Three-dimensional ultrasound evaluation of the effects of pomegranate therapy on carotid plaque texture using locality preserving projection

Computer Methods and Programs in Biomedicine 184 (2020) 105276

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Three-dimensional ultrasound evaluation of the effects of pomegranate therapy on carotid plaque texture using locality preserving projection Xueli Chen a, Mingquan Lin a, He Cui a, Yimin Chen a, Arna van Engelen b, Marleen de Bruijne b,c, M. Reza Azarpazhooh d, Seyed Mojtaba Sohrevardi d,e, Tommy W.S. Chow a, J. David Spence d, Bernard Chiu a,∗ a

Department of Electrical Engineering, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong Biomedical Imaging Group Rotterdam, Department of Radiology and Nuclear Medicine, Erasmus MC, Rotterdam, the Netherlands c Machine Learning Section, Department of Computer Science, University of Copenhagen, Denmark d Stroke Prevention & Atherosclerosis Research Centre, Robarts Research Institute, London, Ontario, Canada e Pharmaceutical Sciences Research Center, Faculty of Pharmacy, Shahid Sadoughi University of Medical Sciences, Yazd, Iran b

a r t i c l e

i n f o

Article history: Received 14 February 2019 Revised 19 November 2019 Accepted 11 December 2019 Available online xxx Keywords: 3D ultrasound imaging Carotid atherosclerosis Pomegranate therapy Plaque texture

a b s t r a c t Background and objective: Dietary supplements are expected to confer a smaller beneficial effect than medical treatments. Therefore, there is a need to develop cost-effective biomarkers that can demonstrate the efficacy of such supplements for carotid atherosclerosis. The aim of this study is to develop such a biomarker based on the changes of 376 plaque textural features measured from 3D ultrasound images. Methods: Since the number of features (376) was greater than the number of subjects (171) in this study, principal component analysis (PCA) was applied to reduce the dimensionality of feature vectors. To generate a scalar biomarker for each subject, elements in the reduced feature vectors produced by PCA were weighted using locality preserving projections (LPP) to capture essential patterns exhibited locally in the feature space. 96 subjects treated by pomegranate juice and tablets, and 75 subjects receiving placebo-matching juice and tablets were evaluated in this study. The discriminative power of the proposed biomarker was evaluated and compared with existing biomarkers using t-tests. As the cost of a clinical trial is directly related to the number of subjects enrolled, the cost-effectiveness of the proposed biomarker was evaluated by sample size estimation. Results: The proposed biomarker was more able to discriminate plaque changes exhibited by the pomegranate and placebo groups than total plaque volume (TPV) according to the result of t-tests (TPV: p = 0.34, Proposed biomarker: p = 1.5 × 10−5 ). The sample size required by the new biomarker to detect a significant effect was 20 times smaller than that required by TPV. Conclusion: With the increase in cost-effectiveness afforded by the proposed biomarker, more proof-ofprinciple studies for novel treatment options could be performed. © 2019 Elsevier B.V. All rights reserved.

1. Introduction Stroke is the second leading cause of death worldwide, with 5.5 million stroke-related deaths in 2016 [1,2]. China, accounting for one-fifth of the population, has a disproportionate share of stroke mortality, which stood at 1.8 million in 2016 and accounted for one-third of the total number of deaths from stroke worldwide

∗

Corresponding author. E-mail address: [email protected] (B. Chiu).

https://doi.org/10.1016/j.cmpb.2019.105276 0169-2607/© 2019 Elsevier B.V. All rights reserved.

[1,2]. Carotid atherosclerosis is a major source of atherosclerotic emboli (platelet aggregates and plaque debris) that would block cerebral arteries, leading to ischemic strokes. Fortunately, for patients with high stroke risk, 75–80% of stroke can be prevented by lifestyle/dietary changes and medical therapies [3]. With recent advances in the pathogenesis of atherosclerosis, the numbers of new interventions are expected to rise rapidly. Effects of these treatment or management strategies are required to be thoroughly validated in clinical trials. Therefore, in parallel to the development of novel therapies, there is a critical requirement of measurement tools for cost-effective serial monitoring of carotid atherosclerosis.

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X. Chen, M. Lin and H. Cui et al. / Computer Methods and Programs in Biomedicine 184 (2020) 105276

Carotid intima-media thickness (IMT) measured from 2D Bmode ultrasound was an early imaging biomarker introduced to increase the sensitivity of carotid disease monitoring, but recent investigations suggest two major weaknesses of IMT. First, the annual change of IMT is small ( ~ 0.15 mm, below the spatial resolution of carotid ultrasound) and does not permit the measurement of change in individuals within a clinically affordable timeframe [4]. Second, IMT measures vascular wall thickening, which is not directly related to atherosclerosis [5], rendering it a weak predictor of cardiovascular risk [6,7]. Although total plaque area (TPA) measurement has emerged as a more accurate metric for stroke risk prediction [8], both IMT and TPA are measured from 2D ultrasound images, acquisition of which requires an operator to choose an imaging plane to be scanned, making an image difficult to reproduce, even for the same operator. Therefore, 2D ultrasound measurements are sub-optimal in serial monitoring of plaque [9]. Development of 3D ultrasound has allowed for more sensitive and reproducible quantification of carotid atherosclerosis. Total plaque volume (TPV) measured from 3D ultrasound has been shown to be reproducible [10], able to predict vascular events [11] and sensitive to disease progression and regression in a clinical trial involving high-dose atorvastatin [12]. The risk of cardiovascular events is related to the presence of vulnerable plaques and the vulnerability of a plaque is determined by its composition. Changes in plaque textural features have served as a surrogate for plaque composition assessment. Textural analysis was shown to be more accurate than TPV in showing plaque regression with high-dose atorvastatin versus placebo subjects [13]. Van Engelen et al. [14] showed that textural change was more accurate than TPV change in predicting cardiovascular events. Zhou et al. [15] showed that fractal dimension texture analysis was more able than TPV to discriminate subjects receiving atorvastatin and placebo. A number of investigations performed in 2D ultrasound have also shown that textural features were useful in identifying symptomatic patients [16,17]. Roy-Cardinal et al. [18] showed that quantitative tissue information extracted from ultrasound imaging was useful in classifying carotid artery plaque components, including lipid, calcification and ruptured fibrous cap. These results suggest that a biomarker based on plaque textural features would be more able than TPV to highlight treatment effects. The increased discriminative power conferred by such a texture-based biomarker could substantially reduce the sample size, duration and therefore cost required to establish the efficacy of novel dietary/lifestyle interventions. Many textural features have been extracted from carotid ultrasound images in investigations involving the stratification of stroke risk [16,19,20]. Christodoulou et al. [16] extracted 61 texture features and shape parameters from 2D longitudinal carotid ultrasound images to classify symptomatic statuses using a combination of classifiers. Kyriacou et al. [19] extracted 43 texture features from 2D longitudinal ultrasound images in a stroke risk assessment study. The probabilistic neural network (PNN) and support vector machine (SVM) were used to classify the symptomatic statuses of patients. Araki et al. [20] extracted 16 textural features from 2D longitudinal images and classified the stroke risk into high and low using SVM. The ground truth classification was determined by lumen diameter. Huang et al. [21] extracted 300 texture features in classifying plaques into 3 categories (i.e., hyperechoic, intermediate and anechoic) using the K-nearest neighbour classifier. The ground truth labels were manually assigned by expert observers. These techniques were evaluated in cross-sectional analyses based on 2D carotid ultrasound images, but not in longitudinal studies of plaque change. The increased reproducibility afforded by 3D carotid ultrasound imaging techniques has allowed for 3D textural analysis of plaque change. Awad et al. [13] extracted 270 textural features to detect statin-related changes in carotid atherosclerosis and showed

