Muscle area estimation from cortical bone


  • Astrid Slizewski,

    Corresponding author
    1. Paleoanthropology, Department of Early Prehistory and Quaternary Ecology, Senckenberg Center for Human Evolution and Paleoenvironment, Eberhard Karls University of Tübingen, Tübingen, Germany
    • Correspondence to: Astrid Slizewski, Paleoanthropology, Department of Early Prehistory and Quaternary Ecology, Senckenberg Center for Human Evolution and Paleoenvironment, Eberhard Karls University of Tübingen, Tübingen, Germany. E-mail:

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  • Eckhard Schönau,

    1. Klinik und Poliklinik für allgemeine Kinderheilkunde, Klinikum der Universität zu Köln, Cologne, Germany
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  • Colin Shaw,

    1. University of Cambridge, PAVE Research Group and The McDonald Institute for Archaeological Research, Cambridge, UK
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  • Katerina Harvati

    1. Paleoanthropology, Department of Early Prehistory and Quaternary Ecology, Senckenberg Center for Human Evolution and Paleoenvironment, Eberhard Karls University of Tübingen, Tübingen, Germany
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This article investigates the relationship between the cortical bone of the radius and the muscle area of the forearm. The aim of this study was to develop a method for muscle area estimation from cortical bone area at 65% of radius length where the muscle area at the forearm is largest. Muscle area and cortical area were measured directly in vivo by peripheral Quantitative Computed Tomography (pQCT). We found significant correlations between muscle area and cortical area (r = 0.881) in the forearm that are in line with previous studies. We have set up a regression model by testing relevant parameters such as age, sex, forearm length, and stature that were all highly correlated to muscle area. The influence of age and sex on the proportion of muscle area to cortical area is strong and potentially related to the effects of testosterone and estrogen on the muscle-bone-unit. Muscle area estimation from cortical bone is possible with a Percent Standard Error of Estimate (%SEE) ranging from 12.03% to 14.83%, depending on the parameters available and the age and sex of the individual. Muscle area estimation from cortical bone can provide new information for the study of skeletal and/or fossil human remains. Anat Rec, 296:1695–1707, 2013. © 2013 Wiley Periodicals, Inc.

This article presents the results of a study that investigates the relationship between the cortical bone of the radius and the muscle area of the forearm. The underlying question of the study is whether it is possible to reasonably estimate muscular properties of the forearm from the cross sectional properties of the forearm bones, and if so, which parameters are required for such an estimation. We hypothesize that cortical bone cross-sectional area can predict muscle cross-sectional area, and that such estimations of muscle area could provide valuable information for the study of human skeletal remains. Therefore, we aim to develop a prediction model for muscle area from cortical area.

Paleoanthropologists, prehistoric human biologists, and forensic anthropologists almost always rely on skeletal material alone for the reconstruction of body shape and physical capabilities of fossil hominines, prehistoric humans, or unidentified recent skeletal human remains. The reconstruction of soft tissue properties from bone has therefore always been an aim in anthropology, from early attempts to assess the muscularity of Neanderthals from their postcranial dimensions (Klaatsch, 1901; Heim, 1976) to comparative studies on primates (e.g., Baumann, 1926; DeRousseau et al., 1983; Marzke et al., 1999) and modern in vivo studies on muscle activity using electromyography (Wall-Scheffler et al., 2010) or 3D neuromusculoskeletal models for fossil hominids (Nagano et al., 2005). It has also been recognized that data on postcranial muscle tissue might provide anthropologists with valuable information on physical strength, metabolic costs, body shape, and lifestyle of individuals and/or populations (e.g., Miller, 1932; Reynolds and Asakawa, 1950; Tobias, 1972).

