The plasticity of the human body with respect to surface and composition in connection with a lack of a standard model was the reason thatDahlmann et al. searched for a population of reference, which was found in the Schlegel material 10.

It is based on measurements taken by W. Schlegel on 1749 young adults aged 18 to 30 years for men and 17 to 30 for women, all living in Hamburg, Germany and includes the variables height (Ht), weight (Wt) and hand circumference (HdC). The studies were carried out between 1955 and 1973, at a time when no ready-to-eat environments for the risk of incident heart failure [11) and the corresponding restaurant chains existed in Germany.

Deduced from this reference population and on the basis of multiple regression equations including the parameters height, weight and hand circumference, the DBA system allowed for the first time the calculation of a reference weight (RefWt) for each individual. Details of the calculation were previously published 5. It is a standard independent of age.

The limitation of the model at this stage of design was the inability to distinguish between muscularity and fat tissue. For that reason, the circumference of the waist (WC), a marker for central obesity, was integrated into the model. Processed by a network of algorithms, it enables the differentiation of the difference weight - that means the difference between the actual weight (ActWt) and the reference weight (RefWt) - into fat mass (FM, kg) and muscle mass (MM, kg). The implementation of waist circumference in the DBA model as a proxy for body fat resulted in a strong concordance with BIA measurements 7. The quantification of fat mass made it possible to determine the lean body mass (LBM), which is defined as a fat free corpse and is calculated by subtracting the fat-mass values from body weight. A schematic illustration of the DBA model is shown in Figure 1 (Figure 1).

The purpose of this study is to discuss how meaningful the calculation of muscle mass is. It should be emphasised here that the DBA model calculates the delta (Δ) muscle mass. That is, the increase in muscle mass compared to the reference population, in contrast to DXA-based measurements, which result in the appendicular soft tissue (ASM). ASM is calculated as the sum of bone-free lean tissue in the arms and legs 12. Evaluation of the DBA results is possible by calculating the DXA-based muscle mass of the study population and the corresponding population of reference. The difference should correspond to the DBA results.

For this cross-sectional study, subjects were recruited from October 2019 to July 2021 at the obesity consultation hour of the endocrinology department of the University Hospital of Bonn, Germany, and were candidates for bariatric surgery. All participants were of European descent and inhabitants of the district Bonn. They had a BMI ≥ 29.7 kg/m^² and their age ranged from 18 to 72 years for men and 18 to 65 years for women. Exclusion criteria were pregnancy, oedema, skeletal malformation, acute diseases (i.e., overt organ failure), and inability to stand in an upright position. The list of participants is largely identical to that published previously in the supplementary material 7. All study procedures were performed according to the ethical standards of the World Medical Association s Declaration of Helsinki, and were approved by the institutional ethics review board. Written informed consent was obtained from each patient prior to enrolment.

The equations are taken from a scoping review, which gathered 122 DXA based formulas of 18 countries 8. All equations were copied from this review with the exception of Tian 13, Kulkarni 12, and Wen 14. These formulas are based on the original paper. Other estimation formulas not derived from DXA measurements e.g. those of Heymsfield et al. 15 were not considered - although of interest.

Equations are selected according to the following variables sex, age, weight (Wt), height (Ht), waist circumference (WC), and derived indices such as BMI (kg/m^²). The weight is given in (kg), the height in (cm). Inclusion criteria were formulas, selected according to sex, healthy condition, sample size ≥ 100, age ≥ 18 years, and accuracy (coefficient of determination, R^²) ≥ 0.7, with the exception of Tanko E11 (R^²=0.58).