that textural features were more accurate than TPV in classifying patients who received high-dose atorvastatin and placebo. Van Engelen et al. [14] extracted 376 features to predict cardiovascular events in high-risk patients and showed that textural change was more accurate than TPV change in predicting cardiovascular events. The 376 features extracted in this study were generated by 9 textural extraction techniques and encompass most features used in the 2D and 3D studies discussed above. In the current study, we aim to develop a cost-effective texturebased biomarker capable of quantifying the degree of plaque change. The 2D and 3D textural analyses discussed above primarily involved feature-based classification. The classifiers generated discrete class labels but did not allow the quantification of how much change has occurred in a plaque. To address this issue, we developed a scalar, easy-to-interpret and discriminative biomarker integrating the 376 plaque features extracted in Ref. [14], which encompass textural features used in previous studies. In addition, a physical understanding of the biomarker should be established for it to be accepted by clinicians. One way of characterizing the biomarker is to identify important textural features that contribute to the biomarker’s ability for discriminating treatment and placebo subjects. A metric was proposed in this study to determine the weight of each of the 376 features in the proposed biomarker (Eq. (7)). The proposed biomarker was validated in a clinical trial aiming to evaluate the effect of pomegranate juice and tablets. Lipid oxidation in arterial macrophages and lipoproteins is a major contributor to carotid atherosclerosis. As a rich source of potent antioxidants [22], pomegranate juice has been shown to inhibit LDL oxidation and attenuate atherosclerosis development in animal studies [23,24]. However, a recent 18-month randomized placebocontrolled trial aiming at assessing the effect of pomegranate juice in 289 subjects at risk of coronary disease and stroke showed that no difference in carotid IMT change was found between the pomegranate and the control group (p = 0.65) [25], thereby casting a doubt on whether pomegranate juice is effective in slowing the progression of atherosclerosis. As pomegranate is a dietary supplement expected to confer smaller beneficial effect than high-dose atorvastatin, the requirement on the discriminative power for the proposed biomarker is higher than that required for detecting the effect of atorvastatin in Ref. [13]. We hypothesized that the proposed biomarker has enough discriminative power in detecting the effects of pomegranate juice/tablets in a placebo-controlled study. This hypothesis was extensively evaluated in the current study. 2. Materials and methods 2.1. Study subjects and ultrasound image acquisition and preprocessing Subjects were recruited at the Stroke Prevention & Atherosclerosis Research Centre at Robarts Research Institute (London, Ontario, Canada) for a registered clinical trial (ISRCTN30768139). The 171 subjects involved in this study were randomized into two groups. 96 subjects received pomegranate extract in a tablet and juice form once daily, and 75 subjects received a placebo-matching tablet and juice lacking the active ingredients once daily. A total of 629 carotid plaques were identified from the 3D ultrasound images of 171 subjects. Baseline characteristics are provided in Table 1. Subjects on cardiovascular medications were allowed to enter the study provided that they were on a stable medication regimen for at least 6 weeks prior study entry and agreed to remain on the same regimen for the duration of the study. The background medications taken by pomegranate and placebo subjects were compared as detailed in Section 2.6 and reported in the Results

X. Chen, M. Lin and H. Cui et al. / Computer Methods and Programs in Biomedicine 184 (2020) 105276

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Table 1 Baseline characteristics of subjects involved in this study. BMI: body mass index; HDL: high-density lipoprotein; LDL: low-density lipoprotein. Continuous variables are given as median (interquartile range). Categorical variables are given as percentages. P-values were obtained using Kruskal-Wallis test for continuous variables and χ 2 testing for categorical variables.

