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. 2020 Oct 29;41(1):491–500. doi: 10.1161/ATVBAHA.120.314838

Low-Carbohydrate Diet Score and Coronary Artery Calcium Progression

Results From the CARDIA Study

Jing-Wei Gao 1, Qing-Yun Hao 1, Hai-Feng Zhang 1, Xiong-Zhi Li 1, Zhi-Min Yuan 2, Ying Guo 3, Jing-Feng Wang 1, Shao-Ling Zhang 3,, Pin-Ming Liu 1,
PMCID: PMC7752248  PMID: 33115269

Supplemental Digital Content is available in the text.

Keywords: cardiovascular diseases; diet, carbohydrate-restricted; follow-up studies; risk factors; young adult

Objective:

To investigate whether low-carbohydrate diets (LCDs) were associated with coronary artery calcium (CAC) progression.

Approach and Results:

We included the participants who completed computed tomography assessment of baseline CAC in 2000 to 2001 (year 15) and follow-up (year 20 or 25) and food frequency questionnaire (years 0, 7, and 20) in the CARDIA study (Coronary Artery Risk Development in Young Adults). CAC progression was defined as CAC >0 at follow-up among participants with baseline CAC of 0 and an annualized change of 10 or percent change of ≥10% for those with 0<baseline CAC<100 or baseline CAC≥100, respectively. Among 2226 included participants (age, 40.4±3.5 years; 45.4% men), the carbohydrate intake accounted for 47.8±6.5% of total energy, and 204 (9.2%) had CAC at baseline (year 15). Over a mean follow-up of 8.3 years, 591 (26.5%) participants had CAC progression. After adjustment for traditional cardiovascular risk factors and other dietary factors, carbohydrate intake as a percentage of total energy was inversely associated with the risk of CAC progression (hazard ratio, 0.731 [95% CI, 0.552–0.968]; P=0.029). Furthermore, the animal-based but not plant-based LCD score was significantly associated with a higher risk of CAC progression (animal-based LCD score: hazard ratio, 1.456 [95% CI, 1.015–2.089]; P=0.041; plant-based LCD score: hazard ratio, 1.016 [95% CI, 0.821–1.257]; P=0.884; both comparing extreme groups).

Conclusions:

LCDs starting at a young age are associated with an increased risk of subsequent CAC progression, particularly when animal protein or fat are chosen to replace carbohydrates.

Registration:

URL: https://www.clinicaltrials.gov; Unique identifier: NCT00005130.


Highlights.

  • Low-carbohydrate diets in young adults were associated with a higher risk of coronary artery calcium progression in middle age.

  • Replacement of carbohydrates with predominantly animal but not plant protein or fat in low-carbohydrate diets has the potential of enhancing CAC progression.

  • These data suggest that as a popular strategy for weight management, long-term animal-based low-carbohydrate diet should be advocated cautiously to avoid its potential impact on coronary atherosclerosis.

Cardiovascular disease (CVD) is a major public health issue and the leading cause of death globally.1,2 Healthy lifestyle choices are crucial for the prevention of CVD. Adopting a healthy lifestyle earlier in life holds the potential to have a greater impact on CVD risk reduction, whereas unhealthy lifestyle changes are associated with an increased risk for subclinical atherosclerosis in middle age.3 Low-carbohydrate diets (LCDs), which restrict carbohydrates, in favor of increased protein or fat intake, have gained substantial popularity because LCD can induce at least short-term weight loss, which is considered to be beneficial for cardiovascular health.4,5 However, due to relatively high levels of protein, fat, and cholesterol in the diets, long-term LCD may raise concerns over ketosis, abnormal lipid profiles, and renal effects,5 which in turn counteracts the potential cardiovascular benefits on CVD.68 Lagiou et al9 found that low-carbohydrate, high-protein intake predicted higher total and cardiovascular mortality in relatively young Swedish women. More recently, results from a pooled analysis of the data from the US National Health and Nutrition Examination Survey 1999 to 2010 and 8 other relevant prospective studies (a total of 462 934 participants, mean follow-up of 16.1 years) suggested a potentially unfavorable association of LCD with overall and cause-specific mortality, including CVD mortality.10

