A coupled multidomain method for computational modeling of blood flow

Flow and pressure waves emanate from the heart and travel through the major arteries where they are damped, dispersed, and reflected due to changes in vessel caliber, tissue properties, and branch points. As a consequence, solutions to the governing equations of blood flow in the large arteries are highly dependent on the outflow boundary conditions imposed to represent the vascular bed downstream of the modeled domain. The most common outflow boundary conditions, especially for three-dimensional simulations of blood flow, are prescribed constant pressure or traction and prescribed velocity profiles. In many simulations, however, the flow distribution and pressure field in the modeled domain are unknown and cannot be prescribed at the outflow boundaries. The size and complexity of the cardiovascular system necessitate a multidomain approach with models of the "upstream" regions of interest (large arteries) coupled to reduced-order models of "downstream" vessels (smaller arteries and microcirculation). To this end, I began by coupling the non-linear, one-dimensional equations of blood flow to various downstream models through a conservative variational formulation. In particular, a boundary condition was derived using the analytical solution of the linear one-dimensional equations through Green's functions. Results showed minimal artificial wave reflection. Alternative downstream models were compared by solving idealized and patient-specific problems. The coupled multidomain method was then extended to the three-dimensional setting following a similar approach and development. A new convective variational formulation was implemented into a stabilized three-dimensional finite element method. This method was used to accurately model flow distribution in a network of arteries and obtain realistic pressure, which is particularly relevant for fluid-solid interaction problems. The three-dimensional coupled multidomain method was then applied to numerous patient-specific cases including abdominal aortic aneurysms, cerebral aneurysms, thoracic-aortic coarctations, pulmonary arteries of patients with pulmonary hypertension, and surgical plans for patients with hypoplastic left heart and tricuspid atresia undergoing the Fontan procedure. Finally, limitations and opportunities to improve boundary conditions for cardiovascular flow modeling were analyzed.