Body segment parameters such as segment mass, center of mass, and radius of gyration are used as inputs in static and dynamic ergonomic and biomechanical models used to predict joint and muscle forces, and to assess risks of musculoskeletal injury. Previous work has predicted body segment parameters (BSPs) in the general population using age and obesity levels as statistical predictors (

Body segment parameters (BSPs), which include the length, segment mass, center of mass (COM), and radius of gyration (R_{G}) of body parts, are used in human factors and ergonomics, as well as biomechanical modeling applications. These applications include the design of tools, protective clothing, equipment, and workstations (

Previously developed approaches used to estimate BSPs are discussed in detail in

The accuracy of the estimated BSPs can significantly impact the validity of biomechanical tools needing these sets of anthropometric data. For example, inverse dynamics models related to lifting and associated injury risk have been shown to be sensitive to errors in estimated COM position, joint rotation center location, length, and segment mass values (

Our previous work has quantified associations of age and BMI with BSPs in American adults (

The study was approved by the University of Pittsburgh Institutional Review Board. A total of 280 working adults participated. Recruitment was stratified by age group, BMI group and gender in an attempt to represent all sections of the working population. More specifically, working men and women were recruited in approximately equal numbers in four BMI categories (normal weight: 18.5 ≤ BMI < 25.0, overweight: 25.0 ≤ BMI < 30.0, obese: 30.0 ≤ BMI < 40.0, and morbidly obese BMI ≥ 40.0 kg m^{−2}) across three age groups (21 ≤ age < 40), middle (40 ≤ age < 55), and old (55 ≤ age < 70), such that each of the twenty four gender, age, and BMI subgroups contained approximately the same number of participants.

After obtaining written informed consent, height and mass were measured in order to confirm eligibility based on BMI was confirmed and female participants of child bearing age took a pregnancy test, with a negative result being required for continued participation. Next, approximately 78 anthropometric measurements were collected (

The processing consisted of each scan being split into each major body segment of interest (torso, left and right upper arm, forearm, thigh, and shank), defined using bony landmarks and anatomically defined planes (^{−3} for bone, 0.9 g cm^{−3} for fat, and 1.08 g cm^{−3} for lean tissue (_{G} were then calculated from the known slice heights and masses using a custom MATLAB script (Mathworks, Natick, MA, USA). Details regarding the specific parameter calculations from the slice masses are included in

For brevity purposes, all reported data for the forearm, upper arm, thigh, and shank were analyzed on the participants’ self-reported dominant side. Segment mass was expressed as percent of the total body mass. COM locations were reported as percent of the segment length from the proximal (superior for the torso) segment border, where a higher value indicates that the COM is located further in the distal (inferior for the torso) direction. The R_{G} values were also expressed as percent of the segment length, with the R_{G} location being measured from the calculated COM.

All statistical analyses were stratified due to significant gender differences and complex interactions of gender with age and BMI findings, previously reported by our group (_{G} for the torso, thigh, shank, upper arm, and forearm) were checked for normality, then log transformed as necessary before any further analysis. The full data set of 280 participants was randomly split into two subgroups: the training set, which contained 200 participants, and the testing set, which contained the remaining 80. A multiple regression analysis was performed on the torso, thigh, shank, upper arm, and forearm segment parameters in the training subset with a backward elimination strategy for variable selection and stratified by gender. The initial models contained age, BMI, age and BMI interaction terms, waist, hip, and neck circumferences, and all relevant physical measures taken of the body segment of interest. In each step of the analysis, the predictor with the largest

While not direct measurement of all segments, the waist, hip, and neck circumferences were included to all initial models due to their relationship with overall body shape and mass distribution, specifically their ability to define central adiposity, which when included with BMI, can help describe the relative distribution of mass throughout the torso and appendages within differing degrees of obesity. For example, individuals with more central adiposity will have higher waist and/or hip circumferences than individuals with less central adiposity, meaning that at given BMI, individuals with larger circumferences will have less total and normalized limb mass, along with COM and Rg values more representative of those seen in less obese individuals.

