Modelling blood motion in deformable vessels

This project aims to introduce a novel approach in studying blood flow in deformable vessels by simultaneously considering both the fluid (blood) and the structure (vessel) through analytical and numerical approaches.

Blood distribution in body is achieved through a complex network of five types of nearly cylindrical vessels of different diameter namely arteries, arterioles, capillaries, venules, and veins. The blood flow is generated by an impulsive, pressure gradient, that is provided by heart. The vessel walls are deformable and have various thickness and elasticity properties. Blood pressure results in formation of stresses on the walls and this causes contraction of the blood vessels. The vessel wall deformation is also initiated by the attached muscles. The precise coupling between blood pressure and the vessel wall deformation results in an extremely efficient and controlled blood motion through the body. Any irregularity in the distribution system due to cardiovascular diseases may result in an unbalanced blood motion, and this could be fatal.

Cardiovascular diseases are the leading cause of death and disability in the developed world. The elasticity (and smoothness) of the wall modifies the hemodynamics (the blood flow dynamics in human vessels), which in turn affects wall stress and the associated mechanobiology, and may set into motion a complex feedback mechanism that leads to various vascular disease processes, including hypertension (high blood pressure). Understanding the blood flow in arteries requires simultaneous consideration of hemodynamics and the deformable arterial wall mechanics.

This PhD studentship project at the University of Dundee aims to introduce a novel approach in studying blood flow in deformable vessels by simultaneously considering both the fluid (blood) and the structure (vessel). This will be achieved by applying concepts that have used in studying hydroelasticity of wave interaction with deformable bodies in engineering. In this project, the blood flow will be governed by the fluid-sheet theory and the deformation of the blood vessels will be determined by use of the classic elastic-plate theory. The two-way coupling between the fluid and structure occurs at the boundaries, where the fluid pressure distribution results in the deformation of the vessel, and deformation of the wall (due to the attached muscles) modifies the flow field.

This model will allow for a wide range of studies on how the blood flow and the blood vessel affect each other; and how formation of irregular obstacles in the vessels (atherogenesis; the chronic build up of fatty material in arteries) would change the flow; or how change in the vessel wall properties (due to aging, for example) would alter the blood flow. This study will be performed primarily through analytical and numerical approaches and results of the model will be compared with available data. In this project, the student will benefit from engaging with world-renowned experts in Engineering Sciences as well as Life Sciences of the University of Dundee. 

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