A FOURTEEN SEGMENT GEOMETRIC-BASED MULTIPLE LINEAR REGRESSION MODEL FOR CALCULATING SEGMENT MASSES

K.J. Chesnin (1), M.P. Besser (2),
L. Selby-Silverstein (2), W. Freedman (1), R. Seliktar (1)
(1) Biomedical Engineering and Science Institute,
Drexel University, Philadelphia, PA 19104
(2) Human Performance Laboratory,
Thomas Jefferson University, Philadelphia, PA 19107

Presented at the 20th Annual Meeting of the American Society of Biomechanics
Atlanta, Georgia. October 17-19, 1996

INTRODUCTION

The accurate calculation of segment masses, in vivo, is important for the determination of whole-body center of mass (COM) and joint kinetics. A geometric-based multiple linear regression model for the calculation of the mass of fourteen body segments has been developed. This model is customized to the individual using thirty four anthropometric measurements and is gender specific. The accuracy of this model has been evaluated and compared with two previously published models4,9, using data available from three published cadaver studies1-3. The output of our model was found to correlate well with the measured data and it compared favorably with the two other models that were evaluated.

REVIEW AND THEORY

There are many methods available for estimating segment masses, in vivo, including: MRI, CT, scaling cadaver data to body mass, regression equations, and stereophotometrics. Some of these methods are excessively time consuming and/or prohibitively expensive. Ratios of segment mass to body mass and regression equations are quick and inexpensive1-4. However, the methods in the literature1-4,6,8 often are developed from small, homogeneous cadaver samples, comprised mostly of men. Thus, their application to various living populations, especially those that vary from the cadavers samples, e.g: children, women, and people with disabilities, may result in significant error. Other methods, such as geometric models and stepwise regression equations, have been developed to increase the sensitivity of the models to individual morphological variations. However, many of these methods are limited in their applicability, since they are derived from small, homogeneous cadaver samples. Further, due to the difficulty in testing the accuracy of segment mass models in vivo, their accuracy is often unknown. Our model is based on the model of Vaughan et al8. They developed geometric-based multiple linear regression equations for the determination of lower extremity segment masses, using data from six male cadavers1.

The model developed here has an advantage in that its theoretical basis seeks to parallel the natural geometric form of the human body, rather than relying purely on statistical inference from a generally small and homogeneous sample of cadavers. The purpose of this work is to develop an accurate model for the calculation of body segment masses in vivo, that is quick, inexpensive, and can be applied to various populations. The model is intended for use in calculating whole-body COM and joint kinetics. .

METHODS

Multiple linear regression equations were derived from published anthropometric and stereophotometric volume data, from 31 men5 and 46 women7, collected in vivo, and density data from cadavers3. The body segments were modeled as regular geometrical solids and were assumed to have a constant density. All the body segments were modeled as cylinders, except the feet and head, which were modeled as right pyramids and a sphere, respectively. The regression equations for estimating segment masses all have the general form of equation 1, where is segment density, and length is a composite anthropometric parameter that depends on the geometric model of the segment.

The accuracy of our model has been estimated using anthropometric and segment mass data from three published cadaver studies (Clauser et al., 1969; Chandler et al., 1975; Clarys et al., 1986). The accuracy of our model has also been compared with two commonly used methods; a ratio method3,4,6 that scales segment mass as a ratio of total body mass and a multiple linear regression model9 that uses total body mass and stature as predictors. The former was developed from the data of eight cadavers segmented by Dempster (1955), and adjusted by Clauser et al., and is a commonly used method6. The latter model (Zatsiorsky et al., 1990) was developed from in vivo gamma radiation experiments, with a large sample of young Russians: 100 men and 15 women9.

Percent errors, sum of absolute error as percent total body mass (equation 2, where Mi is the measured mass of segment i, Ci is the calculated mass of segment i, and Mb is total body mass.), and intraclass correlation coefficients (ICC) for segment mass data were calculated comparing each of the segment mass estimation models to data from three published cadaver studies1-3. Several foot and hand anthropometric measurements were not directly measured in the cadaver studies, but were estimated from the data available. Further, the raw data from Clauser et al. were not available; the data used were right and left side averages for each subject.

