There was a time when blood flow in the human body could only be represented in "still" images, which were acquired through magnetic resonance (MRI). At the National Center for Supercomputing Applications (NCSA) supported by the University of Illinois, Dr. George Karniadakis and Dr. Spencer Sherwin recently have developed and adapted the so-called NekTar computer codes to accurately model various kinds of fluid flows. The true-to-life simulation of the human blood flow allows the researchers to find adequate surgical treatment for atherosclerosis, which occurs as a fatty blockage in the vessels and causes the arteries to slowly obstruct until the heart finally stops beating. A major change in the shape of arterial grafts might encourage the blood flow to swirl down the tortuous veins. The corkscrewing turbulence prevents the arteries from silting up with plaque.
Dr. Karniadakis already started to work on the NekTar codes in 1983 as a graduate student at the Massachusetts Institute of Technology. He based his research on the spectral methods, developed by Steve Orszag at the University of Princeton, in order to display fluid flows by means of simple geometric patterns. Using this approach, which relies on Fourier analysis, Dr. Karniadakis succeeded to generate far more complex grids to simulate structured flows, affixed to the object they represent, or unstructured ones, with material flowing across them, or a mixture of both. NekTar is currently applied at NCSA by the Karniadakis-team to check out an innovative theory of turbulence. The central algorithm builds on a new class of computational calculation methods as well as on complex equations to supply an increased resolution. Hence the exceptional accuracy.
Nektar enables the researchers to zero in on selected areas of a calculation, such as the junction of an arterial graft, while the simulation is running, to introduce corrections or alterations on the spot. In this way, the overall cost for memory and computing power can be kept within limits. The complexity of the human circulatory system constitutes a challenging field of research for Dr. Karniadakis, who currently is a professor of applied mathematics at Brown University. The blood channels not only function as a transportation means for oxygen and wastes but also regulate the heating and cooling of the body. Its natural defences against atherosclerosis are impossible to detect with MRI. As a result, stent graft operations to repair blockages or replace damaged arterial tissue show a relatively high failure rate. No less than half of the prosthetic grafts tend to block likewise or fall out within ten years.
Usually, obstruction occurs at the graft junction. The majority of the grafts is joined in the same plane, perpendicular to the existing artery in order to create a U-shape around the blocked area. Dr. Spencer Sherwin, who is a former student of Professor Karniadakis, has now discovered that this type of shape is far from ideal. At the Imperial College of Science, Technology and Medicine in London, Dr. Sherwin and his team have applied a variation of one of the NekTar codes on NCSA computers to study in detail the strange nature of the blood flow. In contrast with former scientific beliefs, there is no symmetry whatsoever in the circulatory behaviour. Instead, the researchers observed two opposite corkscrew-like flows, surrounded by a similar third one. As a result, the blood moves in spirals, enhanced in this peculiar flow by the natural curves and bends of the human arteries.
The typical corkscrew swirl literally scrubs the plaque from the arteries as a natural cleaning system to slow down the process of atherosclerosis. To create a similar effect in surgical procedures, the grafts have to be attached in such a way they curve in to the blocked artery like highway on-off ramps. The Sherwin team applies the NekTar code on the SGI CRAY Origin2000 to define the most adequate shape for arterial grafts by running several blood flow simulations. In this way, the scientists are able to precisely determine at which angle sufficient friction occurs between blood and arterial wall to avoid both blockage and damage. To this purpose, a 5000-element prototype of an arterial graft has been designed from hundreds of MRI images in order to test the right angle position.
In addition, some variable parameters have been integrated into the model to take into account all changes relating to the body's different postures, such as standing up and lying down. The physical position indeed might have an influence on the blood flow velocity as does the pulsing beat of the heart, as it is pumping the blood through the veins. Due to the complex setting, every single simulation will require over 3000 computing hours. In any case, the NekTar code is performing very well since comparisons of MRI blood velocity in actual arterial grafts in the same plane as the blocked artery, as well as in the curved fashion, corresponded marvellously with the simulations. In the near future, Dr. Karniadakis and Dr. Sherwin will refine the codes in order to accurately compute the continuum of fluid flows between microscopic and atomic levels. As such, they will pay large services to the automotive and aerospace industries.
For a full account of the story, we invite you to check out the Web page of the National Center for Supercomputing Applications to explore the secrets behind the medical use of the NekTar codes in the fight against atherosclerosis.