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.
