Patient-specific modeling
A geometry taken from an image is only half a model. The other half is what happens at its inlets and outlets, which decides the answer as much as the anatomy does.
Boundary conditions carry the physiology
A vessel model cut out of the body must be told what the rest of the circulation does at every cut. We couple lumped-parameter models of the downstream vasculature and of the heart to the three-dimensional domain, so that pressure and flow at the boundaries follow from physiology rather than being prescribed.
For coronary flow this matters more than elsewhere: the vessels are compressed by the contracting myocardium, so the downstream model has to include intramyocardial pressure over the cardiac cycle. Regulatory mechanisms can be built into the same boundary models, letting the simulation respond to changes in demand rather than holding flow fixed.
Numerical formulation
Constraining velocity profiles at outlets keeps the problem stable at physiological Reynolds numbers without distorting the interior solution. The formulations developed for this — an augmented Lagrangian treatment of outlet profiles, and stable coupling of lumped models to the finite element domain — underlie the rest of the work in the laboratory.
Selected work
Patient-specific modeling of blood flow and pressure in human coronary arteries
Annals of Biomedical Engineering 38(10):3195–3209
Incorporating autoregulatory mechanisms of the cardiovascular system in three-dimensional finite element models of arterial blood flow
Annals of Biomedical Engineering 38(7):2314–2330
On coupling a lumped parameter heart model and a three-dimensional finite element aorta model
Annals of Biomedical Engineering 37(11):2153–2169
Augmented Lagrangian method for constraining the shape of velocity profiles at outlet boundaries for three-dimensional finite element simulations of blood flow
Computer Methods in Applied Mechanics and Engineering 198(45–46):3551–3566