The existing FSI model is not a suitable representation of CSF flow in CF-LVAD patients. More studies are needed to elucidate the role of pulsatility in CSF flow and the compensatory changes in CSF production and absorption that occur in patients with CF-LVADs in whom pulsatility is diminished.

Reduced fluid-structure interaction models have received a considerable attention in recent years being the key component of hemodynamic modeling. A variety of models applying to specific physiological components such as arterial, venous and cerebrospinal fluid (CSF) circulatory systems have been developed based on different approaches. The purpose of this paper is to apply the general approach based on Hamilton's variational principle to create a model for a viscous Newtonian fluid -structure interaction (FSI) in a compliant bifurcated network. This approach provides the background for a correct formulation of reduced FSI models with an account for arbitrary nonlinear visco-elastic properties of compliant boundaries. The correct boundary conditions are specified at junctions, including matching points in a combined 3D/1D approach. The hyperbolic properties of derived mathematical model are analyzed and used, constructing the monotone finite volume numerical scheme, second-order accuracy in time and space. The computational algorithm is validated by comparison of numerical solutions with the exact manufactured solutions for an isolated compliant segment and a bifurcated structure. The accuracy of applied TVD (total variation diminishing) and Lax-Wendroff methods are analyzed by comparison of numerical results to the available analytical smooth and discontinuous solutions.

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-A modified reduced fluid-structure interaction model is derived based on expanded Hamilton's variational principle governing the coupled incompressible viscous fluid -structure interaction (FSI) in a compliant bifurcated network. To enforce the continuity equation a Lagrange multiplier is utilized which in case of an incompressible fluid coincides with fluid pressure. The first variation of an expanded action functional yields the nonlinear governing Euler-Lagrange equations for the fully coupled nonlinear fluid -structure problem with account for fluid gravity potential. The correct boundary conditions are specified at junctions as natural boundary conditions following from the variational principle. The hyperbolic properties of derived mathematical model are analyzed and used, constructing the monotone finite volume numerical scheme, second-order accuracy in time and space. The accuracy of applied TVD (total variation diminishing) and Lax-Wendroff methods are analyzed by comparison of numerical results to the available analytical smooth and discontinuous solutions.