Men

Tian, North America

ASM = 0.443*Wt + 0.011*Ht - 0.284*WC ─ 0.013*Age + 16.36 (E1)

Lee, Korea

ASM = 0.327*Wt + 0.079*Ht - 0.124*WC - 0.012*Age -1.55 (E2)

Furushima, Japan

ASM = 0.46*Wt - 0.251*WC + 12.87 (E3)

Tian,North America

ASM = 0.214*Wt + 0.144*Ht - 0.071*Age - 12.70 (E4)

Visvanathan, Australia

ASM = 0.353*Wt - 0.621*BMI ─ 0.023*Age + 15.14 (E5)

Kulkarni, India

ASM = 0.2*Wt + 0.14*Ht - 0.045*Age - 13.43 (E6)

Wen, China

ASM = 0.193*Wt + 0.107*Ht - 0.037*Age - 6.79 (E7)

Women

Tian, North America

ASM = 0.229*Wt + 0.081*Ht - 0.055*WC - 0.024*Age - 5.14 (E8)

Lee, Korea

ASM = 0.21*Wt + 0.09*Ht - 0.037*WC - 0.002*Age ─ 7.82 (E9)

Tian, North America

ASM = 0.184*Wt + 0.103*Ht - 0.033*Age - 10.11 (E10)

Tanko, Denmark

ASM = 0.11*Wt + 0.161*Ht - 0.05*Age - 13.3 (E11)

Visvanathan, Australia

ASM = 0.353*Wt - 0.621*BMI - 0.023*Age + 10.05 (E12)

Furushima, Japan

ASM = 0.138*Wt + 0.155*Ht - 16.29 (E13)

Kulkarni, India

ASM = 0.17*Wt + 0.10*Ht - 0.028*Age - 9.85 (E14)

Wen, China

ASM = 0.193*Wt + 0.107*Ht - 0.037*Age - 10.95 (E15)

The same equations are used for the Study Population and the Reference Population, which address the corresponding body weights in the formula.

A dataset of 44 men and 64 women was analysed with regard to their muscle mass processed by the DBA system. Characteristics of participants are presented in Table 1, stratified by sex (Table 1). Details about the Ref. Population have been previously published (10, 5). The Ref. Weight plus ΔFM plus Δ SMM equals the Actual Weight.

Age ranged between 18 and 72 years. All the subjects had a BMI ≥29.7 (kg/m^²). Men had greater height, weight, waist and hand circumferences but age, BMI and ΔSMM, notably if adjusted to height (ΔSMMI), were similar regardless of sex. In detail, the mean values of ΔSMM as an estimate of muscle mass increase calculated by the DBA-system were 11.8 ±3.6 for men and 8.9 ±2.6 for women, respectively. The derived index ΔSMMI revealed values of 3.7 ±1.0 for men and 3.2 ±0.9 for women, respectively.

Pearson`s correlation coefficients (r) between Age and Actual Weight, LBM, ΔSMM and ΔSMMI are -0.01, -0.04, -0.06, and -0.06 for men and -0.16, -0.12, -0.09, and -0.05 for women, respectively. All values are not significantly different from zero (p > 0.05). Consequently, the association (slope) between age and muscle mass adjusted for height (ΔSMMI), calculated as a univariate linear regression model, was not significantly different from zero (ß = 0) for men (p = 0.74) and women (p = 0.72), respectively (Figure 2).

The association between BMI and Actual Weight, LBM, ΔSMM and ΔSMMI are presented for men and women in Figure 3 (Figure 3a – Figure 3h).

The graphical representation shows a linear relationship for all the parameters. The equations of the corresponding regression lines are given in Table 2. The indicated regression coefficient represents the slope ß, which is a measure of the contribution of muscle mass toward the corresponding BMI. A positive relationship is represented by a rising (ß > 0) regression line. The t-test revealed significant rising slopes for all the anthropometric parameters (p < 0.001).

Actual Weight includes fat mass and presents in comparison with BMI a goodness of fit described by coefficient of determination (R^²) of 0.78 for men and 0.77 for women, respectively. This value decreases to 0.39 and 0.35 for men and women, respectively, concerning LBM and increases again, when only the increase in muscle mass is considered, in particular, when it is adjusted by height^² (ΔSMMI), to a level of 0.77 for men and 0.76 for women, respectively. This process of transformation reduces the variance of residues (SEE) from 2.74 to 2.04 for men and from 2.45 to 2.16 for women, if the outlier is not considered (Figure 3h).

