Numerical methods and applications for reduced models of blood flow

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dc.contributor.advisorRiviere, Beatrice
dc.contributor.advisorRusin, Craig G.
dc.creatorPuelz, Charles
dc.date.accessioned2017-08-01T18:12:08Z
dc.date.available2017-08-01T18:12:08Z
dc.date.created2017-05
dc.date.issued2017-04-11
dc.date.submittedMay 2017
dc.date.updated2017-08-01T18:12:08Z
dc.description.abstractThe human cardiovascular system is a vastly complex collection of interacting components, including vessels, organ systems, valves, regulatory mechanisms, microcirculations, remodeling tissue, and electrophysiological signals. Experimental, mathematical, and computational research efforts have explored various hemodynamic questions; the scope of this literature is a testament to the intricate nature of cardiovascular physiology. In this work, we focus on computational modeling of blood flow in the major vessels of the human body. We consider theoretical questions related to the numerical approximation of reduced models for blood flow, posed as nonlinear hyperbolic systems in one space dimension. Further, we apply this modeling framework to abnormal physiologies resulting from surgical intervention in patients with congenital heart defects. This thesis contains three main parts: (i) a discussion of the implementation and analysis for numerical discretizations of reduced models for blood flow, (ii) an investigation of solutions to different classes of models in the realm of smooth and discontinuous solutions, and (iii) an application of these models within a multiscale framework for simulating flow in patients with hypoplastic left heart syndrome. The two numerical discretizations studied in this thesis are a characteristics-based method for approximating the Riemann-invariants of reduced blood flow models, and a discontinuous Galerkin scheme for approximating solutions to the reduced models directly. A priori error estimates are derived in particular cases for both methods. Further, two classes of hyperbolic systems for blood flow, namely the mass-momentum and the mass-velocity formulations, are systematically compared with each numerical method and physiologically relevant networks of vessels and boundary conditions. Lastly, closed loop vessel network models of various Fontan physiologies are constructed. Arterial and venous trees are built from networks of one-dimensional vessels while the heart, valves, vessel junctions, and organ beds are modeled by systems of algebraic and ordinary differential equations.
dc.format.mimetypeapplication/pdf
dc.identifier.citationPuelz, Charles. "Numerical methods and applications for reduced models of blood flow." (2017) Diss., Rice University. <a href="https://hdl.handle.net/1911/96093">https://hdl.handle.net/1911/96093</a>.
dc.identifier.urihttps://hdl.handle.net/1911/96093
dc.language.isoeng
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.
dc.subjectone-dimensional blood flow
dc.subjectdiscontinuous Galerkin
dc.subjecterror estimates
dc.subjectcongenital heart defect
dc.subjecthypoplastic left heart syndrome
dc.subjecthyperbolic conservation law
dc.titleNumerical methods and applications for reduced models of blood flow
dc.typeThesis
dc.type.materialText
thesis.degree.departmentComputational and Applied Mathematics
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy
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