Subjects
A total of 136 subjects (among them 66 are diabetic and 70 are non-diabetic) suffering from carotid plaques were investigated in present study. From October 2011 to February 2015, the patients received carotid artery examination at the department of ultrasound, the third affiliated hospital of Sun Yat-sen University. All participants provided the written informed consent. The study protocol was approved by the Institutional Review Board of the third affiliated hospital of Sun Yat-sen University (Guangzhou, China).
In this study, the diagnostic criteria for diabetes are defined as fasting plasma glucose (FPG) level of ≥7.0 mmol/L, and/or 2-h plasma glucose value of ≥11.1 mmol/L, and/or HbA1c level of ≥6.5 %, and/or treatment with either hypoglycemic agents or insulin [13, 14]. Patients with acute or chronic infectious disease, alcohol or drug abuse, retinopathy, or uncontrolled hypertension were excluded. Information regarding age, gender, total number of plaques, systolic blood pressure (SBP), diastolic blood pressure (DBP), body mass index (BMI), total cholesterol, triglyceride, low density lipoprotein cholesterol, high density lipoprotein cholesterol, lipoprotein, apolipoprotein A1, apolipoprotein B100, FPG, HbA1c and medication use were collected.
Carotid ultrasonography
The study was performed by a specialized physician with 5 years vascular ultrasound working experience using a Toshiba AplioXG SSA-790A ultrasound Platform equipped with a 5–12 MHz linear-array transducer (PLT-805AT) and Esaote MyLab90 ultrasound Platform equipped with a 4–13 MHz linear-array transducer (LA523). 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.
To improve the comparability of the plaque images obtained by different ultrasound systems at different settings, all images were standardized according to the scheme proposed by Sabetai et al. [15] before texture analysis. Furthermore, it is more clinically significant to focus on echolucent plaques, since these plaques are more potentially unstable than echo-rich plaques [16]. Gray-scale median (GSM) analysis is an objective and reproducible method for evaluating the echogenicity of carotid plaque [15]. In case there were multiple plaques in one individual, the plaques with the lowest GSM value among them was selected as the representative for the following texture analysis [17]. Two operators performed the GSM measurement independently, and the interoperator reproducibility was evaluated with a kappa value. The disagreement of the two operators were discussed and re-evaluated, then an agreement was finally achieved.
Many studies have shown that carotid intima-media thickening (IMT) is a high risk factor of the future cardiovascular events [18–20]. Maximum IMT (Plaque-IMTmax) was defined as the greatest axial thickness among the plaques in the carotid arteries [21, 22], and was measured in this study.
Texture analysis
MaZda is an effective tool for texture analysis and offers an approach for texture feature extraction, selection and reduction [23]. In MaZda, we can draw regions of interest with arbitrary shapes, as shown in Fig. 1. It provides six various algorithms, such as histogram, absolute gradient, run-length matrix, co-occurrence matrix, autoregressive model and wavelet for features extraction [5, 23]. In present study, about 300 texture features of carotid plaques were extracted using MaZda, as shown in Table 1.
Texture feature selection and reduction
In order to select optimal features among the large number of texture features of the plaques from diabetic and non-diabetic patients, the methods based on Fisher coefficient and mutual information measure were used to select 15 optimal features, respectively. Furthermore, linear discriminant analysis (LDA) was implemented for the combined feature set, and the most discriminating features (MDF) were obtained.
Fisher coefficient
Fisher coefficient is defined as a ratio of between-class scatter D to within-class variance V [24]:
$$F = \frac{D}{V}{ = }\frac{{\frac{1}{{1 - \sum\nolimits_{k = 1}^{K} {P_{k}^{2} } }}\sum\nolimits_{k = 1}^{K} {\sum\nolimits_{j = 1}^{K} {P_{k} P_{j} (\mu_{k} - \mu_{j} )^{2} } } }}{{\sum\nolimits_{k = 1}^{K} {P_{k} v_{k} } }}$$
(1)
where \(u_{i}\), \(v_{i}\) and \(P_{i}\) denote the mean, the variance and the priori probability of class i, respectively. Texture features with larger Fisher coefficient are selected as optimal features.