Age Men, % Systolic blood pressure, mm Hg Diastolic blood pressure, mm Hg TPV, mm3 BMI, kg/m2 Heart rate, beats/min Smoking (never, quit, and still smoking) Smoking pack-years Alcohol Total cholesterol, mmol/L HDL cholesterol, mmol/L LDL cholesterol, mmol/L Triglyceride, mmol/L

Placebo (n = 75)

Pomegranate (n = 96)

P-value

67 (62–70) 65 122 (115–129) 71 (65–78) 136 (68–245) 28 (25–31) 65 (56–73) 39%, 15%, 47% 0.01 (0–10) 72% 3.5 (3.1–4.3) 1.4 (1.2–1.7) 1.5 (1.2–2.2) 1.0 (0.7–1.4)

65 (59–70) 71 123 (116–132) 72 (66–78) 142 (67–228) 28 (25–32) 66 (57–73) 41%, 24%, 35% 1 (0–20) 73% 3.5 (2.9–4.6) 1.3 (1.1–1.6) 1.6 (1.1–2.4) 1.0 (0.8–1.4)

0.11 0.44 0.73 0.89 0.94 0.78 0.41 0.80, 0.13,0.14 0.33 0.89 0.97 0.13 0.88 0.10

section. The subjects provided written informed consent to the study protocol approved by Western University Health Science Research Ethics Board (file number 102516). High-resolution 3D US images were obtained by translating an ultrasound transducer (L12-5, 8.5 MHz central frequency, Philips, Bothel, WA, USA) mounted on a mechanical assembly at a uniform speed along the neck for about 4 cm, centred on the bifurcation. Ultrasound frames acquired using an ultrasound machine (ATL HDI 50 0 0, Philips, Bothel, WA, USA) were digitalized at a rate of 30 Hz and reconstructed into a 3D image with a field of view of 50 × 40 × 60 mm3 [26]. For each subject, a sonographer optimized the image quality for plaque analysis by controlling the overall gain, time gain control settings and the focal points considering the neck size and carotid anatomy. Participants were scanned at baseline before the study and at a follow-up session, which took place ranging from 283 to 579 days after the initial scan. Although the sonographer attempted to standardize ultrasound image acquisition, his judgement is prone to bias and variability. For this reason, linear normalization was carried out in order to standardize the image intensity of the acquired images. The 10th percentile of the image volume was scaled to a gray level of 10 and the 90th percentile was scaled to 150 [27]. 2.2. Plaque segmentation and extraction of textural features Carotid plaques in 3D ultrasound images were segmented following the workflow previously described [10] by an observer who had acquired an intra-class correlation (ICC) of 95% in TPV measurements obtained in five repeated segmentation sessions for 20 arteries involved in this study. A set of 376 textural features generated by 9 different texture extraction techniques was computed for each plaque in both arteries as described in [14]. These 9 techniques were summarized below. Most of these texture measures have been involved in previous 2D and 3D carotid ultrasound investigations, and the parameters involved were based on these studies [13,16,28,29]. The value of jth feature for pth plaque from Subject i at Visit k, is denoted as vi, j, k, p , where, in this study, i = 1, 2, . . . , 171, j = 1, 2, . . . , 376, k = 0, 1 (Baseline and follow-up respectively). For each feature and each visit, a subject average vi, j, k was computed by weighting the value computed for each plaque p with its volume PVp : vi, j,k =  p∈{All plaques for Subject i } PVP × vi, j,k,p /T PV, where  T PV = p∈{All plaques for Subject i } PV p . Since the time intervals between the baseline and follow-up scans (t in years) vary among subjects, the changes of jth feature for Subject i, denoted as  f (i, j ), was normalized to its annual rate:  f (i, j ) = (vi, j,1 − vi, j,0 )/t.

Min-max scaling technique was then applied to ensure that all features have the same range of 0 to 1 so that the weighting factor generated by the dimensionality reduction techniques introduced in Section 2.4 can be interpreted in a consistent manner. The normalized feature change f(i, j) was computed as follows. For each textural feature j ∈ {1, 2, . . . , 376}:

minumum = min  f (i, j ) i maximum = max  f (i, j ) f (i, j ) =

i  f (i, j )−minumum maximum−minumum

(1)

The 9 texture extraction techniques were summarized below, with the number of features per technique given in parentheses: Gray-level distribution (GLD, 34) GLD features were statistics of the image intensity inside the plaques, including (1) the mean, (2) standard deviation, (3) median, (4) minimum, (5) maximum, (6) entropy, (7) mode, (8) energy, (9)-(13) the third to seventh moments around the mean, (14)-(33) the normalized histogram of 20 gray-level bins, and (34) the histogram bin with the highest count. Gray-level co-occurrence matrix (GLCM, 78) GLCM pioneered by Haralick et al. [30] is a two-dimensional histogram with each element Cdθ (i, j ) specifying the joint probability of having two pixels with gray-level i and j separated with a distance of d along the direction defined by θ . As in [14], GLCMs with d = 1 pixel were computed for four directions with θ = 0◦ , 45◦ , 90◦ , 135◦ . GLCM features were computed separately for each of the axial, coronal and sagittal orientations. For each of these three orientations, 4 GLCMs of different θ were computed for all consecutive slices covering a plaque. The following 13 features were extracted from each GLCM [30]: (1) autocorrelation, (2) contrast, (3) correlation, (4) cluster prominence, (5) dissimilarity, (6) energy, (7) entropy, (8) homogeneity, (9) maximum probability, (10) sum average, (10) sum entropy and (11) and (12) two information measures of correlation. The mean and the standard deviation of the 4 different θ s were calculated for each of the axial, coronal and sagittal orientations, resulting in 78 features in total (13 features × 2 quantities (mean or SD) × 3 orientations). Gray-level run-length matrix (GLRLM, 66) GLRLM is a twodimensional matrix in which each element pθ (g, l) specifies the number of length-l runs at gray-level g along the θ direction [31]. For each of the axial, coronal and sagittal orientations, GLRLM of four directions (θ = 0◦ , 45◦ , 90◦ , 135◦ ) were constructed. The following 11 features were computed

