Computational Analysis of Blood Flow in Arteries Incorporating Reduced-Order Models of the Downstream Vasculature.

Computational models are essential to biomechanical analyses of the cardiovascular system, enabling characterization of force and motion that is difficult to measure and prediction of a patient's response to a variety of potential treatments. To perform such feats, models must first be able to reproduce measured features of blood flow and pressure. Recent progress in simulation techniques has produced multiscale models that capture the details of blood flow in large vessels and incorporate reduced-order representations of hemodynamics in the downstream vasculature. Automatic methods are needed to make such models consistent with in vivo measurements. This dissertation describes tuning of multiscale cardiovascular models to reproduce measured hemodynamic features by adjusting reduced-order descriptions of the downstream vasculature. Detailed analyses of blood flow in proximal regions of models are performed with finite element methods, and reduced-order models of the downstream circulation are included as boundary conditions. First, three-dimensional analysis of blood flow in deformable vessels is combined with downstream three-element windkessels, which are lumped-parameter models for which the parameter values must be found. Examples of hemodynamics in the common carotid artery, the iliac bifurcation, and the abdominal aorta demonstrate the ability to achieve desired maximum and minimum pressures, the shape of the pressure waveform, and the shape of a flow waveform within the model. Next, complete models of the pulmonary arteries are developed coupling nonlinear one-dimensional blood flow analysis with analytic one-dimensional models in downstream arterial trees based on morphometric data. Determination of the hemodynamic significance of unilateral pulmonary arterial stenoses, a challenge that is typical of treatment decisions in congenital cardiovascular disease, is studied with computational models and porcine experiments. Tuning methods for the first two types of multiscale models are based on quasi-Newton algorithms. Finally, three-dimensional hemodynamic models are combined with four-element windkessel representations of morphometry-based pulmonary arteries to further analyze unilateral stenoses. A novel tuning approach is introduced employing a reduced-order surrogate that incorporates the intrinsic impedance of the multiscale model. Results of these studies suggest general application of automatic tuning methods and future developments in experimental work and more complete cardiovascular modeling.