Fractal geometry of coronary plaque images within optical coherence tomography: A novel approach of plaque vulnerability in patients with acute coronary syndrome versus stable angina pectoris

doi:10.21203/rs.3.rs-2705155/v1

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Fractal geometry of coronary plaque images within optical coherence tomography: A novel approach of plaque vulnerability in patients with acute coronary syndrome versus stable angina pectoris

https://doi.org/10.21203/rs.3.rs-2705155/v1

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Background and Purposes:

The main cause of acute coronary syndrome (ACS) is plaque rupture and thrombus formation. However, it has not been fairly successful to identify vulnerable plaque to rupture using conventional parameters of intravascular imaging modalities. Fractal analysis is one of the mathematical models to examine geometrical features of picture image using a specific parameter called as fractal dimension (FD) which suggests geometric complexity of the image. This study examined FD of the optical coherence tomography (OCT)-derived images of the culprit plaque in patients with ACS versus stable angina pectoris (SAP) in order to evaluate the feasibility of FD for identifying vulnerable coronary plaques, because coronary plaques in ACS patients are known to be more vulnerable than those in patients with SAP.

Methods and Results

We examined 65 cases (34 ACS patients, 31 SAP patients) in which the culprit lesion was imaged by OCT before percutaneous coronary intervention in patients with ACS and SAP. The culprit plaque lesion in the ACS group had a significantly larger mean lipid arc (203.8 ± 39.4° vs 152.3 ± 34.5°, p < 0.001) and a larger lipid plaque length (12.6 ± 5.1mm vs 7.7 ± 2.7mm, p < 0.001) and a thinner fibrous cap thickness (75.3 ± 22.3 µm vs 134.8 ± 53.2 µm, p < 0.001) than those in the SAP group. The prevalence of OCT -derived macrophage infiltration (MφI) in the entire culprit coronary vessel as well as that of the OCT-derived thin-cap fibroatheroma (TCFA) at the culprit lesion were significantly greater in the ACS group than those in the SAP group, respectively (MφI: 61.8% vs 35.5%, p = 0.048; TCFA: 44.1% vs 6.4%, p < 0.001). The FD of culprit plaque in the ACS group was significantly greater than in the SAP group (2.401 ± 0.073 vs 2.341 ± 0.051, p < 0.001). In multivariate regression analysis, the presence of MφI was a significant determinant of FD (regression coefficient estimate 0.049, CI: 0.018–0.079, p = 0.002).

Conclusions

The FD of OCT-derived image of culprit coronary plaque in the ACS group was significantly greater than that in the SAP group, indicating that the culprit plaque in ACS were structurally more complex. Therefore, fractal analysis of coronary OCT images might be clinically useful for identifying vulnerable coronary plaques.

Atherosclerosis

vulnerable plaque

acute coronary syndrome

optical coherence tomography

fractal

The main cause of acute coronary syndrome (ACS) is a rapid stenosis or an abrupt occlusion of coronary arterial lumen due to coronary plaque rupture and thrombus formation [1]. Pathological features of vulnerable plaques, which are prone to plaque rupture, include a thin-cap fibroatheroma (TCFA) and infiltration of inflammatory cells such as macrophages [2]. Since identifying these kinds of vulnerable plaque would be important for preventing ACS, attempts have been made to identify vulnerable plaque by using several intravascular imaging modalities such as color intravascular ultrasound (IVUS), optical coherence tomography (OCT), near-infrared spectroscopy, and coronary angioscopy [3]. However, all the approaches of tissue characterization by these modalities have not been successful in order to precisely identify a vulnerable plaque prone to rupture in the very near future with a high predictive value [4, 5]. One of the reasons might be due to sticking of investigators of intravascular imaging with trying to develop a method for identification only of TCFA, which inherently has a low absolute degree of prevalence for rupture, although it is relatively prone to rupture compared to the other tissue types of plaque.

