Evaluation of carotid plaque echogenicity based on the integral of the cumulative probability distribution using gray-scale ultrasound images

Objective Carotid plaque echogenicity is associated with the risk of cardiovascular events. Gray-scale median (GSM) of the ultrasound image of carotid plaques has been widely used as an objective method for evaluation of plaque echogenicity in patients with atherosclerosis. We proposed a computer-aided method to evaluate plaque echogenicity and compared its efficiency with GSM. Methods One hundred and twenty-five carotid plaques (43 echo-rich, 35 intermediate, 47 echolucent) were collected from 72 patients in this study. The cumulative probability distribution curves were obtained based on statistics of the pixels in the gray-level images of plaques. The area under the cumulative probability distribution curve (AUCPDC) was calculated as its integral value to evaluate plaque echogenicity. Results The classification accuracy for three types of plaques is 78.4% (kappa value, κ = 0.673), when the AUCPDC is used for classifier training, whereas GSM is 64.8% (κ = 0.460). The receiver operating characteristic curves were produced to test the effectiveness of AUCPDC and GSM for the identification of echolucent plaques. The area under the curve (AUC) was 0.817 when AUCPDC was used for training the classifier, which is higher than that achieved using GSM (AUC = 0.746). Compared with GSM, the AUCPDC showed a borderline association with coronary heart disease (Spearman r = 0.234, p = 0.050). Conclusions Our experimental results suggest that AUCPDC analysis is a promising method for evaluation of plaque echogenicity and predicting cardiovascular events in patients with plaques.

Introduction Cardiovascular diseases significantly threaten human health and are the primary cause of death and disability worldwide [1]. Most myocardial infarctions, strokes, and acute coronary syndromes are caused by the rupture of unstable atherosclerotic plaques [2]. In recent years, growing evidence has been presented to support the association between plaque echogenicity and its vulnerability [3,4]. Echolucent plaques are dominated with lipid content, less calcification, less fibrous tissue, and tend to be more prone to rupture [5,6]. In addition, previous studies have demonstrated that plaque echolucency is associated with coronary events and future stroke [7,8]. Therefore, it is of significant interest to evaluate the plaque echogenicity, which may contribute to the identification of unstable plaques and for predicting cardiovascular events.
It is well-known that ultrasound imaging is a non-invasive technique for carotid atherosclerosis plaque examination. Ultrasound measurement of plaque echogenicity can provide a risk factor for predicting cardiovascular events [9][10][11]. Visual classification has been used to assess the plaque echogenicity in many previous studies [11][12][13], however, the results are operatordependent. Recent studies have shown that computer assisted methods of plaque characterization using B-mode images can provide measurements in predicting clinical outcome [4,[14][15][16][17][18][19]. Percentage white (PW) has been proposed as a metric for evaluation of echogenicity in carotid plaques, but it needs an intensity threshold to determine which pixels are echogenic (white) [14]. The process of PW feature extraction is relatively complex because the intensity threshold of each image is different. Texture analysis has been utilized to characterize carotid atherosclerotic plaques in symptomatic and asymptomatic patients [15][16][17], and it shows promise in the assessment of plaque echogenicity by combining the morphological characteristics of plaques [20]. However, the extraction of texture features requires high computational complexity. Recent studies have indicated that computerized measurement of the gray-scale median (GSM) is an objective and useful metric for assessment of the plaque echogenicity [4,18,19]. It is worthwhile noting that GSM is the fiftieth percentile of the probability distribution of gray-scale pixels, and it ignores the details of the probability distribution of plaques. Shankar et al. proposed a method to model the statistics of the pixels in the gray-level images of soft and hard plaques [21]. The cumulative probability distribution curves showed significant trends for these two types of plaques. Therefore, we suggest that the area under the cumulative probability distribution curve (AUCPDC) may be an effective parameter for evaluating plaque echogenicity.
The aim of this study is to examine whether the AUCPDC analysis is a useful method for the evaluation of plaque echogenicity and to further compare its efficiency with GSM.

A. Patients
The study protocol was approved by the Institutional Review Board of the third affiliated hospital of Sun Yat-sen University (Guangzhou, China). All participants provided written informed consent.
From September 2013 to March 2016, a total of 130 carotid plaques were collected from 74 volunteers, and 5 controversial plaques were excluded after visual classification by two sonographers. The remaining 125 carotid plaques (43 echo-rich, 35 intermediate and 47 echolucent plaques) from 72 volunteers were used in the in the following analysis.

