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28 February 2023: Clinical Research  

Proposal for a Simple Equation for Limb Muscle Weight Calculation

Yasutaka Kurokawa12ABCDE*, Takayuki Kurokawa3BCDEF, Misato Fujii4B, Masatoshi Tanifuji5B, Takashi Nakajin6B, Tsukasa Sato7B, Ikuko Machida4B

DOI: 10.12659/MSM.938606

Med Sci Monit 2023; 29:e938606



BACKGROUND: Although body mass index (BMI) is currently being utilized frequently as an indicator of obesity, it provides little information concerning body composition; key components such as fat and muscle cannot be differentiated. It is especially non-sensitive in identifying muscle mass, which can be challenging to examine without the use of radiologic methods. We sought to identify whether biometric values such as upper arm subcutaneous fat thickness/circumference could provide an adequate indicator of muscle mass.

MATERIAL AND METHODS: Patients admitted to our clinic for various causes were retrospectively studied in 95 consecutive cases. Physical parameters including upper arm subcutaneous fat thickness, upper arm circumference, weight, and height were measured. Then, values such as limb muscle weight (LMWDXA) and total fat weight (FWDXA) were obtained from dual-energy X-ray absorptiometry. Pearson’s correlation coefficients were calculated and linear regression analysis was conducted.

RESULTS: Neither upper arm subcutaneous fat thickness nor upper arm circumference was correlated with LMWDXA. FWDXA also showed a correlation with BMI (r=0.823, P<0.001). LMWDXA also significantly correlated with measured body weight (BWm)-BMI (r=0.719, P<0.001).

CONCLUSIONS: From our analytic data we propose an equation for calculating muscle mass, designated the Simple Muscle Weight (SMW): SMW=289.2×(BWm-BMI)+3631. SMW calculation has potential for use as an easy and simple first-line diagnostic tool to identify diminished muscle mass.

Keywords: Body Mass Index, sarcopenia, Humans, Retrospective Studies, Muscles, Upper Extremity, Body Weight


Overall health in older patients is influenced by the degree of decrease in muscle mass [1]. Despite the fact that methods of diagnosis vary, from measuring walking speeds and grip strength to radiological investigations, the majority of these methods have faced difficulties, due to the myriad of tests or parameters required [2,3].

Theoretically, diminished muscle volume can be diagnosed easily by radiological modalities such as computed tomography, magnetic resonance imaging, and/or dual-energy X-ray absorptiometry (DXA). These methods are practically not available in the majority of smaller clinics, and the demand for a simple method is high.

We aimed to assess the statistical correlations between biometric values such as weight, height, upper arm subcutaneous fat thickness, and upper arm circumference to find a combination of parameters that correlates with the values obtained by DXA scans such as total fat weight (FWDXA) and limb muscle weight (LMWDXA).

Material and Methods


FWDXA and LMWDXA of all 4 limbs were measured by DXA [5] using a PRODIGY Fuga Advance system (GE Healthcare, Chicago, Illinois, USA) with enCORE: Ver. 17 SP1 software.


Statistical analysis was performed using JSTAT: Ver. 22.0E [6]. The Pearson’s correlation coefficient and probability values were determined for each of the physical parameters compared with the values obtained using DXA. Probability less than 0.01 was regarded as significant.



The gender distribution in the 95 cases was 27: 68 for Men: Women, respectively. BMI, upper arm subcutaneous fat thickness, and upper arm circumference were measured (mean±standard deviation) as seen in Table 2.

Age ranged from 47 to 102 years of age (85±8.3). Measured body weight (BWm) ranged from 26.8 to 64.0 kg (43.1±8.17). Height ranged from 134 to 175 cm (153±8.85). BMI ranged from 11.6 to 28.1 kg/m2 (18.4±3.18). Upper arm subcutaneous fat thickness ranged from 0.6 to 18 mm (7.9±4.0). Upper arm circumference ranged from 12 to 27 cm (20±3.0).

The mean values as measured by DXA were as follows: FWDXA was 3563–25 823 g (11 823±5203.9) and LMWDXA was 6951–17 595 g (10 772±2388.2).


Upper arm subcutaneous fat thickness was significantly correlated with BMI (r=0.558, P<0.001) and FWDXA (r=0.666, P<0.001). Upper arm circumference was also significantly correlated with BMI (r=0.629, P<0.001) and FWDXA (r=0.743, P<0.001) (Table 3).

In contrast, upper arm subcutaneous fat thickness had no correlation with LMWDXA (r=0.163, P=0.114). A moderate correlation, however, was suggested between upper arm circumference and LMWDXA (r=0.458, P<0.001).


