Institutional Repository
Technical University of Crete
Technical University of Crete
EN
|
EL
| URI: | http://purl.tuc.gr/dl/dias/90B51476-698C-4932-8FAA-A05C36D29755 | ||
| Year | 2024 | ||
| Type of Item | Peer-Reviewed Journal Publication | ||
| License |
|
||
| Bibliographic Citation | S. Singh and N. Bekiaris-Liberis, "Numerical and Lyapunov-based investigation of the effect of stenosis on blood transport stability using a control-theoretic PDE model of cardiovascular flow," IEEE Control Syst. Lett. https://doi.org/10.1109/LCSYS.2024.3484635 | ||
| Appears in Collections |
We perform various numerical tests to study the effect of (boundary) stenosis on blood flow stability, employing a detailed and accurate, second-order finite-volume scheme for numerically implementing a partial differential equation (PDE) model, using clinically realistic values for the artery’s parameters and the blood inflow. The model consists of a baseline 2×2 hetero-directional, nonlinear hyperbolic PDE system, in which, the stenosis’ effect is described by a pressure drop at the outlet of an arterial segment considered. We then study the stability properties (observed in our numerical tests) of a reference trajectory, corresponding to a given time-varying inflow (e.g., a periodic trajectory with period equal to the time interval between two consecutive heartbeats) and stenosis severity, deriving the respective linearized system and constructing a Lyapunov functional. Due to the fact that the linearized system is time varying, with time-varying parameters depending on the reference trajectories themselves (that, in turn, depend in an implicit manner on the stenosis degree), which cannot be derived analytically, we verify the Lyapunov-based stability conditions obtained, numerically. Both the numerical tests and the Lyapunov-based stability analysis show that a reference trajectory is asymptotically stable with a decay rate that decreases as the stenosis severity deteriorates.
Copyright © DIAS 2013
