Nearly 100,000 heart valve replacements or repairs are performed in the US every year. Mathematical models of heart valves are used to improve artificial valve design and to guide surgeons performing valve-repairing surgeries. Models can be used to define the geometry of a valve, predict blood flow dynamics, or demonstrate operating mechanisms of the valve. In this thesis we reviewed features that are typically considered when developing a model of a heart valve. The main modeling methods include representing a heart valve using lumped parameters, finite elements, or isogeometric elements. Examples of a lumped-parameter model and isogeometric analysis are explored. First, we developed a simulation for the lumped-parameter model of Virag and Lulić, and we demonstrated its ability to capture the dynamical behavior of blood pressures, volumes, and flows in the aortic valve region. A Newton-Krylov method was used to estimate periodic solution trajectories, which provide a basis for examining the response to perturbations about initial conditions. Next, an isogeometric model of a heart valve was constructed based on NURBS geometry. The mechanical stiffness of the valve was computed. We discussed how the isogeometric representation could be used in a more complex fluid-structure interaction model to measure surface shear and estimate fatigue failure.

Library of Congress Subject Headings

Heart valves--Mathematical models; Fluid-structure interaction

Publication Date


Document Type


Student Type


Degree Name

Applied and Computational Mathematics (MS)

Department, Program, or Center

School of Mathematical Sciences (COS)


Laura Munoz

Advisor/Committee Member

Nathan Cahill

Advisor/Committee Member

Tamas Wiandt


Physical copy available from RIT's Wallace Library at QP113 .K65 2016


RIT – Main Campus

Plan Codes