# Developing and Validating an Age-Independent Equation Using Multi-Frequency Bioelectrical Impedance Analysis for Estimation of Appendicular Skeletal Muscle Mass and Establishing a Cutoff for Sarcopenia

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## Abstract

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^{2}/Z

_{50}) and impedance ratio of high and low frequency (Z

_{250}/Z

_{5}) of hand to foot values were calculated. Multiple regression analyses were conducted with ALM as dependent variable in men and women separately. Results: We created the following equations: ALM = (0.6947 × (Ht

^{2}/Z

_{50})) + (−55.24 × (Z

_{250}/Z

_{5})) + (−10,940 × (1/Z

_{50})) + 51.33 for men, and ALM = (0.6144 × (Ht

^{2}/Z

_{50})) + (−36.61 × (Z

_{250}/Z

_{5})) + (−9332 × (1/Z

_{50})) + 37.91 for women. Additionally, we conducted measurements in 1624 men and 1368 women aged 18 to 40 years to establish sarcopenia cutoff values in the Japanese population. The mean values minus 2 standard deviations of the skeletal muscle mass index (ALM/Ht

^{2}) in these participants were 6.8 and 5.7 kg/m

^{2}in men and women, respectively. Conclusion: The current study established and validated a theoretical and age-independent equation using MF-BIA to estimate ALM and provided reasonable sarcopenia cutoff values.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Participants

#### 2.2. Multi-Frequency Bioelectrical Impedance Analysis

_{5}, Z

_{50}, and Z

_{250}, respectively). Routine quality assurance procedures were conducted using a custom-made impedance tester and no instrument drift or shift was detected during the measurement period. Participants were evaluated in their underwear, in a standing position, and were asked to stand barefoot on toe-and heel electrodes and to hold the handgrips with arms hanging down a few centimeters from the hip. The eight-electrode method enables segmental impedance measurement. The electrical current is ≤90 μA. Minimum weight graduation was 0.1 kg. Participants were instructed to refrain from vigorous exercise and consuming alcohol for the 24-h period before the experiment, to finish the last meal at least 2.5-h before the measurement, and to empty their bladder before the measurement. Measurements were conducted between 15:00 to 17:30, and room temperature was adjusted to maintain a thermoneutral environment.

^{2}/Z

_{50}) or resistance index of 50 kHz (Ht

^{2}/R

_{50}) calculated by Ht and Z

_{50}or resistance at 50 kHz (R

_{50}) as a predicting variable for AMM or ALM [17,30,38]. In the human body, reactance is less than 10% of resistance, and correlation between impedance and resistance are >0.99; thus Ht

^{2}/Z

_{50}and Ht

^{2}/R

_{50}are interchangeable. We chose to use Ht

^{2}/Z

_{50}as a candidate independent variable to estimate ALM in this study. One of the most well-known equations for estimating muscle mass by BIA was developed by Janssen et al. using MRI as follows: SMM (kg) = ((Ht

^{2}/R

_{50}× 0.401) + (sex × 3.825) + (age × −0.071)) + 5.102 [30], and many BIA equations are age-dependent. Yamada et al. indicated that expansion of ECW relative to ICW or total body water (TBW) is observed with aging, and may mask actual age-related decrease of muscle cell mass [32,34,39,40,41]. The Z at low-frequency (≤50 kHz, for example, Z

_{5}or Z

_{50}) currents mainly reflects ECW. In contrast, the Z at high-frequency (≥250 kHz) reflects TBW. Thus, the impedance ratio of Z

_{250}against Z

_{5}(Z

_{250}/Z

_{5}) is an index of ECW/TBW, and we chose to use Z

_{250}/Z

_{5}as another candidate independent variable to estimate ALM. In addition, the possibility of edema affects ALM estimation, i.e., if the person has edema, particularly peripheral edema, the BIA overestimates actual ALM. The index of 1/Z

_{5}or 1/Z

_{50}could potentially be applied as an adjusting variable for this situation. Thus, we selected 1/Z

_{50}as an additional candidate independent variable to estimate ALM. We developed estimating equations for men and women separately, because body composition and fat and muscle distribution are quite different between men and women.