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and averaged over the four directions: (1) Short-run emphasis, (2) long-run emphasis, (3) low gray-level emphasis, (4) high gray-level emphasis, (5) gray-level non-uniformity, (6) run-length non-uniformity, (7) run percentage, (8) shortrun low gray-level emphasis, (9) long-run high gray-level emphasis, (10) short-run high gray-level emphasis and (11) long-run low gray-level emphasis. These 11 measurements were computed for each of the axial, coronal and sagittal orientations, and for two bin width settings of 5 and 20, resulting in 66 features in total (11 features × 3 orientations × 2 bin widths). Gray-level difference statistics (GLDS, 12) GLDS computes the absolute gray-level difference between a pair of pixels with a distance of 1 pixel for four directions (θ = 0◦ , 45◦ , 90◦ , 135◦ ) [32]. Four features were computed and averaged over the four directions, including (1) mean, (2) contrast, (3) angular second moment and (4) entropy. These 4 features were obtained on each of the axial, coronal, sagittal orientations, resulting in 12 features (4 features × 3 orientations). Neighbourhood gray tone different matrix (NGTDM, 10) NGTDM quantifies the local gray-level variations at each gray-level bin [33]. A number of features are derived from this matrix describing different aspects of human visual perception: (1) coarseness, (2) contrast, (3) busyness, (4) complexity and (5) texture strength. These 5 features were computed for gray-level bins with widths 1 and 10, resulting in 10 features (5 measures × 2 bin widths). Laws texture (105) Laws developed textual features by convolution with the following 1D kernels: L = [1 4 6 4 1], E = [−1 − 2 0 2 1], S = [−1 0 2 0 − 1], R = [1 − 4 6 − 4 1], W = [−1 2 0 − 2 1]. For feature extraction in 3D images, 125 3D convolution kernels were generated by convolving these 1D kernels in the vertical, horizontal and out-of-plane orientations. Rotated kernels, such as LES, LSE, ELS, ESL, SEL and SLE, were averaged to produce a single kernel, reducing the total number with 3D kernels to 35. The mean, absolute mean and standard deviation were computed for each of the convolutions with the 35 kernels, resulting in 105 features in total [35 kernels × 3 quantities/kernel (mean or absolute mean or SD)]. Local binary pattern (LBP, 27) Rotationally invariant LBP measures textural homogeneity by quantifying the number of transitions from intensities higher than the central pixel to those lower than the central pixel [34]. We quantified the transitions of intensity in a 26- and 98-neighbourhood of each voxel inside the plaque as in [14]. Measurements include: (1)–(4) the mean and standard deviation of the number of regions in both the 26- and the 98-voxel neighborhood, (5)-(11) a normalized histogram of 1 up to 6 and > 6 areas for the 26-neighborhood, and (12)–(27) 1 up to 15 and > 15 areas for the 98-neighborhood. Gaussian filter bank (24) 3D Gaussian filters of 3 scales, 0.16 mm, 0.32 mm and 0.64 mm, were used to generated smoothed images, from which the intensity, gradient magnitude, Laplacian and curvature were obtained on a voxelby-voxel basis. The mean and standard deviation of these 12 measures were computed over all voxels inside the plaque, resulting in 24 features [12 measures × 2 quantities (mean or SD)]. Structure tensor (20) The structure tensor characterizes the distribution of the gradient around a centering voxel. (1– 3) The 3 eigenvalues, (4) the determinant of the 3D structure tensor and (5) the fractional anisotropy were computed for each voxel inside the plaque region. Two scale settings were applied: (i) a local scale of 0.16 mm and an integration scale of 0.48 mm, (ii) a local scale of 0.32 mm and an

integration scale of 0.80 mm. Readers are referred to Lindeberg and Gårding [35] for the definitions of local and integration scales. The mean and standard deviations of these 5 features were computed over each plaque region in the two scale settings, resulting in 20 features in total [5 measures × 2 settings × 2 quantities (mean or SD)]. 2.3. Dimensionality reduction using principal component analysis (PCA) In the current study, the development of a scalar biomarker was formulated as a supervised dimensionality reduction problem aiming at maximizing the discriminative power of the lowdimensional (one-dimensional here) representation. Linear discriminant analysis (LDA) is a widely used method, but it has two major issues when the feature dimension (376 in this study) is higher than the number of samples (171 in this study). First, the covariance matrix is often singular, which does not allow LDA to generate a result [36]. Second, even if a result could be generated, discriminative power would be low in high-dimensional settings. In particular, Bickel et al. [37] showed that Fisher LDA performs only as well as random guessing if the ratio of feature dimensions and sample size approaches infinity. For this reason, the dimensionality of the feature space is first reduced by principal component analysis (PCA) before a supervised dimensionality reduction method is used to generate the biomarker. The number of principal components to be retained, denoted by Nx , is a parameter in the PCA model that was required to be determined. Two types of methods have been developed to determine Nx : (i) Heuristic methods, which include scree plot [38], total variance thresholding [39] and broken stick model [40], and (ii) statistical methods, which include cross-validation [39], bootstrapping [39] and Horn’s parallel analysis [41]. While some methods are inherently subjective (e.g., scree plot, total variance thresholding), other methods are computationally intensive (e.g. crossvalidation, bootstrapping). Horn’s parallel analysis is a computationally efficient and objective method and therefore was applied in this paper to determine Nx . One common stopping criterion in PCA is the Kaiser rule [42], which stated that principal components with an eigenvalue larger than 1 should be retained. This rule is based on the Guttman’s conclusion [43] that in an infinite dataset with P variables, the number of eigenvalues larger than 1 forms a theoretical lower bound on the number of components that can produce a correlation structure based on the P variables through linear combination. Horn showed that the application of the Kaiser rule may result in an excessive number of principal components due to sampling error from a finite-sized data set. In Horn’s parallel analysis, the bias in the Kaiser rule was estimated by generating an uncorrelated random data of the same size as the actual data set [41]; PCA was performed in the random and actual data set in parallel, thereby obtaining eigenvalues from each of the two PCA operations. The eigenvalue of the ith principal component obtained in the PCA for the random and actual data was denoted by λr,i and λa,i respectively. The corrected eigenvalue for the ith component of the actual data was then de = λ − λ + 1. The Kaiser rule was then applied termined by: λ a,i a,i r,i  greater than 1 [41,44]. The to retain principal components with λ a,i method is widely used [44–46] because it does not involve subjective judgement and is computationally efficient. In this study, Horn’s parallel analysis was used to determine Nx based on the entire set of 171 subjects. After Nx had been determined, PCA was performed for the whole dataset (i.e., 171 subjects), resulting in Nx eigenvectors x {φ j }Nj=1 . The 376-dimensional feature change vector of each subT

ject, denoted by fi = [ f (i, 1 ), f (i, 2 ), . . . , f (i, 376 )] , was projected

