Magazine article American Scientist

Blood in Motion

Magazine article American Scientist

Blood in Motion

Article excerpt

Applied mathematician George Karniadakis models how diseases alter the body's circulation.

Precisely describing how blood flows through the smallest vessels is no simple matter. Fluid dynamics comes into play, but so does particle dynamics at the level of atoms and molecules. Including every atom and molecule in a numerical model of blood circulation is not feasible, even using today's fastest computers. So applied mathematician George Karniadakis of Brown University and his colleagues have simplified. They begin on a slightly larger scale-bundling atoms and molecules into groups of 10 or more-and model blood circulation. Their technique, aided by scientists at Argonne National Laboratory, is producing new insight into the ways that diseases disrupt normal blood flow. Karniadakis spoke with American Scientist contributing editor Catherine Clabby about the work.

What are a few of the biggest challenges to modeling blood flow through vessels?

Blood is a really complex fluid with many yet-unexplored properties. Any modeling errors greatly affect simulation results. For capillaries and vessels such as arterioles and venules, which connect capillaries to arteries and veins, the difficulty is how to scale up the molecular-based modeling. So we have developed a m'ultiscale approach to capture the effects of both the flow and the particle dynamics and to quantify their interactions. The geometric complexity of the human arterial tree is another big challenge. For large arteries, MRI scans can be used to extract and reconstruct patientspecific arterial geometries, but this is not possible at the small scale. Finally, the viscous and elastic properties of blood cells and arterial walls introduce big uncertainties.

What is your multiscale technique, and how could it be medically useful?

We need to span a range of spatial and temporal scales so that we can numerically portray many components accurately. That includes proteins such as spectrin, which is part of the cytoskeleton of red blood cells, and fibrinogen, which is involved in blood coagulation. At the same time we need to reach up to the vessel scale, and we need to model how those two scales influence one another. There are no standard ways of doing that. But there have been some recent advances in coarse-graining molecular dynamics methods: ways to represent systems with less than all-atom resolution. These methods do a good job of modeling blood cells, plasma, proteins, and arterial walls while simplifying the computational complexity. The coarser-grain approach still requires supercomputers to carry out realistic simulations, but it makes the problem more manageable. We have used these models to explore what specific changes to blood flow occur in vessels affected by sickle cell disease, malaria, and brain aneurysms.

What have your new simulations revealed about how diseases disrupt blood flow?

One recent example is new insight into what causes painful episodes in people with sickle cell disease. Healthy red blood cells are round and flexible, and easily change shape to move through even the smallest blood vessels. Among people with sickle cell disease, blood cells can be hard, sticky, and abnormally shaped. They resemble sickles. The common wisdom has been that this distorted shape causes blood cells to get stuck in tiny vessels and block the flow of oxygenated blood. …

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