Semi-analytical solution of a constrained fourth-order integro-differential equation of steady flow–structure interaction in a model collapsible tube

摘要

We provide accurate, non-perturbative, semi-analytical solutions to a constrained fourth-order integro-differential equation derived by Djorjevic and Vukobratovic [On a steady, viscous flow in two-dimensional channels, Acta Mech. 163 (2003) 189–205] in the study of a steady incompressible flow through a flexible 2D tube. Our numerical experiments motivate the introduction of a global parameter that monitors the deformation of the tube as a function of material properties and flow characteristics. Physically, this parameter is proportional to the work done by the longitudinal tension on the wall. An example is provided on how this global parameter can be used to monitor coronary lesion progression. In particular, this parameter is used to define an index of criticality of such lesions.