Once the models were finalized, they were used for prediction in the independent validation data set, so that the predicted and actual segment (in-vivo DXA-based) parameters could be compared using the absolute percent error, as well as the root mean square error (RMSE). The total variability explained by the models when applied to the testing set (R^{2}), along with the improvements of these models (ΔR^{2}) over previously established models using only age and BMI terms (

The final study sample consisted of 280 working adults (148 female) ages 21-70 (mean: 44.9 ± 13.4 years). A number of predictors simultaneously remained significant in models for women and men (_{G}) of the models showing improvement over a previously established method (

The initial torso models included the following variables as potential predictors of the torso BSPs (COM, mass and R_{G}): age, BMI, their squared and interaction terms in addition to waist, hip, and neck circumference, torso widths, depths, and axis depths (_{G}) (

The thigh models initially included neck, waist, hip, knee, and three thigh circumferences, taken at the upper, middle, and lower thigh levels (^{2}) in proportion of explained variability (^{2} for R_{G} predictions; however, the model for females retained almost all of the age, BMI, and interaction terms, while the male model was solely based on circumference measurements.

When applied to the test data set, the thigh COM and R_{G} models had normalized RMSE values below 5%, while the mass RMSE was much higher, at 11.6% (_{G} mean error was comparable to the torso prediction errors, at about 1.1%; however, the COM and mass predictions were slightly higher, at 3.8 and 7.0%, respectively. All three of the actual thigh parameters had errors of 16-38% when predicted with the deLeva methods (

The shank prediction models started with neck, waist, hip, knee, calf, and ankle circumferences, as well as knee and ankle widths, and shank length. With the exception of shank COM in males, all of the other parameter predictions included at least one BMI term and calf circumference. In both genders, hip and calf circumferences were included in the final mass models, while waist, knee, and calf circumferences were used in the R_{G} models.

All of the models other than COM in males showed R^{2} increases of over 0.2 (^{2} values over 0.85 for mass in both genders (^{2} increase of 0.004 over the previous model using only age and BMI terms. The model only included hip circumference and ankle width, but none of the age terms, or any of the other terms generally associated with obesity, such as BMI or waist or hip circumferences. When applied to the test data set, the COM and R_{G} predictions were especially accurate, with RMSE under 2.5%, and average errors of all three shank parameters under 5% (_{G} predictions, with average of over 60%.

In addition to the age and BMI terms, the upper arm models started with waist, hip, neck, upper arm, and elbow circumferences, and elbow width. The final model for predicting mass in females had an R^{2} of about 0.5 (^{2} of under 0.25. Even though the variance explained by the models approximately doubled for R_{G} in males and COM in females, the overall values still remained under 15%. The models for mass and R_{G} in males, and mass and COM in females all included waist and elbow circumferences.

The final model for predicting R_{G} in females is notable because it did not improve over the previous model, which included all of the age, BMI, quadratic, and interaction terms. None of the anthropometric terms were significant in the final model, and the final R^{2} ended up slightly less than the previous model because the non-significant age, BMI, and interaction terms were removed during the backward elimination process. While the total variance explained by the model was under 20% for R_{G} for both genders, the RMSE was under 4% when applied to the test data set, with an average error of less than 3% (_{G}.

The initial model for the forearm included the age and BMI terms along with waist, hip, neck, forearm, elbow, and wrist circumferences, wrist and elbow widths, and forearm length. All of the final models included at least one of the age or BMI terms, and all except for mass in females included wrist circumference (^{2} values, they also had larger prediction errors in the test data set, with normalized RMSE of about 9%, and average errors over 7% (_{G} predictions were more accurate when applied to the test data set, with RMSE under 2.5%, and average errors under 2%. The deLeva parameter predictions forearm mass prediction error was slightly higher than the anthropometric model errors, at a little over 11%; however, the average error in R_{G} calculation was nearly 60%.

The new prediction models including individual anthropometric measures in addition to age and BMI terms have increased the accuracy over previous methods which only considered gender (

The torso parameter predictions in females, particularly COM and R_{G}, were found dependent not only on age and BMI factors, but also on a number of torso width and depth measurements. While all of the final R^{2} values for the female torso predictions are above 0.5, the increases are especially notable for mass and COM predictions (

In females, the models for thigh COM and R_{G} retained most of the age and BMI predictors as being significant, suggesting that while individual thigh anthropometry explains most of the variation in thigh mass (ΔR^{2} = 0.49), age and obesity status explain the distribution of mass within the thigh. In males, most of the age and BMI factors are significant in COM prediction, while thigh mass and R_{G} predictions are almost entirely dependent on circumference measurements. The thigh R_{G} prediction in males is entirely dependent on circumference measurements (neck, hip, knee, and upper and mid-thigh), and does not include any of the initial age or BMI predictors, indicating that this parameter is only dependent on the shape of the individual, and independent of age or obesity status.

