• body mass index;
  • elderly;
  • fat;
  • lean mass;
  • mortality


  1. Top of page
  2. Abstract

OBJECTIVES: To evaluate the correlation between body mass index (BMI), body composition, and all-cause mortality in an elderly Asian population.

DESIGN: A prospective observational cohort study with 3.5-year follow-up.

SETTING: The Korean Longitudinal Study on Health and Aging Project for elderly residents in Seongnam City, Korea.

PARTICIPANTS: Eight hundred seventy-seven subjects aged 65 and older for whom baseline body composition data was available.

MEASUREMENTS: BMI, waist circumference, and body composition of each subject was evaluated. Body composition was examined using bioelectrical impedance analyses of measures, including lean mass (kg), fat mass (kg), and fat proportion (%). In addition, lean mass index (LMI, kg/m2) was calculated by dividing lean mass by the square of height. Participants were divided into three groups: Group 1 (<25th percentile), Group 2 (25–75th percentiles), and Group 3 (≥75th percentile) for BMI, waist circumference, body composition, and LMI.

RESULTS: In the fully adjusted Cox proportional hazard model, BMI, waist circumference, and fat composition were not correlated with mortality, but higher lean mass and LMI were considered predictors of lower mortality when comparing Group 3 and Group 1 (in lean mass, relative risk reduction of 84%, 95% confidence interval (CI)=45–96%, P=.004; in LMI, relative risk reduction of 69%, 95% CI=12–89%, P=.03).

CONCLUSION: The present study indicates that the recommendation of low BMI as a means of obtaining a survival advantage in the elderly is not supported. Instead, higher lean mass and higher LMI are associated with better survival in the elderly Asian population.

Obesity is an important risk factor for diabetes mellitus, cardiovascular disease, chronic kidney disease (CKD), and mortality.1–4 Accordingly, the World Health Organization (WHO) recommends the screening and treatment of obesity to prevent further morbidity. Despite widespread knowledge of the health consequences of obesity, its prevalence continues to increase worldwide. Data from the National Health and Nutrition Examination Survey indicate that half of the American population is overweight or obese.5 In Korea, the prevalence of obesity has increased rapidly since the 1990s, with 30.6% of the population considered overweight in 2001.6

Body mass index (BMI) is commonly used as an indicator of obesity for practical reasons. The WHO grades obesity according to BMI: underweight (<18.5 kg/m2), normal range (18.5–24.9 kg/m2), overweight (25.0–29.9 kg/m2), and obese (≥30.0 kg/m2),7 although variables such as age, sex, and race affect BMI.8,9 For example, older adults have a particular body size, shape, and composition, and they tend to lose fat-free mass and increase fat mass.10 Furthermore, Asians have a higher proportion of body fat for a given BMI than Caucasians.11 Therefore, it is almost certain that the relationship between BMI and other variables is different for elderly Asians than for younger Asians or Caucasians (who have been the subjects of most previous research).

Epidemiological studies have demonstrated that high BMI, consistent with being overweight or obese, is associated with a greater risk of mortality,2 but this relationship is not evident in older adults or in patients with chronic disease.12,13 Rather, a higher BMI appears to be correlated with a lower risk of mortality in what is known as the “obesity paradox.” A possible explanation for this reverse correlation is the insensitivity of BMI; nutrition and body composition might be factors of greater importance in relation to mortality in these populations. In the present study, the correlations between BMI, body composition, and mortality were evaluated in elderly Asians, who have a body composition that differs from that of people of other races.


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  2. Abstract

Study Participants

The present study was designed as a population-based, prospective cohort study of a population aged 65 and older. Participants resided in Seongnam City, a satellite city of Seoul, Korea. The study design has been described in detail elsewhere as an element of the Korean Longitudinal Study on Health and Aging (KLoSHA).14 The baseline phase of KLoSHA began in September 2005. From a random sample of 1,000 participants, 877 subjects who had a bioelectrical impedance analysis (BIA; Biospace Inbody 720; Biospace Company, Ltd., Seoul, Korea) were evaluated. BIA has been found in the literature to be reliable in the calculation of body composition.15 The evaluated participants did not differ from the 123 unevaluated participants in relation to hypertension, diabetes mellitus, chronic kidney disease (CKD), serum creatinine (Cr), and glomerular filtration rate (GFR) (data not shown), but the study subjects were younger than the unevaluated participants (mean age 75.3 vs 83.9). All assessments were performed at Seoul National University Bundang Hospital in Gyeonggi-do, Korea.