B. Clinical and biochemical analyses
Blood samples were collected after an overnight fast for analysis of total cholesterol, triglyceride, high density lipoprotein cholesterol, low density lipoprotein cholesterol, apolipoprotein A1, apolipoprotein B100, fasting plasma glucose, and HbA 1c . The diagnostic criteria for hypertension was defined as systolic blood pressure ! 130 mmHg and/or diastolic blood pressure ! 80 mmHg or current use of antihypertensive agents. Diabetes was defined as fasting plasma glucose level of ! 7.0 mmol/L, and/or 2-hour plasma glucose value of ! 11.1 mmol/L, and/or HbA 1c level of ! 6.5%, and/or treatment with either hypoglycemic agents or insulin [22,23].

C. Images acquisition and preprocessing
Ultrasound images of carotid plaques were collected by a sonographer that has 5 years of experience in vascular imaging using an Aplio XG (SSA-790A) (Toshiba Medical Systems, Japan) equipped with a 5-12 MHz linear-array transducer (PLT-805AT). The carotid artery was examined with the head tilted slightly upward in the mid-line position. The transducer was manipulated so that the near and far walls were parallel to the transducer footprint, and the lumen diameter was maximized in the longitudinal plane.
According to the criteria of the European carotid plaque study group, plaques were classified into three different types: echolucent, intermediate and echo-rich plaques [12]. The visual classification of plaque echogenicity was independently performed by two sonographers with at least 5 years of experience in vascular imaging, and a kappa value (κ) was calculated to evaluate the between-observer agreement.

D. Image normalization
The ultrasound system settings (e.g. system gain, time gain compensation etc.) can impact the brightness and contrast of the B-mode images. In this study, all images were normalized according to the scheme proposed by Sabetai et al [24]. After normalization, the GSM of the blood range from 0 to 5, whereas the GSM of adventitia range from 185 to 195.

E. Statistics of the pixels in gray-level images of plaques
In this study, the plaque was manually segmented by one operator in the gray-level image, and the statistics of the pixels of plaques were obtained. Then, the AUCPDC analysis and GSM analysis were performed for each plaque based on their pixel statistics.

F. Gray-scale median
Here, we let x represents the gray scale pixel value, f(x) is the probability density function of x, and f(x) can be calculated as follows: The number of pixels ðgray value ¼ xÞ Total number of pixels ðgray value range from 0 to 255Þ : ð1Þ The GSM is defined as follows:

G. Area under cumulative probability distribution curve
For each plaque, the cumulative distribution function F(x) of the gray scale distribution, can be expressed as follows, The AUCPDC is measured as follows,

H. Classification
The k-nearest-neighbor (KNN) classification was performed for classifying the three different types of plaques based on AUCPDC or GSM. In order to improve the reliability of classification, a leave-one-out cross validation was implemented in this study. The kappa statistic (κ) was calculated to evaluate the agreement between visual classification and the KNN classification. Furthermore, the receiver operating characteristic (ROC) curves for the KNN classifier were developed to compare the ability of AUCPDC and GSM in identifying echolucent plaques.

I. Intra-operator agreement
In order to examine the intra-operator agreement, the AUCPDC analyses were performed at two different times within a 2-month period. Based on the same visual classification, a total of

J. Bootstrapping for estimating Youden's index J
Youden's index J [26] is a single statistic that can summarize the performance of a diagnostic test, and it is defined as: It has been widely utilized in many studies to evaluate the accuracy of diagnostic tests and the performance of risk assessment model [27,28].
Bootstrap is a useful tool to provide statistical inference to estimate the accuracy and the precision of any statistic through resampling with replacement from the original datasets [29,30]. In this study, the bootstrapping is implemented to estimate the 95% confidence intervals (CIs) of Youden's index J.

K. Statistical analyses
All statistical analysis was performed with PASW Statistics 18 and all values were presented as the mean value ± SD, or real number of patients with the percentage in parentheses. Spearman's rank correlation analysis was also implemented between the GSM, AUCPDC and the status of hypertension, diabetes, coronary heart disease (CHD). Youden's index J was calculated using MedCalc statistical software.