General consensus today (Korhonen et al., 2012; McCarthy et al., 2012; Nilsson et al., 2012) agrees with the long held conviction of anatomists (von Meyer, 1867; Roux, 1881; Wolff, 1892) that the geometry of long bone shafts is influenced by the loadings placed on the skeleton during lifetime. On the basis of this relationship researchers often reconstruct activity patterns of fossil hominines and prehistoric humans (Ruff et al., 1993; Stock and Pfeiffer, 2001; Shackelford, 2007). Muscular strength, on the other hand, has been assessed by measuring the size of joints (Wolpoff, 1999; Katzenberg and Saunders, 2000), and the shape and perimeter of long bone diaphyses (Genovés, 1967; Wolpoff, 1999; Weaver, 2003). Although enthesopathies are the basis on which muscular properties are most frequently discussed (Plummer, 1984; Stirland, 1993; Churchill and Morris, 1998), it remains unclear how the interaction between various factors influences their development (Churchill and Morris, 1998; Stirland, 1998) despite growing work on the topic (Robb, 1998; Stirland, 1998; Wilczak, 1998; Weiss, 2003). Genetic factors may also influence the degree of expression of enthesopathies (Churchill and Morris, 1998), making it even more difficult to determine the influence of muscular strength on them. Another problem inherent in evaluating muscular strength from enthesopathies is the subjectivity of the visualization system that has been used to characterize them (e.g., Robb, 1994; Hawkey and Merbs, 1995). Efforts to develop an objective, quantitative technique for rating enthesopathies provided results that are inconsistent within and among individuals, and with other indicators of physical strength (Plummer, 1984; Stirland, 1993; Churchill and Morris, 1998; Wilczak, 1998). Therefore, the statistical analysis of the degree of expression of enthesopathies remains a difficult task (Robb, 1998) even though some recent studies that take into account the current anatomical understanding of muscle insertion sites have provided promising results (Benjamin et al., 2002; Villotte, 2006; Havelková and Villotte 2007; Villotte et al., 2010). Other studies (Ruff and Runestad, 1992; Trinkaus et al., 1994) have demonstrated that articular surfaces, and perhaps the entire joint, are less “plastic” than the diaphysis. Articular size does not seem to change in response to alternating mechanical loadings in adults, but the cross-section of the diaphysis does (Ruff et al., 1991). Furthermore, evolutionary changes in joint morphology appear more slowly than changes in the diaphysis (Ruff et al., 1993), which might indicate that genetic factors could influence the shape and size of articular surfaces.

Bone cross-sections can provide insights into the mechanical properties of long bones, and can give information about the peak forces (bending, torsion compression, and tension) that have been placed on the bone during a lifetime (Lovejoy et al., 1976; Ben-Itzhak et al., 1988; Grine et al., 1995; Churchill et al., 1996; Pfeiffer and Zehr, 1996; Pearson and Grine, 1997; Katzenberg and Saunders, 2000; Stock and Shaw, 2007; Shaw and Stock 2009a,b). There are different ways of interpreting bone cross-sectional areas. While some researchers focus on the geometry of the cross-section in order to derive information about the potential distribution of cortical tissue along the shaft (e.g., Trinkaus and Churchill, 1999; Trinkaus and Ruff, 1999; Trinkaus et al., 2006), others place greater emphasis on cross-sectional area size relative to other measurements and estimations such as body mass or limb length (e.g., Ruff, 2000a) or cortical thickness distribution along the shaft (Bondioli et al., 2010). For any analysis of cross-sectional information the choice of the most suitable location(s) along the bone shaft is crucial and can be difficult. As the influences of muscle and bone on each other are not yet fully understood in detail, different approaches may lead to inconsistent results (Roberts, 1978; Collier, 1989; Ruff, 1994). Furthermore, the questions of how to standardize cross sectional properties is a hotly debated one, which has not been definitively solved, yet (for details on discussions and methods see, e.g., Ruff et al., 1991, 1993; Churchill, 1994; Trinkaus and Churchill, 1999; Ruff 2000a,b; Pearson and Liebermann 2004; Ruff et al., 2006; Stock and Shaw 2007).

Julius Wolff was the first to describe the relationship between bone loss or gain and muscular activity (Wolff, 1892). Since then, the processes of modeling and remodeling of bone have been described in more detail through the Mechanostat Model (Frost, 1960), the Functional-Muscle-Bone-Unit concept (Schoenau and Frost, 2002; Schoenau, 2005), and the Bone Functional Adaptation principle (Ruff et al., 2006). The Mechanostat Model comprehensively extends and refines Wolff's law. It defines four stages of bone response (Disuse, Adapted State, Overload, and Fracture), and introduces the terms “modeling” for the build-up of bone mass and “remodeling” for the adaptive processes without a gain of bone mass (Frost, 1960). Some researchers argue against the restrictive nature of the Mechanostat Model (Carter and Beaupre, 2001) and have proposed the existence of several, independently acting Mechanostats (Skerry, 2006). The Functional-Muscle-Bone-Unit concept explains the regulatory circuit of bone adaptation on a cellular level (Schoenau et al., 1996). It was published as a diagnostic tool for clinical evaluation of bone health and strength (Fricke and Schoenau, 2007). Some researchers have proposed additional ways of refining the Functional-Muscle-Bone-Unit concept by skeletal compensation mechanisms (Sugiyama et al., 2002). The Bone Functional Adaptation principle pointed out that even though juvenile bone is more responsive to mechanical loading than adult bone, the mechanical properties of adult bone are not simply a reflection of loading on the bone during childhood and adolescence. Rather, adult bone properties are the result of several factors including genetics as well as past and more recent mechanical demands on the bone, and properties vary between skeletal locations (Ruff et al., 2006). However, there is a broad agreement that muscular activity and cortical thickness are strongly correlated, and that, in a healthy subject, there is a strong relationship between muscle area and cortical area (Frost and Schoenau, 2000; Schoenau, et al., 2002).

