How to asses, visualize and compare the anisotropy of linear structures reconstructed from optical sections--a study based on histopathological quantification of human brain microvessels.

Three-dimensional analyses of the spatial arrangement, spatial orientation and preferential directions of systems of fibers are frequent tasks in many scientific fields, including the textile industry, plant biology and tissue modeling. In biology, systems of oriented and branching lines are often used to represent the three-dimensional directionality and topology of microscopic blood vessels supplying various organs. In our study, we present a novel p(χ²) (chi-square) method for evaluating the anisotropy of line systems that involves comparing the observed length densities of lines with the discrete uniform distribution of an isotropic line system with the χ²-test. Using this method in our open source software, we determined the rose of directions, preferential directions and level of anisotropy of linear systems representing the microscopic blood vessels in samples of various regions from human brains (cortex, subcortical gray matter and white matter). The novel method was compared with two other methods used for anisotropy quantification (ellipsoidal and fractional anisotropy). All three methods detected different levels of anisotropy of blood microvessels in human brain. The microvascular bed in the cortex was closer to an isotropic network, while the microvessels supplying the white matter appeared to be an anisotropic and direction-sensitive system. All three methods were able to determine the differences between various brain regions. The advantage of our p(χ²) method is its high correlation with the number of preferential directions of the line system. However, the software, named esofspy, is able to calculate all three of the measures of anisotropy compared and documented in this paper, thus making the methods freely available to the scientific community.