In summary, severe obesity induces a mean increase in muscle mass in a magnitude of 11.8 kg for men and 8.9 kg for women, as deduced from the DBA model, showing a linear relationship to BMI and a low variability between both parameters. However, as emphasized, this is a model and raises the question of validity: does the study evaluates what it is intended to evaluate? For this reason, the data are compared with DXA-based muscle mass analysis data from 7 studies performed in 7 countries including 15 formulas and adapted to the Study and Reference Population.

The results are presented in Table 3 for men and Table 4 for women. The formulas E1, E2, and E3 for men and E8 and E9 for women include WC measurements. The mean values of E1, E2, and E3 are equal (p = 0.55) for men and those of E8 and E9 are equal (p = 0.08) for women, tested by ANOVA. The formulas E4-E7 for men and E10-E15 for women show a heterogeneous picture between different countries. The mean values are significantly different (p < 0.005), for both men and women of the Study Group and the Reference Group as well, as tested by ANOVA.

The mean ASM value ±SD of all the formulas is 34.6 ±1.2 kg for the Study Population and 25.1 ±0.7 kg for the Ref. Population resulting in a difference of 9.5 kg compared to 11.8 kg derived by the DBA model with reference to the male population. Concerning the female population, the mean ASM value ±SD of all the formulas was 24.7 ±1.0 kg for the Study Population and 17.1 ±0.8 kg for the Ref. Population resulting in a difference of 7.6 kg compared to 8.9 kg derived by the DBA model.

If the ASM values are adjusted to the SMM tissue in a magnitude of +20%, the results are 11.4 kg vs. 11.8 kg for men and 9.1 kg vs. 8.9 kg for women, respectively, when the DXA derived results are compared with the DBA model.

Skeletal muscle mass, a key component of human body composition, is highly correlated with physical function and health status 16. Sarcopenia, characterized by the loss of skeletal muscle mass and strength with age, has been associated with low endurance capacity, physical disability, poor quality of life and death. 17. Therefore, accurate and practical measurement of skeletal muscle mass is important for research and clinical practice related to sarcopenia. Appendicular skeletal muscle mass (ASM) measured by DXA is a relevant indicator of body muscle mass, and is widely used in the diagnosis of sarcopenia 18. However, CT, MRI and DXA are impractical for large epidemiological studies because of their high cost, radiation exposure and lack of access to technical equipment. Simple, valid, reliable and inexpensive methods for measuring skeletal muscle mass are still needed. A practical alternative for estimating muscle mass could be anthropometry.

The present study investigated the impact of obesity on the development of SMM. Figure 3 demonstrates an increase in the association (R^² and SEE) between Actual Weight, LBM, ΔSMM and ΔSMMI with BMI. The result underlines that the relationship between BMI and SMM becomes more specific, when body weight is virtually stripped of fat mass and organs and normalized for height squared (for discussion see 5). Other studies have reported that skeletal muscle mass measured by MRI increases with body weight, but the data were not height adjusted 19. The increase in muscle mass is speculated to be the result of impaired obesity-associated insulin resistance with increased chronic insulin levels, which may stimulate muscle hypertrophy through an enhanced protein synthesis 20. A histogram shows that a cluster of BMI values (25 < 40 kg/m^²) associated with increasing amounts of muscle mass (kg) is significant (ANOVA), but no further characterization (mean values, correlation, regression) is reported 20.

Pearson´s correlation coefficients between Age and Actual Weight, LBM, ΔSMM and ΔSMMI, did not significantly differ from zero (p > 0.05) and showed no signs of decrease with age (Figure. 2), meaning that there is no association between age and muscle mass up to a life-span of 65 years. This result is consistent with the observation that there is a curvilinear relationship between age and SMM, with a change in the slope of the regression line occurring approximately at 45 years of age in both men and women 21.

The IMAT compartment assessed as the percentage difference between ASM (kg) and total body SMM (kg), was estimated to be 20% in our study group for men and women. These results far exceed the values measured in subjects with anorexia nervosa (1.4%) and male and female athletes (approximately 11.0%) (9, recalculated from Table 2). The data highlight the impact of nutritional status as a variable on muscle structure. Our data support the finding that greater adiposity is accompanied by enlargement of the SMM compartment, meaning that people who are overweight have more SMM in terms of age and height than normal weight people do 22.

