Derivation and validation of simple equations to predict total muscle mass from simple anthropometric and demographic data

Background: Muscle mass reflects and influences health status. Its reliable estimation would be of value for epidemiology.

Objective: The aim of the study was to derive and validate anthropometric prediction equations to quantify whole-body skeletal muscle mass (SM) in adults.

Design: The derivation sample included 423 subjects (227 women) aged 18–81 y with a body mass index (BMI; in kg/m2) of 15.9–40.8. The validation sample included 197 subjects (105 women) aged 19–83 y with a BMI of 15.7–36.4. Both samples were of mixed ethnic/racial groups. All underwent whole-body magnetic resonance imaging to quantify SM (dependent variable for multiple regressions) and anthropometric variables (independent variables).

Results: Two prediction equations with high practicality and optimal derivation correlations with SM were further investigated to assess agreement and bias by using Bland-Altman plots and validated in separate data sets. Including race as a variable increased R2 by only 0.1% in men and by 8% in women. For men: SM (kg) = 39.5 + 0.665 body weight (BW; kg) − 0.185 waist circumference (cm) − 0.418 hip circumference (cm) − 0.08 age (y) (derivation: R2 = 0.76, SEE = 2.7 kg; validation: R2 = 0.79, SEE = 2.7 kg). Bland-Altman plots showed moderate agreement in both derivation and validation analyses. For women: SM (kg) = 2.89 + 0.255 BW (kg) − 0.175 hip circumference (cm) − 0.038 age (y) + 0.118 height (cm) (derivation: R2 = 0.58, SEE = 2.2 kg; validation: R2 = 0.59, SEE = 2.1 kg). Bland-Altman plots had a negative slope, indicating a tendency to overestimate SM among women with smaller muscle mass and to underestimate SM among those with larger muscle mass.

Conclusions: Anthropometry predicts SM better in men than in women. Equations that include hip circumference showed agreement between methods, with predictive power similar to that of BMI to predict fat mass, with the potential for applications in groups, as well as epidemiology and survey settings.


Alex’s Notes: Our body mass is a composite of skeletal muscle, fat mass, organs, bones, fluid, etc. Knowing one’s body composition has many implications in health and performance, but the most accurate methods (DXA, bod-pod, MRI) are expensive and impractical for most people. However, anthropometric measurements are simple, quick, safe, noninvasive, cheap, and readily accessible. Unfortunately, they are less accurate and can be influenced by numerous variables not the least of which is the skill of the person doing the measurements. Regardless, they are quite useful for observational studies and some clinical settings as well.

The researchers of the current study sought to create an equation based on anthropometric variables that could predict the amount of skeletal muscle an individual has. This is no different than the various equations for estimating energy expenditure. To do so, a total of 423 men and women aged 18-81 years old with BMIs ranging from 15.9-40.8 that were free of disease from previous studies were used to formulate the equations from their anthropometric measurements. To test the validity of the equations, a second group of 197 men and women (18-83 years old; 15.7-36.4 BMI) who were ambulatory nonsmokers, free of medical conditions or metabolic characteristics that could affect the variables under investigation, and not regularly engaging in vigorous exercise underwent whole-body MRI scans for a skeletal muscle mass comparison to the equations created from the first group.

For both groups the average age was roughly 42-years, and the BMI was just over 25. Notably, all of the most powerful prediction equations included hip circumference as a significant independent variable, although bodyweight was the most powerful predictor of skeletal muscle mass. The equations had negligible improvements when race was included as a variable, and were far more accurate for men than women. In men, the equation had a predictive power of 76% and an error range of 2.7kg, while women had a predictive power of only 58% and an error range of 2.2kg. In both, the equations consistently underestimated skeletal muscle in those with more of it and overestimated skeletal muscle in those with less of it. With all this in mind, the equations are below.

  1. For men: Skeletal Muscle Mass (kg) = 39.5 + 0.665 body weight (kg) − 0.185 waist circumference (cm) − 0.418 hip circumference (cm) − 0.08 age (y)
  2. For women: Skeletal Muscle Mass (kg) = 2.89 + 0.255 body weight (kg) − 0.175 hip circumference (cm) − 0.038 age (y) + 0.118 height (cm)

Anthropometric measurements are as follows,

  • the waist was measured midpoint between the lowest rib and the upper border of the iliac crest;
  • hips were measured at the level of the pubic symphysis and the greatest gluteal protuberance;

So for kicks let’s see how it plays out.

  • Bodyweight = 160 lbs / 2.2 kg/lb = 72.73 kg
  • Waist circumference = 32 inches * 2.54 cm/inch = 81.28 cm
  • Hip circumference = 37 inches * 2.54 cm/inch = 93.98 cm
  • Age = 22 years
  • Skeletal muscle mass = 39.5 + .665(72.73) - .185(81.28) - .418(93.98) - .08(22)
    • Skeletal muscle mass = 31.79 kg = 69.93 lbs

The above result may seem surprising, and it was to me at first. With the error range, I could be anywhere between 64-76 lbs of skeletal muscle, although the equation did likely underestimate rather than overestimate. I recently had a DXA scan tell me that my lean body mass was 150 lbs, so the difference must be my bones, organs, and fluids. Not sure how useful the information is to me, but still interesting.

Have fun.

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