Study on Natural Vibration Characteristics Based on the Coupled Wave Theory of Spring Supported Elastic Pipes and Fluids

According to WHO, cardiovascular diseases that are heart disease and stroke are the world’s biggest killers. Since the cardiovascular diseases have remained the leading causes of death globally in the last 15 years, prevention of an arteriosclerosis that is a main cause of the cardiovascular disease is important. Although an atherosclerosis is a disease which a plaque accumulates inside a blood vessel, plaque accumulation does not occur with the development of an arteriosclerosis. An early lesion of arteriosclerosis progress as functional change of endothelial cells that is uniformly distributed on the luminal surface of a blood vessel.  Focusing on dysfunction of endothelial cells as an early lesion of arteriosclerosis, an arteriosclerosis may be detectable before the blood vessels change irreversible. Since dysfunction of endothelial cells is generally caused by a wall shear stress on the endothelial cells, an estimation of the wall shear stress on the endothelial cells is one of clinical medicine concerns. Since it is difficult to non-invasively measure a wall shear stress on the endothelial cells in clinic, a wall shear stress on the endothelial cells is generally calculated from a gradient of a blood flow velocity on the endothelial cells. However, from the viewpoint of cost, it is difficult to newly apply an ultrasonic diagnostic apparatus to evaluation of the endothelial cells functions. Therefore, we focused on a blood pressure data that is obtained non-invasively by tonometry method. In previous study, we formulated a relationship between the pressure and a flow velocity based on the coupled wave theory of elastic pipes and Newtonian fluids. In addition, we estimated a flow velocity distribution and a wall shear stress by using a blood pressure data that is obtained by a tonometry method. However, the coupled wave theory is applied to elastic pipes that is assumed to be an infinite length. Hence, natural vibration characteristics that depend on boundary condition at both end of elastic pipes and fluids are not considered. A little has been reported on a relationship between the natural vibration characteristics and the boundary condition based on the coupled wave theory. On the other hand, a spring supported elastic pipe that can reflect constraint by surrounding blood vessels has not been applied to the coupled wave theory. In this study, we applied spring supported elastic pipes to the coupled wave theory and formulated a relationship between a natural vibration characteristics and boundary conditions. In addition, we investigated a natural vibration characteristics of spring supported elastic pipes and Newtonian fluids based on the coupled wave theory.