Wave propagation through vascular networks: Effects of stiffness of the vascular wall

The following work is a theoretical investigation into the influence of vascular mechanics and geometry on wave propagation through diverging, bifurcating networks with emphasis on wall stiffness.; The analysis is restricted to vessels with thin walls and to waves whose length is large compared with tube radius. The flow is axially symmetric, incompressible, inviscid and Newtonian. The model is carried out under idealized geometric conditions where the vessels of the network are modelled as straight linearly elastic tubes. Analytical expressions describing the pressure distribution and reflection coefficients are based on D'Alembert's solution of the wave equation in one dimensional theory. An iterative scheme is presented for computing the local characteristics of pressure and flow waves as they progress along a tree structure and become modified by wave reflections.; We use our method to examine wave propagation and primary wave reflections in a tube consisting of multiple segments of variable elasticity, which is extended to simulate the physiological condition of a blood vessel containing a vascular stent. Results indicate that a stiffer stent generally acts to abate wave propagation while a more elastic stent facilitates in wave propagation with the length and relative location of the stent playing an important role.; Next, we examined wave propagation due to changing wall elasticity in symmetrical and asymmetrical branching structures. The asymmetrical structures mimic three typical vascular networks; two of which represent various degrees of the arterial system and the third, the branching patterns in the vascular system of the human heart. Analysis is carried out on composite pressure waveforms as well as those of a single harmonic. It is found that the distensibility of a vessel wall directly affects the degree to which wave propagation will exist and inherently how wave reflections will be generated. A stiffened vessel located close to the tree's entrance will effectively abate wave propagation, whereas a stiffened vessel embedded internally will have a moderate affect on wave propagation globally.; The local hemodynamics in a bypass loop model with dimensions typical of those in a human coronary circulation are also studied, we find that in the absence of a bypass graft, wave reflections resulting from a narrowing and stiffening of a diseased coronary artery have the effect of actually aiding the flow in the diseased vessel. In the presence of a bypass graft, however, the effects of wave reflections are reversed and become adverse to flow in both the bypass graft and the diseased coronary artery. A stiffer bypass graft moderates these effects and is therefore preferable to a more elastic bypass. Results also indicate that a bypass of equal or smaller diameter than that of the native coronary artery can moderate and even reverse the adverse effects of wave reflections resulting from the presence of the bypass.