Nonlinear Dynamics : міжнародна конференція
Постійне посилання на розділhttps://repository.kpi.kharkov.ua/handle/KhPI-Press/24521
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Документ Mathematical Modeling of Mitral Valve Dynamics: Nonlinear vs Linear Models(NTU "KhPI", 2016) Romashov, Yu.; Kizilova, N.; Gaidulis, G.A tractable mathematical model of the valve dynamics is developed for the real time computations and in silico planning of the biomechanically consistent surgery on the ruptured chordae of the mitral valve. The geometry and dynamics of the heart contraction and valve closure are restored by digitization of the 2d echocardiography data measured on a patient. The chordae are modeled as branched systems of viscoelastic strings with zero bending rigidity. Both linear and nonlinear rheology of the heart tissues are considered. The corresponding numerical procedure is worked out. The developed model can be used for comparative study of different existing strategy of surgical restoration for individual patients as well as for fast real time computations of optimal location of the neochordae directly during the surgery.Документ Nonlinear Model of Blood Flow Through Stenosed Coronary Arteries(NTU "KhPI", 2016) Solovyova, H.; Kizilova, N.; Mizerski, J.Blood flow and pulse wave propagation in the blood vessels are usually studied on the incompressible linearized axsymmetric Navier-Stokes equations (Womersley model) coupled with linear and nonlinear viscoelastic equations for the vessel walls. A brief review of the nonlinear models is given. Blood flow and wave propagation through the stenosed artery terminated by a viscoelastic chamber with different resistivity and compliance has been considered. The material parameters of the wall corresponded to healthy elastic and degenerated compliant human arteries. Both 2d linearized and 1d nonlinear models have been applied for numerical solution of the problem. The computational results for the pressure P(t), flow U(t) and diameter d(t) oscillations have been compared to the measurement data. It is shown that the dynamics of the fluid-filled vessels with healthy elastic walls is satisfactory described by the linearized equations while for the age-related degenerative walls, stenosed or diluted vessels the nonlinear models are preferable.