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Original article
Computational fluid dynamic measures of wall shear stress are related to coronary lesion characteristics
  1. Jun-Bean Park1,
  2. Gilwoo Choi2,3,
  3. Eun Ju Chun4,
  4. Hyun Jin Kim2,
  5. Jonghanne Park1,
  6. Ji-Hyun Jung1,
  7. Min-Ho Lee5,
  8. Hiromasa Otake6,
  9. Joon-Hyung Doh7,
  10. Chang-Wook Nam8,
  11. Eun-Seok Shin9,
  12. Bernard De Bruyne10,
  13. Charles A Taylor2,11,
  14. Bon-Kwon Koo1,12
  1. 1Department of Medicine, Seoul National University Hospital, Seoul, South Korea
  2. 2HeartFlow, Inc., Redwood City, California, USA
  3. 3Department of Surgery, Stanford University Medical Center, Stanford, California, USA
  4. 4Department of Radiology, Seoul National University Bundang Hospital, Seongnam-si, Gyeonggi-do, South Korea
  5. 5Department of Medicine, Soonchunhyang University Hospital, Seoul, South Korea
  6. 6Department of Medicine, Kobe University Graduate School of Medicine, Kobe, Japan
  7. 7Department of Medicine, Inje University Ilsan Paik Hospital, Goyang-si, Gyeonggi-do, South Korea
  8. 8Department of Medicine, Keimyung University Dongsan Medical Center, Daegu, South Korea
  9. 9Department of Cardiology, Ulsan University Hospital, University of Ulsan College of Medicine, Ulsan, South Korea
  10. 10Cardiovascular Center Aalst, OLV-Clinic, Aalst, Belgium
  11. 11Department of Bioengineering, Stanford University, Stanford, California, USA
  12. 12Institute of Aging, Seoul National University, Seoul, South Korea
  1. Correspondence to Dr Bon-Kwon Koo, Department of Internal Medicine and Cardiovascular Center, Seoul National University Hospital, 101 Daehang-ro, Chongno-gu, Seoul 110-744, Korea; bkkoo{at}


Objective To assess the distribution of pressure and shear-related forces acting on atherosclerotic plaques and their association with lesion characteristics using coronary CT angiography (cCTA)-based computational fluid dynamics (CFD) model of epicardial coronary arteries.

Methods Patient-specific models of epicardial coronary arteries were reconstructed from cCTA in 80 patients (12 women, 63.8±9.0 years). The pressure and wall shear stress (WSS) in left anterior descending coronary arteries were assessed using CFD. High-risk plaques were defined as the presence of at least one of the following adverse plaque characteristics: low-density plaque, positive remodelling, napkin-ring sign and spotty calcification.

Results At resting condition, 39.5% of stenotic segments (% diameter stenosis 52.3±14.4%) were exposed to high WSS (>40 dyne/cm2). When the stenotic lesion was subdivided into three segments, the distribution of WSS was different from that of pressure change and its magnitude was highest at minimal lumen area (p<0.001). High pressure gradient, proximal location, small lumen and short length were independent determinants of WSS (all p<0.05). The plaques exposed to the highest WSS tertile had a significantly greater proportion of high-risk plaques. The addition of WSS to % diameter stenosis significantly improved the measures of discrimination and reclassification of high-risk plaques (area under the curves from 0.540 to 0.718, p=0.031; net reclassification index 0.827, p<0.001).

Conclusions The cCTA-based CFD method can improve the identification of high-risk plaques and the risk stratification for coronary artery disease patients by providing non-invasive measurements of WSS affecting coronary plaques.

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Although atherosclerosis is a systemic process, it remains a geometrically focal disease, suggesting the importance of local haemodynamic factors. Furthermore, it is well known that plaque rupture predisposes at certain locations within a plaque and within a vessel.1–3 Mounting evidence has shown that haemodynamic parameters of coronary arteries such as pressure and wall shear stress (WSS) contribute to plaque development, progression, instability and acute clinical events.4–6 The pressure-derived index, fractional flow reserve (FFR), is an independent prognosticator in patients with coronary artery disease (CAD), and FFR-guided revascularisation can improve outcomes of patients with CAD.7 On the other hand, WSS is considered as another important haemodynamic parameter influencing plaque development, progression and transformation.8 ,9 Recently, very high WSS has been reported to contribute to plaque transformation and rupture.10–12 Despite these potential clinical implications of WSS in managing CAD, its distribution in advanced coronary atherosclerosis and the underlying geometric and haemodynamic parameters affecting WSS have not been adequately described in patient-specific coronary models.

