Biomechanical stress profiling of coronary atherosclerosis identifying a multifactorial metric to evaluate plaque rupture risk

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R uptured thin-cap fibroatheromas (TCFAs), frequently implicated at the site of culprit coronary thrombi, are hallmarked by the presence of a thin, inflamed fibrous cap overlying a large necrotic lipid core (1,2).Motivated by the need to identify rupture-prone plaques prospectively in patients, a number of intravascular modalities, including optical frequency domain imaging (OFDI), virtual histology, intravascular ultrasound (IVUS), and near-infrared spectroscopy, have been investigated to detect TCFAs (3,4).A critical challenge is that TCFAs with similar morphological features do not all possess an equal likelihood of rupture.In 70% of patients with acute coronary syndrome (ACS), multiple nondisrupted TCFAs are found remote from the culprit site and in nonculprit arteries (5,6).Moreover, 20% of plaque ruptures are observed in necrotic core (NC) lesions with thicker fibrous caps (>100 mm), intraplaque hemorrhage, or calcifications (5)(6)(7).These findings call into question the effectiveness of an imaging paradigm that relies entirely on detecting TCFA features and highlight the need to augment morphological findings with critical biomechanical metrics to evaluate the risk of plaque rupture accurately.
The contours are discretized into meshes, and tensile stress is mathematically derived in response to physiological pressure and information on the material properties of the constituent tissues (8,12).Several FEM studies have underscored the importance of local maximum (peak) tensile stress in the fibrous cap and indicated that peak stress is profoundly related to the propensity of plaque rupture and ensuing risk of acute coronary events (12)(13)(14).Various morphological factors, including fibrous cap thickness (8,11), NC size (11,12,14), plaque burden (13), stenosis severity (8), and presence of calcifications (13), have been shown to influence peak stress.Clinical studies suggest that the measurement of peak stress may improve the prediction of future major adverse cardiovascular events, thus highlighting the clinical need for prospectively quantifying biomechanical stress in coronary plaques (13,15).However, despite the demonstrated relevance and clinical need for measuring plaque tensile stress, the computational complexity and long processing times render the FEM approach impractical as a routine clinical tool for biomechanical stress profiling of coronary plaques.
In this study, we introduce a novel approach using a straightforward multifactorial stress equation (MSE), which may circumvent the need for FEM by estimating peak stress in necrotic core fibroatheromas (NCFAs) directly from 6 independent morphometric measurements of plaque geometry.To improve the precision of quantifying peak stress, the MSE uses a dualmodality OFDI-IVUS approach to obtain plaque morphology.Through studies conducted in 33 patients, we demonstrate that the new MSE can accurately estimate peak stress to potentially locate rupture-prone plaques in patients.