Measurements and Definitions

The clinical parameters investigated were age, sex, weight (kg), height (cm), and waist circumference (cm), as well as history of hypertension, diabetes mellitus, smoking, coronary heart disease (CHD), or cerebrovascular accident (CVA). Systolic blood pressure (SBP) and diastolic blood pressure (DBP) were measured after participants had rested for at least 3 minutes. One person's height was not measured. BMI was calculated as weight (kg) divided by height (m2). Body composition, including lean mass (kg), fat mass (kg), and fat proportion (%), was measured using BIA. Lean mass indexed according to the square of height was calculated (LMI, kg/m2). Numerous laboratory measurements were obtained. Serum measurements included blood urea nitrogen (BUN), Cr, glucose, total cholesterol, triglycerides, high-density lipoprotein cholesterol (HDL-C), and low-density lipoprotein cholesterol. Urine measurements included a dipstick test for albumin and a red blood cell (RBC) count per high-power field using light microscopy. GFR was calculated for 866 participants using the Modification of Diet in Renal Disease study equation.16

Hypertension was defined as one of the following conditions: SBP of 140 mmHg or greater, DBP of 90 mmHg or greater, or the use of antihypertensive medication irrespective of BP. Diabetes mellitus was defined as a fasting glucose level of 126 mg/dL or greater or the use of hypoglycemic agents. CHD was defined as a self-reported history of angina pectoris, acute myocardial infarction, percutaneous coronary intervention, or coronary artery bypass operation. Anemia was defined as a serum hemoglobin level of less than 13 g/dL in men or less than 12 g/dL in women.17 Low HDL-C was defined as an HDL-C level less than 40 mg/dL in men and less than 50 mg/dL in women.18 Proteinuria was defined as albumin 1+ or greater and hematuria as a RBC count of more than 5 per high-power field. On the basis of WHO definitions,7 32.3% of participants were overweight (BMI 25.0–29.9 kg/m2) and 3.8% were obese (BMI≥30.0 kg/m2). Because most of the participants were normal weight or underweight, the following BMI quartile-based groups were established: Group 1 (<25th percentile, BMI<22.0 kg/m2), Group 2 (25th–75th percentile, BMI 22.0–26.1 kg/m2), and Group 3 (≥75th percentile, BMI≥26.1 kg/m2). Values for waist circumference, body composition, and LMI were also divided into three groups based on quartiles. Regular exercise was defined as an exercise regimen of at least 30 minutes, three or more times per week. All-cause mortality data were obtained from the Ministry of Public Administration and Security national database.

Statistical Analysis

All analyses were performed using SPSS software (SPSS version 16.0, Chicago, IL). Data are presented as means ± standard deviations for continuous variables and as proportions for categorical variables. Demographic and clinical data were described and compared across the LMI groups. Differences between the LMI groups were analyzed using the chi-square test for categorical variables and one-way analysis of variance (ANOVA) test for continuous variables. The Duncan method was used for post hoc analysis in ANOVA. Correlations between BMI, waist circumference, body composition, and LMI were evaluated using the Pearson correlation method. The unadjusted hazard ratios for all-cause mortality were calculated using the Cox proportional hazards analysis (Model 1). Adjustments were made for age, sex, hypertension, diabetes mellitus, CHD, CVA, ever drinking alcohol, smoking, hemoglobin, albumin, cholesterol, and regular exercise (Model 2). P<.05 was considered significant.


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  2. Abstract

Baseline Characteristics and Factors Associated with LMI

Table 1 shows the baseline characteristics of all participants and the factors related to LMI. The mean age of participants was 75.3 (range 65–98). Mean BMI was 24.0 kg/m2 (range 15.3–35.9 kg/m2). Women (n=412) had a higher mean BMI (24.2 kg/m2) than men (n=465; mean 23.7 kg/m2). A median age split revealed a mean BMI of 24.7 kg/m2 for participants younger than 74 and 23.1 kg/m2 for participants aged 74 and older. Group 1 contained high proportions of older participants and women and those with hematuria and high serum levels of cholesterol and triglyceride; the proportion of alcohol drinkers, smokers, and subjects who regularly exercised was lower in Group 1 than in the other groups. The same was true for levels of glucose, albumin, HDL-C, and albumin. A GFR of less than 60 mL/min per 1.73 m2 was found in 47.7% of all participants, with six (0.7%) having a GFR between 30 and 15 mL/min per 1.73 m2 and two (0.2%) having a GFR of less than 15 mL/min per 1.73 m2. GFR level did not differ between the LMI groups.