Actually, Stone GW, et al reported that radiofrequency IVUS-derived TCFA has a rate for major adverse cardiovascular events of only 4.9% at a median follow-up of 3.4years [6]. In order to overcome this limitation, we may have to shift our perspectives from simply seeking for intravascular imaging-derived TCFA rather to finding specific characteristics of image texture directly related to plaque rupture with a higher predictability. One of the other possible ways might be a geometrical and mathematical evaluation of pixel-based texture of intravascular images. Fractal analysis has been used in other imaging modalities such as CT or MRI for evaluating the degree of a specific pathology [7, 8]. Fractal analysis is a mathematical model to express a complex and irregular geometric structure that cannot be simply described by classical geometry indices, because such structures have the same degree of non-regularity on all scale, in other words, any suitably chosen part of it is similar in shape to a given larger or smaller part when magnified or reduced to the same size. This feature is called as self-similarity. Mathematically, fractal is defined by Mandelbrot BB who founded the academic paradigm of fractal geometry as follows: "A fractal is by definition a set for which the Hausdorff–Besicovitch dimension (called as fractal dimension) strictly exceeds the topological dimension."[9]. This dimension is a geometric measure of roughness or complexity [10]. Fractal analysis measures a degree of this fractal dimension within a structure of interest, examining how complex and complicated the structure is for having self-similarity.

The purpose of the present study was to evaluate the feasibility of the fractal analysis for OCT images of coronary plaque for identifying vulnerable ones. However, the gold standard of plaque vulnerability cannot be readily obtained unless each of all plaque is observed for long years with repetitive invasive imaging methods to examine whether it ruptures and provokes ACS. Therefore, this study was to compare fractal dimension in patients with ACS versus stable angina pectoris (SAP), both of which have been reported to have a different plaque vulnerability [11–13].

Patient selection

This was a single-center, retrospective, exploratory, and non-randomized observational study. A total of 65 patients who underwent percutaneous coronary intervention (PCI) for ACS or SAP with coronary OCT imaging were enrolled by the following criteria from all the consecutive patients with PCI between February 2014 and March 2020 at Nihon University Itabashi Hospital. They were divided into two groups: the ACS group (n = 34) and the SAP group (n = 31). ACS included ST-segment elevation myocardial infarction (16 patients, 47.1%), non-ST-segment elevation myocardial infarction (6 patients, 17.6%), unstable angina (12 patients, 35.3%). ST-segment elevation myocardial infarction was diagnosed on the basis of characteristic symptoms of myocardial ischemia in association with persistent electrocardiographic (ECG) ST elevation and subsequent release of biomarkers of myocardial necrosis. Diagnostic ST elevation in absence of left ventricular hypertrophy or left bundle-branch block is defined as new ST elevation at the J point in at least 2 contiguous leads of ≥ 2mm (0.2mV) in men or ≥ 1,5mm (0.15mV) in women in leads V₂-V₃ and/or of ≥ 1mm (0.1mV) in other contiguous chest leads or the limb leads. Non-ST-segment elevation myocardial infarction was defined as exacerbated exertional angina or new-onset resting angina without ST-segment elevation on 12-lead ECG but with elevated myocardial biomarkers. Unstable angina was defined as exacerbated exertional angina or new rest angina without elevated myocardial biomarkers but with a specific electrocardiogram change [14]. Stable angina was defined as chest pain due to significant coronary artery stenosis only on exertion without exacerbation of chest pain threshold. The culprit lesions were determined from coronary angiography findings, ECG changes, and wall motion abnormality on echocardiography. All patients included had an angiographically determined coronary diameter stenosis of at least 75% (relative to the diameter of adjacent normal coronary artery). All the OCT images of the culprit lesion were obtained just before PCI. Patients with poor OCT image quality were excluded. This study was approved by the clinical research ethics review committee of Itabashi Hospital, Nihon University School of Medicine (RK-200908-06), and was carried out in accordance with the Declaration of Helsinki. In addition, this study was conducted after obtaining written consent from all patients regarding the use of image information for research purposes, with careful consideration given to the conduct of catheterization and the protection of personal information.

Coronary Plaque Imaging With Oct

Coronary angiography was first performed using a standard technique from the radial or femoral artery. A guide wire was then inserted to the periphery of the coronary artery branch, and the following intravascular imaging was performed via the guide wire. Immediately before imaging, 1.5 mg of isosorbide dinitrate was injected into coronary artery. The imaging catheter of OCT (Dragonfly ™ JP Imaging Catheter ILUMIEN ™, OPTIS ™, St. Jude Medical, St. Paul, MN, USA) was inserted through the guide wire into the culprit vessel including a culprit lesion of interest as peripheral as possible before performing PCI. The OCT imaging was then performed at a pullback speed of 40 mm / sec with an imaging frame-rate of 180 frames / sec. At the time of imaging, a low-molecular-weight dextran solution was flushed using a syringe to remove erythrocytes. As for a totally occluded coronary segment, blood flow recanalization was performed using a guide wire with the smallest diameter just before the OCT imaging.