METHODS
STUDY GROUP.This study details a retrospective analysis of an investigational study that included 33 patients with ACS (n ¼ 13) and stable angina pectoris (n ¼ 20) who underwent imaging using IVUS according to standard of care, followed by OFDI imaging between August 2008 and July 2015 at the Thorax Center, Erasmus Medical Center, Rotterdam, the Netherlands (Supplemental Table 1).The Ethics Committee at Erasmus Medical Center approved the protocol (Ref: 100-mm axial resolution) was performed with 0.5 mm/s pullback speed at 10 frames/s.Separate OFDI pullbacks were performed following IVUS through the same guide wire and using an imaging protocol that has been well established (16).Using 2.6-F catheters (Terumo Fast View, Terumo Corporation, Somerset, New Jersey), OFDI (console built at Massachusetts General Hospital, Boston, Massachusetts; 1300-nm center wavelength, 9.4-mm axial resolution) was performed at 20 mm/s pullback speed with an imaging rate of 100 frames/s during injection of nonionic contrast solution at 1 to 3 ml/s (17).
OFDI-IVUS IMAGE CO-REGISTRATION.OFDI and IVUS image co-registration was performed using previously established criteria for plaque identification (18) with ImageJ (National Institutes of Health, Bethesda, Maryland).Image cross sections with stent struts, side branches spanning beyond the field of view, or visible thrombi were excluded from the analysis because these features obstructed the accurate determination of luminal geometry.IVUS datasets were co-registered with OFDI pullbacks with the aid of landmarks, such as side branches, presence of calcifications, lumen shape, plaque shape, and the relative distance from such landmarks and structures.
From OFDI images, we identified all NCFAs defined as plaques with a high-intensity fibrous cap overlying an NC with low-intensity, diffused signal, with a lipid arc >90 .A total of 61 nonruptured NCFA plaques were identified in 39 coronary arteries of 30 patients.
Co-registered OFDI-IVUS image pairs at the location of the thinnest fibrous cap in all 61 NCFAs were selected for analysis using FEM (detailed later).In addition, to investigate the influence of plaque morphological parameters, OFDI-IVUS image pairs were further selected for analysis at 1-mm increments over the entire length for each NCFA.Thus, a total of 195 co-registered OFDI-IVUS image pairs from 61 nonruptured NCFAs were analyzed.In 3 additional patients, ruptured NCFAs were observed at the sites of culprit coronary thrombosis; these patients' datasets were used to test the use of the MSE for localizing plaque ruptures as detailed later.Boston, Massachusetts) to perform FEM.An anisotropic, linear-elastic, quasi-incompressible material model was used to conduct FEM, similar to other published reports (8,12).The material properties of the plaque constituents were obtained from published reports (8,15,19) (Supplemental Table 2).We also observed that the presence, location, and thickness of calcium modulated peak stress.
Furthermore, the interactions among multiple morphometric plaque parameters greatly influenced the magnitude and location of peak stress.For instance, because of the presence of thin calcium near the lumen, an elevated peak stress of 321 kPa (Figure 3D3) was measured in the NCFA with the smallest arc angle (98 ), and a peak stress of 346 kPa (Figure 3D4) was measured in the NCFA with a relatively thicker fibrous cap (116 mm).A high peak stress of 490 kPa was observed at the summit of the plaque with a thick NC and large arc angle, as seen in Figure 3D4.observed between FEM-derived peak stress and FC thick , and the best fit was obtained using power law (8,11,12).

MOST INFLUENTIAL PARAMETERS AND THE MSE.
We used stepwise multivariate regression analysis to identify the most influential plaque parameters and exclude redundant variables (Table 2).We observed that both plaque thickness and total area were excluded by the multivariate stepwise regression analysis from the predictor list.This was because plaque thickness was found to be collinear with the plaque area.Total area was found to be redundant because it is the sum of lumen and plaque areas, and it was excluded from the final MSE model.Thus, only (Table 2), the MSE was developed by combining the cumulative interactions of 6 plaque parameters to compute the PSM as follows:.

