CORRESPONDENCE: LETTER TO THE EDITOR
Reply
Takafumi Hiro, MD, PhD, FACC*,
Yusaku Fukumoto, MD, PhD,
Takashi Fujii, MD, PhD and
Masunori Matsuzaki, MD, PhD, FACC
* Division of Cardiology, Department of Clinical Science of Medicine, Yamaguchi University Graduate School of Medicine, 1-1-1 Minami Kogushi, Ube, Yamaguchi 755-8505, Japan (Email: thiro{at}yamaguchi-u.ac.jp).
We would like to express our gratitude to Drs. Li and Gillard for giving us their honest comments regarding our article (1). The key points of their criticism were: 1) we have to recognize the inherent limitations of computational fluid dynamics; and 2) we should consider the degree of stenosis, pressure distribution across the stenosis, as well as in-plaque stress, all of which may be more important in plaque rupture. We agree entirely with these comments.
Any kind of computational analysis, especially for life systems, requires many assumptions and hypotheses. To ensure its validity, all we can examine is the correspondence between the calculated results and the real-world data. The location of shear stress concentration obtained by our program, which is commercially available, corresponded almost exactly to the real location of plaque rupture. It may be true that the maximum shear stress should be at the location of the maximum stenosis; however, it comes to effect only if the cross-sectional lumen is circular or uniform in shape. The lumen shapes we analyzed were much more complicated, having non-negligible side branches, and the top of plaque hill usually did not correspond to the maximum stenosis. Furthermore, shear stress is dependent on not the peak value but the maximum "derivative" of flow velocity with respect to the distance from the vessel wall. Even if our data did not indicate the real shear stress, our method can still be useful for predicting the future rupture point.
Regarding other critical factors in plaque rupture, such as wall-distending pressure, the degree of stenosis, and in-plaque stresses, we responded to the previous letter to the editor (2). In addition to their work in 2006 (3), we also published an article in the Journal in 2005 (4) demonstrating the importance of fibrous cap thickness, lipid core, and calcification in plaque rupture. Wall-distending pressure or in-plaque stress may be much more important in driving the plaque rupture, because the degree of shear stress is very small compared with such forces. Therefore, we think that the local elevation of shear stress might become a trigger rather than a major driving force of plaque rupture. When one attempts to tear a thin paper into 2 parts, just stretching the paper is not sufficient. However, if one makes just a tiny cut in an edge of the paper, it will tear it very easily. We think that the local elevation of shear stress might form such a tiny cut-line, which may be derived from the modification of endothelial cell functions.
In our study (1), we demonstrated just such a statistical relationship between shear stress and plaque rupture. We are under the impression that plaque rupture is a multifactorial multiprocess as well as multi-interaction phenomenon that is deterministic in some ways and stochastic in others.
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References
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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. Hiro T, Fukumoto Y, Fujii T, Matsuzaki M. Local blood pressure rather than shear stress should be blamed for plaque rupture (reply) J Am Coll Cardiol 2008;52:500.[Free Full Text] 3. 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] 4. Imoto K, Hiro T, Fujii T, et al. A computational analysis of stress distribution using vessel models and three-dimensional intravascular ultrasound imaging J Am Coll Cardiol 2005;46:1507-1515.[Abstract/Free Full Text]
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