The combination of computational fluid dynamics (CFD) and CT technologies enables a simulation of coronary flow conditions in the patient-specific coronary model and allows non-invasive assessment of in vivo haemodynamic parameters including blood velocity, pressure, pressure gradients, FFR and WSS.13–15 CFD methods have been thoroughly validated in many research areas and actively used in assessing coronary haemodynamics using models derived from invasive intravascular images.12 ,16 The non-invasive CT-based CFD model is particularly advantageous in assessing the haemodynamics over the entire coronary trees, which invasive method cannot accomplish.

We sought to non-invasively assess the distribution of pressure and shear-related forces acting on atherosclerotic plaques and their association with lesion characteristics using coronary CT angiography (cCTA)-based CFD analysis of coronary haemodynamics.


Study population

The study population comprised 80 stable patients with suspected or known CAD who underwent invasive coronary angiography (ICA) and FFR with the available cCTA within 3 months of ICA and FFR. Patients with a history of myocardial infarction, previous coronary revascularisation or complete occlusion of any coronary artery were excluded. This retrospective study protocol was approved by the institutional review boards of each site, and is in accordance with the Declaration of Helsinki.

Invasive coronary angiography and fractional flow reserve

Selective ICA was performed by standard techniques. All angiograms were reviewed at a core laboratory in a blind fashion. Quantitative coronary angiography (QCA) was performed by an independent analyser blinded to FFR results. Using the guide catheter for calibration and an edge detection system (CAAS 5.7 QCA system, Pie Medical, Maastricht, the Netherlands), the reference vessel diameter and minimal lumen diameter were measured and the per cent (%) diameter stenosis was calculated. The FFR was measured using a 0.014-inch pressure-monitoring guidewire (Pressure-Wire Certus, St Jude Medical Systems, Uppsala, Sweden). Maximal hyperaemia was induced with a continuous intravenous infusion of adenosine or ATP at the rate of 140 μg/kg/min.

Image acquisition of cCTA and CFD analysis

The cCTA images were obtained in accordance with the Society of Cardiovascular Computed Tomography Guidelines on Performance of cCTA, with 64 or higher detector row scanner platforms. Oral β-blocker was administered for any subjects with a heart rate ≥65 bpm. Immediately before the cCTA acquisition, 0.2 mg sublingual nitroglycerine was administered. All cCTA data were analysed by a single core laboratory (HeartFlow, Redwood City, California, USA) in a blinded manner.

Coronary segmentation was achieved following the same procedure as FFRCT computation as described by Taylor et al,14 ,17 including the extraction of topology of the coronary artery trees, identification of coronary plaques and segmentation of lumen boundary along the coronary trees. Coronary flow and pressure were computed by solving the Navier-Stokes equations numerically based on finite element methods in a computational domain of patient-specific coronary geometry with assumptions of a rigid wall and a Newtonian fluid.18 The boundary conditions of CFD were assigned based on myocardial mass, vessel sizes at each outlet and the response of the microcirculation to adenosine.14 ,17 Specifically, total coronary flow at rest was estimated on the basis of myocardial mass of individual patients to compute a total baseline coronary resistance. The total baseline resistance was distributed to each coronary artery based on vessel calibre and reduced to model hyperaemia according to the effect of adenosine on the resistance change of the coronary microcirculation. To compare CFD analysis of coronary arteries according to disease state, vessel segments were labelled as stenotic when a stenosis was >30% by visual estimation. The other segments without stenosis and major bifurcation were defined as non-stenotic. For qualitative visual comparison, CFD results were displayed in straightened and unfolded configurations using coordinate transformations in a curvilinear coordinate system defined by the directions of vessel length, radius and circumference (see online supplementary figure S1). For quantitative analyses, haemodynamic metrics including non-invasive FFR from cCTA data (FFRCT), WSS, pressure, pressure drop over length (ie, pressure gradient) and traction were computed from CFD results (see online supplementary figure S2). A detailed description of each metric and processing method is provided in the online supplementary method. To investigate haemodynamic characteristics over the entire coronary length, metrics were averaged over a thin strip (2 mm thickness) of the coronary model with 0.5 mm intervals along the coronary centrelines. To investigate local characteristics within stenotic lesions, each stenotic lesion was divided into upstream, minimal lumen area (MLA) (3 mm length) and downstream segments with respect to the identified MLA location. The haemodynamic quantities were then averaged over the subdivided segments.

