Bo Duan

Date of Award


Degree Type


Degree Name

Doctor of Philosophy


The subject of this thesis is wave propagation in fluid-filled distensible tubes, with emphasis on the effects of wave reflections in pulsatile flow through vascular networks.;A computing scheme for wave propagation in vascular trees with branching junctions is developed. Due to the large number of junctions usually present in vascular trees, only one-dimensional theory is practical. The propagating waves consist of transmitted and reflected components. A generalized model of branching trees is considered. An iterative formula for pressure in each vessel is derived, which leads to explicit expressions for pressure and flow distributions in the entire tree. Pressure distributions in different tree structures are then calculated and flow features are examined.;Analytical expressions for reflection coefficients at a converging junction are derived, and the distributions of pressure and flow in a closed bypass loop with two branching vessels are obtained. Distributions of pressure amplitude in two loops simulating a coronary bypass and an abdominal bypass are then calculated using these solutions, and flow features are examined. A converging junction with multiple inflow vessels is also considered, and general governing equations which can be solved for the reflection coefficients in each of the inflow vessels are derived.;A bypass loop consisting of three branching vessels are also considered. Reflection coefficients at the junctions are obtained by transforming the loop into a tree. Analytical expressions for the distributions of pressure and flow are then derived. Again, pressure amplitude in a loop simulating a coronary bypass is calculated and wave characteristics are examined.;The main feature of our approach is that the solutions are obtained in terms of elementary functions and give transmitted and reflected wave components explicitly, hence both global and local flow properties can be studied for waves propagating in complex vascular networks. Results obtained in this thesis can be used not only to investigate wave characteristics in actual blood vessel systems, but also to lay down the necessary ground for more sophisticated real-time simulation of pulse wave propagation, which can eventually provide a useful tool for clinical analysis and diagnosis of cardiovascular diseases relating to blood flow problems.



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