pattern is obviously of zero, but the artificial result of the algorithm can be related to the complexity of shape. We fitted the log-log plot by the modified rounded ramp function and the slope of the oblique part was used as the fractal based descriptor. We demonstrated on histological samples of the heart that this fractal-based parameter has the property of scale and rotation invariance.
Highlights
Main approach to the analysis of tissues under both physiological and pathological conditions is usually based on the analysis of two-dimensional sections
Changes of the microvascular network are associated with several pathologies including cardiovascular diseases [3], metabolic syndrome [4], and tumors [5]
Main derivation of the fractal dimension is described in the paper [9], we briefly recall important steps
Summary
Main approach to the analysis of tissues under both physiological and pathological conditions is usually based on the analysis of two-dimensional sections. Tissue processing for the histological analysis is accompanied by some artifacts including shrinkage. The magnitude of shrinkage depends on the composition of the tissue [1, 2]. The shrinkage affects quantitative analysis of the structure of tissues. The microvascular density, i.e., the surface density of capillaries on the two-dimensional histological section, is commonly used to description of the microvascular network. Changes of the microvascular network are associated with several pathologies including cardiovascular diseases [3], metabolic syndrome [4], and tumors [5]
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