Since upper arm subcutaneous fat thickness and circumference did not significantly correlate with LMWDXA but did correlate with FWDXA, we tested the correlation between BMI and FWDXA. As a result, we found that BMI does correlate significantly with FWDXA (r=0.823, P<0.001) (Figure 1). The linear correlation suggests that BMI can mathematically substitute for FWDXA in the studied population. Therefore, we additionally hypothesized that there may be a correlation between LMWDXA and the difference between BWm and BMI (BWm-BMI) (Appendix 1).

Since LMWDXA correlated significantly with (BWm-BMI) (r=0.719, P<0.001), in our subjects, we can regard (BWm-BMI) as muscle mass, which might help to predict sarcopenia (Figure 2).

In conclusion, we propose the Simple Muscle Weight (SMW) equation [SMW=289.2×(BWm-BMI)+3631] as a possible first-step indicator of muscle mass.



While DXA remains unchallenged as the criterion standard for measuring muscle mass, emerging modalities have been identified to be useful in the identification of sarcopenia, but with certain difficulties [12]. Although ethnic and disease-specific modifications apply, the accuracy of DXA has been backed by numerous research studies in the literature [13].

The use of radiological measurement to obtain accurate values requires special equipment and qualifications, compared with the cheaper and lighter devices used for impedance adipometry [14] and ultrasonic measurement of muscle thickness [15].


A common way to start the initial investigation for sarcopenia is measurement of the patient’s calf circumference, grip strength, and ambulatory abilities, which can be inaccurate and inconsistent in patients with physical disabilities. Functional tests such as the Sit to Stand test, 30-second Chair Stand Test, muscle strength, physical performance, and physical functioning have also been examined to determine the loss of muscle mass in the elderly [16]. These functional tests give quantitative and descriptive analyses of the patient population, with numerous modifications requiring adjustment for different patient populations [17].


The lack of availability of a way to easily measure muscle mass has resulted in increased use of non-radiological methods. Fayh et al [18] and Evans et al [19] have proposed methods using biochemical markers. Other markers, such as blood albumin levels and molecular markers, have been speculated to reflect the existence of diminished muscle mass. Although these biomarkers have the potential to aid in the diagnosis of decreased muscle mass, difficulties remain, including coverage of the costs, difficulty/lack of accessibility, and patient cooperation.


While there is a substantial body of literature examining the relationship between BMI and fat weight, the estimation of body composition without the use of radiological or biochemical methods seems to be challenging.

Our study showed significant correlations between FWDXA and upper arm subcutaneous fat thickness and/or circumference. More importantly, BMI was significantly correlated with FWDXA. These findings are in accord with the international literature, especially when measured by impedance adipometry or DXA [20].

To better understand the dynamic relationship between FWDXA and BMI, we re-examined the correlations between these parameters, and found that LMWDXA is also significantly correlated with (BWm-BMI). From this correlation and the linear regression, the equation SMW=289.2×(BWm-BMI)+3631 was devised. This equation serves as a way, by applying it as a relative index, to identify underlying muscle mass. In Figure 3 we see a large portion of patients’ LMWDXA indicating low muscle mass. Even when BMI offered no information on sarcopenia in these patients, the results of the SMW calculation showed that most patients were sarcopenic. Indeed, the majority of the patients in our study were admitted with limb fractures caused by falls, and pneumonia – conditions which are highly associated with sarcopenia [21,22].

On the other hand, patients with low BMI did not necessarily show low LMWDXA, as can be seen in Figure 4. High BMI did not necessarily mean that the patients did not have diminished muscle mass; some patients with relatively high BMI even presented with low LMWDXA. This is important, since obesity coexisting with sarcopenia, known as sarcopenic obesity, can lead to especially high morbidity in the elderly [23].


Although our study suggested that muscle weight could be roughly calculated without radiographic, biochemical, or functional data, there were a few factors that it did not take into consideration. While SMW appears to be able to be calculated on the basis of body weight and BMI for a homogenous population, we have yet to understand modifying factors, as well as the accuracy of SMW in different ethnicities. Our subject population was mostly elderly patients, but it would be interesting to observe whether the same principles apply in younger, healthier patients as well. Male and female differences should also be considered, and modifying factors must be addressed and identified.

Clinical pictures based on multiple parameters are of the utmost importance, and assessment for risk of falls, debilitation, and ambulatory function should also be considered if SMW is to be applied in a realistic clinical situation, where indication of therapy would be determined on its basis.


From our analytic data we propose the possibility of calculating muscle mass as a variable called the Simple Muscle Weight. The equation is: SMW=289.2×(BWm-BMI)+3631. SMW calculation has the potential to be used as an easy and simple first-line diagnostic tool to identify diminished muscle mass.


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