Analysis of coronary plaque characteristics

Coronary lesions were defined as plaques of an area ≥1 mm2 within and/or adjacent to the vessel lumen, which could be clearly distinguished from the lumen and surrounding tissue.19 For each coronary lesion, the presence of adverse plaque characteristics (APC), which were defined as low-density plaque, positive remodelling, napkin-ring sign and spotty calcification, was assessed in the MLA segment. This interpretation was performed by an independent observer blinded to the clinical data and CFD results, based on previous studies.13 Briefly, plaque density was assessed using an automated software programme that can analyse each pixel within the plaque. The low-density plaque was defined as the plaque density with lower than 30 Hounsfield units (HU). To identify the presence of low-density plaque, a region of interest was placed on at least five randomly selected points within each plaque, and the mean value was defined as the plaque density.20 The remodelling index was calculated as the outer vessel diameter at the site of maximal stenosis divided by the reference diameter. A remodelling index threshold of ≥1.10 was used to define positive remodelling. The napkin-ring sign was defined as a ring-like attenuation pattern of the coronary plaque with peripheral high attenuation tissue surrounding a central lower attenuation portion (see online supplementary figure S3), which has been increasingly recognised as a key feature of high-risk plaques.20 ,21 Spotty calcification was defined as a small (<3 mm), dense (>130 HU) plaque component surrounded by non-calcified tissue of the plaque. A plaque with at least one feature of APC was defined as a high-risk plaque. The WSS averaged over the MLA segment was used to assess the association between APC and WSS.

Statistical analysis

Categorical and continuous variables are given as counts (percentages) and as mean±SD or median (IQR), respectively. Mean values of FFRCT and invasive FFR were compared using the paired t-test. To compare APC across WSS tertiles, we used the χ2 test for categorical variables and analysis of variance for continuous variables, respectively. Pearson's correlation coefficients were calculated to determine the relationship among haemodynamic parameters pertaining to plaque stress. Lesion-based bivariate and multivariate analyses were performed using the generalised estimating equation approach to account for the clustered nature of data, that is, several lesions within the same patient. The association between WSS and high-risk plaques was modelled with logistic regression, and non-linearity was explored using multivariable fractional polynomials (MFP). We constructed receiver operating characteristic curves and determined their area under the curves (AUC) to assess the ability of the variables of interest to discriminate plaques with APC. The incremental value of WSS in discriminating APC was explored by constructing two models, one with luminal narrowing alone and the other with luminal narrowing plus WSS. The AUC in each model was calculated and compared for statistical significance. The category-free net reclassification index (NRI) and integrated discrimination improvement (IDI) analyses were conducted. All statistical analyses were conducted with SPSS V.22 (IBM SPSS Statistics, Chicago, Illinois, USA) and R V.3.2.1 ( A two-sided p value <0.05 was considered as significant.


Baseline characteristics

Baseline characteristics are summarised in table 1. The median interval between cCTA and ICA was 29 (IQR 13–49) days, with no clinical events between the tests. The mean values of FFRCT and invasive FFR were 0.79±0.11 and 0.78±0.12 (p=0.480), respectively. Seventy-nine stenotic lesions were found and the distribution of lesions was as follows: left main coronary artery (n=8), proximal left anterior descending coronary artery (LAD) (n=37) and mid-LAD (n=34). The MLA by cCTA and % diameter stenosis by QCA were 2.1±1.0 mm2 and 52.3±14.4%, respectively. High-risk plaques were found in 44 of 79 stenotic lesions (55.7%) and the most common feature was positive remodelling (50.6%).