With the exception of shank COM prediction in males, all of the prediction models included calf circumference. The calf circumference measurement is notable because it is defined as the largest measurement around the calf, as opposed to other measurements, which are defined relative to anatomical landmarks. The calf circumference is a highly significant predictor (p < 0.001) for shank mass in both genders because it is proportional to the maximum cross section of the shank, instead of being in a predefined location. Similarly to the thigh R_{G} in males, the COM value in males is also only predicted by anthropometric measurements, meaning that this value is also independent of age and obesity status.

Including individual anthropometric measurements in the prediction of the upper extremity’s BSPs variables had varying and complex effects. For example, while the female upper arm COM prediction model was dependent only on individual geometry, in males, this BSP variable was dependent both on age and individual anthropometry data. The forearm BSP predictions were highly dependent on individual anthropometric measures, in addition to age and BMI terms, in both males and females.

Overall, nearly all of the observed statistical models benefitted from including individual anthropometric measurements. In addition to observing the effects of age and BMI, data points such as waist and hip circumference provide additional measures of obesity, and whole body mass distribution. By using separate randomly selected training and test data sets, this study was able to develop and validate anthropometry based prediction models for the segment parameters of interest. The independent validation is imperative in such settings to assess true model performance, and not an overly optimistic metric attainable due to over fitting. These anthropometric models were able to predict the parameters more precisely than previous modeling methods (

In summary, the findings of the present study provide statistical tools that allow the prediction of BSPs using simple individual characteristics such as age, BMI and body measurements. The final models presented have shown large improvements over the

Compared to the method explained by

Limitations of this study involve the study population, which consisted only of healthy American working aged adults with full time jobs. Factors such as activity levels and overall fitness were not considered, and would likely impact body mass distribution. While ethnicity was not taken into account in the statistical analysis, the participants recruited reflected the diversity of the American working population, and the use of the multiple anthropometric measurements accounted for differences in whole body and segment shaped in a more detailed manner than including ethnicity as a single predictor.

Because the DXA scans were collected only in the frontal plane, with the participants lying supine, some degree of weight shifting may have occurred, which would not be present during standing. Additionally, the specific segment definition used for the torso was chosen for its applicability to inverse dynamics calculations and individual variability (_{G} values using frontal plane values (

For the purpose of brevity, only the dominant side arm and leg segment parameters were analyzed. Only observing the dominant side has the most relevance for performing many occupational tasks and sports activities, and symmetry may be assumed for other tasks.

Finally, our sample size may not be as large as it appears at the first glance, considering the large numbers of independent variables that we considered in the models. We could have examined more complex models had we recruited an even larger number of participants. Thus, the prediction equations we were able to formulate and improvements elicited should be considered preliminary, needing further refinement and validation. Despite the limitations, we feel the many strengths of our study outweigh them in investigating the complex associations between anthropometrics and body segment parameters, and exploiting the same for more accurate prediction of the latter.

CDC /NIOSH- R01-OH010106, “Obesity and Body Segment Parameters in Working Adults.”

NIH/NIA- P30-AG024827, “The Pittsburgh Claude D. Pepper Older Americans Independence Center.”

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Conflict of Interest Statement

The authors have no financial interests in relation to the work described in this research manuscript.

Example of a whole body DXA scan prior to division into the segments of interest. The differences in bone, fat, and lean tissue can be visualized based on the individual pixel brightness.

Segmental boundaries of interest: (a) forearm, (b) upper arm, (c) torso, (d) thigh, (e) shank. During the scan analysis process, each of these segments is separated into a series of 3 pixel (3.9 cm) tall slices, so that the BSPs can be calculated as described by

Anthropometric measurements collected for use as predictive terms in the BSP models. All arm and leg measurements were performed on left and right sides.

Circumference at the umbilicus | |

Around largest part of the hip | |

Around proximal thigh | |

Around point midway between proximal border of patella and inguinal crease | |

Around thigh1 cm above proximal border of patella | |

Around medial and lateral femoral epicondyles | |

Around largest part of calf | |

Around medial and lateral malleoli | |

Around midpoint between acromion and olecranon processes | |

Around medial and lateral humeral epicondyles | |

Around midpoint between lateral humeral epicondyle and ulnar styloid process | |

Around radial and ulnar styloid processes | |

Thickness at center of palm | |

Distance between medial and lateral humeral epicondyles | |

Between radial and ulnar styloid processes | |

Between medial and lateral epicondyles | |

Between medial and lateral malleoli | |

Lateral humeral epicondyle to acromion | |

Ulnar styloid process to lateral humeral epicondyle | |

Greater trochanter to knee joint center | |

Knee joint center to lateral malleolus | |

Between left and right ASIS | |

Width at shoulder joint center level | |

Width at nipple level | |

Width at level midway between nipple and L3-L4 | |

Width at L3-L4 level | |

Depth at shoulder joint center level | |

Depth at nipple level | |

Depth at level midway between nipple and L3-L4 | |

Depth at L3-L4 level | |

Depth from the shoulder joint center/greater trochanter plane to the back at shoulder joint center level | |

