Key result
A mathematical model of blood flow demonstrated that blood viscosity attenuates nonlinear wave amplitude in small arteries, while varying arterial parameters amplify it in large arteries.
This mathematical model demonstrates how blood viscosity and arterial parameters influence the propagation, attenuation, and reflection of blood pressure waves in inhomogeneous vessels.
A model for describing blood pressure propagation wave in artery is proposed. Considering blood viscosity, slowly varying arterial parameters and arterial bifurcations, we obtain the dynamical equation of blood flow. We show that the blood viscosity attenuate the nonlinear blood wave amplitude mainly in small artery. On the other hand, the variation of arterial parameters (such as radius and Young's modulus) amplify the amplitude of the nonlinear blood wave in large arteries. We also investigate how the nonlinear blood wave (or a soliton) is reflected and transmitted at the arterial bifurcations. It can be concluded that the parameters at the bifurcation determine whether there is substantial reflection or not, but the transmission in each bifurcation is approximately the same as the incident wave.
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Wen-Shan et al. (1997) studied Blood pressure propagation wave in artery. Mathematical model of blood flow was evaluated on Blood wave amplitude and reflection/transmission at bifurcations. A mathematical model of blood flow demonstrated that blood viscosity attenuates nonlinear wave amplitude in small arteries, while varying arterial parameters amplify it in large arteries.
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