Numerical and Lyapunov-based investigation of the effect of stenosis on blood transport stability using a control-theoretic PDE model of cardiovascular flowNumerical and Lyapunov-based investigation of the effect of stenosis on blood transport stability using a control-theoretic PDE model of cardiovascular flow Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2024-10-292024enWe 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.Funded by the European Union (ERC, C-NORA, 101088147). Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them.http://creativecommons.org/licenses/by-nc-nd/4.0/IEEE Control Systems LettersEarly AccessSingh_et_al_IEEE Control Syst. Lett_preprint.pdfChania [Greece]Library of TUC2024-10-26application/pdf1.4 MBhttps://ieeexplore.ieee.org/document/10729875free Singh Shantanu Shantanu Singh Bekiaris-Liberis Nikolaos Μπεκιαρης-Λυμπερης Νικολαος Institute of Electrical and Electronics Engineers Blood flow Cardiovascular stenosis Hyperbolic PDE Lyapunov stability