Stents are expandable tubes that are inserted into blocked or damaged blood
vessels. They offer a practical way to treat coronary artery disease, repairing
vessels and keeping them open so that blood can flow freely. When stents
work, they are a great alternative to radical surgery, but they can deteriorate or
become dislodged. Mathematical models of blood vessels and stents are helping
to determine better shapes and materials for the tubes. These models are so
accurate that the FDA is considering requiring mathematical modeling in the
design of stents before any further testing is done, to reduce the need for expensive
experimentation.
Precise modeling of the entire human vascular system is far beyond the reach of
current computational power, so researchers focus their detailed models on small
subsections, which are coupled with simpler models of the rest of the system.
The Navier-Stokes equations are used to represent the flow of blood and its
interaction with vessel walls. A mathematical proof was the central part of recent
research that led to the abandonment of one type of stent and the design of
better ones. The goal now is to create better computational fluid-vessel models
and stent models to improve the treatment and prediction of coronary artery
disease the major cause of heart attacks.
For More Information: Design of Optimal Endoprostheses Using Mathematical Modeling,
Canic, Krajcer, and Lapin, Endovascular Today, May 2006.