Table 1

Baseline characteristics

Distribution of haemodynamic parameters

Online supplementary figure S2 illustrates that idealised stenosis models were constructed to demonstrate the distribution of haemodynamic parameters in an idealised model. Representative examples of patient-specific CFD analyses are shown in figure 1. In non-stenotic segments, mean WSS was 13.7±7.0 dyne/cm2 and 86.8% had WSS of <20 dyne/cm2 at resting condition. The WSS values in stenotic segments were higher than those in non-stenotic segments and 39.5% of stenotic segments were exposed to WSS of >40 dyne/cm2 at resting condition (figure 2A, B).

Figure 1

Representative examples. Two representative cases showing ICA, invasively measured FFR (left), FFRCT and WSS along the length of the vessel (right). The elevation of WSS was observed at the point where pressure gradient, and thus ΔFFRCT existed. (A) The ICA demonstrated diffuse luminal narrowing along the LAD, which was also displayed on luminal surface extracted from the cCTA image. The change of WSS was not prominent as FFRCT decreased gradually along the diffuse stenotic segment. (B) Two discrete stenoses in the proximal and mid-LAD caused abrupt decrease in FFRCT in a stepwise manner. Notable peaks of WSS were coupled with marked drops of FFRCT at these two stenotic lesions. cCTA, coronary CT angiography; FFRCT, coronary CT angiography-derived fractional flow reserve; ΔFFRCT, delta of FFRCT; ICA, invasive coronary angiography; LAD, left anterior descending coronary artery; WSS, wall shear stress.

Figure 2

Distribution of wall shear stress (WSS) in non-stenotic and stenotic segments at resting condition. Higher WSS was shown in stenotic (B) than in non-stenotic segments (A) at resting condition.

The analysis using the three divided regions of a stenotic lesion demonstrated the different distribution of WSS and Δ pressure (figure 3A, B). The WSS was highest in the MLA segment at resting and hyperaemic conditions. However, the Δ pressure was similar in upstream and MLA segments.

Figure 3

Difference in spatial distribution of haemodynamic parameters according to sublesion region. The MLA segment exposed to the highest WSS (A) at resting and hyperaemic conditions. The upstream shoulder was the segment where Δ pressure (B) was greatest at both conditions. *p<0.001. MLA, minimal lumen area; NS, not significant; WSS, wall shear stress; Δ pressure, delta of pressure.

Determinants of WSS

There was a strong positive relation between WSS and pressure gradient across the lesions at resting (r=0.969, p<0.001) and hyperaemic conditions (r=0.962, p<0.001) (see online supplementary figure S4). When stenotic lesions were classified according to lesion locations, the WSS was significantly higher with a more proximal location of stenotic lesions, at both resting and hyperaemic conditions (see online supplementary table S1). By multivariate analyses, peak pressure gradient, blood flow, MLA, lesion length and lesion location were independent determinants for the magnitude of WSS at both resting and hyperaemic conditions (table 2).

Table 2

Anatomic and haemodynamic determinants of WSS

WSS and plaque characteristics

Characteristics of coronary plaques stratified by the tertiles of WSS are shown in table 3. The plaques exposed to the highest WSS tertile had a significantly greater proportion of high-risk plaques. Specifically, low-density plaque or napkin-ring sign was significantly more prevalent in the highest WSS tertile, whereas positive remodelling tended to be more frequent in the highest tertile. Spotty calcification was not observed in the lowest tertile. When the logistic regression model with MFP was used to explore the association between WSS and high-risk plaques, the OR of high-risk plaques increased as the value of WSS increased. Notably, we found that the OR of high-risk plaques also increased when the value of WSS decreased below 40 dyne/cm2 (figure 4). The strong association of WSS with high-risk plaques was reflected by the significant AUC (0.673, p=0.005). However, the AUC value of % diameter stenosis for high-risk plaques was not significant (0.540, p=0.539) (see online supplementary table S2). The addition of WSS to % diameter stenosis significantly improved the measures of discrimination and reclassification of high-risk plaques (AUC from 0.540 to 0.718, p=0.031; category-free NRI 0.827, p<0.001; IDI 0.131, p<0.001) (table 4). This incremental value of WSS over % diameter stenosis was observed for each feature of APC except for spotty calcification.

