The Promise of Computational Fluid Dynamics As a Tool for Delineating Therapeutic Options in the Treatment of Aneurysms

In this issue of the AJNR American Journal of Neuroradiology, Steinman et al, in their article, “Image-Based Computational Simulation of Flow Dynamics in a Giant Intracranial Aneurysm,” show the potential usefulness of computational fluid dynamics (CFD) as a practical tool that can be used in the diagnosis, therapeutic planning, and postoperative monitoring of patients with intracranial aneurysms. Clearly, the computer resource requirements for the simulations performed in their study preclude such immediate applications with the use of single personal computers or workstations. However, as discussed later, this gap can actually be bridged by using currently available, state-of-the-art supercomputer systems.

One of the most important points made by Steinman et al is that the technology is now available (eg, computed rotational angiography) to generate patient-specific geometric data that can be directly integrated into a flow simulation code, which can then be used to accurately describe, in spatial and temporal detail, the hemodynamics relevant to that specific patient’s aneurysm. This is a logical extension of computational modeling of aneurysms in which great progress has been made during the last decade (1–4). Armed with this information, and with the additional capability of using the code to make predictions of the hemodynamic implications of several possible therapeutic options, the physician will be in a much better position to find an optimal procedure for the patient.

Steinman et al include examples showing how the very complex 3D, unsteady velocity, pressure, and shear stress fields associated with aneurysmal flow can be visualized. It is important to note that because of the constraints imposed by publication in a paper journal, the authors have been unable to show the true power currently available in computer visualization. In practice, physicians and researchers using these tools can watch the flow evolution through the pulsatile cycle in slow motion or freeze-frame while zooming in on the relevant area of interest. Fully 3D visualization tools are now in common usage. I suspect that physicians engaged in careful study of these simulations will eventually develop powerful intuition regarding the behavior of fluid flow within the arteries, which has eluded them until now because such information has not been available in a comprehensible form.

Accurately simulating human blood flow is a daunting task. Blood is a very complex fluid, and the human vascular tree is too intricate to even consider representing in detail on any computer in the present or foreseeable future. Potentially important factors affecting hemodynamic evolution are two-phase fluid dynamics (particulates and liquids), non-Newtonian behavior, unsteadiness of pulsatile flow, and flexibility and motion of vessel walls (5). Although present research to develop and improve models of all these elements of hemodynamics is extensive and ongoing, it is not possible to include all of them in any realistic, practical simulations. The real challenge is to establish a hierarchy of these factors and include those that are most important to the calculations at hand, considering computer resource constraints. Steinman et al chose to neglect wall motion and non-Newtonian and two-phase flow effects in their study. This is a reasonable approximation to make, considering that the emphasis in this work was on realistic vessel geometry. As the accuracy of the simulations improves or the type of blood flow being studied changes, the relative importance of the mathematical models being used must continually be reassessed. For example, the model used by Steinman et al may not be appropriate for the study of coronary artery flow, with constantly moving vessels, or the microcirculatory system, in which the erythrocyte diameter is comparable with that of vessels.

Equally important in performing hemodynamic simulations is striking a reasonable balance among the errors caused by the inadequacy of the mathematical models, the resolution limitations of the input geometry (computed rotational angiographic data), the accuracy of the numerical methods, and the spatial and temporal resolution due to the mesh generation and choice of time stepping. It is important to understand the inherent limitations of the computational simulations. It may make no sense to compute flow fields accurate to 1% if the input geometry is only accurate to 10%. Thus, code validation is an essential continuing component of CFD simulation work. In particular, any relevant fluid dynamic data that can be obtained from laboratory or clinical studies should be compared regularly with the simulations. At a minimum, this can help alert the investigator, for example, to significant errors in input geometry, which could be catastrophic in a patient-specific analysis. Improvements in laboratory and clinical fluid dynamic measurement capabilities can have a direct, positive impact on the accuracy and usefulness of the CFD simulations by helping to identify the relevant sources of error so improvements can be made. As more accurate in vivo data become available, validation comparisons such as those presented by Steinman et al can become more precise; instead of pointing out that the simulation dynamics were “broadly consistent” with the clinical data, more useful quantitative error estimates could be provided.

Future investigation in the study of the application of CFD to aneurysm treatment has two major tracks. The first is to understand as fully as possible the fluid dynamic factors leading to aneurysm formation and rupture in general. The second, which was the main focus of Steinman et al, is to predict the hemodynamics for a specific patient and to predict the resulting flows after various possible types of intervention to assist the physician in making an optimal therapeutic choice. As the authors point out, “A number of specific hemodynamic factors—notably wall shear stress, pressure and mural stress, impingement force, flow rate, and residence time—have been implicated in aneurysm growth and rupture.” However, additional research is needed to quantify the relative importance of these factors, how they might interact or correlate, and how they might relate to other factors such as mural imperfections and vessel geometry. For example, in locations common to the formation of saccular aneurysms, such as at the apex of an arterial bifurcation, it is known that maximal pressures can be two to three times greater than in the proximal artery (6). However, it is not clear whether aneurysm growth is due to a secular pattern of repeated stresses at that level or perhaps to an acute incidence in which pressures exceed those values. Once we have a better quantitative understanding of these hemodynamic issues, the value of the simulations in treating specific patients will significantly increase.

Although the application of the methods used by Steinman et al to real patients may seem unrealistic, considering the 72 hr per pulsatile flow cycle required for the computations on a 1-Hz Pentium III workstation, it is within the capability of present technology to reduce these numbers to a very realistic value. For example, the ASCI White System now running under the Accelerated Strategic Computing Initiative at Lawrence Livermore National Laboratory, has 8192 processors. On such a machine, the present calculations could be sped up by a factor of approximately 10,000, thereby reducing the computation time per cycle to a couple of minutes. With Moore’s law (a doubling of data attenuation on computers every 18 months) appearing to be on track for the next 10 to 20 years, the sorts of simulations shown by Steinman et al will become accessible in the not-too-distant future. If the medical community had sufficient interest in being able to avail themselves of such simulations, a national computational facility could be established (or an expansion of the 1000+ processor Beowulf cluster “Biowulf” at the National Institutes of Health Center for Information Technology could be planned), connected by the high speed Internet 2, that, with appropriate scheduling, would enable this application in the very near future at clinics around the country.

Since the late 1950s, CFD has played a major role in the development of more versatile and efficient aircraft. It has now become a “crucial enabling technology for the design and development of flight vehicles” (7). No serious aeronautical engineer today would consider advancing a new aircraft design without extensive computational testing and optimization. The potential of CFD to play a similar role in cardiovascular intervention is very high.