Multiple Reflection Theory for Fluid-Structure Interaction in Viscoelastic Vessels and Experimental Validation

Fluid-structure interaction in viscoelastic vessels is often modelled with the motivation to understand arterial blood flow. Traveling waves in flexible vessels have been analyzed and experiments have been performed by many researchers. Theoretical models often focus either on the flow of the liquid (assuming that the wall is rigid), or on the displacement of the wall (assuming that the wall is elastic). Analytical theories on the interaction between the fluid and the wall are limited; models are typically based on numerical techniques. For assessing the validity of analytical and numerical models well-defined in-vitro experiments are of great importance. The objective of this paper is to present a transmission line analytical theory and validate it against experimental data obtained for aortic analogues. Transition line theory allows for including non-uniformities of vessels by capturing them as several uniform segments. The analytical theory is set up by multiple sections and a formulation is derived that incorporates the multiple reflections and transmissions of propagating waves through the interfaces of these sections. The pressure, flow and wall distention results obtained from the analytical model are compared with experimental data from a straight uniform tube and a tapered one with aortic relevance. The analytical results and the experimental measurements were found to be in good agreement for both the uniform and tapered tubes.