#### 2.3. Dual-Energy X-ray Absorptiometry

#### 2.4. Statistical Analysis

^{2}/Z

_{50}, and Z

_{250}/Z

_{5}against age, and determination coefficients were obtained. To examine the effect of age on BIA estimation, we investigated the association between age and the residual of the ALM obtained by DXA and the ALM estimated by one of the previous BIA equations for Japanese older adults aged 65 years and over using TANITA BIA according to the following Equations [38]:

^{2}/Z

_{50})) + (0.179 × Weight) − 0.019

^{2}/Z

_{50})) + (0.117 × Weight) + 0.881

^{2}/Z

_{50}, Z

_{250}/Z

_{5}, and 1/Z

_{50}as independent variables and ALM as the dependent variable, where entry probability of F was 0.05 and removal was 0.10. To validate the newly developed equation, the association between the ALM estimated with the newly developed MF-BIA equation and the ALM obtained by DXA was examined in the validation groups and pair t-test was conducted between measured and estimated ALM. To establish sarcopenia cutoff values based on Baumgartner et al. [42], we calculated the mean minus 2SD in 1624 men and 1368 women aged 18 to 40 years using the equation. All analyses were performed using SPSS software (Version 22.0 for Windows, IBM Corp., Armonk, NY, USA). For all analyses, p < 0.05 was used to indicate statistical significance.

## 3. Results

_{5}, Z

_{50}, Z

_{250}, Ht

^{2}/Z

_{50}, Z

_{250}/Z

_{5}and 1/Z

_{50}were significantly different between men and women.

^{2}= 0.49 and 0.44 for men and women, respectively). Figure 1C,D shows the correlation between age and the residual of the ALM obtained by DXA and the ALM estimated by the previous BIA equation. The residual significantly correlated with age, and the previous BIA equation underestimated ALM in young adults. Thus, the previous equation cannot be used to examine age-related ALM loss.

^{2}= 0.42 and 0.29 in men and women, respectively. In contrast, as Figure 3 shows, the determinant coefficients of quadratic regression analysis between age and Ht

^{2}/Z

_{50}obtained by BIA were R

^{2}= 0.11 and 0.04 in men and women, respectively.

_{250}/Z

_{5}) of the ratio between extra- to intra-cellular water compartments obtained by MF-BIA in men (A) and women (B). The determinant coefficients of quadratic regression analysis were R

^{2}= 0.37 and 0.23, respectively.

^{2}/Z

_{50}was a significant independent variable to estimate ALM, but the determinant coefficient was moderate and the standard error of estimation (SEE) was relatively large (2.27 and 1.88 kg in men and women, respectively). In contrast, in the final model (model 3), all impedance variables became significant independent variables to estimate ALM, the determinant coefficients became significantly greater than model 1, and SEE became lower than models 1 and 2 (1.46 and 1.22 kg in men and women, respectively). The variance inflation factor (VIF), an index to detect multicollinearity, was less than 5, so that the final model is acceptable to use. The negative coefficients of 1/Z

_{50}indicated that 1/Z

_{50}did work as a suppressor variable in the model.

^{2}/Z

_{50})) + (−55.24 × (Z

_{250}/Z

_{5})) + (−10940 × (1/Z

_{50})) + 51.33

^{2}/Z

_{50})) + (−36.61 × (Z

_{250}/Z

_{5})) + (−9332 × (1/Z

_{50})) + 37.91

^{2}= 0.87 and 0.86, respectively. The SEE was 1.53 and 1.15 kg in men and women, respectively. The intercept was not significantly different from zero and the slope was not significantly different from one (p < 0.05). There were no significant differences between measured and estimated ALM both in men (p = 0.57) and women (p = 0.24) by the paired t-test. We calculated the skeletal muscle index (SMI) as follows: SMI = ALM/Ht

^{2}, and the determinant coefficients of the association between SMI by DXA and SMI by MF-BIA in the validation group were R

^{2}= 0.69 and 0.67, in men and women, respectively. Figure 6 shows the correlation between age and ALM obtained by the new MF-BIA and the correlations with age were very similar to that of DXA (Figure 1 and Figure 6).

^{2}, and thus the sarcopenia cutoff values (mean minus 2SD) were 6.8 and 5.7 kg/m

^{2}in men and women, respectively.

## 4. Discussion

^{2}/Z

_{50})) + (0.179 × Weight) − 0.019 for men, and ALM = (0.221 × (Ht

^{2}/Z

_{50})) + (0.117 × Weight) + 0.881 for women [38]. The impedance index (Ht

^{2}/Z

_{50}) has been used for estimating ALM and/or SMM in many articles. However, when we applied this equation to individuals over a wide age range (18 to 86 years), the equation underestimated ALM significantly in the younger population. We examined the mechanism of this underestimation. The Ht

^{2}/Z

_{50}did not seem to reflect age-related ALM decline, because Ht

^{2}/Z

_{50}was not correlated with age (R

^{2}= 0.11 and 0.04, in men and women, respectively) compared with DXA (R

^{2}= 0.42 and 0.29, in men and women, respectively), which led to age-related underestimation of the BIA.