Depth from the shoulder joint center/greater trochanter plane to the back at nipple level | |

Depth from the shoulder joint center/greater trochanter plane to the back at level midway between nipple level and L3-L4 | |

Depth from the shoulder joint center/greater trochanter plane to the back at L3-L4 | |

Distance from ground to C7 | |

Distance from ground to shoulder joint center | |

Distance from ground to ASIS | |

Distance from ground to greater trochanter |

Torso center of mass, mass, and radius of gyration multiple regression model estimated coefficients for the final models following the backwards elimination process.

Thigh center of mass, mass, and radius of gyration multiple regression model estimated coefficients for the final models following the backwards elimination process.

Shank center of mass, mass, and radius of gyration multiple regression model estimated coefficients for the final models following the backwards elimination process.

Upper arm center of mass, mass, and radius of gyration multiple regression model estimated coefficients for the final models following the backwards elimination process.

Forearm center of mass, mass, and radius of gyration multiple regression model estimated coefficients for the final models following the backwards elimination process.

R^{2} values for the final multiple regression models, compared to the values (R^{2}_{0}) from the regression models from ^{2}) are provided to demonstrate the improvement between the sets of models.

Female | Torso COM | Torso Mass | Torso Rg | Thigh COM | Thigh Mass | Thigh Rg | Shank COM | Shank Mass | Shank Rg | Arm COM | Arm Mass | Arm Rg | Forearm COM | Forearm Mass | Forearm Rg |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

R^{2} | 0.509 | 0.633 | 0.677 | 0.358 | 0.663 | 0.242 | 0.505 | 0.861 | 0.441 | 0.099 | 0.503 | 0.181 | 0.375 | 0.672 | 0.320 |

R^{2}_{0} | 0.279 | 0.138 | 0.563 | 0.122 | 0.163 | 0.049 | 0.304 | 0.174 | 0.122 | 0.046 | 0.197 | 0.184 | 0.249 | 0.272 | 0.108 |

ΔR^{2} | 0.230 | 0.495 | 0.114 | 0.236 | 0.500 | 0.193 | 0.201 | 0.687 | 0.319 | 0.053 | 0.306 | −0.003 | 0.126 | 0.400 | 0.212 |

Male | Torso COM | Torso Mass | Torso Rg | Thigh COM | Thigh Mass | Thigh Rg | Shank COM | Shank Mass | Shank Rg | Arm COM | Arm Mass | Arm Rg | Forearm COM | Forearm Mass | Forearm Rg |

R^{2} | 0.635 | 0.660 | 0.739 | 0.387 | 0.558 | 0.570 | 0.209 | 0.853 | 0.622 | 0.131 | 0.218 | 0.133 | 0.338 | 0.446 | 0.400 |

R^{2}_{0} | 0.506 | 0.453 | 0.573 | 0.107 | 0.440 | 0.292 | 0.205 | 0.502 | 0.253 | 0.114 | 0.180 | 0.062 | 0.174 | 0.352 | 0.245 |

ΔR^{2} | 0.129 | 0.207 | 0.166 | 0.280 | 0.118 | 0.278 | 0.004 | 0.351 | 0.369 | 0.017 | 0.038 | 0.071 | 0.164 | 0.094 | 0.155 |

Root mean square error (RMSE) for the model predictions expressed as a percentage of the actual measured values in the test data set, and their comparison to those of

Torso | Thigh | Shank | Arm | Forearm | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

COM | Mass | Rg | COM | Mass | Rg | COM | Mass | Rg | COM | Mass | Rg | COM | Mass | Rg | |

RMSE | 1.675 | 5.241 | 1.596 | 4.812 | 10.951 | 1.665 | 2.408 | 5.681 | 1.468 | 4.623 | 10.032 | 3.374 | 2.122 | 9.030 | 1.432 |

Diff (predicted) | 1.34 | 4.35 | 1.25 | 3.01 | 6.17 | 1.23 | 1.98 | 4.46 | 1.15 | 3.63 | 7.48 | 2.68 | 1.57 | 6.81 | 0.88 |

Diff (deLeva) | 19.65 | 6.36 | 33.94 | 16.85 | 27.09 | 38.78 | 9.66 | 15.02 | 62.81 | 16.83 | 26.22 | 39.67 | 9.84 | 11.60 | 59.82 |