Atherosclerosis 221 (2012) 432–437
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Choosing the optimal wall shear parameter for the prediction of plaque location—A patient-specific computational study in human left coronary arteries Farhad Rikhtegar a,1 , Joseph A. Knight a,1 , Ufuk Olgac a , Stefan C. Saur b , Dimos Poulikakos a , William Marshall Jr. c , Philippe C. Cattin b,d , Hatem Alkadhi e , Vartan Kurtcuoglu a,∗ a
Laboratory of Thermodynamics in Emerging Technologies, Department of Mechanical and Process Engineering, ETH Zurich, Zurich, Switzerland Computer Vision Laboratory, Department of Information Technology and Electrical Engineering, ETH Zurich, Zurich, Switzerland c College of Medicine, University of South Florida, USA d Medical Image Analysis Center, University of Basel, Basel, Switzerland e Institute of Diagnostic and Interventional Radiology, University Hospital Zurich, Zurich, Switzerland b
a r t i c l e
i n f o
Article history: Received 28 January 2011 Received in revised form 4 January 2012 Accepted 7 January 2012 Available online 18 January 2012 Keywords: Computed tomography Wall shear stress Oscillatory shear index Relative residence time Computational fluid dynamics Plaque prediction
a b s t r a c t Objective: While the correlation of atherosclerotic plaque locations with local wall shear stress magnitude has been evaluated previously by other investigators in both right (RCA) and left coronary arteries (LCA), the relative performance of average wall shear stress (AWSS), average wall shear stress gradient (AWSSG), oscillatory shear index (OSI) and relative residence time (RRT) as indicators of potential atherosclerotic plaque locations has not been studied for the LCA. Here we determine the performance of said wall shear parameters in the LCA for the prediction of plaque development locations and compare these results to those previously found in the RCA. Methods: We obtained 30 patient-specific geometries (mean age 67.1 (±9.2) years, all with stable angina) of the LCA using dual-source computed tomography and virtually removed any plaque present. We then performed computational fluid dynamics simulations to calculate the wall shear parameters. Results: For the 96 total plaques, AWSS had a higher sensitivity for the prediction of plaque locations (86 ± 25%) than AWSSG (65 ± 37%, p < 0.05), OSI (67 ± 32%, p < 0.01) or RRT (48 ± 38%, p < 0.001). RRT had a higher PPV (49 ± 36%) than AWSS (31 ± 20%, p < 0.05) or AWSSG (16 ± 12%, p < 0.001). Segment 5 of the LCA presented with overall low values for sensitivity and PPV. Parameter performance in the remainder of the LCA was comparable to that in the RCA. Conclusions: AWSS features remarkably high sensitivity, but does not reach the PPV of RRT. This may indicate that while low wall shear stress is necessary for plaque formation, its presence alone is not sufficient to predict future plaque locations. Time dependent factors have to be taken into account as well. © 2012 Elsevier Ireland Ltd. All rights reserved.
