Understanding Effect of Arterial Viscoelasticity on Blood Hammer Using Multi-Scale Perturbation Analysis

The blood hammer in arteries is a common phenomenon that may be frequently caused by the blooding flowing and stopping from the heart system and other unexpected or external interference on the blooding system (e.g., blood clots or drastic body movement). Particularly, the existence of blood clots and severe blood hammer may lead to potential problems in arterial systems (e.g. intracerebral hemorrhage and cerebral thrombosis). Thus, it is of great practical significance to understand the behavior of the blood hammer and its associated issues.

This paper aims to examine the transient blood flows in arteries under the different influence conditions. Specifically, the commonly used water hammer analysis method in water piping systems is adapted and applied to mimic and analyze the transient blood flows in arteries. As a preliminary study in this paper, the impact of the arterial viscoelasticity on the transient blood flow behavior is firstly investigated by the multi-scale perturbation method that has been widely applied to other fluid systems such as free surface water and water supply systems. To this end, the blood flow is assumed to be laminar, since for most of the blooding flow cases, Re < 200. As a result, the linear steady friction equation and the analytical weighting function based unsteady friction model can be implemented into the analytical analysis by the multi-scale perturbation method. In the meantime, the deformable arterial wall is mimicked by imposing the viscoelastic deformation in the continuity equation as it has been conducted in the plastic pipe water hammer problems in the literature.

Through this study, it is expected to obtain an analytical expression for describing the blood pressure wave propagation in arteries under different conditions of flow oscillation and arterial scales. Thereafter, the analytical results are further applied to examine the influence of anomalous condition in the arteries such as blood clots, so as to explore the possibility of a new and innovative method of using transient blood flow signals (blood hammer waves) to identify and analyze the blood clots in arteries. The results and findings of this study may provide useful information and tool for the diagnosis of organic blooding systems.