Promising mathematical methods for early diagnosis of human circulatory disorders

Abstract

The aim of the study is elaboration of efficient mathematical models for early diagnostics of the cardiovascular diseases based on the blood flow rate Q(t) curves measured noninvasively in different parts of human body. Ultrasound, rheography, magnetic resonance imaging techniques could be useful for the purpose. In this paper a set of rheographic curves Q(t) has been measured in the abdominal aorta Q_c(t), left and right upper Q₁(t) and Q₂(t) and lower Q₃(t) and Q₄(t) extremities of 36 volunteers of the age 36-65. Correlation analysis has been used for each pair {Q_i(t),Q_j(t)} of the measured discrete signals and some statistical indexes have been found significant for reliable early diagnostics of blood insufficiency due to arterial narrowing, improper control and age-related degenerative changes in the blood vessel walls. It is shown that in most individuals the digital curves Q₁(t) and Q₂(t) well correspond to a linear correlation with a small dispersion, while the curves Q₃(t) and Q₄(t) are usually weakly correlated, characterized by some time shift between them, significant dispersion and in some patients have unpredictable (chaotic) dynamics. Covariance indices  for all the pairs {Q_i(t),Q_j(t)} of the curves, their spectra and the Lyapunov exponents  are calculated. It is shown that in young healthy subjects all the covariances , the spectrum has 3-4 fundamental harmonics, and all  Lyapunov exponents <0 that corresponds to regular or quasi-regular dynamics. In most elderly subjects the covariances , especially in the curves measured in the lower extremities, the spectra are complicated, and have positive Lyapunov exponents > 0, that corresponds to the possibility of chaotic dynamics. In the young healthy individuals without diseases and age-related degenerative changes of the cardiovascular system, there are some complications of the spectrum, the presence of both <0 and > 0. Thus, the values ,   and spectrum of the curves can be important parameters for early diagnosis of age-related changes and circulatory disorders. Their prompt computations can be easily done on any type of cheap and noninvasive ultrasound or impedance rheography curves. Regular measurements and accumulation of such curves in a personal database will increase the quality of individual and population healthcare.