Table 1. Baseline Demographics According to the Lean Mass Index Groups
CharacteristicAll Participants (N=876)Group 1 (n=218)Group 2 (n=439)Group 3 (n=219) P-Value
  1. Subscript numbers (1–3) are differential subgroups after post hoc analysis.

  2. Lean mass index groups: Group 1, <14.6 kg/m2; Group 2, 14.6–16.8 kg/m2; Group 3, ≥16.8 kg/m2.

  3. SD=standard deviation.

Lean mass index, kg/m2, mean ± SD15.7 ± 1.713.7 ± 0.7115.7 ± 0.6217.9 ± 0.93<.001
Lean mass, kg, mean ± SD39.1 ± 7.731.2 ± 3.7138.3 ± 4.7248.5 ± 5.23<.001
Body mass index, kg/m2, mean ± SD24.0 ± 3.320.9 ± 2.5124.3 ± 2.7226.3 ± 2.83<.001
Age, mean ± SD75.3 ± 8.378.3 ± 8.5175.0 ± 8.2272.9 ± 7.13<.001
Female %<.001
Regular exercise, %54.438.655.368.0<.001
Hypertension, %
Diabetes mellitus, %<.001
Coronary heart disease, %
Cerebrovascular accident, %
Alcohol, %40.620.036.668.9<.001
Smoking, %39.826.435.362.1<.001
Systolic blood pressure, mmHg, mean ± SD132.0 ± 17.4130.2 ± 17.3131.9 ± 17.9133.8 ± 16.5.10
Diastolic blood pressure, mmHg, mean ± SD82.5 ± 10.581.6 ± 10.882.4 ± 10.483.7 ± 10.2.10
Pulse pressure, mmHg, mean ± SD49.4 ± 12.248.7 ± 11.549.5 ± 12.750.1 ± 11.8.46
Glucose, mg/dL, mean ± SD108.8 ± 24.7100.2 ± 15.81109.5 ± 25.62115.9 ± 27.43<.001
Protein, g/dL, mean ± SD7.47 ± 0.467.43 ± 0.487.49 ± 0.447.45 ± 0.45.20
Albumin, g/dL, mean ± SD4.11 ± 0.234.06 ± 0.2514.12 ± 0.2324.13 ± 0.202.001
Cholesterol, mg/dL, mean ± SD202.4 ± 38.0205.6 ± 38.01204.3 ± 38.12195.6 ± 37.12.008
Triglyceride, mg/dL, mean ± SD133.7 ± 81.6120.4 ± 57.21136.5 ± 85.62141.6 ± 92.22.01
High-density lipoprotein cholesterol, mg/dL, mean ± SD60.5 ± 15.264.2 ± 15.8160.5 ± 14.9256.7 ± 14.33<.001
Hemoglobin, g/dL, mean ± SD13.8 ± 1.513.0 ± 1.2113.8 ± 1.4214.6 ± 1.43<.001
Creatinine, mg/dL, mean ± SD1.12 ± 0.341.05 ± 0.2311.12 ± 0.4121.21 ± 0.233<.001
Glomerular filtration rate, mL/min/1.73 m2, mean ± SD61.2 ± 12.660.0 ± 14.661.2 ± 12.562.2 ± 10.5.19
Proteinuria, %
Hematuria, %10.917.310.35.6<.001

Correlations Between Baseline BMI and Results of BIA

The degree of correlation between baseline BMI, waist circumference, body composition, and LMI were evaluated. Waist circumference, lean mass, fat mass, fat proportion, and LMI increased in relation to BMI. All correlationswere significant (P<.001). The correlation coefficient between lean mass and BMI was 0.35 and that between fat mass and BMI was 0.91. Correlation coefficients of LMI with BMI, waist circumference, lean mass, fat mass, and fat proportion were 0.67, 0.53, 0.86, 0.39, and −0.08, respectively.