Table 3

Adverse plaque characteristics according to tertiles of resting WSS

Table 4

Incremental value of WSS over luminal narrowing for assessing adverse plaque characteristics

Figure 4

Association between wall shear stress (WSS) and high-risk plaques. Adjusted fractional polynomial logistic regression showed the relationship between WSS and high-risk plaques (red line: log OR, shaded area: 95% CI). Note that the OR of high-risk plaques increased at both extremes of WSS with the lowest OR at the physiological range of WSS (≈40 dyne/cm2). The OR has been adjusted for the distance from left main ostium and % diameter stenosis.


The major findings of our study are as follows: (1) stenotic segments were exposed to much higher WSS levels compared with non-stenotic segments; (2) the distribution of WSS was different from that of pressure change in a stenotic segment; (3) WSS was closely associated with pressure gradient, lesion location, MLA and lesion length; and (4) WSS had an incremental value over luminal narrowing in discriminating high-risk plaques. These findings suggest that this cCTA-based CFD method can be potentially used to assess various haemodynamic parameters and to elucidate the link between haemodynamic forces and plaque-related clinical events and help to improve the risk stratification for patients with CAD.

Extensive studies on the contribution of WSS to plaque development and progression have been published.22 ,23 Recently, the implication of high WSS in atherosclerosis has gained increasing interest, especially due to its relationship with plaque vulnerability and rupture.2 ,11 ,12 ,24 High WSS is reported to induce thinning of plaque caps by promoting plasmin-induced metalloproteinase activity, smooth muscle cell apoptosis and decreased matrix synthesis.8 Our study showed that 39.5% of stenotic segments were exposed to very high WSS (>40 dyne/cm2) at resting condition. The prevalence of high WSS in patients with CAD observed herein contrasts to a previous study that focused on the analysis of low WSS in relation to plaque progression.23 We think that this difference is mainly caused by the significant difference in the degree of stenosis enrolled in the studies.8 Indeed, the lower tertile limit for MLA in our study was 1.5 mm2, whereas that in the previous study was approximately 6 mm2. Moreover, other studies in carotid and coronary arteries with clinically significant stenoses also demonstrated that those lesions were exposed to the high WSS.11 ,16 ,25 ,26

The distribution of haemodynamic parameters differed according to the sublesion regions in our study. Specifically, the highest WSS and pressure difference were located at the MLA and upstream shoulder, respectively. Our findings are consistent with previous studies evaluating plaque rupture sites within plaques.1 ,11 ,24 ,27 Fukumoto et al2 demonstrated that all coronary plaque ruptures occurred at the upstream or mid-portion of plaques and the distribution of high WSS was frequently colocalised with that of plaque rupture. However, WSS is not the only mechanical force causing plaque disruption since the pressure-related force across the stenotic lesion can also contribute to plaque rupture.5 ,6 Furthermore, due to the significantly smaller magnitude of WSS-related force than pressure-related force, the high WSS was suggested to weaken the plaque rather than act as a direct force for the occurrence of plaque rupture.26 As plaque rupture occurs due to the imbalance between the mechanical force and the plaque strength, a complete understanding of haemodynamic forces and plaque characteristics can help improve the accuracy in estimating the risk of plaque-related clinical events.

Interestingly, higher WSS values were observed at the stenotic lesions characterised by more proximal location, narrower lumen or shorter length (table 2). These findings can provide an explanation for known patterns of plaque rupture reported in previous studies.3 ,28–32 Previous autopsy and intravascular ultrasound studies demonstrated that ruptured plaques were predominantly localised in the proximal portion of coronary arteries.3 ,29 ,30 Our findings suggest that plaques with proximal location, severe luminal narrowing or discrete stenosis are exposed to high WSS, which can increase plaque vulnerability,8 ,33 thrombogenic potential34 and consequently the risk of plaque-related clinical events.