Coronary artery calcium (CAC) assessed by computed tomography (CT)—an established marker of atherosclerotic coronary artery disease—is a strong predictor of cardiovascular morbidity and mortality and a potent CVD risk stratification tool.11,12 It is shown that nutrition and diet are of importance in the progression of vascular calcification.13 Notably, the associations between dietary carbohydrates, CAC, and other atherosclerotic markers have been an area of scientific interest recently.14 The CARDIA study (Coronary Artery Risk Development in Young Adults) is a prospective, multicenter cohort study sponsored by the National Heart, Lung, and Blood Institutes. It is designed to identify the influences of potentially risk factors began in young adulthood on CVD development in later life.15 Findings from the CARDIA study have contributed substantially to the knowledge about the importance of lifestyle and environmental factors during young adulthood to the development of CAC through their midlife.3,1618

In the present study, we aimed to provide new evidence about the contribution of LCD starting early in adulthood to future CVD risk. By using the longitudinal CARDIA study data, we examined the association of LCD patterns (including animal- and plant-based LCD score) with the risk of subsequent CAC progression.

Materials and Methods

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Subjects

Details of the CARDIA study design and examinations have been reported previously.19 Briefly, it is a prospective cohort study designed to investigate the evolution of CVD risk. Participants were recruited from 4 field centers (Birmingham, Alabama; Chicago, Illinois; Minneapolis, Minnesota; and Oakland, California). In 1985 to 1986 (year 0 of the cohort), a total of 5115 Black and White men and women aged 18 to 30 years were enrolled in the study. Until now, 8 follow-up examinations have been conducted: years 2, 5, 7, 10, 15, 20, 25, and 30.

As CAC was first measured by CT scans at year 15 (2000–2001) in the CARDIA study, for the purpose of the present study, we included all the participants at year 15 (n=3671). As Figure 1 shows, participants were excluded if one of the following data could not be available: baseline CAC data (n=629), follow-up CAC data (n=271), covariate data (n=244), or validated dietary data (without complete dietary information or with implausible energy intake defined as <800 or >8000 kcal for men and <600 or >6000 kcal for women; n=301). The final study sample for this analysis was 2226 adults.

Figure 1.

Figure 1.

Flowchart for selecting the CARDIA (Coronary Artery Risk Development in Young Adults) participants for analysis. CAC indicates coronary artery calcium.

All participants provided informed consent, and the study was approved by the institutional review boards at each field center.

Assessment of the Diets

Dietary data were assessed by using a trained interviewer-administered CARDIA dietary history (years 0, 7, and 20 after inclusion in the cohort) as described previously.20 Briefly, interviewers asked the participants open-ended questions about dietary consumption of 100 food categories that referenced 1609 separate food items within the past month. Foods consumed were assigned to 1 of 166 food groups devised by the Minnesota Nutrition Coordinating Center. Food group intake was assessed as servings per day of constituent foods based on their gram weight information. In the present study, we calculated the average of years 0 and 7 dietary data in analyses to reduce potential confounding from a single assessment only and to avoid the possibility that macronutrient consumption measured at year 20 may have been influenced by the measurement of CAC at year 15 as reported previously.16,21 The macronutrients (carbohydrates, fat, and protein) were expressed as the percentage of total energy, calculated as the daily calories derived from each macronutrient divided by the total number of calories for the day.

It is supposed that the effects of long-term carbohydrate restriction can be varied since different sources of protein or fat (animal or plant sources) in the diets are chosen to replace carbohydrates to provide enough energy. Therefore, we calculated animal- and plant-based LCD score, respectively, as reported previously.6 As shown in Table 1, the points of each of the 3 macronutrients were summed to create the overall LCD score. Plant-based LCD score was calculated by summation of the points for carbohydrates, plant protein, and plant fat as a percentage of total energy; similarly, animal-based LCD score was calculated by summarizing carbohydrates, animal protein, and animal fat as a percentage of total energy. As a result, the highest score represented low-carbohydrate and high animal or plant protein or fat intake.

Table 1.

Criteria Determining the Low-Carbohydrate-Diet Scores

graphic file with name atv-41-491-g002.jpg

CAC Measurements

CAC was measured at years 15, 20, and 25 using a standardized protocol.22 At years 15 and 20, the CARDIA study conducted either a cardiac-gated electron-beam CT or a multidetector CT depending on the study site to detect CAC. At year 25, given the high reproducibility at previous examinations, a single CT scan was performed using only multidetector CT scanners. The comparability of electron-beam CT and multidetector CT has been demonstrated previously.23 Scans were read centrally by a trained reader who was blinded to the participant’s characteristics.