Clinical Risk Factors for Mortality

Participants were followed up for a period of 3.5 years, during which time 6.3% (55) of the cohort died. Clinical risk factors were evaluated as potential causes of mortality (Table 2), and it was found that participants who exercised regularly and had high serum albumin had a higher survival rate. The present study did not find any correlation between mortality and a history of hypertension, diabetes mellitus, CHD, or CVA. Serum cholesterol levels did not influence mortality during the same period.

Table 2. Clinical Factors: Risk of All-Cause Mortality in Univariate and Multivariate Analyses (n=877)
FactorHazard Ratio (95% Confidence Interval) P-Value
Model 1*Model 2
  • *

    Univariate analysis.

  • Adjusted for age, sex, hypertension, diabetes mellitus, preexisting history of coronary heart disease and cerebrovascular accident, ever drinking alcohol, smoking, hemoglobin, albumin, cholesterol, and regular exercise.

Age (1-year increase)1.10 (1.07–1.14) <.0011.09 (1.06–1.13) <.001
Male (vs female)1.37 (0.81–2.33) .241.56 (0.74–3.30) .25
Hypertension1.05 (0.59–1.89) .861.21 (0.66–2.25) .54
Systolic blood pressure, mmHg
 120–1401 (Referent)1 (Referent)
 <1201.77 (0.89–3.53) .111.73 (0.83–3.61) .14
 ≥1401.30 (0.71–2.37) .401.05 (0.53–2.12) .88
Diastolic blood pressure, mmHg
 80–901 (Referent)1 (Referent)
 <801.83 (0.97–3.46) .061.62 (0.83–3.18) .16
 ≥901.36 (0.72–2.58) .341.54 (0.76–3.13) .23
Pulse pressure (1-mmHg increase)0.99 (0.96–1.01) .250.98 (0.95–1.00) .06
Orthostatic hypotension1.76 (0.80–3.89) .161.44 (0.63–3.31) .39
Diabetes mellitus0.94 (0.48–1.81) .841.06 (0.53–2.12) .88
Preexisting history of coronary heart disease0.69 (0.21–2.20) .520.69 (0.21–2.25) .54
Preexisting history of cerebrovascular accident1.22 (0.52–2.84) .651.42 (0.59–3.42) .43
Alcohol1.01 (0.59–1.73) .981.04 (0.54–1.98) .91
Smoking1.60 (0.94–2.71) .081.29 (0.68–2.45) .43
Regular exercise0.28 (0.15–0.51) <.0010.24 (0.13–0.47) <.001
Anemia1.32 (0.65–2.69) .450.68 (0.23–1.97) .47
Serum albumin (1-g/dL increase)0.08 (0.03–0.23) <.0010.17 (0.06–0.50) .001
Serum cholesterol (1-mg/dL increase)1.00 (0.99–1.00) .281.00 (0.99–1.01) .80
Serum triglycerides (1-mg/dL increase)1.00 (0.99–1.00) .381.00 (1.00–1.01) .90
Low high-density lipoprotein cholesterol1.05 (0.33–3.36) .940.46 (0.11–1.96) .29
Glomerular filtration rate <60 mL/min per 1.73 m2 (vs ≥60)1.55 (0.91–2.64) .111.36 (0.77–2.39) .28

Influence of BMI and Body Composition on Mortality

Hazard ratios for mortality were calculated for BMI and body composition (Table 3). In univariate analysis, higher BMI appeared to be associated with a greater risk of mortality, although this relationship was no longer significant after adjustment for multiple variables. Waist circumference, fat mass, and fat proportion were also not associated with mortality. In contrast, there was an association between lean mass, LMI, and mortality. No interaction between men and women was shown in the correlation between lean mass parameters and all-cause mortality. Participants in lean mass Group 3 had a relative risk of mortality that was 74% lower in univariate analysis and 84% lower in multivariate analysis than those in Group 1. In the LMI group, Group 3 had a relative risk of mortality that was 74% lower in univariate analysis and 69% lower in multivariate analysis than those in Group 1. Fat mass indexed according to the square of height was not correlated with all-cause mortality in univariate or multivariate analyses.

Table 3. Body Mass Index (BMI) and Body Composition: Risk of All-Cause Mortality in Univariate and Multivariate Analyses
GroupHazard Ratio (95% Confidence Interval) P-Value
Model 1*Model 2
  • *

    Univariate analysis.