X. Chen, M. Lin and H. Cui et al. / Computer Methods and Programs in Biomedicine 184 (2020) 105276

on the eigenvectors, resulting in an Nx -dimensional vector, denoted T T by xi = [xi,1 , xi,2 , . . . , xi,Nx ] with xi, j = φ j fi . 2.4. The proposed biomarker for effect evaluation To generate the biomarker for detecting plaque textural changes in the pomegranate and placebo groups, a supervised dimensionality reduction technique was subsequently applied. In this work, three techniques were evaluated and compared based on leaveone-out cross-validation. In each of the 171 leave-one-out trial, a biomarker was generated for a single subject while the features of the remaining 170 subjects (i.e., the whole population excluding the subject being evaluated) were used to train the biomarker. 2.4.1. Linear discriminant analysis (LDA) LDA is the most commonly used supervised dimensionality reduction method. It maximizes the trace ratio of the betweenand within-class matrices for the entire dataset and may have a lower discriminative power if the feature space is highly inhomogeneous. More specifically, LDA finds a projection yi = wT xi , where w is a 376-dimensional weighting vector, that maximizes the ratio between the separation of the means associated with different classes and the within-class variances in the reduced dimension, which can be expressed as:

w∗ = arg max w

wSb wT , wSw wT

(2)

where Sb and Sw are the between- and within-class scatter matrices defined in [47]. 2.4.2. Locality alignment discriminant analysis (LADA) The locality alignment discriminant analysis (LADA) [47] divides the entire feature space into local patches; the trace ratio between the traces of sum of scatter matrices obtained in all local patches is maximized instead of those of the global scatter matrices, thereby capturing local patterns in the feature space. We hypothesize that the biomarker generated using LADA is more able than LDA to detect the difference in textural change features exhibited in placebo and pomegranate subjects. LADA has been described in detail previously [47]. Its relation with and advantages over LDA are briefly summarized here. The Sb and Sw in Eq. (2) were calculated for the entire dataset and therefore less capable of capturing local structures of the dataset. To address this issue, LADA considers the cost function in Eq. (2) on a patch-by-patch basis first and then sums up the contribution from each patch, resulting in the following problem:

w∗ = arg max w

l

w( i=1 Sb,i )wT ,  w( li=1 Sw,i )wT

(3)

where Sb,i and Sw,i are the between- and within-class scatter matrices of Patch i and the total number of patches is l. This formulation better represents the local patterns in the feature space and has been shown to provide more discriminative results between features of malignant and benign prostate lesions [47]. The number of data points in each patch for LADA, denoted by K, was required to be tuned. In this study, 3-fold cross-validation was applied to tune K in each leave-one-out trial. In each trial, the 170 subjects (i.e., the whole study population excluding the subject being evaluated) were split into three equal partitions. One partition was assigned to be the validation set whereas the remaining two partitions were used for training. K varied from 5 to 100 with an increment of 5. For each K setting, after the optimum w (i.e., w∗ ) has been obtained by solving Eq. (3) based on the training set, the LADA biomarker for each of the subjects in the validation set was obtained by w∗T xi . A t-test was then performed on the validation set; the absolute value of the t-statistic, denoted by |t|, was

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recorded, which indicated how well the LADA biomarker separated the pomegranate from the placebo groups. This process was repeated 3 times for each K setting, thereby resulting in three |t|s, which were then averaged; the average |t| was used as the metric assessing how well the two groups were discriminated at K. K associated with the largest average |t| was chosen as the optimal K, denoted by K∗ . The final model for the current leave-one-out trial was trained with the 170 subjects based on K∗ . 2.4.3. Locality preserving projections (LPP) A major weakness of LADA is that K is required to be tuned in each leave-one-out trial. The computational time required to tune K would be high for investigations involving a large population. Similar to LADA, the Locality Preserving Projection (LPP) method [48], preserves local geometry of a dataset, but does not involve any parameter; and as such, the computational time required for tuning would be saved. For this reason, we evaluated the ability of LPP in discriminating textural features exhibited in the pomegranate and placebo subjects and hypothesize that LPP can generate a discriminative and computationally efficient biomarker. LPP produces an optimal linear approximation that preserves local structures relating to the proximity of data points in the lowdimensional manifold. It preserves local relations of data points by imposing a heavy penalty if a pair of neighbouring points xi and xj having a high similarity aij are mapped far apart. Cosine similarity is widely used to measure cohesion within clusters in the field of data mining [49] due to its low computational complexity. The similarity aij are defined as:



ai j =

cos(xi , xj ) 0

if xi , xj are in the same group elsewhere

(4)

Mathematically, LPP minimizes the following cost function:

1 ai j ( xi T w − xj T w )2 , 2

(5)

i, j

The optimization problem can be written in a matrix way as follows:

w∗ =

argmin

{w:wT XDXT w=1}

wT XLXT w,

(6)

where X = [x1 , x2 , . . . , x171 ]. D is a diagonal matrix with dii =  j ai j , known as the degree matrix. L = D − A with A = {ai j } is known as the Laplacian matrix. w∗ can be obtained by perform-



ing eigenvalue decomposition of the matrix XDXT

−1

XLXT .

2.5. Feature weighting In addition to evaluating whether the proposed scalar biomarker is able to detect the difference in plaque texture change between the pomegranate and placebo groups, it is also important to gain an insight into the biomedical meaning of the proposed biomarker. Here, we introduced a metric evaluating how much each of the 376 features contributed to the proposed biomarker. The importance of the jth eigenvector obtained in PCA (i.e., the 376-dimensional φj ) is quantified by the jth component of w∗ obtained using LADA or LPP. For this reason, the strengths of each of the 376 features can be rated by the weighted sum of Nx eigenvectors. Specifically, the strength of each textural feature d can be quantified by S(d) defined as follows:

S (d ) =

Nx 

w j φ j (d )

for d = 1, 2, . . . , 376,

(7)

j=1

where wj denotes the jth component of w∗ , the weighting vector generated by LADA or LPP. The average absolute value of S(d)s from the 171 leave-one-out trials serves as a metric on how important the textural feature d is in the LADA or LPP biomarker.