CAC was scored using the Agatston method,24 which was calculated for each calcified lesion; and the scores were summed across all lesions within a given artery and across all arteries (left anterior descending, left main, circumflex, and right coronary artery) to obtain the total calcium score. CAC progression was defined as one of the following: (1) CAC >0 at follow-up among participants with baseline CAC=0; (2) an annualized change of ≥10 at follow-up among those with 0<baseline CAC<100; (3) an annualized percentage change (annualized change in CAC score divided by the baseline CAC score) ≥10% among those with baseline CAC ≥100.25

Measurements of Other Covariates

The demographic, lifestyle, and education characteristics of participants (eg, age, race, sex, smoking status, alcohol consumption, levels of physical activity, and educational attainment) were assessed during interviews. Educational attainment was categorized as ≤12 years (representing ≤high school degree), 13 to 16 years (representing college degree or similar level of education), and ≥17 years (representing>college degree, such as MSc, MD, JD, and PhD). Smoking status was classified as current, former, or never. Participants rested in the sitting position for 5 minutes before resting systolic and diastolic blood pressures were measured 3× at 1-minute intervals with a random-zero sphygmomanometer on the right arm. The second and the third measurements were averaged and recorded. Laboratory tests were also performed. Briefly, overnight fasting blood samples were drawn using the EDTA vacutainers; plasma was isolated and frozen at −70 °C until shipment on dry ice to the laboratory.26 Detailed descriptions of measurements of total cholesterol, LDL (low-density lipoprotein) cholesterol, HDL (high-density lipoprotein) cholesterol, triglycerides, serum creatinine, and fasting plasma glucose of the participants have been published previously.26 Diabetes was defined as fasting plasma glucose ≥126 mg/dL or a history of diabetes medication use. Hypertension was defined as taking antihypertensive medications, having a diagnosis of hypertension, or having 3 consecutive systolic blood pressure readings ≥140 mm Hg or diastolic blood pressure ≥90 mm Hg. Body mass index was calculated as weight divided by the square of height (kg/m2).

Statistical Analysis

Normally distributed continuous data were expressed as mean±SD, and the non-normally distributed continuous data, otherwise, were expressed as the median (interquartile range). Categorical data were expressed as numbers (percentage). Since we evaluated baseline CAC at year 15, all continuous characteristics reflect the average of years 0, 7, and 15, except age (year 15) and dietary data (the average of years 0 and 7). Differences among groups were evaluated using ANOVA or Kruskal-Wallis h test when appropriate for the continuous variables and the χ2 test for the categorical variables. The follow-up period was defined as the time from 2000 to 2001 (year 15) to the incidence of CAC progression or loss to follow-up, whichever occurred first. X-tile (version 3.6.1; Yale University School of Medicine) software was used to determine the optimal cutoff points for carbohydrate intake as a percentage of total energy according to the highest χ2 value defined by the Kaplan-Meier survival analysis.27 Kaplan-Meier estimates were used to compute cumulative incidence of CAC progression by carbohydrate intake groups, and the differences in estimates were compared using the log-rank procedure. Cox regression was used to compute hazard ratios and 95% CIs for the association between carbohydrate intake and CAC progression. Covariates of known established or suspected risk factors for CAC progression were considered in the multivariable models. As reported in the literature,6 because LCD may decrease subsequent energy intake, we did not control for total energy intake in multivariate models. Likewise, we did not perform adjustment for intake of other macronutrient components, as LCD in turn may increase intake of protein or fat. However, we performed adjustment for dietary intake of micronutrients, which have been reported to be associated with the risk of CAC progression in multivariate nutrient density models. We further used a restricted cubic spline regression model with 3 knots to assess the nonlinear dose-response association between carbohydrate intake and CAC progression. We did a time-varying sensitivity analysis for participants who were identified with CAC progression before year 20; carbohydrate intake was calculated on the basis of the mean of years 0 and 7 food frequency questionnaire responses. From year 20 onward, carbohydrate intake was calculated on the basis of the mean of years 0, 7, and 20 food frequency questionnaire results. As a total of 327 participants did not have dietary information at year 20, we first did the sensitivity analysis excluding these people with missing data, and again, we used average values of dietary information at years 0 and 7 to replace missing data to conduct the sensitivity analysis for all our included participants. In addition, we performed specified subgroup analysis by age, sex, race, body mass index, presence of hypertension, and baseline CAC and tested for potential interactions of these covariates with carbohydrate intake separately. All analyses were conducted in SPSS, version 23 (SPSS, Inc, Chicago, IL). A 2-sided P of <0.05 was considered statistically significant.