_{250}against Z

_{5}(Z

_{250}/Z

_{5}), an index of ECW/TBW. Previously, Yamada et al. [32,34,39,40,41] indicated that the impedance ratio of low to high frequency strongly correlated with age and muscle strength, and suggested that the impedance ratio is an important marker of muscle quality. They stated that the impedance ratio reflects the ratio of actual muscle cell mass against total body water. In the present study, Z

_{250}/Z

_{5}correlated significantly with age (R

^{2}= 0.37 and 0.23 in men and women, respectively). In the multiple regression model 2, Z

_{250}/Z

_{5}significantly improved the accuracy of ALM prediction, which means that it is essential to take into account the water distribution within the body to estimate ALM by BIA.

_{5}or 1/Z

_{50}may be applied as an adjusting variable in this situation. In the multiple regression model 3, 1/Z

_{50}significantly improved the accuracy of ALM prediction. This final model did not have multicollinearity (VIF < 2.5) and had high determinant coefficients. The coefficients of 1/Z

_{50}were negative, which means the variables work as a suppressor when an individual had possible edema or water shift into peripheral extra-water segments.

^{2}, and thus the sarcopenia cutoff values (mean minus 2SD) based on Baumgartener et al. [42] were 6.8 and 5.7 kg/m

^{2}in men and women, respectively. For the Japanese population, Sanada et al. [46] established a cut off using DXA (QDR-4500A, Hologic, MA, USA) as 6.87 and 5.46 kg/m

^{2}in men and women, respectively. Tanimoto et al. [47] established a cut off using BIA (TANITA MC-190) of 7.0 and 5.8 kg/m

^{2}in men and women, respectively. Yoshida et al. [38] used a BIA (MC-190) and suggested cut offs of 7.09 and 5.91 kg/m

^{2}in men and women, respectively. Yamada et al. [48] established a cut off using a BIA (Inbody 720, Biospace) and reported values of 6.75 and 5.07 kg/m

^{2}in men and women, respectively. It is important to note that Yamada et al. [49] reported that if we used the manufacturer’s own formula, which is undisclosed, different MF-BIA devices provided different SMI values, but if we used one disclosed equation, even with different devices, MF-BIAs provided the same SMI values over a wide age range (18 to 89 years). The sarcopenia cut off value established in the current study was very similar to the value from the previous publication using DXA [46], and within the range previously published in the literature. Thus, we consider that the values of 6.8 and 5.7 kg/m

^{2}from 1624 men and 1368 women, aged 18 to 40 years, can be reasonably used as sarcopenia cut off levels for the Japanese population.

## 5. Conclusions

^{2}/Z

_{50})) + (−55.24 × (Z

_{250}/Z

_{5})) + (−10940 × (1/Z

_{50})) + 51.33 for men, and ALM = (0.6144 × (Ht

^{2}/Z

_{50})) + (−36.61 × (Z

_{250}/Z

_{5})) + (−9332 × (1/Z

_{50})) + 37.91 for women. In the cross validation group, the equation had high determinant coefficients (R

^{2}= 0.87 and 0.86, respectively) with reasonable SEE (1.53 and 1.15 kg in men and women, respectively). The current study established and validated this theoretical and age-independent equation of MF-BIA for estimating ALM and provided a sarcopenia cutoff value using the equation for the Japanese population. This MF-BIA device is distributed worldwide, thus it is an interesting challenge to develop equations and establish the sarcopenia cut off for various countries with different population as an area of future research. Readers should examine our results and evaluate how they can be interpreted from the perspective of previous studies and the working hypotheses. The current findings and their implications should be discussed in the broadest context possible. Areas for future research may also be identified.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**A and B shows the relationship between the appendicular lean mass (ALM) estimated by one of the previous bioelectrical impedance analysis equation for a standing-posture 8-electrode TANITA MF-BIA and the ALM obtained dual X-ray absorptiometry (DXA) in 319 men (

**A**) and 437 women; (

**B**) The equation was established and validated for Japanese older adults aged 65y and over as a previous equation by [38]. The determinant coefficient were just moderate (R

^{2}= 0.50 and 0.44, men and women, respectively) because of the wide range of the age in the current participants (18 to 86 years). (

**C**,

**D**) shows the relationship between age and the residual of the ALM obtained DXA and the ALM estimated by the previous BIA equation. The residual was significantly correlated with age, which indicated that the previous BIA equation underestimated ALM in young adults. The previous equation cannot be used to examine age-related ALM loss.

**Figure 2.**Relationship between age and the appendicular lean mass (ALM) obtained by DXA in 319 men (

**A**) and 437 women (

**B**) aged 18 to 86 years old. The determinant coefficients of quadratic regression analysis were R

^{2}= 0.42 and 0.29, respectively.

