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Blood-vessel simulations provide valuable data for doctors
by Scott Jenkins
Computer simulations of blood flow in arteries and veins can enhance information from imaging devices and may soon help doctors make better individualized treatment decisions.
 FORCE OF FLOW – Argonne researchers are studying the force of blood flow through damaged arteries. |
Argonne computer scientist Paul Fischer has developed a computer code that calculates forces and stresses inside partially blocked blood vessels, simulating the turbulence that blockage creates. These simulations are based on medical images of the vessel from ultrasound, computer tomography (CT) or magnetic resonance imaging (MRI).
Working with Frank Loth at the University of Illinois-Chicago, Hisham Bassiouny of the University of Chicago's department of surgery, Henry Tufo of Argonne and Loth's graduate student Seung Lee, Fischer has constructed algorithms that simulate turbulence in the carotid artery, which supplies the brain's oxygen, and also in grafted veins and arteries of dialysis patients.
Understanding blood flow mechanics
Biomedical researchers studying the progression of arterial diseases are interested in the role played by the mechanical forces of blood flow.
"We want to know what forces blood exerts inside the vessels," says Fischer. For example, forces on vessel walls may be important in causing plaque to break off and to cause strokes. Also, some diseases form downstream from certain features such as grafts and blockages.
But experiments aimed at understanding forces inside blood vessels are difficult and expensive to do. That's where computer simulations can help.
Fischer has taken up the study in two areas. In the first, he works to simulate blood flow in places called stenoses, where arteries are abnormally pinched or narrow. A stenosis creates turbulence that can form blood clots or cause plaque ruptures that result in strokes. In the second, Fischer is investigating turbulence resulting from places where grafts have been stitched onto an existing vessel. His goal is to determine the role of blood turbulence in graft failures.
 TURBULENT FLOW – These pictures illustrate the turbulence during blood flow in a stenosed, or narrowed, carotid artery. See an online animation of this drawing. |
Many medical scientists suspect a link between turbulence in arteries and strokes, but very little is known in the area.
"There haven't been any published papers on direct numerical simulation of turbulence in blood vessels," says Fischer. Computer simulations offer a way to predict turbulence and resulting forces that may be relevant to diseases of the blood vessels.
From images to calculation
The computer simulations work in concert with imaging instruments to get more specific and higher-quality information on a case-by-case basis. For example, each person's carotid artery is shaped in a slightly different way. Previous studies have shown that the most important quality for gauging forces and simulating turbulence in a carotid is its shape or geometry. The shape for a given patient is provided by the image data. By taking an image of the artery from, say, an MRI machine, and converting it into a computerized model of the artery, the calculations are specific to a particular patient.
The software models the artery's image, translating the data into a set of cross-sectional slices that reproduce the shape. The cross-sections are then translated into a finite-element mesh consisting of small, deformed "bricks." Several hundred grid points are associated with each brick.
For every grid point on the bricks, the forces will be calculated over time. From the calculations will come predictions of force distributions on the vessel walls. "What we'd like to do is to give doctors quantitative information about the forces to go with the geometric information," says Fischer. The combination of the images with definite values for forces in specific locations could eventually be a powerful tool in diagnosis and treatment.
While turbulent flow in a blood vessel is an extremely complex system, certain forces are especially relevant to medicine. These include the "wall normal stress," the force exerted by the blood outward on the walls of the vessel, similar to pressure. Another is the "wall shear stress," which acts tangentially to the surface of the vessel in the direction of the flow. Fischer hopes that such data will help doctors "better quantify the stress environment for that patient rather than basing it on heuristics."
Computer power
Much of the physics behind the behavior of flowing fluids is described by the Navier-Stokes equations. These equations are solved to get the force profile of an artery. But even though the physics is known, the amount of data involved is so great that a parallel computing system is needed to do the work.
 ABNORMALLY NARROW – Blood flow simulation of an abnormally narrowed carotid artery. |
Calculations must be made for each grid point in each brick in every cross section over the time in which the calculation runs. "So you get into a system of equations with 15 to 20 million unknowns at every time step, and there might be tens of thousands of time steps," says Fischer. Even with a 256-node parallel computer, the calculations take a few days to simulate ten cardiac cycles (heartbeats) that researchers feel are adequate for capturing the details of the flow correctly.
In the future, Fischer will work on improving the algorithms to speed the calculations. Coupled with faster computers, improved algorithms will make possible the goal of taking an image, generating the finite mesh and making the simulation all in one day.
With computer systems becoming less expensive, the hope is to have a parallel computer attached to each imaging machine. The data would be fed directly from the imaging device into the computer, and the force calculations and turbulence simulations could be in the doctor's hands with the image by the end of the day.
Into the future
Before this kind of quantitative information can be used routinely, a large number of studies must be done to build a body of knowledge from which statistically relevant correlations can be drawn. Fischer and his co-workers would like to follow up their initial simulation with others, and in the next few years, have around a hundred cases for doctors to consult.
"Once that's done," says Fischer, "doctors will have some data and will be able to observe correlations - for example, associating shear stress levels with a specific disease." Fischer believes that simulations will allow doctors to make better decisions about patient treatment.
Fischer's work is funded by DOE's Office of Advanced Scientific Computing Research, the National Institutes of Health and the Whitaker Foundation. The graphics were rendered using software developed by Mike Papka in the Futures Laboratory in Argonne's Mathematics and Computer Science Division. Additional graphics assistance was provided by Mick Coady of the University of Colorado-Boulder's BP Center for Visualization.
For more information, please contact Catherine Foster (630/252-5580 or cfoster@anl.gov) at Argonne.
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