Results

Characteristics According to Carbohydrate Intake

The characteristics of all the included participants were summarized in Table 2. The average age at the first CT scans was 40.4±3.5 years (year 15), 1011 (45.4%) participants were men, 454 (20.4%) were current smokers, and 329 (14.8%) were hypertensive. In addition, 204 (9.2%) participants exhibited CAC at baseline, and the mean carbohydrate intake as a percentage of total energy was 47.8±6.5%. Here, according to results of X-tile analysis (Figure 2), individuals were categorized into 3 groups by the percentage of total energy from carbohydrates: low (<43%), moderate (43%–53%), and high (≥53%) carbohydrate intake group. Participants with lower energy from carbohydrate intake were more likely to be men, current smokers; to have a lower education level; to drink more; and to have higher levels of body mass index, systolic blood pressure, fasting plasma glucose, total cholesterol, LDL cholesterol, and triglycerides. With regard to dietary patterns, participants with lower energy from carbohydrates tended to have higher intake of total energy, protein, fat (both animal and plant sources), and higher dietary magnesium, calcium, and vitamin D, along with lower dietary fiber intake. However, there were no significant differences regarding race, hypertension and diabetes prevalence, physical activity, and serum HDL cholesterol levels among the 3 groups.

Table 2.

Characteristics of Study Participants According to the Average of Carbohydrate Intake as a Percentage of Total Energy at Years 0 and 7

graphic file with name atv-41-491-g003.jpg

Figure 2.

Figure 2.

Determination of cutoff values of carbohydrate intake as a percentage of total energy for coronary artery calcium (CAC) progression by X-tile analysis in the CARDIA study (Coronary Artery Risk Development in Young Adults). X-tile analysis was performed on dietary and CAC data from the CARDIA study, equally divided into training and validation sets. X-tile plots of training sets are shown in the left. The plot shows the χ2 log-rank values produced when dividing the cohort with 2 cut points, producing high, middle, and low subsets. The x axis represents all potential cut points from low to high (left to right) that define a low subset, whereas the y axis represents cut points from high to low (top to bottom) that define a high subset. Green coloration of cut points indicates a direct association. The optimal cut point occurs at the brightest pixel. The cut point highlighted by the black dot in the left is shown on a histogram of the entire cohort (middle) and a Kaplan-Meier plot (right; low subset, blue; middle subset, gray; high subset, magenta). P was determined by using the cut point defined in the training set and applying it to the validation set. Finally, the cutoff points for the carbohydrate intake as a percentage of total energy were <43% (low carbohydrate intake group), 43% to 53% (moderate carbohydrate intake group), and ≥53% (high carbohydrate intake group).

Association Between Dietary Carbohydrate Intake and CAC Progression

During a follow-up period of 8.3±2.3 years, 591 (26.5%) cases exhibited CAC progression. As Table 3 shows, the percentage of CAC progression decreased as the carbohydrates in diets increased (low versus moderate versus high carbohydrate intake group: 170 [34.6%] versus 337 [25.7%] versus 84 [19.7%]). As results yielded from both unadjusted and adjusted models, the most significant CAC progression was found in participants with the lowest carbohydrate intake (P<0.05; Table 3). In the final model, the hazard ratios (95% CI) for CAC progression comparing the moderate and the highest carbohydrate intake group with the lowest carbohydrate intake group were 0.841 (95% CI, 0.694–1.020) and 0.731 (95% CI, 0.552–0.968), respectively (Table 3; Figure 3). Figure 4 shows the restricted cubic splines of the risk of CAC progression across levels of carbohydrates as a percentage of total energy. Consistent with the above analysis, spline regression analysis confirmed that carbohydrate intake was inversely and nonlinearly associated with the risk of CAC progression, compared with the reference level of 47.5% (Figure 4). Similar results were found in the time-varying sensitivity analyses when we combined dietary data at years 0 and 7 with those at year 20 (Tables I and II in the Data Supplement).

