Phase maps for networks of polycrystalline human biological liquids: Statistical and fractal analyses

Abstract

Performed in this work are complex statistical and fractal analyses of phase properties inherent to birefringence networks of liquid crystals consisting of opticallythin layers prepared from synovial fluid taken from human joints. Within the framework of a statistical approach, the authors have investigated values and ranges for changes of statistical moments of the 1-st to 4-th orders that characterize coordinate distributions for phase shifts between orthogonal components of amplitudes inherent to laser radiation transformed by synovial fluid layers for human joints with various pathologies. Using the Gramm-Charlie method, ascertained are correlation criteria for differentiation of phase maps describing pathologically changed liquid-crystal networks. In the framework of the fractal approach, determined are dimensionalities of self-similar coordinate phase distributions as well as features of transformation of logarithmic dependences for power spectra of these distributions for various types of human joint pathologies.