RESULTS AND DISCUSSION

Due to varying segmentation procedures and experimental protocols, data from the three cadaver studies were analyzed separately. Our model segments the body in a manner most similar to Chandler et al. The other models and cadaver studies segment the body slightly differently.

Table 1 reveals the total percent of body mass that is allotted to the wrong segment by each model, and is indicative of the accuracy of the models when used for calculating whole-body COM. The results indicate that our model worked best with the data of Chandler et al. The Dempster model worked best with the cadaver data of Clauser et al. However, the data from Clauser et al. were right and left side averages, thus the resultant error is an underestimate of the actual error, as there are normally right and left side asymmetries. The regression model of Zatsiorsky et al. showed higher errors than the other two models.

Table 2 indicates that the model developed here shows good correlation (> 0.70) for most segments. The model is least correlated with the smaller body segments: the hand, foot, and forearm. However, foot height, foot breadth, and hand length, which are used in our model, were not directly available and were estimated from the data. This would result in increased errors in the calculation of foot and hand masses for those cadavers. Also, when calculating the whole-body COM the smaller segments have less of an impact, as seen in figure 1, depending on the motion of interest. However, errors in segment mass may result in increased errors in calculated joint forces due to inertial forces, depending on the motion and joint of interest.

Figure 1 shows that our model compared favorably with the other two models that were evaluated. This figure also illustrates that errors in calculating the mass of larger segments has more influence on the calculation of whole-body COM. It should be recognized that varying segmentation procedures will affect these results.

Using cadaver data to examine the accuracy of models used for calculating body segment masses in vivo, is not ideal, due to pre- and post-mortem tissue changes, fluid losses, etc. Further, it is difficult to combine the data from different studies, due to varying experimental protocols. However, we are unable to safely, directly measure segment masses in vivo, and hence must rely on cadaver data. While the data analyzed do not provide a direct measure of the accuracy of the models when applied in vivo, it provides insight into their utility.

The model developed here is customized to the individual using anthropometric measurements. Therefore, it should be better suited for calculating segment masses of populations not well represented in cadaver studies (e.g: children, women, and people with disabilities), than are simple statistical models that assume some average morphology. Our model was developed using in vivo data5,7 and thus should represent the shape of the living human better than data from cadavers. Further, these data were collected from a much larger and morphologically diverse sample than that used in most cadaver segmentation studies1-4. Our model has been shown to calculate segment masses with some accuracy and compared favorably to the two other models evaluated. Our model is inexpensive, quick, and accounts for individual fluctuations in segment shapes using anthropometric measurements, thus increasing its clinical and research utility.

REFERENCES

1) Chandler , RF et al., Investigation of the Inertial Properties of the Human Body, AMRL Technical Report 74-137, 1975.

2) Clarys, JP et al., Hum Bio 58, pp. 771-782, 1986.

3) Clauser, CE et al., Weight, Volume, and COM of segments of the Human Body, AMRL-TR-69-70, 1969.

4) Dempster, WT, Space Requirements of the Seated Operator, WADC Technical Report 55-159, 1955.

5) McConville, JT et al., Anthropometric Relationships of Body and Body Segment Moments of Inertia, AFAMRL Technical Report 80-1191, 1980.

6) Winter, DA, Biomechanics and Motor Control of Human Movement, John Wiley & Sons, 1990.

7) Young, JW et al., Anthropometric and Mass Distribution Characteristics of the Adult Female, FAA-AM-83-16, 1983.

8) Vaughan , CL et al., Dynamics of Human Gait, Human Kinetics Publishers, 1992.

9) Zatsiorsky, VM et al., Contemporary problems of Biomechanics, CRC Press, 1990 pp. 272-291.