Previous work has shown that muscular function and anatomy dominate the mechanisms that determine the strength of load-bearing bones in humans after birth (Frost and Schoenau, 2000), and possibly even in utero (Rauch and Schoenau, 2001). Still, other factors such as gravitational loading might also influence the response of bone to mechanical signals (Judex and Carlson, 2009) even though evidence is scarce. Other studies have also shown that cortical area and muscle area are strongly correlated in all living mammals (Runge et al., 2002), and that muscle area and bone area are highly correlated (r > 0.93) in the human forearm and lower leg (Schießl and Willnecker, 1998). The capability of an individual to produce force is determined by the properties of his or her muscles (e.g., muscle mass, muscle cross-sectional area) and the lever arm of the limb (limb bone length). Therefore, estimation of muscle cross-sectional area could provide a crucial parameter for determining the physical capabilities of an individual.

The implications of these medical studies, Wolff's Law, and the Mechanostat Model are that it should be possible to reconstruct muscle from bone. In this study, the question of muscle reconstruction from bone is addressed using a large in vivo sample to assess the relationship between cortical area and muscle area. We focused on the forearm as a non-weight-bearing limb in order to minimize the influence of locomotor loading and body weight on the results (Ruff and Hayes, 1983; Brock and Ruff, 1988; Collier, 1989; Ruff, 1994; Larsen et al., 1995; Ruff, 1999).


In Vivo Human Sample

Our in vivo sample consists of participants from the “Dortmund Nutritional and Longitudinal designed Study” (DONALD). The non-dominant forearms of 695 healthy subjects aged 5.79–59.95 years were measured at the Universitätsklinikum Köln using a Peripheral Quantitative Computed Tomography (pQCT, XCT-2000, Stratec Medizintechnik GmbH, Pforzheim, Germany) at 4% and 65% of forearm length (Fricke et al., 2008). Measured parameters in the forearm included cortical area and muscle area at each location (4% and 65%). The study was approved by the Ethics Committee of the University of Cologne and the Bundesamt für Strahlenschutz (Federal Agency for Protection of Radiation). Table 1 displays the distribution of age and sex within the sample population. Data on nutrition, height, sex, weight, and life history was recorded for each individual. The study population was comprised mainly of individuals from German middle-class families. All participants were of European background.

Table 1. Composition of study sample
SexAgeTotal number
5–6 years7–12 years13–20 years20–40 years40–60 years


pQCT provides information on cortical bone area, cortical bone density, bone geometry, and mechanical properties including bending strength, all calculated from the density and geometry of a 2D cross-sectional image. In living humans, pQCT scans also provide information on soft tissue area (muscle and fat). The Stratec software automatically differentiates between different types of hard and soft tissues by thresholds and absorptiometric density. In this study the threshold for cortical bone was defined as 710 mg/cm3 and muscle was defined as an absorptiometric density of 20 to 60 mg/cm3. Detailed descriptions of the pQCT technology are available in Jämsä et al. (1998), Schießl et al., (1998), Schießl and Willnecker (1998), Sievänen and Vuori (1998), Leonard et al., (2004), Kalender (2005), and Shaw and Stock (2009). The Stratec XCT 2000 works with a constant high voltage of 60kV and a low radiation of only 0.3 µSv/CT Slice.

Throughout this article, the terms “cortical/muscle area at 4%/65%” will refer to the measuring sites at 4% and 65% of forearm length starting distally. “Forearm length” was defined as the distance from the ulnar styloid process to the olecranon to facilitate the in vivo clinical determination. In adults, the reference line from which the 4% and 65% measuring sites are determined is placed on the incisura ulnaris to define a homologous anatomical position. Figure 1 shows the placement of the 4% measuring site for individuals with open and closed growth plates. The measuring sites are standard locations for pQCT measurements at the forearm in clinical applications. Those locations have been defined based on the fact that at the distal measuring site (4%) the radius holds more area than the ulna. The 65% measurement site was chosen because the circumference of the musculature of the forearm is largest at that location (Schoenau et al., 2000). At the 65% measuring site, both forearm bones would be equally suitable for analysis, but the radius is preferred in order to perform both standard pQCT measurements of the forearm (4% and 65%) on the same bone (Schneider and Börner, 1991). Figure 2 shows the measurement locations at the forearm. Unfortunately, no data on muscle area at the 4% measurement site was recorded during the DONALD study, even though data on cortical area is available for this measurement site. Therefore, correlations can only be computed against muscle area at 65%.

Figure 1.

Placement of reference line for determining the 4% and 65% pQCT locations in children and adults.

Figure 2.

In vivo pQCT slices at 4% and 65% of forearm length. Schematic view.

All analyses were performed using IBM SPSS Statistics (V.19). The available parameters were checked for normal distribution first, using the Shapiro–Wilk Test. If the null hypothesis of normal distribution is rejected, application of the Pearson Product Moment Correlation can be problematic and non-parametric testing is required (Leonhart, 2010).