The OCT image was first analyzed using conventional indices. The angular span of the lipid core from lumen area gravity center within short-axis images was measured over the entire length of the culprit plaque for every 1 mm slice, and the average was calculated. The lesion length of the lipid core was measured on the long axis view. The minimum fibrous cap thickness was measured along the entire length of the culprit plaque. The presence of TCFA was defined as the thinnest fibrous cap less than 65 µm. The presence of macrophage infiltration was determined based on the presence of a line-like high luminance within the wall of the coronary artery having a striped shadow [15]. Because of the low prevalence of identifying macrophage infiltration just at the culprit lesion, this determination was performed for the entire culprit vessel rather than the specific culprit plaque. The OCT data were analyzed by two experienced physicians blinded to angiography and clinical findings.

Fractal Analysis Of The Oct Image

Fractal analysis was performed for an OCT cross-sectional image at the culprit plaque with the narrowest luminal area. However, when the segment was considered to be filled with thrombus or to be associated with a significant ulceration, the adjacent closest site of the minimal liminal area without any thrombus and ulceration was selected for obtaining the OCT image.

According to Fractal theory, fractal dimension is an indicator to describe the complexity and self-similarity of a certain geometry, and the box-counting analysis is proved to be an effective and appropriate method for measuring fractal dimension. The concept of fractal was originated from the coastline paradox that measuring the length of the coastline is too difficult [16]. Actually, the length of a coastline is uncertain since it is determined by the length of the straight ruler used to measure. A shorter ruler measures more of small details inlets while a larger ruler ignores those details, so the measured length increases as the ruler length decreases. Fractal dimension is related to how the change of the ruler length affect the measured result. The box-counting method is one of the ways to evaluate fractal dimension. In order to calculate the dimension, a coastline curve is first split into foursquares as boxes with side length of ε, which cover the curve without any doubling (Fig. 1a). When the total quantity of boxes to be able to cover all the curve figure is N(ε), fractal curve has a feature that N(ε) increases very unexpectedly more and more associated with a less decrease of ε.

In fractal structures, there usually exists a correlation between N(ε) and ε as:

$$\text{N}\left({\epsilon }\right) =\text{k}{{\epsilon }}^{-D}$$

where k is constant, and D is the fractal dimension.

In the present study, this 2D box-counting method was applied to 3D rough surface world (Fig. 1b). Using open-source image processing software Fiji (Rasband WS, National Institutes of Health, Bethesda, USA), an OCT probe image and guidewire artifacts were removed from the gray-scale OCT short-axis image of the plaque lesion of interest. A trimming was performed into a 4 mm × 4 mm foursquare box with a center corresponded to the OCT probe center. The OCT image has a three-dimensional information as (x, y, z), where x and y correspond to the location coordinates on a pixel-by-pixel basis, and z is the value of grey scale from 0 to 256. This analysis was performed by a fractal analysis software [FLANA] (TAOS Institute, Yokohama, Japan) covering the entire image by a cube calculated using the box counting method. The value of fractal dimension (FD) for a complex 3D rough surface is between 2 and 3, meaning that the structure is more complex than 2D structures.

Statistical Analysis

Continuous variables with a normal distribution were expressed as mean ± standard deviation, and the comparisons were made by Student t-test. Non-normal distributions were expressed as medians (interquartile ranges) and the comparisons were made with the Mann-Whitney U test. Categorical variables were compared using the chi-square test or Fisher's exact test. The correlation between two continuous indices was evaluated using Spearman's correlation coefficient. In the multivariate multiple regression analysis, explanatory variables were selected from significant indices in a univariate comparison, the total number of which did not exceed 1/15 of the total number of cases. All statistical analyzes were tested using the software EZR (version 1.37, Saitama Medical Center, Jichi Medical University, Saitama, Japan) and P < 0.05 was determined to be statistically significant.

Clinical Characteristics

A total of 65 cases were enrolled in this study. Mean age was 64 ± 14 years (40–87 years), and 50 cases (77%) were male. These variables were not significantly different between the ACS and the SAP groups. There were no significant differences in the prevalence of atherosclerotic risk factors and comorbidities, except that the prevalence of old myocardial infarction was significantly lower in the ACS group than the SAP group (5.9% vs 25.8%, P = 0.039). As for laboratory values, LDL cholesterol levels were statistically significantly higher in the ACS group than SAP group(133 ± 55 mg/ dL vs 107 ± 42 mg/dL, P = 0.039), whereas the level of HDL cholesterol (41 ± 11 mg/dL vs 50 ± 12 mg/dL, P = 0.003), creatinine, triglycerides, and HbA1c, were not significantly different. The concomitant use of β-blockers (14.7% vs 38.7%, P = 0.012), statin (29.4% vs 64.5%, P = 0.006), and ACE-I/ARB (17.6% vs 64.5) %, P < 0.001) was significantly lower in the ACS group.