**Figure 3.**Relationship between age and the impedance index (height squired divided by impedance at 50 kHz: Ht

^{2}/Z

_{50}) obtained by bioelectrical impedance analysis in 319 men (

**A**) and 437 women (

**B**) aged 18 to 86 years old. The determinant coefficients of quadratic regression analysis were R

^{2}= 0.11 and 0.04, respectively, which is significantly lower than that of the age-ALM relationship in DXA.

**Figure 4.**Relationship between age and the impedance ratio of high and low frequency (impedance at 250 kHz divided by impedance at 5 kHz: Z

_{250}/Z

_{5}) obtained by multi-frequency bioelectrical impedance analysis (MF-BIA) in 319 men (

**A**) and 437 women (

**B**) aged 18 to 86 years old. The determinant coefficients of quadratic regression analysis were R

^{2}= 0.37 and 0.23, respectively. The Z

_{250}/Z

_{5}is the index of the ratio between extra- and intra-cellular water compartments in the body.

**Figure 5.**Relationship between ALM estimated by new equation of MF-BIA established with the developing group (222 men and 301 women) against ALM by DXA in validation group with 97 men and 136 women. The determinant coefficients of linear regression analysis were R

^{2}= 0.87 and 0.85, respectively. The intercept was not significantly different from zero and the slope was not significantly different from one.

**Figure 6.**Relationship between age and ALM obtained by new MF-BIA in 319 men (

**A**) and 437 women (

**B**) aged 18 to 86 years old. The determinant coefficients of quadratic regression analysis were R

^{2}= 0.40 and 0.31, respectively.

