Study of the evolution of the shear stress on the restenosis after coronary angioplasty

https://doi.org/10.1016/j.jbiomech.2005.02.005Get rights and content

Abstract

In this article, we analyze the influence of fluid dynamics variables on the development of obstructive coronary artery disease in the medium term after percutaneous coronary intervention with stent implantation. We have analyzed a group of seven patients and the study is focused on the mid-right coronary artery. In these patients we have studied the relationship between wall shear stress and arterial wall thickness both immediately after stent implantation and six months later. The realistic three-dimensional (3D) reconstruction of the arteries is performed with the data obtained with intravascular ultrasound (IVUS) and angiography. The commercial code Fluent is used to solve the Navier–Stokes equations. Special attention is paid to the shear stress on the wall arteries and the corresponding thickness. The results show that there is a negative correlation for most of the cases between the wall shear stress and increase in wall thickness. A model is proposed to study the instability at the wall, and qualitative agreement is found.

Introduction

The appearance and progression of the atherosclerotic disease depend on individual characteristics, determined genetically, the presence of risk factors and local factors related to the vascular anatomy and hemodynamic variables. These local effects are indirectly inferred from the preferential distribution of the atherosclerotic plaque on specific locations, such as bifurcations and curved arteries. Also, the eccentric morphology appearing in most damaged regions and the differential composition of the plaque are due to local factors influencing the atherosclerotic disease.

Restenosis after percutaneous dilation is the major drawback of coronary angioplasty. It represents a special form of atherosclerosis due to the healing process secondary to extensive vessel trauma induced after intracoronary balloon inflation. The use of coronary stents may decrease the incidence of this phenomenon. Unfortunately, intra-stent restenosis still occurs in 20–30% of the cases following the stent implantation.

The low and oscillating wall shear stress appears to coincide with early intimal thickening in the carotid artery (Ku et al., 1985) and abdominal aorta (Moore et al., 1994). The consequences of local variations in the flow have been studied in different experimental models (Benard et al., 2003). Most of them suggest a correlation between low endothelial shear stress and wall thickness, although there is discrepancy in the results (Zarins et al., 1983; Gnasso et al., 1997; Shaaban and Duerinckx, 2000). The contribution of the hemodynamics variations to the loss of lumen after coronary angioplasty has been less studied. Wentzel et al., 2000, Wentzel et al., 2003 have made a realistic three-dimensional (3D) reconstruction similar to the method followed in this paper. They observed an inverse relationship between the shear stress and neointimal thickness. However, there is little information about the neointimal growth or decrease in stent edges and the change in fluid dynamics parameters over time after stent implantation. This work analyzes this aspect and also the neointimal behavior inside the stent.

We also present a simple model that explains the evolution in wall thickness, assuming that wall shear stress plays a significant role in the process. The model is based on the growth of the plaque wall associated to low wall shear stress. This mechanism may be unstable, and using linear theory it is shown that under some conditions it may lead to exponential growth of the wall thickness.

Section snippets

Three-dimensional reconstruction and mesh

The technique of 3D reconstruction used in this study is similar to that proposed by Wentzel et al. (2000). Briefly, intravascular ultrasound (IVUS) cross-sections with 2-mm intervals were selected, taking as the first section the one located at 4 mm distal to the stent distal edge. The last section (or the most proximal one) corresponded to the aorto-ostial junction. From each section, the luminal and external contours were manually identified. By matching the angiographically obtained catheter

Physical model

Blood has been considered as a Newtonian fluid with constant viscosity. Johnston et al. (2004) made an analysis of non-Newtonian blood models in human right coronary arteries and they found that for mid-range velocities, around 0.2 m/s, which is the value used in our case, the models were virtually indistinguishable and the Newtonian model is a good approximation. The physical properties for blood have been established from the data found in the bibliography (Ku, 1997). The values chosen for the

Results

A group of seven patients was studied with a stent implanted in the right coronary artery. Numerical simulations were done both immediately after stent implantation and 6 months later, in order to check if the fluid dynamics factors play a significant role in the development of restenosis. The geometry analyzed in this work is basically a curved artery without bifurcation. To determine the development of the atherosclerosis in the intra-stent region and at the edges of the stent, two

Instability wall growth model

An alternative model is proposed that is based in the previous ideas. It is assumed that there is a tendency for the wall thickness to increase in places where there is low wall shear stress. Apparently this mechanism is stable for flow in a tube. If the shear stress is low, the wall thickness will increase, and the cross-section of the tube will decrease; because of continuity, if the total flow rate is maintained, the velocity will increase, originating an increase in the shear stress that

Conclusions

A numerical study is made for seven patients just after stent implantation and 6 months later. Steady-state simulations for different flow rates are made and the results corresponding to an average value are presented. The results show that the implantation of a stent is not a definitive measure against the restenosis. In six out of seven cases there is a clear tendency for the wall thickness to increase where the wall shear stress is low. If only the largest wall shear stresses are considered,

Acknowledgement

This work has been carried out with the financial support of the Spanish Government through the project MOTRICO TIC2000-1635-C04.

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