Oct Analysis

As for conventional OCT indices, the lipid plaque length was significantly longer (12.6 ± 5.0 mm vs 7.7 ± 2.7 mm, p < 0.001), the mean lipid arc was significantly greater (204 ± 39° vs 152 ± 34°, p < 0.001), and the minimal fibrous cap thickness was significantly thinner (75.3 ± 22.3 µm vs 134.8 ± 53.2 µm, p < 0.001), in the ACS group than these values of the SAP group, respectively. The prevalence of OCT-derived macrophage infiltration OCT-derived TCFA within the entire culprit vessel were significantly higher in the ACS group than in the SAP group (macrophage infiltration: 61.8% vs 35.5%, p = 0.048; TCFA: 44.1% vs 6.4%, p < 0.001).

Fractal Analysis

The value of FD at the culprit lesion was significantly greater in the ACS group compared with the SAP group (2.400 ± 0.072 vs 2.342 ± 0.051, p < 0.001). There was a significant but rough correlation between FD and minimum fibrous cap thickness (r=-0.385, P = 0.002 as well as between FD and mean lipid arc (r = 0.33, P = 0.007).

In order to explore the determinants of FD (Table 2), a univariate analysis was first performed, then fibrous cap thickness (p = 0.002), lipid plaque length (p < 0.001), mean lipid arc (p = 0.007) at the culprit lesion, and the presence of macrophage infiltration within the entire culprit vessel ( p < 0.001), and the presence or absence of TCFA (p < 0.001) were found to be significant variables. In the multivariate analysis, four explanatory variables were selected for candidates as determinants of FD, and then fibrous cap thickness, lipid plaque length, mean lipid arc, and the presence of macrophage infiltration within the entire culprit vessel, all of which were considered to be no multicollinearity neither confounding, were enrolled, with reference to the p-value. As a result, only the presence of macrophage infiltration within the entire culprit vessel was a significant determinant (regression coefficient estimate 0.049, CI: 0.018–0.079, p = 0.002).

The present study revealed that fractal dimension of OCT cross-sectional images at the culprit lesion in patients with ACS was significantly greater than that in patients with SAP. This study also showed that the culprit plaques in the ACS group had significantly larger mean angle-span of lipid core, longer lipid core lesion lengths, and smaller minimum fibrous cap thickness than those in the SAP group. In addition, TCFA was more frequently observed close to the culprit lesion, and the prevalence of macrophage infiltration within the entire culprit vessel was more frequent, in the ACS group than those in SAP group. These findings with conventional OCT parameters were compatible with previous reports using OCT, coronary angioscopy or near-infrared spectroscopy that coronary culprit plaques in patients with ACS are more vulnerable than those with SAP [17–20].

Therefore, it can be speculated that fractal dimension of the OCT coronary plaque image might be related to coronary plaque vulnerability. Actually, the fractal dimension of the OCT images in the present study showed a positive correlation with mean lipid arc and a negative correlation with the minimum fibrous cap thickness. Furthermore, a multivariate analysis suggested that the infiltration of macrophages might be considered as a determinant of fractal dimension.

Higher fractal dimension of the OCT images in the ACS group, which was considered to have a greater prevalence of vulnerable plaques, indicated that the images were more complicated as well as self-similar than those in the SAP group. The complexity of the OCT images with a grey-scale suggests that the brightness or strength of infrared light reflection from each tissue component and/or the light energy attenuation within plaque tissue is not monotonic but non-uniform and heterogeneous. The OCT images are reconstructed by the degree of infrared light reflection which comes from several boundary surfaces between two tissue components, the strength of which is determined by the difference in refractive index between the two materials. The present study showed that there was a positive correlation between lipid content and fractal dimension. Lipid core of atherosclerotic plaque usually includes various tissue component such as necrotic substances, cholesterol crystal, bleeding, and inflammatory cell infiltration [21] so that there are various reflection points as well as various attenuation through materials within. On the contrary, fibrous tissue usually comprises very uniform arrays of collagen fibers, which would yield simple and monotonous patterns of light reflection within the tissue. This consideration may explain the fact that there was a negative correlation between the minimum fibrous cap thickness and fractal dimension as shown in the present study, because thinner fibrous cap means less tissue uniformity of the entire plaque. Furthermore, a multivariate analysis showed that macrophage infiltration within the entire culprit vessel was a significant determinant of the fractal dimension. Abundance of macrophage infiltration, which has been reported to be greater in patients with ACS [18], might be associated with more complex change of tissue structure due to various chemical reactions, edema, infiltrations of other type of cells or new material involvements, making complex OCT images. From these results, it can be speculated that the value of fractal dimension would be able to evaluate the vulnerability of plaque as well as the degree of macrophage infiltration within a coronary vessel.