Muscle cross-sectional area predictors were checked for correlation with all other predictors before being entered into the regression. This was done so as to reduce the negative effects of multi-collinearity on the quality of the regression (Belsley et al., 1980; Greene, 1993). If two variables were highly likely to represent the same explanatory factor, one was excluded from the model to assure the reliability of the individual predictors. Variables were checked for bivariate correlations using a two-tailed approach. Pearson's Product Moment Correlation (r) was calculated as a parametric test while Spearman's rank correlation coefficient (ρ) was computed as an additional non-parametric test.

Variables were then analyzed by performing multiple linear regression with a confidence interval of 95%. The method was forward to allow for the software to exclude independent variables that would not improve the quality of the model. The dependent variable was muscle area at 65%. The value for a perfect regression model would be a coefficient of determination (r2) of 1. With respect to the predictive power of the model and following Shaw (2010) only values higher than r2 = 0.250 were considered as significant.

All correlation values and regression parameters were analyzed both on unstandardized raw data and on cortical area and muscle area standardized by forearm length. The formula for standardization of muscle area and cortical area by forearm length was adapted from the equation by Marchi and Sparacello (2005):

display math

This method of standardization has been proposed by several authors as an appropriate way of comparing non-weight-bearing upper limb parameters of individuals of different body height and proportions (Ruff et al., 1993; Churchill, 1994; Trinkaus and Churchill, 1999). In medicine, it is common to scale both muscle and cortical area to forearm length, as this method minimizes the potential source of error caused by varying body proportions due to genetic factors, illness or growth patterns. Standardization to body mass or body height might in this case cause a misinterpretation of muscular and skeletal strength and health of an individual (see Fricke et al., 2009). In a previous study (Schoenau et al., 2000), it was found that body mass has no significant influence on muscle area and cortical area of the forearm bones. Accordingly, standardization to forearm length seems to be the appropriate method for this study, although Ruff et al. (1991) found a significant correlation between body mass and cross sectional properties of the weight bearing femur. The results of Ruff et al. (1991) indicate that lower limbs indeed require standardization to body mass, and that for weight bearing bones standardization to bone length might be an oversimplification (Ruff et al. 1993; Ruff 2000a,b).

As further indicators of the model quality, the Standard Error of Estimate (SEE) and the Percent Standard Error of Estimate (%SEE) are indicated. The SEE is a parameter that provides information about the expected accuracy of a prediction equation under the condition that the individual for which a variable is estimated derives from the same population as the study sample on which the regression was based. The SEE is calculated from the square root of the mean residual of the model (Riffenburgh, 2012). The percent standard error of estimate (%SEE) allows for an evaluation across studies by providing a value that makes different units of measurement and varying size ranges comparable. It is an essential criterion for the evaluation of the quality of prediction equations. The %SEE is calculated by dividing the SEE by the mean value of the dependent variable (here: muscle area) of the regression (Ruff, 2007).


The Shapiro–Wilk Test demonstrated that the age distribution within the DONALD sample is not consistent with the null hypothesis, indicating that additional, non-parametric, testing is required beyond the Pearson Product Moment Correlation. There is a data gap with no participants between the age of 23.15 years and 29.65 years, while the majority of participants cluster in two groups: 6–18 years of age and 38–48 years of age. This distribution was to be expected as the sample comprises mainly parents and their children. There is also a slight difference in sex distribution with 44.46% of the sample being male and 55.54% being female. Visualization of muscle area values against age in a scatterplot (Fig. 3) demonstrates that age is related to a rapid increase of muscle mass in children while the effect of age on adult muscle mass is small. This effect has been described previously and is also known for bone area and mineral density (e.g., Schießl et al., 1998; Specker, 2006; Guadalupe-Grau et al., 2009). Therefore, a spline was modeled for the age variable with the knot set at the beginning of the data gap between the young and the older ages at 23.15 years. A spline model is hypothesized when the relationship between a prediction variable and a dependent variable is altered at a certain value along the range of the predictor. The knot is set at a point where a shift in the form of the relationship between the two variables is estimated to take place. Such a change could, for example, be a shift from a quadratic to a linear relationship or from a linear to another linear relationship. The spline allows for the regression line to alter its direction at the knot, while the two directions of this line will be joined where the knot is set (Poirier, 1976; Eubank, 1999; Hurley et al., 2004). A t-test for the computed knot (here: XB1 = Age – 23.15; XB2 = XB12) indicates if there is a significant change in slope at the set knot. The t-test was significant at <0.001.

Figure 3.

The relationship of the variables age and muscle area within the sample.

Spearman's non-parametric rank correlation coefficient was additionally calculated for all variables. Correlation values provided by the Spearman and Pearson tests are very similar for all tested variables (Table 2), indicating that for the present study the Pearson's Product Moment Correlation is applicable, even though age is not normally distributed within the sample.