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X. Chen, M. Lin and H. Cui et al. / Computer Methods and Programs in Biomedicine 184 (2020) 105276 Table 2 Background medications taken by subjects involved in this study. The number and percentage (in parentheses) of subjects who took specific medications in the two groups are tabulated below. The term “Statins” used in the table encompasses Atorvastatin, Rosuvastatin and Pravastatin. Note that only two subjects took low-intensity Pravastatin and Pravastatin is thus not listed below. †: 3 cases with missing information; ††: 3 cases with missing information; ∗ Low intensity: Atorvastatin 10 mg/day or Rosuvastatin 5 mg/day or Pravastatin 10–20 mg/day; ∗∗ Medium intensity: Atorvastatin 20–40 mg/day or Rosuvastatin 10–20 mg/day; ∗ ∗ ∗ High intensity: Atorvastatin > 40 mg/day or Rosuvastatin 40 mg/day. Medications Antihypertensive medications Statins Intensity of statins Intensity of Atorvastatin Intensity of Rosuvastatin Ezetimibe Niacin Fibrate Combination therapy

Low∗ Medium∗ ∗ High∗ ∗ ∗ Low∗ Medium∗ ∗ High∗ ∗ ∗ Low∗ Medium∗ ∗ High∗ ∗ ∗

Statin with ezetimibe Statin with fibrate Statin with ezetimibe and fibrates

2.6. Statistical tests The background medications taken by pomegranate and placebo subjects were analyzed. Kolmogorov-Smirnov test was performed to test the normality of the data. Group comparisons were performed using the independent sample t-test for normally distributed data or Mann-Whitney U test for non-normally distributed data. For the variables with three categories (i.e., intensities of statins, Atorvastatin and Rosuvastatin in Table 2), subjects who did not take and who took a low, moderate and high dose were coded by 0, 1, 2 and 3 respectively and then the Mann-Whitney U test were performed. All statistical analyses were performed using SPSS version 25.0 (IBM Inc, Armonk NY). The discriminative power of the LDA, LADA, LPP biomarkers and TPV was evaluated by two-sample t-tests. The P-value computed in two-sample t-tests quantified the ability of each parameter in discriminating the change exhibited in the pomegranate and placebo groups. For the above biomarkers, the sample size required to detect a specific effect size δ was computed using the following equation [50]:

(zα/2 + zβ )2 (σ02 + σ12 ) , (8) δ2 where p(Z > zβ ) = β and Z is a normally distributed random variable with zero mean and unity variance. σ 0 and σ 1 are the stann=

dard deviations of the parameters associated with the placebo and pomegranate groups respectively. In this study, the sample size was computed at 90% statistical power (i.e., β = 0.1) and a significant level of α = 0.05. 3. Results Table 2 shows the background medications taken by pomegranate and placebo subjects. No statistically significant difference was observed between the background medications taken by the two groups. Plaque textural and volume measurements were obtained at baseline and 376 ± 23 days (range: 283 - 579 days) later. Since the time interval between baseline and follow-up varies with subjects, TPV and textural change per year were calculated to allow comparisons among subjects. Nx for PCA and K for LADA were tuned according to Section 2.3 and 2.4.2.

Placebo n = 75†

Treatment n = 96††

57 (79.2) 65 (90.3) 9 (12.5) 42 (58.3) 14 (19.4) 3 (4.2) 10 (13.9) 3 (4.2) 5 (6.9) 32 (44.4) 11 (15.3) 41 (56.9) 9 (12.5) 2 (2.8) 40 (54.8) 2 (2.8) 2 (2.8)

74 (79.6) 76 (81.7) 18 (19.4) 42 (45.2) 16 (17.2) 3 (3.2) 15 (16.1) 5 (5.4) 14 (15.1) 27 (29.0) 11 (11.8) 44 (47.3) 10 (10.8) 4 (4.3) 37 (39.8) 3 (3.3) 2 (2.2)

P-value 0.949 0.122 0.083

0.668

0.061 0.220 0.727 0.697 0.054 1.000 0.804

The optimal Nx was 11, and the optimal Ks were 60 in most of the 171 leave-one-out trials for the LADA biomarker (i.e., 156 out of 171 leave-one-out trials). The standard deviation of homogeneity derived from GLCM in the coronal plane (GLCM Coronal std homo) was the strongest individual feature for discriminating the pomegranate and placebo groups according to the P-value. Table 3 shows the P-values for GLCM Coronal std homo, TPV, the LDA, LADA and LPP biomarkers. Table 4 shows the sample size required for the five biomarkers to detect effect sizes ranging from 50 to 100% of that exhibited in the current placebo-controlled trial on the effect of pomegranate in a one-year study. The LDA, LADA and LPP biomarkers took changes of all textural features into account and were more able to discriminate the two treatment groups than TPV. The LADA and LPP biomarkers were more discriminative than the strongest textural feature. The experiments were implemented in MATLAB on a computer with a CPU (Intel(R) Core(TM) i7-6700, 3.40 GHz) and 8 GB memory. Tuning Nx took 6 s. Computation of both the LDA and LPP biomarkers took less than 1 s, whereas the computation of the LADA biomarker took more than 10 min due to the requirement to tune K in all 171 leave-one-out trials. Since LPP is much less time-consuming and has a higher discriminative power than LADA according to the two-sample t-tests, the application of LPP is more clinically feasible than LADA. One of the contributions of this study is the introduction of a metric to rank the importance of textural features (Eq. (7)). The ranking result for LPP is presented here. The top 8 features having the highest absolute average weights generated in 171 leave-oneout trials were tabulated in Table 5. Fig. 1 shows two example plaques belonging to a placebo subject and a pomegranate subject. Three contiguous axial images of each plaque were shown. The LPP scores of the placebo and pomegranate subjects were 0.33 and -0.16, respectively. The GLD mode decreased for the placebo subject and increased for the pomegranate subject. This indicates that the plaque of the placebo subject had become more echolucent, whereas that of the pomegranate subject had become more echogenic as confirmed by the visual comparison of the regions pointed to by the arrowheads. Changes of the normalized histogram in the low-intensity spectrum (Histogram 2 and 3) further echo this observation.