DISCUSSION
The tensile stress distribution in NCFAs, particularly peak stress in the fibrous cap, is a crucial predictor of plaque rupture and major adverse cardiovascular events in patients (12)(13)(14).The traditional FEM modeling approach used to compute the peak stress is mathematically complex, requires specialist operators, and takes hours to report results.In this study, we demonstrate that PSM can be readily calculated directly from morphometric measurements derived from plaque geometry.Our results show that MSEmeasured PSM values are essentially identical to those obtained by FEM, thus suggesting that MSE may circumvent the need for mathematically complex and time-intensive FEM approaches to measure plaque stress.Consequently, in a pilot test in 3 patients, we showed that the locations of elevated PSM coincided with sites of ruptured plaques.
A key finding of our study is that peak stress in the fibrous cap can be directly estimated by using a closed-form equation (Equation 1).Similar to other studies (8,11,12), we demonstrated a nonlinear relationship (Figure 4A) between peak stress and FC thick .
Although the critical FC thick of <65 mm has been extensively reported in published reports as a major determinant of plaque vulnerability (1,18), our study demonstrated that under certain conditions, NCFAs with thicker FC thick similarly exhibited elevated peak stress.We further observed that in plaques with thicker caps (>200 mm), the peak stress is only minimally influenced by FC thick , where NC thick was the major determinant of PSM, whereas when FC thick is reduced to <200 mm, peak stress is exponentially  elevated (Figure 4A).Similar to our results, other studies also showed that peak stress is increased with increasing luminal area, lumen eccentricity, NC thickness, NC area/NC arc, and arterial remodeling index (12,14).
Interestingly, in our study only 56% of the plaques elicited the highest PSM at the frame with the thinnest cap location, and FC thick was a sole determining factor in only 7% of plaques.In fact, prior histopath- Consistent with previous studies implicating the influence of calcium (20), our study demonstrated that peak stress was influenced by the presence, location, and area of calcification in the coronary cross section.When evaluated as an independent variable, Cal area indicated moderate correlation with peak stress (R ¼ 0.35; p < 0.01).However, the overlap of calcification with the NC, specifically the sum of NC area and Cal area , significantly influenced the peak stress (R ¼ 0.62; p < 0.0001).These results suggest that in addition to the presence of calcification, the proximity of calcium deposits with NC is likely an important mediator of plaque rupture.We noticed    that peak stress was considerably elevated when a thin calcific nodule (Cal thick <200 mm) was located in the vicinity of the lumen (CalLu dist <200 mm).
Other biomechanical studies using FEM indicate a large variability in peak stress values (100 to 900 kPa) measured in ruptured and intact coronary plaques in patients (21)(22)(23).In this study, we observed peak stress values ranging from w100 to 1,000 kPa even in nondisrupted plaques.2, Supplemental Table 3).
In our study, FEM was used purely for the purpose of obtaining reference peak stress values and to derive the MSE (Equation 1).We further compared MSE-calculated PSM with the FEM-derived peak stress in 61 nonruptured NCFAs.The excellent correlation with high concordance and low measurement bias between the 2 approaches (Figure 5) shows that MSE can be used interchangeably with FEM.Thus, in practice, in a subset of 3 patients with ruptured NCFAs (Figure 6), through straightforward MSE measurements, we observed that peak stress was significantly elevated in the vicinity of the rupture site.
Although further validation through prospective clinical testing is warranted, this initial result is significant because it indicates that just 6 morphometric measurements of plaque geometry may accurately localize rupture-prone sites.
STUDY LIMITATIONS.In the patient cohort investigated in this study, ruptured plaques were observed in only 3 patients; therefore, the MSE was applied to identify rupture sites in only these patients.In 3 patients with plaque ruptures we observed that the maximum PSM was elevated close to the site of plaque rupture (Figure 6).
NL 22249.078.08).Each patient gave written informed consent before enrollment.All procedures were performed in accordance with local and federal regulations and the Declaration of Helsinki.OFDI AND IVUS IMAGING.OFDI and IVUS imaging were performed following diagnostic coronary angiography in 33 patients (10 before percutaneous coronary intervention [PCI], 8 after PCI, and 15 both before and after PCI).Gray scale IVUS (3.2-F, 30 MHz, Boston Scientific, Marlborough, Massachusetts; SEE PAGE 817 A B B R E V I A T I O N S A N D A C R O N Y M S ACS = acute coronary syndrome CT = computed tomography CTA = computed tomography angiography FEM = finite element modeling IVUS = intravascular ultrasound MSE = multifactorial stress equation NC = necrotic core NCFA = necrotic core fibroatheroma OFDI = optical frequency domain imaging PCI = percutaneous coronary intervention PSM = peak stress metric TCFA = thin-cap fibroatheroma of Coalesenz; and has received grant support from the National Institutes of Health for retrospective analysis of optical frequency domain imaging and intravascular ultrasound images in this study.All other authors have reported that they have no relationships relevant to the contents of this paper to disclose.Gregg Stone, MD, served as Guest Editor for this paper.Manuscript received November 8, 2018; revised manuscript received December 31, 2018, accepted January 2, 2019. Mesh generation and modal solution.The segmented plaque geometries were meshed with 2-dimensional, 6-node triangular and 8-node quadrilateral isoparametric elements.Appropriate boundary conditions and wall thickness of 300 mm were used to suppress the rigid body motion and radial overstretching of the artery, respectively.Static intraluminal pressure of 13.33 kPa was applied as the loading condition to mimic physiological pressure.The distribution of tensile stress was computed within each element, and the average stress of neighboring elements was calculated to obtain the tensile stress at each node.The tensile stress distribution was similarly calculated for all nodes within the coronary cross section, and the location of the maximum tensile stress (peak stress) was noted (Figure2D).Doradla et al.STATISTICAL ANALYSIS.Univariate linear regression analysis was used to analyze the extent of correlation between each of the 13 plaque parameters and the FEM-derived peak stress.Then, a stepwise multivariate regression model (SPSS version 24.0.0,IBM Corp., Armonk, New York) was used to determine the interdependencies among plaque variables and to identify the most influential parameters.In some cases, multiple NCFAs were identified in the same patient; therefore, the generalized estimating equation was used to account for intrapatient dependencies.In all cases, p < 0.05 was considered statistically significant.The principal plaque parameters that significantly influenced the peak stress were used to derive the MSE.The accuracy of the MSE was evaluated by comparing the MSE-calculated peak stress metric (PSM) with the FEM-measured peak stress values using the leave-1-out cross-validation method.RESULTS PEAK STRESS IN NCFA LESIONS.The FEM-derived peak stress in 61 NCFAs ranged from 108.8 to 1048.0 kPa and was located at the shoulder of the NC (n ¼ 32), summit of the NC (n ¼ 11), boundary between calcium and lipid or at the edge of calcific nodule (n ¼ 10), and along the longest diameter (major axis) of the plaque (n ¼ 8) of NCFAs.Figures 3A1 to 3A5 to