Table 2. Correlation values for potential predictors against each other
 Raw valuesCA values standardized by forearm length
CA4CA65StatureForearm lengthCA4CA65StatureForearm length
  1. Bivariate correlations, two-tailed, N = 695.

  2. MA65, muscle cross-sectional area at 65% of forearm length; CA65, cortical area at 65% of forearm length.

Radius length0.8050.8340.9631−0.2030.211x1
Radius length0.790.8340.9461−0.1890.185x1

Correlation values between possible predictors of muscle cross-sectional area, standardized and unstandardized, are displayed in Table 2. The high correlations between cortical area at 4% and cortical area at 65% (r = 0.812) on the one hand, and forearm length and stature (r = 0.963) on the other, require the exclusion of one parameter each. Cortical area at 65% (CA 65%) is more strongly correlated with muscle area at 65% than is cortical area at 4%, both when standardized and unstandardized (Table 3). This is a reasonable result as CA 65% is the corresponding anatomical location to muscle area at 65%. Therefore, cortical area at 4% is excluded from the model and was not entered into the regression. Correlation values for stature and muscle area are higher than for forearm length and muscle area. The correlation value for muscle area (65%) and forearm length is low (r = 0.181), while correlation between muscle area (65%) and stature is higher (r = 0.266). Therefore, forearm length was excluded as a predictor and not entered into the regression.

Table 3. Correlation values for potential predictors against muscle area
  1. Bivariate correlations, two-tailed, N = 695.

  2. MA65, muscle cross-sectional area at 65% of forearm length; CA65, cortical area at 65% of forearm length.

Radius length0.1810.813
Radius length0.1970.819

Values entered into the regression were age (with the computed knot at 23.15 years), sex, stature, and cortical area at 65%. All parameters were included into the regression by the software. The prediction model was significant with both unstandardized and standardized values for muscle and cortical area (Sig. ≤ 0.01). The value for the coefficient of determination was higher when values were not standardized by forearm length (r2 = 0.84), but the coefficient for the model using standardized values is also clearly above the defined limit for r2 in this study, indicating a high predictive power (r2 = 0.352). Results of both multiple-regressions analyses are displayed in Table 4. Although absolute values for the SEE differ largely between the two models as an effect of standardization, the %SEE values show that the error of estimate is equally low for both models (%SEE < 12).

Table 4. Results of multiple linear regressions
Depended variablePredictorsAdjusted R2Sig.ConstantCA65SexAgeStatureSEE%SEE
  1. Method: forward, unstandardized, 95% confidence interval.

  2. The subscript “stand” referes standardized by forearm length.

  3. Age spline, XB1 = age – 23.15; XB2 = XB12; RECODE XB1 (LO THRU 0 = 0); CA65, cortical area at 65% of forearm length; MA65, muscle cross-sectional area at 65% of forearm length; SEE, Standard Error of the Estimate; %SEE, Percent Standard Error of the Estimate.

MA65standCA65stand, age spline, sex, stature0.352≤0.00141.64521.216−4.126−0.016−0.0965.68011211.82
MA65CA65, age spline, sex, stature0.84≤0.001−263.08623.502−324.335−0.91311.232341.787110.88

In the analysis of human skeletal remains the variables age, sex, and stature are often only available as estimations. These variables might therefore add potential sources of error to the regression. To evaluate the quality of a muscle area prediction model in which stature, age and/or sex are unknown, the regression was also computed for forearm length instead of stature as a predictor, and without age or/and sex (Table 5). The regression was also computed for age groups (infants I, infants II, juvenile, adult, and mature) instead of known age, as in many cases anthropologists are able to define the age class of an individual but not the exact age at death. Age groups were classified according to Hermann et al. (1989) and entered as values from 0 to 4, with infants I being coded as 0 and mature individuals as 4. As the defined age groups are an ordinal and not a linear variable the computing of a spline is not required here. All regressions displayed in Table 5 are significant at the ≤0.001 level. Replacing stature with forearm length in the equation does not reduce the strength of the relationship determined by the model. The coefficient of determination is slightly lower if raw values for forearm length are used and slightly higher if standardized values for forearm length are used than for the regression including the parameter stature. %SEE is slightly higher for the raw values regression and slightly lower for the standardized values regression when forearm length replaces stature in the model. However, the difference caused by entering forearm length instead of stature into the regression is minimal, with the divergence for r2 being <0.032 and the divergence for the %SEE being <0.29 between the standardized models.

Table 5. Comparison of the results of multiple linear regressions based on varying sets of predictors
Depended variablePredictorsAdjusted R2Sig.ConstantCA65SexAgeAge groupStatureForearm lengthSEE%SEE
  1. Method: forward, unstandardized, 95% confidence interval.

  2. Age spline, XB15age – 23.15; XB25XB12; RECODE XB1 (LO THRU 050); MA65, muscle cross-sectional area at 65% of forearm length; CA65, cortical area at 65% of forearm length.