X. Chen, M. Lin and H. Cui et al. / Computer Methods and Programs in Biomedicine 184 (2020) 105276

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Table 3 The means and standard deviations (in parentheses) of TPV, the most discriminative feature among the 376 features, the LDA, LADA and LPP biomarkers computed for the placebo and pomegranate groups and the P-values associated with two-sample t-tests. Measurements

Placebo (n = 75)

Pomegranate (n = 96)

P-value

TPV(mm3 )

28 (77) 0.64 (0.16) 0.31 (1.39) 0.14 (0.50) 0.23 (0.42)

17 (77) 0.73 (0.15) −0.19 (1.02) −0.13 (0.40) −0.07 (0.46)

0.34 4.8 × 10−4 9.7 × 10−3 1.8 × 10−4 1.5 × 10−5

GLCM Coronal std homo LDA LADA LPP

Fig. 1. Example plaques for a placebo and pomegranate subject with strong textural features listed. The first and third rows show the plaques in baseline and the second and fourth rows show the plaques in follow-up. Difference in echogeneity between baseline and follow-up were shown for the two example plaques using arrowheads. The LPP scores for the placebo and the pomegranate subjects are 0.33 and −0.16, respectively. H4N3: the normalized number of voxels in the plaque having 4 transitional areas in the 26-voxel neighborhood; HxN5: the normalized number of voxels in the plaque having x transitional areas in the 98-voxel neighborhood, where x = 6, 7, 8. .

LBP measured the number of transitions from a higher to a lower intensity with respect to the center voxel, thereby detecting textural patterns characterized by microstructures (e.g., edges, lines, spots, flat areas) [34]. The four LBP features decreased more in the placebo plaque, whereas a smaller change was exhibited in the pomegranate plaque as shown in Fig. 1, indicating

that the pomegranate plaque was more stable in its textural patterns. The NGTDM contrast decreased more in the placebo subject than in the pomegranate subject as shown in Fig. 1, although the difference was small. This feature, defined in Ref. [33], is related to the dynamic range of grayscale, the amount of local intensity

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X. Chen, M. Lin and H. Cui et al. / Computer Methods and Programs in Biomedicine 184 (2020) 105276 Table 4 Sample sizes per group required for various effect sizes in a one-year study. The sample sizes below give a 90% statistical power and a significant level of 0.05 (two-tailed). The effect sizes are expressed as the percentage of the current placebo-controlled study. Effect size

TPV

GLCM: Coronal, std homo

LDA

LADA

LPP

100% 75% 50%

971 1726 3883

70 125 281

124 220 495

58 104 233

45 80 180

Table 5 Feature ranking for the LPP model. H4N3: the normalized number of voxels in the plaque having 4 transitional areas in the 26-voxel neighborhood; HxN5: the normalized number of voxels in the plaque having x transitional areas in the 98-voxel neighborhood, where x = 6, 7, 8. Texture change LBP H4N3 H7N5 H8N5 H6N5 GLD Histogram 2 Histogram 3 Mode NGTDM Contrast

Weights

Rank Order

0.17 0.16 0.12 0.10

1 2 4 8

0.15 0.11 0.11

3 6 7

0.12

5

variations and the total number of voxels of the plaque. High contrast is achieved with a large dynamic range and a large local intensity variation in a small volume. The involvement of plaque volume in NGTDM contrast confounded the textural difference exhibited in these two sample plaques. In the example shown in Fig. 1, although the change in contrast was more prominent in the placebo plaque, the contrast difference between the two plaques was confounded by the plaque volume change difference (the plaque volume increased by 53 mm3 for the placebo plaque and only 4 mm3 for the pomegranate plaque). 4. Discussion We developed a cost-effective and computationally efficient texture-based biomarker that detected changes in atherosclerotic plaques due to dietary supplements such as pomegranate. A previous study of the effect of pomegranate juice on carotid IMT [25] showed no significant effect, but the finding may be attributed to the insensitivity of IMT in detecting treatment effect. TPV, as a three-dimensional measurement, has shown to be more able to detect change [51,52] and more correlated to atherosclerosis than IMT in previous studies [53,54]. However, TPV was not able to detect a statistically significant effect of pomegranate in this study ( p = 0.34). The proposed biomarker was much more able to detect the difference between the pomegranate and placebo groups than TPV ( p = 1.5 × 10−5 ). The improved discriminative power afforded by the proposed biomarker will benefit the cost-effectiveness of clinical trials involving other dietary supplements, which are expected to confer a smaller effect on atherosclerosis than medical interventions. The proposed biomarker integrated the discriminating power of 376 textural features and provided stronger discrimination than any of the 376 features used individually. The sample size required by the new biomarker was 20 times lower than that required by TPV. The example shown in Fig. 1 provides insights on a major benefit of integrating a larger number of features.