**Table 1.**Physical characteristics and BIA variables of participants for equation developing and validation.

Equation Developing Group (222 Men) | Validation Group (97 Men) | |||||

Mean ± SD | MAX | MIN | Mean ± SD | MAX | MIN | |

Age | 46 ± 17 | 81 | 18 | 49 ± 18 | 78 | 18 |

Ht | 167.5 ± 6.8 | 181.9 | 147.1 | 167.0 ± 7.6 | 184.6 | 150.0 |

Wt | 64.8 ± 9.5 | 93.3 | 45.4 | 67.0 ± 10.4 | 99.0 | 47.3 |

BMI | 23.1 ± 2.8 | 31.5 | 16.2 | 24.0 ± 3.1 | 31.1 | 17.6 |

ALM_{DXA} | 23.5 ± 3.8 | 32.3 | 14.8 | 23.8 ± 4.2 | 34.5 | 16.0 |

Z_{5} | 655.2 ± 64.8 | 837.2 | 498.7 | 636.4 ± 62.5 | 811.1 | 499.4 |

Z_{50} | 573.6 ± 58.0 | 735.6 | 437.2 | 557.0 ± 56.5 | 719.7 | 442.1 |

Z_{250} | 508.6 ± 52.6 | 657.2 | 388.6 | 494.5 ± 50.3 | 641.4 | 391.3 |

Ht^{2}/Z_{50} | 49.5 ± 5.8 | 66.9 | 33.1 | 50.6 ± 6.5 | 72.4 | 34.5 |

Z_{250}/Z_{5} | 0.776 ± 0.020 | 0.838 | 0.724 | 0.777 ± 0.020 | 0.830 | 0.736 |

1/Z_{50} | 0.00176 ± 0.00018 | 0.00229 | 0.00136 | 0.00181 ± 0.00018 | 0.00226 | 0.00139 |

Equation Developing Group (301 Women) | Validation Group (136 Women) | |||||

Mean ± SD | MAX | MIN | Mean ± SD | MAX | MIN | |

Age | 47 ± 18 | 86 | 18 | 44 ± 18 | 85 | 18 |

Ht | 154.7 ± 6.7 | 172.4 | 137.3 | 155.2 ± 7.1 | 170.2 | 138.3 |

Wt | 54.0 ± 7.3 | 83.6 | 38.3 | 54.1 ± 8.3 | 80.4 | 32.5 |

BMI | 22.6 ± 3.1 | 33.7 | 16.6 | 22.4 ± 3.0 | 32.9 | 16.0 |

ALM_{DXA} | 16.5 ± 2.5 | 24.2 | 10.8 | 17.0 ± 3.1 | 28.2 | 10.4 |

Z_{5} | 730.8 ± 81.2 | 965.4 | 536.9 | 736.7 ± 79.9 | 995.7 | 508.5 |

Z_{50} | 657.9 ± 73.0 | 885.1 | 484.3 | 661.1 ± 72.6 | 901.1 | 464.6 |

Z_{250} | 591.0 ± 65.7 | 799.5 | 438.7 | 592.7 ± 66.0 | 815.0 | 420.1 |

Ht^{2}/Z_{50} | 36.8 ± 4.2 | 49.8 | 27.1 | 36.9 ± 5.2 | 52.1 | 24.3 |

Z_{250}/Z_{5} | 0.809 ± 0.018 | 0.861 | 0.746 | 0.805 ± 0.020 | 0.851 | 0.742 |

1/Z_{50} | 0.00154 ± 0.00017 | 0.00206 | 0.00113 | 0.00153 ± 0.00017 | 0.00215 | 0.00111 |

_{DXA}, appendicular lean mass by dual X-ray absorptiometry; Z

_{5}, Z

_{50}, and Z

_{250}, whole body impedance of 5, 50, and 250 kHz.

Men (n = 222) | Coefficients | Sig. | Collinearity VIF | ||

Unstandardized | Standardized | ||||

B | Beta | ||||

1 | Ht^{2}/Z_{50} | 0.5153 | 0.797 | <0.001 | |

(Constant) | −1.941 | 0.1401 | |||

R^{2} = 0.635, SEE = 2.27 kg | |||||

2 | Ht^{2}/Z_{50} | 0.4396 | 0.680 | <0.001 | 1.138 |

Z_{250}/Z_{5} | −62.84 | −0.337 | <0.001 | 1.138 | |

(Constant) | 50.58 | <0.001 | |||

R^{2} = 0.735, SEE = 1.94 kg | |||||

3 | Ht^{2}/Z_{50} | 0.6947 | 1.075 | <0.001 | 2.473 |

Z_{250}/Z_{5} | −55.24 | −0.296 | <0.001 | 1.152 | |

1/Z_{50} | −10941 | −0.513 | <0.001 | 2.254 | |

(Constant) | 51.33 | <0.001 | |||

R^{2} = 0.851, SEE = 1.46 kg | |||||

Women (n = 301) | B | Beta | VIF | ||

1 | Ht^{2}/Z_{50} | 0.3797 | 0.644 | <0.001 | |

(Constant) | 2.567 | 0.008 | |||

R^{2} = 0.415, SEE = 1.88 kg | |||||

2 | Ht^{2}/Z_{50} | 0.3346 | 0.568 | <0.001 | 1.043 |

Z_{250}/Z_{5} | −50.68 | −0.378 | <0.001 | 1.043 | |

(Constant) | 45.22 | <0.001 | |||

R^{2} = 0.552, SEE = 1.65 kg | |||||

3 | Ht^{2}/Z_{50} | 0.6144 | 1.042 | <0.001 | 2.14 |

Z_{250}/Z_{5} | −36.61 | −0.273 | <0.001 | 1.096 | |

1/Z_{50} | −9332 | −0.649 | <0.001 | 2.053 | |

(Constant) | 37.91 | <0.001 | |||

R^{2} = 0.757, SEE = 1.22 kg |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Yamada, Y.; Nishizawa, M.; Uchiyama, T.; Kasahara, Y.; Shindo, M.; Miyachi, M.; Tanaka, S.
Developing and Validating an Age-Independent Equation Using Multi-Frequency Bioelectrical Impedance Analysis for Estimation of Appendicular Skeletal Muscle Mass and Establishing a Cutoff for Sarcopenia. *Int. J. Environ. Res. Public Health* **2017**, *14*, 809.
https://doi.org/10.3390/ijerph14070809

**AMA Style**

Yamada Y, Nishizawa M, Uchiyama T, Kasahara Y, Shindo M, Miyachi M, Tanaka S.
Developing and Validating an Age-Independent Equation Using Multi-Frequency Bioelectrical Impedance Analysis for Estimation of Appendicular Skeletal Muscle Mass and Establishing a Cutoff for Sarcopenia. *International Journal of Environmental Research and Public Health*. 2017; 14(7):809.
https://doi.org/10.3390/ijerph14070809

**Chicago/Turabian Style**

Yamada, Yosuke, Miyuki Nishizawa, Tomoka Uchiyama, Yasuhiro Kasahara, Mikio Shindo, Motohiko Miyachi, and Shigeho Tanaka.
2017. "Developing and Validating an Age-Independent Equation Using Multi-Frequency Bioelectrical Impedance Analysis for Estimation of Appendicular Skeletal Muscle Mass and Establishing a Cutoff for Sarcopenia" *International Journal of Environmental Research and Public Health* 14, no. 7: 809.
https://doi.org/10.3390/ijerph14070809