Our study also showed that coronary plaques exposed to higher WSS had a higher probability of APC. However, the presence of high-risk plaques was not associated with the degree of % diameter stenosis. These results are in line with previous studies demonstrating that the measurement of luminal narrowing by angiography may have a limited role in assessing plaque vulnerability.35 In the present study, the addition of WSS to % diameter stenosis significantly improved the ability to discriminate high-risk plaques. These results imply that WSS is not a simple reflection of luminal narrowing (ie, plaque geometry), but is a more relevant parameter potentially capable of identifying high-risk plaques. Several studies, including genetic, biological and imaging assessments, have also supported the link between WSS and plaque characteristics besides plaque geometry. Particularly, Samady et al12 suggested the causal relationship between WSS and APC by demonstrating that the segments exposed to high WSS develop plaques with a more vulnerable phenotype, such as greater necrotic core and calcium progression, regression of fibrous tissue and excessive expansive remodelling. Furthermore, there is substantial evidence demonstrating local biological effects induced by high WSS can destabilise the plaque cap and turn it into a rupture-prone vulnerable plaque.33 Specifically, high WSS has been reported to stimulate endothelial cells to produce plasmin that dissolves the proteoglycan matrix, which consequently reduces the stability of plaque fibrous cap. Stimulated endothelial cells also increase nitric oxide production and stimulate macrophages to secrete promatrix metalloproteinases, promoting collagen and matrix degradation. In subendothelial space, nitric oxide stimulates macrophages to induce smooth muscle cells apoptosis. Importantly, we observed that the risk of high-risk plaques increased at both extremes of WSS. Given that previous studies suggested that 40 dyne/cm2 could be a physiological cut-off value of arterial WSS,36 ,37 this finding supports the hypothesis that both lower and higher WSS than the physiological level may have adverse effects on coronary atherosclerotic plaques.

This study has some limitations. First, the present analyses were performed using a simulation of the mean, time-averaged flow. A pulsatile simulation of the coronary flow and pressure could further provide maximum haemodynamic quantities over the cardiac cycle. Second, hyperaemic conditions were used for the CFD analysis as a surrogate for exercise conditions. More significant haemodynamic forces could be observed due to the elevation of blood pressure under exercise conditions. Third, the coronary model was assumed to be rigid without consideration of fluid–structure interaction. Such analyses may provide further insight into internal stresses within the plaque as opposed to stresses acting on the plaque surface. Finally, this study did not include serial imaging studies, which could have provided direct information on plaque progression and plaque transformation.

In conclusion, our study findings suggest that the non-invasive haemodynamic assessment using cCTA-based CFD can be helpful to elucidate the mechanistic link between haemodynamic forces and plaque-related clinical events and to improve the risk stratification for CAD. Therefore, this method may expand the usefulness of cCTA in the assessment and treatment planning for patients with CAD.

Key messages

What is already known on this subject?

  • It has been reported that wall shear stress (WSS) plays an important role in plaque formation, progression, vulnerability and plaque-related clinical events. So far, however, the assessment of WSS was largely dependent on invasive imaging techniques, such as coronary angiography and intravascular ultrasound, which limits its usefulness, particularly in asymptomatic patients with coronary artery disease (CAD).

What might this study add?

  • Our findings showed that the patient-specific computational fluid dynamics (CFD) model based on coronary CT angiography (cCTA) enabled to measure WSS in a non-invasive manner. This study also demonstrated that the assessment of WSS had an incremental value over luminal narrowing for the discrimination of adverse plaque characteristics, such as low-density plaque, positive remodelling or napkin-ring sign (a ring-like peripheral high attenuation tissue surrounding a central lower attenuation portion of the plaque).

How might this impact on clinical practice?

  • These findings suggest that cCTA-based CFD method can be useful to improve the risk stratification for patients with CAD, by providing non-invasive measurements of WSS affecting coronary plaques.


View Abstract


  • J-BP and GC contributed equally to this study.

  • Contributors J-BP, GC, HJK, CAT and B-KK contributed to the conception and design, and analysis and interpretation of data. HO, J-HD, C-WN, E-SS and BDB contributed to the conception and design. EJC, JP, J-HJ and M-HL contributed to the analysis and interpretation of data. J-BP, GC and B-KK contributed to the drafting of the manuscript. EJC, HJK, JP, J-HJ, M-HL, HO, J-HD, C-WN, E-SS, BDB and CAT contributed towards revising the manuscript critically for important intellectual content. All authors provided review and final approval of the submitted manuscript.

  • Funding This work was supported by HeartFlow (Redwood City, California, USA).

  • Competing interests CAT, GC and HJK are employees and shareholders of HeartFlow, which provides the FFRCT service.

  • Ethics approval This study protocol was approved by the institutional review boards of each site.

  • Provenance and peer review Not commissioned; externally peer reviewed.

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