Mutual information measure
Mutual information (MI), a measure of dependence between two random variables, is defined as [25]:
$$MI\left( {X,Y} \right) = H\left( X \right) + H\left( Y \right) - H\left( {X,Y} \right)$$
(2)
where X and Y are random variables, H is the entropy. In case of X stores values of texture features and Y stores the classification decision. Then, a large MI between X and Y means that X is a useful texture features for classification. Then the MI for each texture features \(f_{i}\) is calculated by [25, 26]:
$$MI(f_{i} ,d) = \sum\limits_{d = 1}^{{N_{b} }} {\sum\limits_{k = 1}^{Nc} {P\left( {f_{i}^{d} ,c_{k} } \right)\log_{2} \left[ {\frac{{P\left( {f_{i}^{d} ,c_{k} } \right)}}{{P\left( {f_{i}^{d} } \right)P\left( {c_{k} } \right)}}} \right]} }$$
(3)
where \(d = c_{1} ,c_{2} , \ldots ,c_{{N_{C} }}\) means the class category, \(N_{c}\) is the total number of class, \(N_{b}\) is the number of histogram bins used for feature discretization, \(f_{i}^{d}\) denotes discretized value of \(f_{i}\).
Linear discriminant analysis
LDA is a useful method for feature reduction [24]. The aim of LDA is to find a transform matrix W such that the ratio of determinants \(\frac{{\left| {W^{T} S_{B} W} \right|}}{{\left| {W^{T} S_{W} W} \right|}}\) is maximized. Where \(S_{B}\) and \(S_{W}\) are the between-class scatter matrix and the within-class scatter matrix. These matrices can be given as formulas (4, 5).
$$S_{B} = \frac{1}{M}\sum\limits_{k = 1}^{{N_{c} }} {M_{k} \left( {x_{i}^{(k)} - u^{(k)} } \right)\left( {x_{i}^{(k)} - u^{(k)} } \right)^{T} }$$
(4)
$$S_{W} = \frac{1}{M}\sum\limits_{k = 1}^{{N_{c} }} {\sum\limits_{i = 1}^{{M_{k} }} {(x_{i}^{(k)} - u^{(k)} )(x_{i}^{(k)} - u^{(k)} )^{T} } }$$
(5)
where \({\text{X}}_{i}^{(k)}\) denotes the i-th pattern in class k
\((i = 1,2, \ldots ,M_{k} ),\)
\(k = 1,2, \ldots ,N_{c}\), \(u^{(k)}\) is the mean vector of class k. It has proved that such a transform matrix \(\varPhi\) is composed of eigenvectors corresponding to largest eigenvalues of \(S_{W}^{ - 1} S_{B}\). The MDF can be obtained when the original data is transformed by the means of matrix \(\varPhi\) as formula (6).
$$MDF_{i} = \varPhi^{T} (x_{i} - u)$$
(6)
Statistical analysis
All statistical analysis was performed with PASW Statistics 18 and p less than 0.05 was considered statistically significant. All values were presented as the mean value ±SD, or real number of patients with the percentage in parentheses. Independent sample t
test was used to examine the baseline clinical parameters between the diabetic and non-diabetic patients. Pearson correlation analysis was conducted to investigate the relationship between HbA1c and the variables including age, BMI, total number of plaques, SBP, DBP, plaque-IMTmax and MDF. Linear regression analysis was carried out by considering the HbA1c as a dependent variable and regarding the MDF as independent variable. The optimized regression model was obtained to estimate the HbA1c. Further, the receiver operating characteristics (ROC) curve was developed to test the relationship between the estimated HbA1c (models output) and diabetes status.