MA65CA65, age spline, sex, forearm length0.837≤0.001549.09624.821−319.07−1.705××3.927344.809210.97
MA65standCA65stand, age spline, sex, forearm length0.384≤0.00155.17219.579−4.823−0.032××−0.1015.5398611.53
MA65CA65, sex, forearm length0.818≤0.001−768.92229.208−323.911×××7.94443.084314.10
MA65standCA65stand, sex, forearm length0.446≤0.00120.42127.756−4.217×××−0.0016.5835413.70
MA65CA65, age spline, forearm length0.807≤0.001−587.1926.404×−0.342××6.863375.656311.96
MA65standCA65stand, age spline, forearm length0.283≤0.00134.91921.107×−0.011××−0.0455.9789212.44
MA65CA65, stature0.798≤0.001−1536.66229.436×××15.86×466.826814.85
MA65standCA65stand, stature0.398≤0.00111.49627.375×××0.041×6.8634814.28
MA65CA65, forearm length0.796≤0.001−1162.36130.401××××8.448469.389414.93
MA65standCA65stand, forearm length0.394≤0.00113.84128.05××××0.0146.8870514.33
MA65CA65, age group, forearm length0.798≤0.001−1132.86729.475××24.961×8.342467.536714.87
MA65standCA65stand, age group, forearm length0.401≤0.00116.5426.836××0.429×0.0056.8488114.25
MA65CA65, age group, stature0.799≤0.001−1480.56529.022××16.72615.436×466.193114.83
MA65standCA65stand, age group, stature0.402≤0.00114.10526.51××0.3650.025×6.83814.23
MA65CA65, age group, sex, forearm length0.823≤0.001−681.59627.513−354.285×42.683×7.712436.813113.90
MA65standCA65stand, age group, sex, forearm length0.462≤0.00125.12625.903−4.632×0.645×−0.0176.5019513.53

The influence of age and sex on the quality of the model is apparent. If either sex or age are removed from the equation the coefficient of determination decreases by up to 0.093, and %SEE increases by up to 1.48. Thus, the predictive power of the model remains high as long as either sex or age are included in the regression. If both parameters are excluded from the model r2 declines by up to 0.145 and %SEE increases by up to 2.44. Entering age class values to the regression does slightly improve the model (r2 + 0.004; %SEE − 0.1) compared to the parameter age being fully excluded from the regression. A predictive model including both age groups and sex, provides a coefficient of determination that is only slightly lower (−0.059) than that of the original model based on exact numerical age and sex. Additionally, %SEE is only slightly higher (+0.77) for the age-group-plus-sex-model than for the original one.

Table 6 displays the results of single, linear regressions for each parameter predicting muscle area separately. These results indicate that only cortical area can be considered as an appropriate predictor of muscle area on its own. Still, the quality of muscle area estimation from cortical area only (r2 = 0.392) is below that of all combined models. The next best single predictor of muscle cross sectional area was age group (r2 = 0.205).

Table 6. Results of linear regressions predicting muscle area
Depended variablePredictorAdjusted R2Sig.ConstantCoefficientSEE%SEE
  1. Method: forward, unstandardized, 95% confidence interval.

  2. The subscript “stand” referes standardized by forearm length.

  3. CA65, cortical area at 65% of forearm length; MA65, muscle cross-sectional area at 65% of forearm length; SEE, Standard Error of the Estimate; %SEE, Percent Standard Error of the Estimate.

MA65standAge group0.094≤0.00144.6751.3368.4363617.55
MA65Age group0.205≤0.0012558.211230.356926.290729.48
MA65standForearm length0.031≤0.00135.3020.0518.7241718.15
MA65Forearm length0.66≤0.001−3575.03926.586605.846219.28

The influence of sex and age on the quality of the predictive model places special emphasis on the question of how correlations differ between the sexes. Table 7 displays correlation values for muscle area and its predictors in the male and female subsamples. All correlations are higher within the male subsample than within the female. Age is strongly correlated to muscle area in both males and females. In the female subsample, stature and forearm length are not significantly correlated to muscle area, while in the male subsample they are. For females, age is a more important variable in the estimation of muscle area than forearm length or stature. The correlation value for muscle area and cortical area is clearly higher in the male sample (r = 0.555) than in the female (r = 0.298), which indicates that for female subjects an estimation of muscle area from cortical area only is not as reliable as for males.

Table 7. Sex-specific correlations against muscle area
 Male (N = 309)Female (N = 386)
MA 65standMA65MA 65standMA65
  1. Bivariate correlations, two-tailed. MA65, muscle cross-sectional area at 65% of forearm length; CA65, cortical area at 65% of forearm length.

  2. a

    Not significant at the 0.01 level.

