We consider a boundary control problem arising in the study of the dynamics of an arterial system which consists of one arterial segment (modeling the aorta in the cardiovascular system) coupled at the inflow with a pressurized chamber (modeling the left ventricle) via a valve. The opening and closing of the valve is dynamically determined by the pressure difference between the left ventricle and the aortic pressure. Mathematically, this is described by a 1D system of coupled PDEs for the pressure and flow in the arterial segment, with a Dirichlet boundary condition imposed on the flow (when valve is closed) or on the pressure (when valve is open). At the outflow we impose a peripheral resistance model, which leads to a non-homogeneous Dirichlet condition. A numerical scheme based on the discontinuous Galerkin method is used to approximate the solution of the resulting system. Then we use this methodology to simulate the heart rate variability observed in real physiological systems, by optimizing the timing of the heartbeat and the peripheral resistance, modeled using a terminal reflection coefficient, with the goal of achieve a prescribed mean pressure in the system.

### Boundary Control for an Arterial System

#### Abstract

We consider a boundary control problem arising in the study of the dynamics of an arterial system which consists of one arterial segment (modeling the aorta in the cardiovascular system) coupled at the inflow with a pressurized chamber (modeling the left ventricle) via a valve. The opening and closing of the valve is dynamically determined by the pressure difference between the left ventricle and the aortic pressure. Mathematically, this is described by a 1D system of coupled PDEs for the pressure and flow in the arterial segment, with a Dirichlet boundary condition imposed on the flow (when valve is closed) or on the pressure (when valve is open). At the outflow we impose a peripheral resistance model, which leads to a non-homogeneous Dirichlet condition. A numerical scheme based on the discontinuous Galerkin method is used to approximate the solution of the resulting system. Then we use this methodology to simulate the heart rate variability observed in real physiological systems, by optimizing the timing of the heartbeat and the peripheral resistance, modeled using a terminal reflection coefficient, with the goal of achieve a prescribed mean pressure in the system.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/4670705
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