FIGURE 1
FIGURE 1 Intracoronary OFDI and IVUS Assessment of Plaque Geometry in Patients Optical frequency domain imaging and intravascular ultrasound overlay of a necrotic core fibroatheroma (NCFA) cross section showing plaque contours.(B) Extracted contours from (A). (C) Plaque geometry reconstructed from the contours.(D) Finite element quadrangular mesh with inlay showing magnified image of fine mesh.(E) Tensile stress distribution calculated using finite element modeling (FEM) analysis.Arrowhead ¼ peak stress location.EEL ¼ external elastic lamina.Doradla et al.

Finally, we assessed
the ability of the MSE to locate plaque ruptures in 3 patients with ruptured NCFAs observed at the sites of culprit thrombi.Figures 6A1 to 6A3 show the PSM values measured at 2 mm intervals in 3 coronary segments by retrieving the plaque parameters from each cross section and simply substituting the values into the MSE.Figures 6B1 to 6B3 display 2-dimensional cross-sectional OFDI images at 5 discrete locations along each coronary pullback; the coronary cross section with the maximum PSM is highlighted in red.Subsequently, we observed that the location of the maximum PSM with black asterisks is in close proximity to the plaque rupture sites in all 3 patients (Figures 6C1 to 6C3).

J 2 0 6 FIGURE 4 A
FIGURE 4 Influence of Various Plaque Parameters on Peak Stress ological and clinical OFDI studies have suggested that ruptured NCFAs are often observed in locations with thicker fibrous caps, calcific nodules, and increased plaque burden (5-7).Our results similarly showed that the location of the thinnest fibrous cap did not influence the highest PSM in 44% of NCFAs and that other parameters, including largest NC thick , NC arc , Plq area , NCCal area , and smallest CSA lumen, were the determining factors in these cases.The results likely provide a quantitative biomechanical corroboration for the foregoing clinical observations and provide a unique opportunity for further investigations.

FIGURE 5 AFEA
FIGURE 5 Comparison of PSM Measured by the MSE Versus FEM

FIGURE 6 1 (
FIGURE 6 Locating the Culprit Plaque Rupture Using the MSE Tool

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A C C : C A R D I O V A S C U L A R I M A G I N G , V O L . 1 3 , N O . 3 , 2 0 2 0