1. Introduction Hemodynamic parameters of wall shear stress, such as average wall shear stress (AWSS), average wall shear stress gradient (AWSSG), oscillatory shear index (OSI) and relative residence time (RRT) are possible indicators for atherosclerotic lesion prone sites [1–4]. In a previous study, we analyzed the performance of these four parameters in predicting patient-specific plaque locations in the right coronary artery (RCA) [5]. In the study at hand, we have performed a similar analysis for the left coronary artery (LCA) of thirty new patients. Our rationale
∗ Corresponding author. Tel.: +41 44 632 6914; fax: +41 44 632 1176. E-mail address:
[email protected] (V. Kurtcuoglu). 1 These authors contributed equally. 0021-9150/$ – see front matter © 2012 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.atherosclerosis.2012.01.018
is threefold: First, the more tortuous and multi-branching geometry of the LCA and the new set of patients are sufficiently different from the RCA case that a comparable performance of the wall shear parameters would support (while not prove) the validity of our retrospective study design. Second, the optimal wall shear parameter for prediction of plaque may be different in the RCA than in the LCA. And, finally, while the computational model and boundary conditions for the calculation of the wall shear parameters in the RCA were deemed to be sufficiently accurate, flow in the LCA is more complex, potentially requiring a more sophisticated approach. We thus present herein an analysis of the hemodynamic parameters AWSS, AWSSG, OSI and RRT obtained through a CFD study of the LCA of 30 patients with plaques 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
F. Rikhtegar et al. / Atherosclerosis 221 (2012) 432–437
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Table 1 Patient demographics and clinical characteristics of the study population. Total Number of patients Age (years) Male/female ratio Body mass index (kg/m2 )
30 (100%) 64.8 ± 10.3 (43–82) 21/9 (70.0%/30.0%) 25.3 ± 3.1 (20.3–32.8)
Heart rate (bpm)
63.0 ± 11.8 (59.8–66.1)
Risk factors Smoker Diabetes High serum cholesterol Arterial hypertension Positive family history
15 (50.0%) 1 (3.3%) 17 (56.7%) 20 (66.7%) 7 (23.3%)
Reasons for referral Typical angina Atypical angina Non-anginal chest pain
6 (20.0%) 1 (3.3%) 23 (76.7%) Fig. 1. Schematic of left coronary artery segmental anatomy with segment numbering according to the classification of the American Heart Association.
of each parameter with respect to predicting the particular plaque locations. 2. Methods Our patient population consisted of 70% (21/30) males with an average age and body mass index (BMI) of 64.8 ± 10.3 years [range 43–82] and 25.3 ± 3.1 kg/m2 [range 20.3–32.8], respectively. Demographic data and clinical characteristics of the patients are summarized in Table 1. The retrospective study protocol was approved by the local ethics committee who waived the written informed consent requirement. 2.1. CT anatomy acquisition and image processing For each patient, an initial non-contrast enhanced CT scan was performed for calcium scoring. The patient was then injected with a contrast agent in a right antecubital vein. The application was controlled by bolus-tracking in the ascending aorta. The scanning parameters followed a standard protocol [6]: detector collimation 32 mm × 0.6 mm, slice acquisition 64 mm × 0.6 mm by means of a z-flying focal spot, gantry rotation time 330 ms, pitch of 0.2–0.5 depending on the heart rate (HR), tube current time product 330 mA s per rotation, and tube potential 120 kV. Both non-enhanced and contrast-enhanced scans were performed from the level of the tracheal bifurcation to the diaphragm. The nonenhanced scan was reconstructed with a B35f kernel at 70% of the R–R interval (the time elapsing between two consecutive R waves in the electrocardiogram) using 3.0 mm non-overlapping slices. The contrast-enhanced CT angiography dataset was reconstructed during mid-diastole at 70% of the R–R interval using a slice thickness of 0.75 mm (in plane resolution 0.256 mm at 512 × 512 voxels), a reconstruction increment of 0.5 mm, and using the soft-tissue convolution kernel B26f. The lumen of the LCA, as well as any calcified plaques present, were automatically segmented with a progressive region growing technique in MeVisLab (MeVis Medical Solutions AG, Bremen, Germany), a development environment for medical image processing. A surface mesh enveloping the vessel lumen and calcified plaques was defined based on the segmentation. This mesh is regarded to represent the lumen surface of the artery in its healthy state. For the subsequent calculations, the surface mesh was truncated manually to only include the Segments 5, 6, 7, 8, 9, 11, and 16 of the LCA defined according to the classification of the American Heart Association (see Fig. 1).
2.2. Computation of blood flow and wall shear parameters The LCA geometries were smoothed and computational volume grids consisting of approximately one million tetrahedral and prismatic elements were generated for all geometries using ANSYS ICEM CFD (ANSYS Inc., Pittsburg, PA). CFD simulations of second order accuracy in space and time were performed using the finitevolume code CFX 11.0 (ANSYS Inc., Pittsburg, PA) to obtain blood flow velocity and wall shear stress fields. Transient flow replicating systolic and diastolic LCA blood flow [7] (Fig. 2) was applied to the inlet of the proximal portion of the geometry, corresponding to the part of the LCA just distal to the ostium. Zero relative pressure was assumed as boundary condition (BC) at the outlets. No-slip BC was applied at the artery walls. As initial conditions, zero pressure and velocity were prescribed throughout the domain. Two cardiac cycles were calculated using a time step size of 0.01 s, but only the data of the second cycle were evaluated to obtain results independent of the initial conditions. Blood was modeled as an incompressible Newtonian fluid with a density of 1050 kg/m3 and a viscosity of 0.0035 Pa s. Grid independence as well as cycle and time step size independence tests were performed on a representative geometry to ensure results independent of the applied temporal and spatial discretization.
