CORRESPONDENCE: LETTER TO THE EDITOR
Plaque Rupture: Plaque Stress, Shear Stress, and Pressure Drop
Zhi-Yong Li, PhD* and
Jonathan H. Gillard, MD
* University Department of Radiology, Cambridge University Hospitals NHS Foundation Trust, Hills Road, Cambridge CB2 0QQ, United Kingdom (Email: ZYL22{at}cam.ac.uk).
We read with interest the article by Fukumoto et al. (1) in a previous issue of the Journal. They used 3-dimensional intravascular ultrasound and computational fluid dynamics (CFD) to study wall shear stress (WSS) distribution in arteries with ruptured plaques. Their results showed that there are local elevations of WSS concentrations at proximal sites in the plaques and that these correspond to the rupture sites.
We want to emphasize that WSS is calculated as blood viscosity multiplied by the derivative of flow velocity with respect to the distance from the vessel wall ( =  x  u/y). Flow velocity varies along the stenotic artery across the plaque as the lumen narrows. Generally the maximum WSS should be at the location of the maximum stenosis, where the velocity is the highest and the lumen diameter is the smallest. There should not be any local elevation of WSS concentration if the lumen surface is smooth and there are no bad mesh elements. The use of image-based CFD can often cause problems with the geometry reconstruction and mesh generation. WSS is largely dependent on the geometry. Therefore, any effort to improve the model reconstruction and mesh generation is useful to improve the accuracy of the WSS calculation.
Pressure distribution across the stenosis is not shown in the article (1); it is not clear how pressure boundary condition was given in this study, but it is thought to be more important for plaque vulnerability. There is a pressure drop across the plaque because of the stenosis. According to the Bernoulli principle, this increased blood velocity produces a lower lateral blood pressure acting on the plaque. Thus, a pressure gradient build-up is created across the plaque that could rupture it. Any increase in systemic pressure or increase in the narrowing of the lumen would further increase the velocity through the narrowed lumen and increase the pressure drop. Furthermore, the magnitude of the pressure drop is much higher than the WSS. It can be tens to hundreds of times the magnitude of WSS for different degrees of stenosis.
Plaque stress (stress within the plaque) may be a more important factor when the mechanism of plaque rupture is considered. The arterial wall continuously interacts with hemodynamic forces, which include WSS and blood pressure. Plaque stress is the result of external hemodynamic forces. Plaque rupture itself represents structural failure of a component of the diseased vessel, and it is therefore reasonable to propose that the biomechanical properties of atheromatous lesions may influence their vulnerability to rupture. Recognizing which features contribute to this increased vulnerability may improve risk stratification and allow aggressive interventions to be targeted at patients with plaques that are prone to rupture. Therefore, when we model the mechanical process of plaque rupture, we need to look at the plaque stress and compare plaque stress with plaque material strength limit. We previously used a blood flow and plaque interaction model and demonstrated that fibrous cap thickness is critical to plaque stability (2). In this study, we also found that plaque stress in often higher at the shoulder regions at the proximal part of the plaque, and this is where plaque rupture can often be found.
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1. Fukumoto Y, Hiro T, Fujii T, et al. Localized elevation of shear stress is related to coronary plaque rupture: a 3-dimensional intravascular ultrasound study with in-vivo color mapping of shear stress distribution J Am Coll Cardiol 2008;51:645-650.[Abstract/Free Full Text]2. Li ZY, Howarth SP, Tang T, Gillard JH. How critical is fibrous cap thickness to carotid plaque stability?. A flow-plaque interaction model. Stroke 2006;37:1195-1199.[Abstract/Free Full Text]
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- Takafumi Hiro, Yusaku Fukumoto, Takashi Fujii, and Masunori Matsuzaki
J. Am. Coll. Cardiol. 2008 52: 500.
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