Choosing the optimal wall shear parameter for the prediction of plaque location—A patient-specific computational study in human right coronary arteries

doi:10.1016/j.atherosclerosis.2010.03.001

Atherosclerosis

Volume 211, Issue 2, August 2010, Pages 445-450

https://doi.org/10.1016/j.atherosclerosis.2010.03.001 Get rights and content

Abstract

Background

Average wall shear–stress (AWSS), average wall shear–stress gradient (AWSSG), oscillatory shear index (OSI) and relative residence time (RRT) are believed to predict areas vulnerable to plaque formation in the coronary arteries. Our aim was to analyze the correlation of these parameters in patients’ vessels before the onset of atherosclerosis to the specific plaque sites thereafter, and to compare the parameters’ sensitivity and positive predictive value.

Methods

We obtained 30 patient-specific geometries (mean age 67.1 (±9.2) years, all with stable angina) of the right coronary artery (RCA) using dual-source computed tomography (CT) and virtually removed any plaque present. We then performed computational fluid dynamics (CFD) simulations to calculate the wall shear parameters.

Results

For the 120 total plaques, AWSS had on average a higher sensitivity for the prediction of plaque locations (72 ± 25%) than AWSSG (68 ± 36%), OSI (60 ± 30%, p < 0.05), and RRT (69 ± 59%); while OSI had a higher positive predict value (PPV) (68 ± 34%) than AWSS (47 ± 27%, p < 0.001), AWSSG (37 ± 23, p < 0.001) and RRT (59 ± 34%). A significant difference was also found between AWSSG and RRT (p < 0.01) concerning PPV.

Conclusions

OSI and RRT are the optimal parameters when the number of false positives is to be minimized. AWSS accurately identifies the largest number of plaques, but produces more false positives than OSI and RRT.

Introduction

Spatial and temporal variations of arterial endothelial wall shear–stress (WSS) are believed to influence the location of potential atherosclerotic plaque formation [1], [2], [3]. While the correlation between WSS and plaque location is not fully understood, several parameters that are derived from WSS distribution, such as average wall shear–stress (AWSS), average wall shear–stress gradient (AWSSG), oscillatory shear index (OSI) and relative residence time (RRT) have been identified as possible indicators for atherosclerotic lesion prone sites [4], [5], [6], [7]. WSS is the direct result of blood flow and, hence, subject specific variations in arterial anatomy will influence those parameters [8]. Computational fluid dynamics (CFD) has proven to be the method of choice for obtaining accurate readings of flow and WSS distribution in subject specific arterial geometries. However, the process beginning with acquisition of the vessel anatomy using imaging techniques such as computed tomography (CT) to the processing of the CFD results, with numerous steps in between, is complex, costly and time consuming. Most previous CFD studies of the coronary arteries have been limited to a small number of vessel geometries (1–7) [9], [10], [11], [12], [13] or have used an averaged anatomy [14]. Another limitation of previous studies has been their attempt to correlate subject specific WSS parameters to common plaque locations such as vessel bifurcations, rather than with actual lesion sites of the respective subject [15].

We present herein an analysis of the hemodynamic parameters AWSS, AWSSG, OSI and RRT obtained through a CFD study on the right coronary arteries of 30 patients. The plaques in the arteries were virtually removed to replicate the healthy state of the vessels prior to the onset of atherosclerosis. We correlate these parameters to each patient's specific plaque profile, and determine the sensitivity and positive predictive value of each parameter with respect to predicting the particular plaque locations.

Section snippets

Methods

Our patient population consisted of 80% (24/30) males with an average age and body mass index (BMI) of 67.1 ± 9.2 years [range 47–84] and 26.3 ± 4.3 kg/m² [range 15.6–36.3], respectively. Demographic data and clinical characteristics of the patients are summarized in Table 1. All plaques studied were stenotic.

Results

In the 30 patients, we found with the reference standard a total of 44, 45 and 31 plaques in segments 1, 2 and 3 of the RCA, respectively. The sensitivity and PPV of correctly identified plaques for the wall shear parameters over the entire RCA are listed in Table 2A. We found AWSS to be significantly more sensitive in predicting plaque locations than OSI (p < 0.05, Table 2B). OSI proved to have a significantly higher PPV than AWSS (p < 0.001) and AWSSG (p < 0.001), as did RRT (AWSS p < 0.05) and AWSSG

Discussion

Although low AWSS, high AWSSG, high OSI and high RRT are believed to correlate to atherosclerotic lesion prone sites, to our knowledge, the work at hand is the first larger patient study to compare these parameters in patient-specific representations of healthy RCA anatomies to the same patients’ detailed plaque profiles once the vessels have become atherosclerotic.