This is a very tempting result, as it suggests a linear association of the IMAT from anorexia nervosa (1.4%) to obesity (20%). However, the results are based on a heterogeneous picture of equations. It cannot be excluded that the calculated ΔSMM values of the DBA model for women (8.9 kg) equal those of the DXA-derived results, e.g., the difference between the Tian equations (E8-E10 = 8.7 kg), suggesting that the calculated muscle mass of the DBA model resembles that of an IMAT-free structure. The answer to this question is reserved for future investigations and is of crucial interest, as IMAT was found to be a significantly higher independent correlate of insulin resistance in premenopausal African Americans than in their white counterparts 19.

Obesity is associated with functional limitations in muscle performance. There is a consensus that individuals of obesity, regardless of age, have greater absolute maximal muscle strength than normal-weight individuals do, suggesting that increased adiposity acts as a chronic overload stimulus on antigravity muscles. For discussion see Tomlinson et al. 3. The question therefore arises as to whether individuals, who have been overweight for many years, increase muscle strength in the lower limbs by carrying more inert mass during daily activities.

One of the first studies to investigate the effects of obesity on muscle strength in an adult population was conducted by Hulens et al. 23. The authors reported that women with obesity had significantly higher isokinetic knee extension, trunk extension, flexion and rotational torque than lean individuals, whereas no impact of obesity was found on handgrip strength. The importance of age classification and its effect on muscle strength has been demonstrated in a separate study, which accounted for the confounding age factor and reported that older people of obesity (41-65 years) had significantly lower knee extension isokinetic torque than their younger counterparts (18-40 years) 24. This is inconsistent to our results, which revealed no correlation between age and a number of different weight variables (see Figure. 2), indicating that there might exist a discrepancy between muscle mass and muscle strength.

The reason for this observation may be the above-described relationship between adiposity and the accompanying enlargement of the SMM compartment by fat (IMAT), resulting in a disturbed physiology of muscle structure. This assumption is supported by a study showing that increased muscle mass as a result of obesity is not associated with muscle strength 20.

Thus, the effect of obesity on skeletal muscle size, structure and function appears to be a dynamic process involving possible interactions with aging effects, physical activity and fat tissue alterations and remains to be elucidated. Unifying prediction equations including the aforementioned variables might have limitations here, as they describe, at the end, the investigated study population. This impression is supported by leave-one-out validations coming to the point that developed regression equations have high validity when applied to samples of subjects similar to the one on which they were developed 9.

Reference values for SMM vary widely depending on the outcome parameter and reference population. The adverse effects of obesity on muscle quality and function require the normalization of SMM for fat mass, but all current definitions disregard, thus far, the relationship between fat mass and lean mass. For this reason, an attempt has been made to provide novel BMI-dependent SMMI cut-offs 4. The degree to which DBA-derived SMMI results are equal to these values, needs to be analyzed in future studies.

To answer these questions, it becomes clear that the DBA model could provide a unifying platform for further studies to be conducted under standardized conditions. Furthermore, as the DBA model is based on a reference population, whose traits were developed decades ago, it has the characteristic of a time capsule simulating a longitudinal study. The model thus fulfils the criteria required by Wen 14, for example, to be simple, valid, reliable and inexpensive for measuring skeletal muscle mass and does not require access to expensive instruments.

To the best of our knowledge, this is the first study to demonstrate a linear relationship between increasing fat mass and muscle mass. The only data pointing in the same direction can be found in the supplementary material of Hwaung et al. 22.

Our study has several limitations. First, the main limitation of the study is that the results compared with those of the DXA-derived equations are based on descriptive statistics. In particular, the quantification of the IMAT needs to be confirmed by future studies that include anthropometric parameters such as waist circumference, as already proposed by Tian et al. 13, and a trait of skeleton frame such as hand circumference. Second, this study included people with morbid obesity who were candidates for bariatric surgery, which may cause selection bias. Third, our study population did not show a decrease in muscle mass with age. However, most of the equations used in this comparative study include a term for age, and it is questionable whether the validated equations remain accurate with age 8. This factor has the potential to introduce selection bias and limits the generalisability of the results.