  • Adjusted for age, sex, hypertension, diabetes mellitus, preexisting history of coronary heart disease or cerebrovascular accident, ever drinking alcohol, smoking, hemoglobin, albumin, cholesterol, and regular exercise.

BMI, kg/m2
 <221 (Referent)1 (Referent)
 22–26.10.62 (0.35–1.10) .100.93 (0.50–1.72) .81
 ≥26.10.31 (0.13–0.72) .0070.54 (0.22–1.36) .19
Waist circumference, cm
 <81.11 (Referent)1 (Referent)
 81.1–92.61.07 (0.54–2.14) .840.88 (0.43–1.78) .72
 ≥92.60.99 (0.44–2.20) .970.65 (0.27–1.57) .34
Lean mass, kg
 <33.31 (Referent)1 (Referent)
 33.3–44.70.60 (0.34–1.05) .070.53 (0.22–1.26) .15
 ≥44.70.26 (0.11–0.65) .0040.16 (0.04–0.55) .004
Lean percentage, %
 <61.11 (Referent)1 (Referent)
 61.1–71.21.15 (0.60–2.21) .670.90 (0.41–1.95) .78
 ≥71.20.94 (0.43–2.05) .870.54 (0.20–1.48) .23
Lean mass index, kg/m2
 <14.61 (Referent)1 (Referent)
 14.6–16.80.60 (0.34–1.05) .070.79 (0.41–1.52) .47
 ≥16.80.26 (0.11–0.64) .0030.31 (0.11–0.88) .03
Fat mass, kg
 <13.41 (Referent)1 (Referent)
 13.4–20.80.89 (0.48–1.64) .701.31 (0.68–2.50) .42
 ≥20.80.60 (0.27–1.33) .210.97 (0.40–2.34) .94
Fat percentage, %
 <23.81 (Referent)1 (Referent)
 23.8–34.31.22 (0.62–2.38) .561.64 (0.79–3.42) .19
 ≥34.31.06 (0.49–2.33) .881.87 (0.69–5.10) .22


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  2. Abstract

Several studies have found a positive correlation between BMI and all-cause mortality in younger adults, not focused on the elderly population. In the present study, lean mass parameters (lean mass or LMI), rather than BMI, were significant risk factors for all-cause mortality in elderly Asians over a 3.5-year period. Other parameters of body composition (e.g., fat mass and fat proportion) were not associated with all-cause mortality. BMI was significantly correlated with various body composition factors. These correlations occurred at different degrees, and the relationship was weaker for lean mass than for fat mass.

Obesity is a known risk factor for mortality in the general population (in terms of age). In a prospective study from the Cancer Prevention Study cohort, high BMI was identified as increasing the risk of mortality over a 12-year period.4 Subject age could alter the relationship between BMI and mortality, because the mortality risk associated with high BMI in older adults was lower than in younger adults. In Korea, the association between BMI and mortality in the general population has been investigated in a large cohort study.2 Among 1,213,829 Koreans, deaths from any cause were found to have a J-shape association with BMI, but age modified this association, because BMI of 25.0 kg/m2 or greater was not associated with greater risk of all-cause mortality in the population aged 65 and older. Because conventional BMI criteria were not suitable for Asians, new BMI criteria were proposed (underweight, <18.5 kg/m2; normal range, 18.5–22.9 kg/m2; overweight, 23.0–24.9 kg/m2; obese, ≥25 kg/m2),19 but when analyzing these criteria in the current study, a positive correlation was not found between BMI and mortality (data not shown).

Body composition varies according to age, sex, and race. Older adults tend to lose fat-free mass and gain fat mass. Therefore, the generalized application of international BMI classifications7 to clinical practice may not detect malnutrition in older adults. Four-year mortality was evaluated in a large Italian population-based sample, aged 65 to 84.20 BMI less than 20 kg/m2 predicted all-cause mortality, highlighting the importance of nutritional management in older adults. Malnutrition–inflammation–cachexia syndrome has been proposed to explain why low BMI increases the risk of mortality in patients undergoing dialysis.21 Similar to the importance of nutritional support in patients undergoing dialysis, older adults need to pay equal attention to becoming underweight and overweight.22