The prevailing hypotheses that link non-uniform flow as mechanisms for the initiation of abnormal physical and biological events

Conclusion

We have shown a statistically significant difference between AWSS and OSI in sensitivity and PPV for the identification of atherosclerotic lesion prone sites in the RCA. The higher PPV of OSI and its tendency to pinpoint the precise location of plaque initiation warrant further research. Likewise, further studies should investigate RRT and its higher PPV, yet tendency to locate more of the entire plaque region. The high sensitivity of AWSS and its simple calculation would make it the prime

Conflicts of interest

We have no conflicts of interest.

Acknowledgements

We kindly acknowledge the financial support of the Swiss National Science Foundation through the National Center of Competence in Research in Computer Aided and Image Guided Medical Interventions (NCCR Co-Me).

References (28)

J.R. Buchanan et al.
Relation between non-uniform hemodynamics and sites of altered permeability and lesion growth at the rabbit aorto–celiac junction
Atherosclerosis
(1999)
Y.S. Chatzizisis et al.
Role of endothelial shear–stress in the natural history of coronary atherosclerosis and vascular remodeling: molecular, cellular, and vascular behavior
J Am Coll Cardiol
(2007)
B. Berthier et al.
Blood flow patterns in an anatomically realistic coronary vessel: influence of three different reconstruction methods
J Biomech
(2002)
J.V. Soulis et al.
Wall shear–stress in normal left coronary artery tree
J Biomech
(2006)
C.L. Feldman et al.
Determination of in vivo velocity and endothelial shear–stress patterns with phasic flow in human coronary arteries: a methodology to predict progression of coronary atherosclerosis
Am Heart J
(2002)
M. Khakpour et al.
Critical assessment of arterial transport models
Int J Heat Mass Transfer
(2008)
Y. Huo et al.
Flow patterns in three-dimensional porcine epicardial coronary arterial tree
Am J Physiol
(2007)
J.M. Zhang et al.
Numerical investigation and identification of susceptible sites of atherosclerotic lesion formation in a complete coronary artery bypass model
Med Biol Eng Comput
(2008)
D.N. Ku et al.
Pulsatile flow and atherosclerosis in the human carotid bifurcation – positive correlation between plaque location and low and oscillating shear–stress
Arteriosclerosis
(1985)
Y.S. Chatzizisis et al.
Prediction of the localization of high-risk coronary atherosclerotic plaques on the basis of low endothelial shear–stress: an intravascular ultrasound and histopathology natural history study
Circulation
(2008)

H.A. Himburg et al.

Spatial comparison between wall shear–stress measures and porcine arterial endothelial permeability

Am J Physiol Heart Circ Physiol

(2004)

J.G. Myers et al.

Factors influencing blood flow patterns in the human right coronary artery

Ann Biomed Eng

(2001)

E. Wellnhofer et al.

Novel non-dimensional approach to comparison of wall shear–stress distributions in coronary arteries of different groups of patients

Atherosclerosis

(2008)

P.H. Stone et al.

Effect of endothelial shear–stress on the progression of coronary artery disease, vascular remodeling, and in-stent restenosis in humans: in vivo 6-month follow-up study

Circulation

(2003)

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Choosing the optimal wall shear parameter for the prediction of plaque location—A patient-specific computational study in human right coronary arteries

Abstract

Background

Methods

Results

Conclusions

Introduction

Section snippets

Methods

Results

Discussion

Conclusion

Conflicts of interest

Acknowledgements

Atherosclerosis

J Am Coll Cardiol

J Biomech

J Biomech

Am Heart J

Int J Heat Mass Transfer

Flow patterns in three-dimensional porcine epicardial coronary arterial tree

Am J Physiol

Numerical investigation and identification of susceptible sites of atherosclerotic lesion formation in a complete coronary artery bypass model

Med Biol Eng Comput

Pulsatile flow and atherosclerosis in the human carotid bifurcation – positive correlation between plaque location and low and oscillating shear–stress

Arteriosclerosis

Prediction of the localization of high-risk coronary atherosclerotic plaques on the basis of low endothelial shear–stress: an intravascular ultrasound and histopathology natural history study

Circulation

Spatial comparison between wall shear–stress measures and porcine arterial endothelial permeability

Am J Physiol Heart Circ Physiol

Factors influencing blood flow patterns in the human right coronary artery

Ann Biomed Eng

Novel non-dimensional approach to comparison of wall shear–stress distributions in coronary arteries of different groups of patients

Atherosclerosis

Effect of endothelial shear–stress on the progression of coronary artery disease, vascular remodeling, and in-stent restenosis in humans: in vivo 6-month follow-up study

Circulation