Leading the effort is Professor Tayfun Tezduyar, James F. Barbour Professor in Mechanical Engineering at Rice University. Other key members of the team are Dr. Sunil Sathe from Rice, Professor Brian Conklin from Baylor, and Professor Keith Stein from Bethel. The question at hand for Tezduyar and his research colleagues is how computational science and computer modeling can help surgeons make treatment decisions about an aneurysm that may be endangering a patient’s life.
An aneurysm is a weak spot in the arterial wall that begins to bulge due to pressure, much like a weak spot in an inner tube. It is estimated that around five percent of people have cerebral aneurysms, but the simple presence of an aneurysm isn’t necessarily a problem. The real danger comes from an aneurysm that is in jeopardy of rupturing. While surgical intervention is possible, operating on a cerebral artery is highly invasive and comes with very significant risks. So knowing when—and when not—to operate is a serious question that is often difficult to answer.
Will It Rupture?
To give surgeons more information about if and when a rupture could occur, and thus when surgery is required, Tezduyar’s team is simulating blood flow in the cerebral arteries to identify the blood flow characteristics and the conditions under which aneurysms evolve and eventually rupture.
“We want to understand how much an arterial wall with an aneurysm deforms and how this influences the relevant characteristics of the blood flow, such as the wall shear stress generated on the arterial walls,” says Tezduyar.
Understanding exactly how blood flows through and interacts with a cerebral artery is a major computational challenge. The supple nature of the artery—and of the balloonlike aneurysm—makes accurate blood flow simulation very complex. If, for example, an artery were a rigid structure—like a pipeline with oil flowing through it—blood flow calculations would be comparatively easy. That’s because the pipeline can be seen as unchanging in the equations, leaving oil flow characteristics as the only variable. But that’s not so with blood flowing through an artery that deforms with changes in blood flow patterns and pressure.
In the case of an artery, neither the blood flow nor the structure of the artery can be seen as a constant. In other words, not only does blood flow change with each beat of the heart, but the supple artery expands and contracts with it, changing in size and shape continuously. And when the size and shape of the artery changes, this, in turn, influences blood flow conditions. For the engineer, this presents what is known as a fluid-structure interaction, where the two variables cannot be separated for study because they are constantly influencing one another.
Engineering Meets Medicine
Before ever becoming involved with biomechanics research, Professor Tezduyar was interested in designing computational methods and modeling techniques to solve complex fluid-structure interaction problems. Such methods and techniques developed by Tezduyar and his graduate students go back as far as 1992. However, it was only after starting a collaboration with biomechanics and medical researchers from the University of Tokyo in 2000 that he became involved in applying his computational methods to areas outside the traditional realm of engineering. In fact, the first journal he coauthored on this subject was in Japanese.
Today, his team is part of a growing trend where researchers of various disciplines are joining forces to solve problems. As scientists are able to tackle increasingly sophisticated questions, the techniques and knowledge required to answer them are often drawn from multiple disciplines.
Commenting on the trend, Tezduyar points out, “Quite a few people in the mechanical engineering field are looking at computer modeling of biomechanics problems. In my estimation, while a lot of the motivation and direction might be coming from medical schools, most of the computational methods and know-how are coming from engineering schools. Of course, those of us who are developing computational methods and modeling techniques need to work with medical researchers so that we better understand what needs to be modeled and how to interpret what we compute.”
A Virtual Aneurysm
To visualize what takes place within the brain, the team began by creating sections of virtual cerebral arteries with an aneurysm. The arterial sections were created with preprocessing tools and closely approximate real arterial sections that researchers imaged with computer tomography. Computations are then carried out in parallel on the Cray XD1 to simulate numerically how the artery—including the aneurysm—and blood will interact with one another. This data is finally fed into EnSight, a software program from Computational Engineering International (CEI), which allows the blood-artery interactions to be visualized and analyzed in detail.
One of the areas researchers have been studying through the visualizations is a type of stress generated on the arterial walls as a result of blood flow. The existence and extent of this stress, known as wall shear stress, depend on blood flow characteristics, such as flow patterns and velocity, and on the geometry of the artery. The T*AFSM and their Japanese collaborators have found that this is one area in particular where it has been critical to take into account the supple nature of the artery in their calculations.
They found that visual simulations where the artery was assumed to be rigid gave an incomplete view of wall shear stress’s impact on the artery. When they considered arterial wall deformation, wall shear stress results were significantly different. With such realistic modeling, researchers believe that these visualizations will one day help them better understand the progression of aneurysms.
“EnSight visualizations have helped us in many ways—and not just for final presentation media. When we compute something, EnSight also serves as a diagnostic tool to first make some sense out of our work and to check our results. For example, we need to make sure that the laws of physics are accurately represented, and EnSight has good tools that help us do that. EnSight even gives us vorticity if we want to have it, so we can look at it and try to understand what is happening with the true mechanics of the problem. Without EnSight we would have difficulty making much progress in this simulation,” observes Tezduyar.
The T*AFSM is also creating research and training opportunities for future generations of US scientists and engineers interested in computer modeling of biomechanics problems. As the team continues its work with cerebral aneurysms, the researchers already have an eye on future possible endeavors. One area of future work is to continue to adapt and improve on the numerical methods, for more effective techniques and more precise simulations. But in addition to this, the team is planning to next apply its expertise to heart valves.
With the hope of answering some of medical science’s questions and ultimately improving lives through computer modeling, these researchers will continue to wend their way through the human circulatory system, one EnSight visualization at a time.
Blood-flow patterns at an instant during the systolic cycle. The computer model is a close approximation of the computer tomography model of a middle cerebral artery segment of a 57 year-old male with cerebral aneurysm.
Blood-flow patterns at an instant during the systolic cycle. The computer model is a close approximation of the computer tomography model of a middle cerebral artery segment of a 59 year-old female with a cerebral aneurysm.