Forearm length0.2350.843−0.041a0.737
Forearm length0.2420.79−0.137a0.608

Table 8 shows the results of multiple linear regressions computed for males and females separately. Again, r2 values are higher for the male sample than for the female in every model. Exact numerical age computed as a spline is more important for muscle area prediction in females than in males. While the quality of the model increases for males when age is replaced by age class (r2 = 0.590), it strongly decreases for females (r2 = 0.337). The removal of forearm length as a predictor does impair the quality of the model in females (r2 declines by 0.111), but age is clearly the more important factor. In males, the exclusion of forearm length from the regression lowers the quality of the model only slightly (r2 declines by 0.007).

Table 8. Results of sex-specific multiple linear regressions
Depended variablePredictorsAdjusted R2Sig.ConstantCA65AgeAge classForearm lengthSEE%SEE
  1. Method: forward, unstandardized, 95% confidence interval. Age spline, XB15age − 23.15; XB25XB12; RECODE XB1 (LO THRU 050); MA65, muscle cross-sectional area at 65% of forearm length; CA65, cortical area at 65% of forearm length.

MA65CA65, forearm length, age spline0.875≤ 0.0011313.25931.058−3.516×0.191357.96310
MA65standCA65stand, forearm length, age spline0.441≤ 0.00155.57826.951−0.058×−0.1195.7770711.36
MA65CA65, forearm length, age group0.876≤ 0.001−566.97522.402×279.6946.581432.390412.09
MA65standCA65stand, forearm length, age group0.59≤ 0.00135.76323.297×3.814−0.0776.1167912.03
MA65CA65, age spline0.876≤ 0.0011360.91631.158−3.571××356.94129.98
MA65standCA65stand, age spline0.399≤ 0.00118.27428.9−0.011××5.9929511.78
MA65CA65, age group0.865≤ 0.001616.79227.674×331.155×450.030712.58
MA65standCA65stand, age group0.562≤ 0.00116.9426.097×2.061×6.3347712.46
MA65CA65, forearm length, age spline0.82≤ 0.001726.69216.55−1.522×3.683240.08888.59
MA65standCA65stand, forearm length, age spline0.381≤ 0.00161.35815.346−0.024×−0.1354.457059.73
MA65CA65, forearm length, age group0.691≤ 0.001−290.22623.889×25.0045.843381.101113.64
MA65standCA65stand, forearm length, age group0.337≤ 0.00133.88722.781×0.394−0.0566.133513.39
MA65CA65, age spline0.815≤ 0.0011551.93118.919−2.27××243.55528.72
MA65standCA65stand, age spline0.278≤ 0.00122.46516.9760.02××4.8139610.51
MA65CA65, age group0.675≤ 0.001682.1730.942×23.87×390.647913.98
MA65standCA65stand, age group0.307≤ 0.00121.66921.799×0.25×6.2747213.69


This study found significant correlations between muscle area and cortical area in the forearm and computed different models for muscle area estimation from the cortical bone which are of high predictive power. For all models the coefficient of determination was higher than r2 = 0.250 and therefore all models can be considered as predictively significant. We therefore demonstrated that estimation of soft tissue properties from bone is possible if additional parameters are available. As we focused solely on one location at the forearm, further studies are needed in order to identify the relationship between muscle and bone in other limbs. Muscle area estimation can provide a tool for reconstructing both the strength and the body shape of archaeological populations or fossil hominines and it might improve other methods such as the calculation of body mass.

The results of the present study are in line with findings from previous work (e.g., Sumnik et al., 2006; Fricke et al., 2008; Chin et al., 2012; Van Caenegem et al., 2012), which have demonstrated that the muscle-bone-unit is strongly influenced by growth, aging and sex. Age and sex are important predictors of muscle area and their inclusion or exclusion will influence the quality of the model. As the results in this paper have shown, muscle area estimation from cortical bone is possible from a set of various predictors that each influences the quality of the estimate. The ideal muscle area prediction model would include exact numerical age, stature, and sex besides cortical area. For the variable age, a knot has to be set between the young ages in which the relationship to muscle area is clearly linear and the older ages where age is a less important predictor of muscle cross sectional area. The gap between 23.15 years and 29.65 years is a weakness of the data and further studies filling this gap are desirable. Using the current data, muscle area estimations for individuals aged between 23.15 years and 29.65 years are extrapolated. However, if stature and age of skeletal remains cannot be reliably determined, the variables age class and radius length should be preferred to avoid the inclusion of additional sources of error in the prediction of muscle area. In males, age class is an even better predictor of muscle area than exact numerical age. In females, however, the variable age class is associated with a decline in the predictive power of the model. Cortical area on its own can provide a rough estimate of muscle area (r2 = 0.392), but sex should be included in the model whenever possible as the analyses have demonstrated its strong influence on the prediction quality. The coefficient of determination was higher for males than for females in all muscle area estimation regressions that have been computed. This indicates that when using the parameters analyzed in this study, muscle area prediction is more exact for males than for females.