When considering the entire study population, NGTDM contrast was among the most important features that contributed to the discriminative power of the LPP model (Table 5). However, as detailed in the Results section, NGTDM contrast was confounded by plaque volume change and was less able to discriminate the textural difference between individual subjects if there is a large variation in the change of plaque volume across the subjects under comparison. LPP was able to integrate the discriminative abilities of various features and detected a textural difference between these two individual subjects (LPP score: 0.33 vs. −0.16). For future studies involving subjects receiving pomegranate extracts using the same ultrasound system in this study, the tuned parameters (i.e., Nx = 11 for PCA and K∗ = 60 for LADA) can be directly applied for quantifying and monitoring the progression/regression of carotid atherosclerosis. For clinical trials involving the evaluation of new therapeutic options or different ultrasound systems, parameter tuning should be performed for the new population in order to maximize the discriminative power of the proposed biomarker. Nx can be determined in an unsupervised manner and efficiently (6 s in this study) using Horn’s parallel analysis. Therefore, tuning Nx would not be a computational burden for a new investigation. On the other hand, tuning the parameter K in LADA is time-consuming since tuning is required in each of the leave-one-out trials (e.g., more than 10 min in our study involving 171 subjects). As the number of leave-one-out trials is equal to the number of subjects evaluated in an investigation, longer computational time would be required to tune K for a larger study, rendering LADA less suitable for such studies. We recommend LPP for future clinical trials as it does not involve any parameter and has a higher discriminative power than LADA as shown in this study. In agreement with our findings, many of the top discriminative features identified in this study were found to be strong features in risk stratification and treatment effect evaluation in previous studies. Van Engelen et al. [14] found that features extracted using the NGTDM technique were strongest in discriminating symptomatic and asymptomatic patients. Christodoulou et al. [16] found that the NGTDM technique provided the best discrimination between symptomatic and asymptomatic subjects. LBP features were among the top features for classifying symptomatic and asymptomatic patients in a study involving 2D longitudinal ultrasound images [55]. Histogram features and first-order statistics from GLD can predict plaque composition in a histological study [56]. Many of the top textural features highlighted in this study are related to homogeneity and echogenicity. Previous clinical investigations agree that heterogeneous and echolucent plaques carry a higher neurological risk than homogeneous and echogenic plaques [57–66]. Heterogeneous and echolucent plaques are composed of intraplaque hemorrhage [67–69] and calcification [70,71], which contribute to the destabilization of plaques, making them more susceptible to rupture [72,73]. These observations suggest that plaque textural feature changes separating placebo subjects from subjects who receive treatments may be similar to those discriminating symptomatic and asymptomatic patients, which further suggests the applicability of the proposed biomarker in risk stratification. We are currently performing analysis to validate this hypothesis by evaluating the image data acquired from a symptomatic and asymptomatic cohort [11]. Speckle noise is the most important artifact for plaque texture characterization. While there are investigations [74,75] that concluded despeckling is beneficial to the image quality, speckle is not always undesirable. The textural information appeared as speckle may carry important information related to the composition and structure of the plaques [17,76,77]. For this reason, there is a need to strike a balance between image quality and preservation of useful textural information appeared as speckle. Before

X. Chen, M. Lin and H. Cui et al. / Computer Methods and Programs in Biomedicine 184 (2020) 105276

they can be used in clinical analysis, existing despeckling techniques [74,75] should be thoroughly validated to be optimally enhancing image quality and preserving useful textural information. However, there is currently no accepted guideline for such an evaluation and establishing such a guideline would require another full publication. Therefore, we decided against despeckling in the current work. A limitation of this study is that it involves manual delineation of plaques, which cannot be considered as the definitive gold standard due to the existence of segmentation of bias and variability. However, TPV measurements have previously been shown to have high intra-observer and inter-scan reproducibility with intra-class correlations of 0.85 and 0.83 respectively [10]. Until an automated segmentation algorithm is thoroughly validated, manual segmentation must still be used as the surrogate gold standard, and in fact, has been used many previous clinical trials for quantification of total plaque area [78,79] and volume [11,12]. Although TPV has been shown to be sensitive to medical treatment [12] and symptomatic status [11], for dietary treatments that are expected to confer a smaller beneficial effect than highdose statin interventions, such as pomegranate investigated in this study, TPV requires many subjects (10 0 0 subjects in a one-year study for pomegranate as shown in Table 4) to establish efficacy in a statistically significant manner. The proposed biomarker reduces the number of subjects required in a one-year study by more than an order of magnitude, thereby substantially reducing the cost of therapeutic trials. With the increase in cost-effectiveness, more pilot studies involving a smaller population can be performed to evaluate new therapeutic options, thereby shortening the period of time that effective therapies are withheld from patients needing them. Declaration of Competing Interest The patient data were acquired in a clinical study sponsored by POM Wonderful, LLC (USA). Professor Spence is the Scientific Officer of Vascularis Inc. Acknowledgments Dr. Chiu is grateful for funding support from the Research Grant Council of the HKSAR, China (Project nos. CityU 11205917, CityU 11203218) and the City University of Hong Kong Strategic Research Grants (nos. 7004617, 7005226). References [1] S. Wu, B. Wu, M. Liu, Z. Chen, W. Wang, C.S. Anderson, P. Sandercock, Y. Wang, Y. Huang, L. Cui, et al., Stroke in China: advances and challenges in epidemiology, prevention, and management, Lancet Neurol. 18 (4) (2019) 394–405. [2] C.O. Johnson, M. Nguyen, G.A. Roth, E. Nichols, T. Alam, D. Abate, F. Abd-Allah, A. Abdelalim, H.N. Abraha, N.M. Abu-Rmeileh, et al., Global, regional, and national burden of stroke, 1990–2016: a systematic analysis for the global burden of disease study 2016, Lancet Neurol. 18 (5) (2019) 439–458. [3] J.D. Spence, Intensive management of risk factors for accelerated atherosclerosis: the role of multiple interventions, Curr. Neurol. Neurosci. Rep. 7 (1) (2007) 42–48. [4] J.D. Spence, Recent advances in pathogenesis, assessment, and treatment of atherosclerosis, F10 0 0Research 5 (2016) (2016). [5] A.V. Finn, F.D. Kolodgie, R. Virmani, Correlation between carotid intimal/medial thickness and atherosclerosis: a point of view from pathology, Arterioscler. Thrombosis Vasc. Biol. 30 (2) (2010) 177–181. [6] H.M. Den Ruijter, S.A. Peters, T.J. Anderson, A.R. Britton, J.M. Dekker, M.J. Eijkemans, G. Engström, G.W. Evans, J. De Graaf, D.E. Grobbee, H. B, Common carotid intima-media thickness measurements in cardiovascular risk prediction: a meta-analysis, Jama 308 (8) (2012) 796–803. [7] A. Zanchetti, M. Hennig, R. Hollweck, G. Bond, R. Tang, C. Cuspidi, G. Parati, R. Facchetti, G. Mancia, Baseline values but not treatment-induced changes in carotid intima-media thickness predict incident cardiovascular events in treated hypertensive patients: findings in the European Lacidipine Study on Atherosclerosis (ELSA), Circulation 120 (12) (2009) 1084–1090.

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