Table 3.

Risk of CAC Progression for Carbohydrate Intake as a Percentage of Total Energy

graphic file with name atv-41-491-g005.jpg

Figure 3.

Figure 3.

Cumulative incidence of coronary artery calcium (CAC) progression by carbohydrate intake as a percentage of total energy. Cumulative incidence curves are statistically different (log-rank P<0.001).

Figure 4.

Figure 4.

Hazard ratios of coronary artery calcium progression by carbohydrate intake as a percentage of total energy. Each hazard ratio was computed with a carbohydrate intake level of 47.5% as the reference. Red solid line represents the hazard ratio of carbohydrate intake across the whole range. Red dotted lines represent the 95% CI. Black dotted line is the reference line as hazard ratio=1. Histograms represent the frequency distribution of carbohydrate intake as a percentage of total energy.

When participants were stratified by age (<40 or ≥40 years), sex (male or female), race (White or Black), body mass index (<30 or ≥30 kg/m2), hypertension (yes or no), and baseline CAC (yes or no), the association between carbohydrate intake and CAC progression remained similar (Figure 5). However, a differential association was observed if subgroups divided by race, showing a stronger inverse association between carbohydrate intake and CAC in Whites than in Blacks (P for interaction, 0.030; Figure 5).

Figure 5.

Figure 5.

Subgroup analysis of the association between dietary carbohydrate intake and coronary artery calcium (CAC) progression. Cox regression after adjustment for alcohol consumption, diastolic blood pressure, diabetes, dietary calcium intake, dietary fiber intake, dietary magnesium intake, dietary vitamin D intake, education levels (high school, college, and graduate school), fasting plasma glucose, high-density lipoprotein cholesterol, low-density lipoprotein cholesterol, physical activity, serum creatinine, systolic blood pressure, smoking status (current, former, and never), systolic blood pressure, and triglycerides was performed in subgroups according to age (<40 or ≥40 y), sex (male or female), race (White or Black), body mass index (BMI; <30 or ≥30 kg/m2), hypertension (yes or no), and baseline CAC (yes or no). *Hazard ratio (HR) and 95% CI were derived from Cox regression models, and the low carbohydrate intake group was used as the reference in each subgroup analysis.

Association of Animal- or Plant-Based LCD Score With CAC Progression

To further explore the effects of the specific sources of fat and protein alternatives to low-carbohydrate intake, we analyzed the association of animal- or plant-based LCD score with CAC progression. As shown in Table 4, after adjustment for all covariates, the animal-based LCD score was significantly associated with more severe CAC progression (hazard ratio, 1.456 [95% CI, 1.015–2.089]; P=0.041). However, there was no such significant relationship between plant-based LCD score and CAC progression in the fully adjusted model (hazard ratio, 1.016 [95% CI, 0.821–1.257]; P=0.884; Table 5).

Table 4.

Risk of CAC Progression for Animal-Based LCD Score

graphic file with name atv-41-491-g009.jpg

Table 5.

Risk of CAC Progression for Plant-Based LCD Score

graphic file with name atv-41-491-g010.jpg

Discussion

In this large prospective cohort study, we found that lower carbohydrate intake as a percentage of total energy during young adulthood was associated with an increased risk of CAC progression later in life. Moreover, replacement of carbohydrates with predominantly animal but not plant sources of protein or fat exerts potent effects on CAC progression.

To our knowledge, this study presents the first evidence that long-term LCDs beginning at a young age were associated with a higher risk of subsequent CAC progression. This is distinct from the results of the MESA study (Multi-Ethnic Study of Atherosclerosis).14 Several plausible explanations could at least, in part, account for this discordance. The participants included in the present study are much younger than those enrolled in the MESA study (mean age, 40.4 versus 62.5 years). As CAC is an age-related pathological process characterized by mineral deposition within the coronary arteries, CAC severity increases with age28; the prevalence of CAC at baseline was lower in our analysis than in the MESA study (9.2% versus 48.5%). Thus, the potential role of LCD on CAC progression may be overwhelmed among the relatively older adults enrolled in the MESA study. Indeed, our findings confirmed an attenuated tendency between LCD and CAC progression in older participants. On the other hand, the different carbohydrate intake as a percentage of total energy across the study population was also a possible confounder. Since participants in the MESA data generally consumed moderate-to-high levels of carbohydrates, the percentage of participants consuming LCD defined as ≤45% of total energy intake from carbohydrates29 in our sample was 2.3-fold greater than in MESA data (34.9% versus 15.2%).14 Additionally, the interaction was observed when the analysis was stratified by race, indicating the stronger association between LCD and CAC progression among Whites compared with Blacks. It was reported that compared with Blacks, Whites consumed less carbohydrates,8 and they exhibited higher CAC levels at younger ages.28 This implies that there might be a possible link between LCD and a higher risk of CVD among Whites in this cohort.