Our results agree with previous work that has described the influence of estrogen and testosterone on the muscle-bone-unit (Rauch and Schoenau, 2001; Schoenau et al., 2001; Schoenau, 2005). Neu et al. (2001) have proposed that estrogen may lower the remodeling level in females to allow for a higher storage of bone mass as a depot for pregnancy and lactation. On the other hand, Schoenau et al. (2000) have hypothesized that testosterone might support the buildup of muscle mass in men. These differences in hormonal influence on the muscle-bone-unit may account for the discrepancies found between the sexes in the current study. While the testosterone level in men remains relatively constant throughout most of their life and decreases only slightly from the age of thirty for about 1% each year (Brawer, 2004), the estrogen level in women changes dramatically and rapidly by the time of the menopause (Minkin et al., 1997). This may explain why age is a much more important predictor of muscle area in females than in males.

Correlations discovered in this study between muscle area and cortical area at 65% of forearm length were significantly higher than correlations between muscle area and cortical area in a previous study (Shaw, 2010) which analyzed the mid-shaft location of the ulna. We therefore propose that the choice of the measuring site is of great importance for the quality of muscle area estimation from cortical bone. The 65% measuring site seems to be an appropriate location for the radius and a reasonable choice for muscle area estimation, as it marks the area of the largest circumference of the muscle mass at the forearm (Schoenau et al., 2000).

For this study, only data on muscle area and bone properties of the radius of non-dominant forearms (self-stated by participants) were available. According to the Mechanostat Model and the Functional Muscle-Bone-Unit concept, the relationship between muscle area and cortical bone should be the same in dominant and non-dominant forearms and in individuals with higher and lower activity levels. But absolute values for muscle area and cortical area (standardized by forearm length) should differ between the dominant and the non-dominant forearm of one individual. Existing datasets show that cortical area is in fact higher in the dominant than in the non-dominant arm (Steele and Mays, 1995; Mays, 2002; Auerbach and Ruff, 2006) and can provide information on handedness (Shaw, 2011). However, further research is needed in order to analyze the relationship between muscle and bone under different conditions.

A standardization of the estimated muscle area by forearm length is required to obtain a surrogate for forearm muscle strength. Muscle area alone is not a relevant indicator of “strength” in terms of, for example, grip force as long bone length has a significant influence on the physical capabilities (Schoenau, 2005). Longer limb bones are a biomechanical advantage (leverage effect) and “strength” is therefore a result of both limb length and muscle area (Rostock, 2003). Muscle cross-sectional area scaled for long bone length can provide an auxiliary value for comparisons between individuals and groups. Future studies will have to evaluate the correlations between muscle area, long bone length, and different indicators of strength such as grip force, tension force, or punch force in detail.

Muscle area estimations could provide new information on long-discussed topics in Paleoanthropology such as the question of whether or not the Neanderthals were “stocky” (Wolpoff, 1999: 676), had a “general muscular hypertrophy of the upper body” (Cartmill et al., 2009: 378), and how their muscle might have increased or decreased the energetic expenditures related to physiological defenses against cold compared to modern humans (Steegman et al., 2002). Muscle area estimations could also be compared to ratings of enthesopathies and contribute to the ongoing quest for a better understanding of muscle insertion sites. From muscle area reconstructions on different limbs, we could generate a more detailed picture of the activity patterns of our prehistoric ancestors and (re-)address a number of behavioral topics related to weapon use (Pearson et al., 2006), gender-specific division of labor (Eshed et al., 2004; Lieverse et al., 2009), or subsistence (Churchill and Morris, 1998; Rhode, 2006). Furthermore, estimations of muscle area could refine the currently used methods of body mass estimation (e.g., Ruff, Trinkaus and Holliday, 1997; Ruff, 2000a; Auerbach and Ruff, 2004; Pomeroy and Stock, 2012; Ruff et al., 2012) as skeletal muscle makes up for about 42% of the male and 36% of the female body mass (Marieb and Hoehn, 2010).

The aim of this study was to evaluate if muscle area estimations from the cortical bone of the radius were possible or not. The results presented here have demonstrated that muscle area at 65% of forearm length can be predicted from the cortical area of the radius. We have described the correlations of a set of parameters such as age, sex, stature, and forearm length to muscle area and presented a number of regressions exploring the influences of these variables on the quality of a muscle area prediction model. We conclude that sex is an essential parameter for reliable muscle area estimation. Further research will give us a more detailed picture of the relationship between muscle and bone and on how we can gain information about prehistoric lifestyles from this relationship.


We would like to thank everybody involved in this study, especially the team of the University Hospital Köln (in particular Bärbel Tutlewski) and all participants and researchers of the DONALD study. We also thank the reviewers for their comments that improved this manuscript. For this article, we consulted the Institute for Clinical Epidemiology and Applied Biometry of the University of Tübingen and thank the institute for advice on statistical methods and prediction models. A.S. thanks Gerd-Christian Weniger for inspiration and support on this study.