A stable approach for coupling multidimensional cardiovascular and pulmonary networks based on a novel pressure-flowrate or pressure-only Neumann boundary condition formulation

In many biomedical flow problems reversed flows along with standard treatment of Neumann boundary conditions (BC) can cause instabilities. We have developed a method that resolves these instabilities in a consistent way while maintaining correct pressure and flowrate values. We also are able to remove the necessary prescription of both pressure and velocities/flowrates to problems where only pressure is known. In addition the method is extended to coupled 3D/reduced-D fluid and fluid-structure interaction (FSI) models. Numerical examples mainly focus on using Neumann BC in cardiovascular and pulmonary systems, particularly coupled 3D-1D and 3D-0D models. Inflow pressure, traction, and impedance boundary conditions are first tested on idealized tubes for variousWomersley numbers. Both pressure and flowrate are shown to match the analytical solutions for these examples. Our method is then tested on a coupled 1D-3D- 1D artery example, demonstrating the power and simplicity of extending this method towards FSI. Finally, the proposed method is investigated for a coupled 3D-0D patient-specific full lung model during spontaneous breathing. All coupled 3D/reduced-D results show a perfect matching of pressure and flowrate between 3D and corresponding reduced-D boundaries. The methods are straight-forward to implement in contrast to using Lagrange multipliers as previously proposed in other studies.     «

In many biomedical flow problems reversed flows along with standard treatment of Neumann boundary conditions (BC) can cause instabilities. We have developed a method that resolves these instabilities in a consistent way while maintaining correct pressure and flowrate values. We also are able to remove the necessary prescription of both pressure and velocities/flowrates to problems where only pressure is known. In addition the method is extended to coupled 3D/reduced-D fluid and fluid-structu...     »