Modeling of Pressure Pulse Waves in Bypass Grafting *
- PDF / 128,140 Bytes
- 9 Pages / 594 x 792 pts Page_size
- 110 Downloads / 185 Views
SYSTEMS ANALYSIS MODELING OF PRESSURE PULSE WAVES IN BYPASS GRAFTING* I. T. Selezov1 and Iu. G. Kryvonos2
UDC 531/534:57
Abstract. We investigate the dynamics of a bypass in terms of determining the optimal parameters of shunt operation. The equations that describe the propagation of pressure pulse waves in blood vessels are presented in differential form and in approximate form for the averaged values based on the conservation laws. The correspondence of these forms is shown from the solution of the initial–boundary-value problem for vascular junction. The influence of the parameters such as various diameters, wall thicknesses, and elastic properties of blood vessels on the shunt effectiveness is investigated. In particular, we investigate the influence of the shunt form and junction area, as well as the angle of the shunt connection with the vessel, on the passage of the coronary vessels and blood coagulation. On the basis of the calculations, conclusions about the influence of various parameters on the dynamics of bypass are made. Keywords: bypass grafting, coronary artery, hydraulic losses, physicomechanical properties of blood vessels. INTRODUCTION The optimal choice of parameters in bypass grafting faces considerable difficulties caused by the complexity of phenomena and a large number of characteristic parameters. No data are currently available that describe the hemodynamics and elastic–strain properties of coronary arteries taking into account their interaction with myocardium [1]. The paper [2] considers, from the point of view of biological applications (bypass grafting and leakages in shunts), the equations that describe blood flow through the shunt for small Reynolds numbers. The analysis is reduced to a biharmonic equation for the flow function and the analytical solution is constructed by conjugation of biorthogonal expansions of the Papkovich–Fadle eigenfunctions in rectangular subdomains. The general solution is suitable to model problems of flow through two-dimensional shunts for different input and output distributions of flow. Several such profiles of flow are represented; however, the majority of the results are related to the problem of small intestine anastomosis. Various flows through the shunt are considered, a special attention is paid to determining the pressure and recirculation domains. In [3], like in [2], the analysis is based on the Stokes flow (for small Reynolds numbers). In actual practice, where there are pulse waves, the situation can be much more difficult. *
The studies were carried out in cooperation with N. M. Amosov National Institute of Cardiovascular Surgery of the National Academy of Medical Sciences of Ukraine in 2013. 1
Institute of Hydromechanics, National Academy of Sciences of Ukraine, Kyiv, Ukraine, [email protected]. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine, [email protected]. Translated from Kibernetika i Sistemnyi Analiz, No. 1, January–February, 2017, pp. 16–25. Original article submitted March 18, 2016.
Data Loading...