2 0
Because of the presence of culprit thrombi in the field of view, which limited our ability to view subsurface plaque morphology, we were unable to calculate the PSM at the precise image frame of the rupture site obscured by thrombus.Therefore, it is likely that the PSM value measured at the rupture site with thrombus may have been different from the observed PSM value at the adjacent site without thrombus.Future prospective, longitudinal clinical studies will be necessary to determine conclusively the associations among peak stress, coronary plaque ruptures, and subsequent thrombosis.In this study, the most time-consuming post-processing step involved OFDI-IVUS image co-registration through identification of image landmarks (see the Methods section, earlier), which added additional processing time and complexity.Recently, bimodality imaging systems have been approved by the U.S. Food and Drug Administration and likely will be available soon for patient use to enable tandem OFDI-IVUS imaging through a single integrated catheter, which will further reduce procedure time, patients' risks, and post-processing complexities(24,25).Following image co-registration in our study, plaque segmentation and parameter calculation were performed in just 2 min, with an additional 5 s for the MSE calculation of PSM for composite image pair.The use of 2-dimensional FEM in this study did not take into account the longitudinal shape of tortuosity of the coronary wall and out-of-plane deformations that could influence stress distributions.This was because coronary catheterization in patients was performed in conjunction with single-plane angiography, thereby precluding the evaluation of 3dimensional coronary vessel shape.In the future, the use of biplane angiography or CT angiography (CTA) may allow us to include these additional parameters into a further refined MSE model that includes longitudinal coronary geometry and tortuosity metrics.However, drawbacks of biplane angiography and CTA include the substantial increase in procedure time, contrast volume, radiation dose, and cost(26); therefore, these approaches may not be suitable for routine PCI procedures.Future studies in Doradla et al.J A C C : C A R D I O V A S C U L A R I M A G I N G , V O L . 1 3 , N O . 3 , 2 0Biomechanical Stress Profiling in Coronary AtherosclerosisM A R C H 2 0 2 0 : 8 0 4 -1 6patients may likely allow us to investigate the comparative effectiveness of including 3-dimensional geometry metrics in predicting plaque rupture in patients and may help in identifying patient subgroups that may benefit from the inclusion of biplane angiography or CTA.CONCLUSIONSWe present a novel and straightforward approach to estimate peak stress in coronary plaques.With a simple analytical equation that defines the cumulative influence of 2-dimensional plaque geometry, we demonstrated that the PSM could be accurately estimated, which may potentially serve as a pivotal biomechanical indicator of plaque rupture risk in patients.Consequently, this new approach obviates the need for tedious and mathematically intensive FEM.In the future, we anticipate that the MSE could be used in conjunction with routine OFDI and IVUS evaluation, which will enable further investigation into the relationship between biomechanical stress profiling and subsequent plaque-related events.ACKNOWLEDGMENTS The authors thank Dr. Hang Lee of the Harvard Catalyst Program for providing statistical consultation on data analysis, and Xuan Pei for her assistance with the ABAQUS software.ADDRESS FOR CORRESPONDENCE: Dr. Seemantini K. Nadkarni, Wellman Center for Photomedicine, Massachusetts General Hospital, Harvard Medical School, 50 Blossom Street, Boston, Massachusetts 02114.E-mail: snadkarni@mgh.harvard.edu.R E F E R E N C E S 3C1 to 3C5 illustrate 5 multifarious NCFAs with 96 to 424 mm FC thick , 602 to 993 mm NC thick , 98 to 302 NC (8,11,12,19)th or without calcium inclusions.The OFDI images, corresponding OFDI-IVUS composite images with segmented contours, and reconstructed plaque geometries, with the tensile stress distributions, are displayed.Similar to other studies(13), we observed that the location of peak stress was limited to within the superficial 500 mm of the plaque.Similar to prior FEM studies(8,11,12,19), we observed that NC thick , NC arc , CSA lumen , NCCal area, Plq area , Cal thick , Cal depth , Plq thick , NC area , Cal area , Tot area , and %AS.The mean AE SD for each plaque parameter is shown in Table 1.First, by univariate linear regression analysis, we identified FC thick , NC arc , NC thick , Plq thick , CSA lumen , NCCal area , Plq area , and Tot area as the 8 parameters that significantly correlated with FEM-derived peak stress (Figures 4A to 4H).Although 7 plaque parameters showed a linear trend, a nonlinear relationship wasFIGURE 2 FEM to Measure Coronary Tensile Stress Distribution

TABLE 1
The Correlation Between FEM-Derived Peak Stress and the Imaging Plaque *The most influential independent plaque parameters.Doradla et al.

TABLE 2
Multivariate Regression Analysis to Identify the Most Influential Plaque Parameters ¼ calcium; CI ¼ confidence interval; CSA ¼ cross-sectional area; FC ¼ fibrous cap; NC ¼ necrotic core; VIF ¼ variance inflation factor. Cal