An interesting result of our study was that only animal protein or fat chosen to replace carbohydrates in LCD promoted CAC, which was supported by the notion that animal sources of protein and fat in LCD may have an impact on CVD-related mortality.9,30 For example, a large prospective cohort study documented that LCDs with high intake of animal protein and fat were significantly associated with higher long-term CVD mortality.30 It was speculated that increased inflammatory cytokines, oxidative stress, and reduced endothelial progenitor cells under LCD, together with high-fat diet (Western diet) or high animal protein,3133 are possible mechanisms for enhancing CAC development.34 Thus, it is crucial to incorporate quality and types of macronutrients when investigating the associations of LCD with CAC progression.

Some limitations of this study need, nevertheless, to be acknowledged. First, dietary intake is not perfectly measured by the validated food frequency questionnaire, which typically has fewer random errors but may produce systematic errors.35 Second, the analysis of the current study was based on dietary information with cumulative average dietary consumption from years 0 and 7. We have conducted the time-varying sensitivity analysis spanning over 10 years, which showed consistent conclusions. However, the potential influences of dietary pattern changes during the follow-up period could not be completely excluded. Third, despite our careful adjustment for the known and suspected confounders, residual confounding cannot be completely ruled out because of the observational nature of prospective cohort studies.

Taken together, we found that LCDs beginning at early adulthood were associated with an increased risk of subsequent CAC progression in middle age, particularly when animal protein or fat in LCD are increased. As a popular strategy for weight management, long-term animal-based LCD should be advocated with great caution to avoid its potential impact on coronary atherosclerosis.

Acknowledgments

We thank the investigators, the staffs, and participants of the CARDIA study (Coronary Artery Risk Development in Young Adults) for their highly valued contributions. We are grateful to Dominique Vuitton, Professor Emeritus from Université Bourgogne Franche-Comté, Besançon, France, for her assistance with the work.

Sources of Funding

This work was supported by grants from the National Natural Science Foundation of China (81870315, 81900379, 81970683, and 81870334). The CARDIA study (Coronary Artery Risk Development in Young Adults) was funded by contracts N01-HC-48047 through N01-HC-48050 and N01-HC-95095 from the National Heart, Lung, and Blood Institute, National Institutes of Health, of the United States.

Disclosures

None.

Supplemental Materials

Tables I and II

Supplementary Material

atv-41-491-s001.pdf (276.6KB, pdf)
atv-41-491-s002.jpg (1.2MB, jpg)

Nonstandard Abbreviations and Acronyms

CAC
coronary artery calcium
CARDIA
Coronary Artery Risk Development in Young Adults
CT
computed tomography
CVD
cardiovascular disease
HDL
high-density lipoprotein
LCD
low-carbohydrate diet
LDL
low-density lipoprotein
MESA
Multi-Ethnic Study of Atherosclerosis
*

These authors contributed equally to this article.

The Data Supplement is available with this article at https://www.ahajournals.org/doi/suppl/10.1161/ATVBAHA.120.314838.

For Sources of Funding and Disclosures, see page 499.

Contributor Information

Jing-Wei Gao, Email: gaojw5@mail2.sysu.edu.cn.

Qing-Yun Hao, Email: haoqy@mail2.sysu.edu.cn.

Hai-Feng Zhang, Email: zhanghf9@hotmail.com.

Xiong-Zhi Li, Email: njmuwilllee@126.com.

Zhi-Min Yuan, Email: yzmxjd@163.com.

Ying Guo, Email: gying@mail.sysu.edu.cn.

Jing-Feng Wang, Email: wjingf@mail.sysu.edu.cn.

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