Validation and Application of a Physically Nonlinear ID Computational Model for Bifurcated Arterial Networks

Reduced fluid-structure interaction models are the key component of hemodynamic simulation. In this work, a multi-purpose computational model applicable to specific physiological components such as arterial, venous and cerebrospinal fluid circulatory systems has been developed based on the Hamilton's variational principle. This model encompasses a viscous Newtonian fluid structure interaction (FSI) framework for the large compliant bifurcated arterial networks and its subsystems. This approach provides the groundworks for a correct formulation of reduced FSI models with an account for arbitrary non-linear viscoelastic properties of a compliant vascular tree. The hyperbolic properties of the derived mathematical model are analyzed and used to construct the Lax-Wendroff finite volume numerical scheme, with second order accuracy in time and space. The computational algorithm is validated against well-known numerical and in vitro experimental data reported in the literature for the case of human arterial trees, comprising 55 and 37 main arterial vessels. Utilizing the physics based nonlinear constitutive framework, this model can be adequately tested, calibrated and applied for patient-specific clinical diagnosis and prediction.