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Study on Characteristic of Nonlinear Waves in Artery Blood Vessel of Human

Author: YiJinQiao
Tutor: LvKeZuo
School: Northwest Normal University
Course: Applied Mathematics
Keywords: Blood flow Neutral disturbance Blood viscosity Reductive perturbation method KdV equation Burgers equation Stress wave Pressure wave Solitary wave Shock wave
CLC: R318.01
Type: Master's thesis
Year: 2006
Downloads: 39
Quote: 0
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Abstract


In recent years, increasing the incidence of cardiovascular disease, the World Health Organization as one of the three diseases that endanger human health. So, people have been exploring an early non-invasive diagnosis of cardiovascular disease. Thus, the study of the basic law of human blood flow has important practical significance. The essence of life forms are nonlinear, blood circulation system also has a complex non-linear characteristics. Therefore, the development of hemodynamic must rely on the development of nonlinear science. The paper first introduces the basic concepts of nonlinear science of hemodynamic the current development in this field, the practical significance of this work. In the second part first prove the large arteries in the human body, there is stress wave; according to the basic assumptions of one-dimensional long straight tube, speed u, pressure p and strain ε r to meet the basic Equation. On the basis of the analysis of the dispersion relation, the application of the reductive perturbation method has been strain ε r meet the KdV equation, and gives the solitary wave solutions of the KdV equation to calculate the stress wave propagation velocity and were compared with the experimental results. This section describes the the neutral disturbance potential applications in clinical diagnosis, based on basic blood flow - Poisuille flow of appropriate amendments, according to the Navier-Stokes equations, the vorticity equation describing the disturbance stream function, application about The perturbation method proved the neutral disturbance will spread the form of a solitary wave, which concluded provides a good theoretical basis for the early diagnosis of cardiovascular disease. In addition, we also calculated based on the total stream function ψ heart stroke output V The results showed that stroke volume V with a maximum flow rate of the heart at the outlet of u max increases, The wave velocity c almost no effect on the stroke volume V. The study showed that the wave propagation in the arteries may be distorted, and ultimately the formation of shock waves. In the fourth part the description of the blood pressure Burgers equation, thus proving the possibility of shock wave is formed in the human body. However, the actual physiological parameters found in the normal human body will only waveform steepening. The last part of the analysis of a blood viscosity calculated according to the actual physiological parameter influence on the blood flow and the velocity of wave propagation, the position of the shock wave formed. The results showed that under normal physiological conditions, due to viscous dissipation, shock desired vessel length is greater than the actual length of the vessel segment is formed, it is generally the human body does not exist a complete shock.

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