Fig. 2. Blood flow into the left coronary artery during one cardiac cycle used as the inlet boundary condition for the flow computations.
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AWSS, AWSSG, OSI and RRT were derived from the calculated wall shear stress field using MATLAB (The MathWorks Inc., Natick, MA) and Tecplot (Tecplot Inc., Bellevue, WA). These parameters are defined as [5] AWSS =
1 T
2.4. Statistical analysis
T
|w | dt, 0
where |w | is the magnitude of the instantaneous wall shear stress vector w and T is the duration of one cardiac cycle,
2 2 ∂w 2 + ∂w + ∂w WSSG = ∂x ∂y ∂z
and 1 AWSSG = T
identify a plaque, was designated as false-positive. A segment containing three or more false-positives was labeled as a cluster of false positives.
T
(WSSG)dt, 0
where WSSG is the wall shear stress gradient and ∂/∂x, ∂/∂y and ∂/∂z are partial derivatives with respect to the x, y and z coordinates, respectively. OSI is defined as
⎞ T dt w 0 1 ⎝ ⎠. 1− T OSI = 2 ⎛
0
|w | dt
Finally, RRT can be defined through [7] RRT∼[(1 − 2 · OSI) · AWSS]−1 , where the proportionality constant between RRT and the right hand side of the expression can be chosen arbitrarily, because it cancels out in the subsequent normalization process. 2.3. Correlation of wall shear parameters to plaque locations The spatial distributions of the four wall shear parameters’ values were compared to each individual patient’s plaque distribution. The reference standard for each patient’s plaque profile was a combination of (1) the proximal and distal ends of the plaques in each patient’s CT dataset that were marked by a radiologist and (2) the margins of the plaques automatically identified using an intensitybased approach [8] and overlaid onto the transparent rendering of the respective LCA geometry. The plaques that were initially not identified by the radiologist but designated as such by the algorithm were reassessed and either included in the study as actual plaques or dismissed as artifacts. Threshold values were determined from the normalized results for each parameter by balancing the number of regions that accurately identified plaques and the overall number of false positives for 10 patients, ultimately giving approximately one accurately identified plaque location for every two false positive locations. These threshold values were then used for all 30 patients in the study. The LCA geometry was rendered transparently with overlaid plaque margins, and the various wall shear parameters were sequentially projected onto the same transparent RCA surface. In this way, it was possible to determine visually the location of peaks and depressions of the wall shear parameters relative to the reference standard. The following nomenclature was used to classify four basic patterns of plaque prediction: proximal (threshold parameter values are found within the proximal half of the plaque), distal (within the distal half of the plaque), full (within the entire margins of the plaque) and center (focused in the middle region of the plaque). A region indicated by the respective wall shear parameter to be prone to plaque formation, where the reference standard did not
All statistical analyses were performed with the software R, release 2.8.1 (www.r-project.org). Quantitative variables are expressed as mean ± standard deviation. Categorical variables are expressed as frequencies or percentages. A Wilcoxon matched pairs signed rank test was performed to compare the non-Gaussian distributed sensitivity and positive predictive values (PPVs) of AWSS, AWSSG, OSI and RRT. Sensitivity was defined as the number of plaques correctly identified divided by the actual number of plaques for that particular region. PPV was defined as the number of plaques correctly identified divided by the total number of both positively and negatively identified plaques. A p value of 51% and >59% of the correctly predicted plaques were determined by calculated values above the threshold for each shear stress parameter at the proximal section of the respective plaque as identified by the reference standard (“proximal” parameter location). In contrast, AWSS and AWSSG only showed