Another finding which might have to be stressed among the results of the present study was that the culprit plaques in patients with ACS and even SAP had a fractal self-similar nature within the plaque because their fractal dimensions were not an integer value but between 2 and 3. Self-similarity means that an object is exactly or approximately similar to a part of itself, suggesting that the mechanism to form the object can be very simple or energy-efficient, even though the structure finally formed becomes very complicated one [9]. It has been classically accepted that the formation of atherosclerotic plaque is first from proliferation of intimal fibrous tissue and then followed by intrusion of LDL-cholesterol through a local injury of endothelial cell of artery and cholesterol-intake of macrophage, leading to form lipid core and fibrocapsule [22]. Therefore, our findings suggested that these mechanisms to form atherosclerotic plaque might be controlled by very simple and cost-effective pathological system. Furthermore, vulnerable plaques, which have a higher fractal dimension, may have a too complex structure so that a plaque cannot keep them stable and static. This may be because when a structure is more complex it becomes more fragile, where a lot of stress concentrations or weak points are derived. Therefore, it would be reasonably accepted that fractal dimension of plaque structure is related to its vulnerability to rupture.

To precisely predict the likelihood of cardiovascular events would be very important to prevent them. However, it has been unsuccessful to identify using conventional parameters of intravascular imaging modalities a highly vulnerable plaque which is prone to rupture in the very near future. To overcome this limitation, a novel parameter which is highly predictable for plaque rupture should be found. Fractal analysis like our study might be a feasible novel way to find a vulnerable plaque in order to enhance the predictability of intravascular imaging modalities for future plaque rupture.

This study was an exploratory observational study conducted in a limited number of cases at a single center. In addition, the inclusion of patients with ACS or SAP only who could undergo OCT at the time of PCI may have included selection bias. In this study, ACS groups usually had a plaque rupture in which critical tissues were already effused, and in such case fractal analysis was performed at a plaque cross-section without ulcer but adjacent to the the culprit lesion, which may yield a selection bias. However, even though such limitations existed, it is noteworthy that there was a significant difference in fractal dimension of the culprit plaque between the ACS and SAP groups.

The fractal dimension of OCT images of vulnerable plaques caused ACS was significantly higher than that of the culprit plaques of the SAP group. Vulnerable plaque, which was not sufficiently identified by conventional parameters of intravascular modalities, may be identified with a higher accuracy by additionally using a fractal analysis of the OCT images.

Funding: none.

Financial Interests: All authors declare they have no financial interests.

Author Contributions:

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by [Tomoyuki Morikawa], [Takafumi Hiro], [Takashi Mineki], [Keisuke Kojima], [Takaaki Kogo], [Korehito Iida], [Naotaka Akutsu], [Nobuhiro Murata], [Mitsumasa Sudo], [Daisuke Kitano], [Daisuke Fukamachi] and [Yasuo Okumura]. The first draft of the manuscript was written by [Tomoyuki Morikawa] and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Ethics approval

This study was performed in line with the principles of the Declaration of Helsinki. Approval was granted by the Ethics Committee of Itabashi Hospital, Nihon University School of Medicine (September 8, 2020/RK-200908-06).

Consent to participate

Informed consent was obtained from all individual participants included in the study. Written informed consent was obtained from the parents.

Consent to publish

The authors affirm that human research participants provided informed consent for publication of the images in Figure 1b.

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Tables are available in Supplementary Files section.

No competing interests reported.

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Version 1

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You are reading this latest preprint version

Fractal geometry of coronary plaque images within optical coherence tomography: A novel approach of plaque vulnerability in patients with acute coronary syndrome versus stable angina pectoris

Status:

Version 1

Abstract

Background and Purposes:

Methods and Results

Conclusions

Figures

Introduction

Methods

Coronary Plaque Imaging With Oct

Fractal Analysis Of The Oct Image

Statistical Analysis

Results

Clinical Characteristics

Oct Analysis

Fractal Analysis

Discussion

Clinical Implications

Limitations

Conclusions

Declarations

References

Tables

Additional Declarations

Supplementary Files

Status:

Version 1