BMI is not a reliable indicator of obesity, especially in older adults, because it does not differentiate lean mass from adipose tissue. BMI also poorly represents central fat mass and nutrition, for which more reliable parameters can be used. It has been found that waist circumference (proxy of central obesity) is a reliable marker of mortality in older adults but that BMI had a paradoxical correlation with mortality.12 Computed tomography (CT) and magnetic resonance imaging (MRI) are the methods of choice for assessing visceral fat,23,24 although in contrast to these expensive techniques, waist circumference and waist to hip ratio are simple and inexpensive methods for making similar assessments.25 Furthermore, the superiority of waist circumference over BMI in predicting CHD has been demonstrated.3 In a study with data from the Korean Acute Myocardial Infarction Registry, the highest level of mortality was observed for patients with the lowest BMI and the highest waist-to-hip ratio.26 In the present study, neither waist circumference nor waist-to-hip ratio was associated with all-cause mortality. This finding was attributed to the body shape of elderly Asians, who are typically leaner than Caucasians. Research shows that fat mass can protect against mortality in patients undergoing hemodialysis, which may help to explain the absence of any clear relationship between mortality and waist circumference or fat mass.27

Muscle mass, as represented by lean mass, is associated with survival, and the protective effect of muscle mass is well known in CKD. Recently, heart failure was reported to be associated with smaller mid-arm muscle circumference in patients undergoing hemodialysis. Muscle mass was measured using 24-hour urinary Cr excretion, and it was found that this influenced cardiovascular and all-cause mortality in patients undergoing hemodialysis.28 The high LMI group in the present study (Group 3) had a greater proportion of younger subjects and of those who exercised regularly and had high levels of serum albumin. These factors could improve survival rates, although those variables were adjusted for in multivariate analyses. Unfavorable factors such as male sex, diabetes mellitus, smoking, and low levels of serum HDL-C were predominant in the high LMI group. This discrepancy may be because patients with metabolic syndrome and those who exercised regularly were included in the high LMI group. Additional large population studies are needed to enable confounding factor stratification.

Although the present observational cohort study of randomly sampled older adults is informative, it is not without limitations. First, the results did not allow for the evaluation of any long-term effects associated with BMI or body composition. Based on the literature, the influence of high BMI on all-cause mortality may easily take 10 years or more to determine. However, similar to the present finding of no association between the short-term effects of BMI and mortality, some long-term studies over 12 years have revealed that elderly individuals with high BMI are not necessarily at greater risk of mortality.6 Second, because all participants in the cohort were elderly Asians, inferences from the data may not be applicable to the general population or to other ethnicities. Third, the sensitivity of BIA used in the present study is not precisely known. Although CT and MRI are more sensitive in measuring visceral adipose tissue, they are also more expensive. BIA is convenient and inexpensive, although the accuracy of this device is limited in older adults.29 Another limitation is that the assessment of lean mass is dependent on fat mass calculation, because weight is held constant, but some studies have demonstrated the reliability and internal validity of BIA.15 Further research is needed to investigate whether the technique used to measure body composition influences associations with mortality. Fourth, the sample size was modest. Thus, although the magnitude of the hazard ratio was large with regard to the potential clinical effect, the confidence intervals were wide. Furthermore, stratifying subjects into the modest sample size may have limited the potential significant results.

Several previous studies of older adults have found obesity to be paradoxically associated with better outcomes, although most studies defined obesity using BMI, which is a poor discriminator of body composition and has been extensively examined only in Caucasians. To the best of the authors' knowledge, the present study is the first to demonstrate the superior predictive power of lean mass parameters (lean mass or LMI), as opposed to BMI, in predicting all-cause mortality in elderly Asians. This suggests that elderly Asians at high risk of mortality could be better identified using body composition measurements, such as lean mass, than BMI measurements.


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  2. Abstract

Conflict of Interest: The editor in chief has reviewed the conflict of interest checklist provided by the authors and has determined that the authors have no financial or any other kind of personal conflicts with this paper.

Author Contributions: Seung Seok Han: drafting and revision of manuscript, analysis and interpretation of data. Ki Woong Kim, Kwang-Il Kim, and Ki Young Na: conception of data. Dong-Wan Chae and Suhnggwon Kim: providing intellectual content of critical importance to the work described. Ho Jun Chin: conception of data, final approval of the version to be published.

Sponsor's Role: None.


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  2. Abstract
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