Наукові роботи. Факультет математики і інформатики
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Документ Novel methods of pulse wave diagnostics based on compression of a superficial artery(2007) Kizilova, N.Pulse wave propagation and reflection in the branching systems of viscoelastic tubes and complex resistances as a model of arterial vasculature is considered. Axisymmetric wave motion of a viscous incompressible liquid in the system is investigated in application to the pressure and flow wave propagation in the system. Expression for the input admittance of the system taking into account wave reflection at the end of the tube is obtained. The dependence of the input admittance on the geometrical and mechanical parameters of the system is investigated. It is shown that the parameters of the pressure wave (the modules and phases of different harmonics) at the inlet of the system give information on the state (normal or pathological) of the inner organs. It is shown that after a proper compression (slight or deep) some harmonics can be amplified while the others are attenuated. Based on the theory of resonant harmonics of different inner organs the novel method of pulse wave palpation is proposed. The results are compared to some other methods as separation of the pressure wave into the forward and backward components, estimation of the parameters of the reflected wave and wave-intensity analysis.Документ Flow distribution and wave propagation in arterial systems with anastomoses(2005) Kizilova, N.; Sechin, R.P.Blood flow and wave propagation in the systems of compliant tubes filled with a fluid have been examined as a model of the systemic circulation and the intraorgan arterial networks have been modeled as Windkessel elements or regular treelike branching structures. Real intraorgan vasculatures possess some geometrical regularity and can be modeled as fractal-like trees. Nevertheless blood flow in the real beds and their self-similar models have some differences. Moreover real vasculatures often have anastomoses which provide additional pathways for blood flow and wave propagation and reflection. Arterial beds in the small and large intestine, in stomach and limbs have arterial anastomoses that influence input admittance spectra of the beds in comparison with the tree-like systems.Документ A Detailed Digital Model of the Human Arterial System(2005) Kizilova, N.A detailed model of the human circulation is developed. The large systemic arteries are presented by the branching system of straight viscoelastic tubes which corresponds topology of the human circulation. Terminal elements at the outlets of the system are presented by tree-like systems with a given topology (with/without anastomoses) and certain geometrical relations between the lengths and diameters of the vessels of different branching orders and the relation between the maximal total length of the vasculature and diameter of the feeding artery. The relations have been obtained by analysis of the morphometric data. They allow correct calculations of the hydraulic resistance and wave impedance of the arterial beds of different organs. The proposed outflow boundary conditions are more preferable then the Windkessels and the regular tree-like systems because they describe both resonant properties of the intraorgan vasculatures and the distributed sources of the reflected waves. The model describes realistic pressure and flow waves and pressure-flow dependences either in the aorta or in the feeding arteries of the inner organs. The latter underlies possibility of the novel noninvasive diagnostics of the state (normal or pathological) of the intraorgan circulation by noninvasive measuring the wall oscillations and blood flow velocity in any cross-section of the feeding artery of the organ.