B. Visual classification
The classification of the carotid plaques (n = 130) into three different types showed a good agreement between two experienced sonographers ( Table 2). The between-observer reproducibility was 96.15% (κ = 0.942). A total of 5 controversial plaques were excluded, and the 125 consensual plaques were retained in the following analysis.
C. The area under cumulative probability distribution curve of plaque

D. Carotid plaque classification
As shown in Tables 3 and 4, when AUCPDC was used for training classifier, the classification accuracy of discriminating the echo-rich, intermediate and echolucent plaques was 78.4% (κ = 0.673), which was higher than that obtained by using GSM 64.8% (κ = 0.460). When classification based on GSM, 8 of 35 intermediate plaques were classified correctly, and 21 of 35 intermediate plaques were misclassified as echolucent plaques ( Table 3). The AUCPDC was more effective in discriminating intermediate and echolucent plaques than GSM. Table 4 indicated that 21 of 35 intermediate plaques were classified correctly, and 11 of 35 intermediate plaques were misclassified as echolucent plaques, when classification based on AUCPDC. Further, ROC curve analysis was developed to test the effectiveness of AUCPDC in the identification of echolucent plaques. The area under the curve (AUC) was 0.817 when AUCPDC was used for training the classifier, whereas AUC was 0.746 when GSM was used (Fig 3).

F. Relationship between GSM, AUCPDC and hypertension, diabetes, CHD
Spearman's rank correlation analysis was implemented to examine the relationship between the GSM, AUCPDC and the status of hypertension, diabetes, CHD (Table 5). Compared with GSM, the AUCPDC showed a statistical association with CHD (Spearman r = -0.121, p = 0.315 vs. r = 0.234, p = 0.050).

Discussion
In the present study, the AUCPDC was proposed to evaluate plaque echogenicity. Our results indicated that it is feasible to classify echo-rich, intermediate and echolucent plaques based on AUCPDC. The classification accuracy was 78.4% (κ = 0.673), when AUCPDC was used to train the classifier. Previous studies have proven that the echolucent plaque is a high risk indicator of cardiovascular events [8,10, 18,31,32]. Compared with GSM, the AUCPDC showed a higher potential feasibility for identifying echolucent plaques (AUC = 0.817) (Fig 3), and it was more related to CHD (Spearman r = 0.234, p = 0.050) ( Table 5). These indicate that AUCPDC analysis of the ultrasound images of carotid plaques might have potential in predicting the cardiovascular risk in patients with plaques.
Many studies have shown that visual classification is a feasible and reliable method for classification of ultrasound plaques with different echogenicity [12,13,33]. Geroulakos et al. classified 70 carotid plaques into five different types (type 1 uniformly echolucent, type 2 predominantly echolucent, type 3 predominantly echogenic, type 4, uniformly echogenic, and type 5 calcified plaques) and the between-observer reproducibility was 85.71% (κ = 0.79). Mayor et al. analyzed 95 carotid bifurcation plaques with the same five-type classification system, and a between-observer reproducibility of 91% (κ = 0.87) was observed. In this study, the plaques were classified into three different types (type 1 echo-rich, type 2 intermediate and type 3 echolucent) according to the scheme of the European carotid plaque study group [12], and a higher between-observer reproducibility of 96.15% (κ = 0.942) was achieved.
Both GSM and AUCPDC are calculated based on the gray scale distribution. Compared with GSM, the AUCPDC calculation takes into consideration the probability density distribution of gray scale values ranging from 0 to 255. The lower gray scale value with a high probability density gives rise to a higher value of AUCPDC. Fig 5 illustrates that the sample 1 has a   same GSM with sample 2 (GSM = 128), but the AUCPDC of sample 2 is larger than sample 1. It may imply that AUCPDC is more effective than GSM in distinguishing the differences in the probability density distributions of gray scale value of plaques. Consistent with the above analysis, Tables 3 and 4 indicate that AUCPDC shows an obvious superiority in discriminating intermediate and echolucent plaques. In this research, compared with GSM, the AUCPDC showed a statistical association with CHD (p = 0.05) ( Table 5), but the correlation is barely significant. Such results may be caused by the relatively small sample size and sample difference. Among a total of 72 patients in this study, only 27 (37.5%) patients had CHD. What's more, there are some methodological limitations on the calculation of AUCPDC. The ultrasound system settings (e.g. system gain, time gain compensation etc.) impact the brightness and contrast of the B-mode images, which will cause calculation bias in AUCPDC. To reduce the impact of instrument settings, normalization of the dynamic range is done by considering minimum and maximum pixel intensities within the region-of-interest. Overall, the AUCPDC is an effective parameter for evaluating the plaque echogenicity.

Conclusion
Compared with GSM, the AUCPDC is more effective in classifying three types of plaques and identifying echolucent plaques, suggesting that AUCPDC analysis is a promising method for