AMERICAN SOCIETY OF BIOMECHANICS Presented at the Twenty-First Annual Meeting of the American Society of Biomechanics Clemson University, South Carolina September 24-27, 1997

INTRODUCTION

The mechanical analysis of human movement often requires knowledge of the inertial properties of body segments. The precision and accuracy of these inertial parameters will have an influence on any mechanical parameters computed using them (Andrews and Mish, 1996). Whilst accuracy of estimated body segmental parameters is difficult to assess precision is relatively easy yet has not been the focus of studies examining the estimation of body segment inertial parameters. It was the purpose of this study to examine the inter- and intra-operator precision with which human limb inertial parameters could be estimated.

REVIEW AND THEORY

Body segment inertial parameters can be estimated in a number of different ways including the use of statistical models (e.g. Hinrichs, 1985), medical imaging techniques (e.g. Mungiole and Martin, 1990), and modeling the body segments as series of geometric solids (e.g. Hatze, 1980). The geometric modeling techniques represent the segments of the body using geometric shapes. The dimensions of these shapes are obtained by taking anthropometric measurements on the experimental subject (e.g. segment length and perimeter). From these data it is possible to obtain an approximation of segment volume, then by providing an estimate of the segment density it is possible to estimate the inertial parameters. The density values are normally obtained from cadaver data.

In this study the precision of body segment inertial parameters determined when modeling the body segments as series of geometric solids was examined.

PROCEDURES

A group of fifty physically active subjects, equally divided into males and females, gave informed consent to participate in the study (height 1.730 m +/-0.073; mass 72.38 kg +/-9.90; age 20.7 years +/-1.8). Each subject was measured three times, twice by measurer A (data sets A1 and A2), and once by measurer B (data set B1), all sets of measurement were conducted in the same session. The measurers had no record of any previous measurements so the sets of measurements were considered to be independent. The measurers were experienced measurers who were familiar, from frequent practice, with the measurement protocols required. In a pilot study prior to the main study reported here, the precisions of the two measurers were assessed and found to be virtually identical. The subjects were measured using anthropometric measuring tapes and calipers, all measurements were made to the nearest millimeter.

Figure 1: the stadium solid and truncated cone used to model the body segments.

The inertial parameters were determined for the limbs by modeling them as series of geometric solids. The thigh, shank, upper arm, and forearm were modeled as a series of truncated cones, the feet and hands were modeled as a series of stadium solids; figure 1 shows these shapes. The dimensions of these shapes were obtained by taking measurements on the subjects; for truncated cones length and perimeters, for the stadium solids lengths, perimeters, and widths. For each segment a system of axes were defined with its origin at the center of mass of the segment. These axes were aligned with approximate body axes: saggital (), frontal (), and longitudinal (); moment of inertia values were referenced to these axes (, , and ). Density values for these solids were taken from the data of Dempster (1955) and were assumed to be uniform throughout a given segment. All segments were measured so that each solid was 3.5 cm in length except for the terminal length which was adjusted to accommodate the remaining portion of the segment.

In addition to modeling each segment as a series of geometric solids (Full Geometric), a reduced model was also employed in which each segment was modeled as two solids only (Reduced Geometric). The segment was divided longitudinally into two equal halves, and a different sized solid used for each half.

There were two measures of precision made, one between data sets A1 and A2 (intra-operator precision), and one between the data sets A1 and B1 (inter-operator precision). Precision was quantified using the percentage root mean square difference (%RMSD) between the data sets, and by computing the intra-class correlation (Fleiss, 1986).

RESULTS

Table 1 shows the inter- and intra-operator precisions for the inertial parameters for the lower limb, similar results were obtained for the upper limb.

Table 1: precisions of inertial parameters for the lower limb.

Segment	Full Geometric		Reduced Geometric
THIGH	Inter	Intra	Inter	Intra
Mass	0.97	0.97	0.96	0.96
C. of M.	0.94	0.95	0.93	0.94
Ixx/Iyy	0.96	0.97	0.95	0.97
Izz	0.98	0.96	0.96	0.94
SHANK
Mass	0.96	0.96	0.97	0.95
C. of M.	0.91	0.91	0.92	0.90
Ixx/Iyy	0.95	0.94	0.96	0.94
Izz	0.96	0.97	0.97	0.95
FOOT
Mass	0.88	0.89	0.89	0.85
C. of M.	0.77	0.75	0.70	0.72
Ixx	0.83	0.81	0.86	0.84
Iyy	0.86	0.84	0.86	0.85
Izz	0.82	0.72	0.80	0.67

DISCUSSION

The mass and center of mass locations estimated using the geometric solid model were compared with the data of Dempster (1955). These data compared favorably, although the Reduced Geometric tended to provide a higher estimate of segment mass than the Full Geometric suggesting that the former did not adequately account for variations in segment shape and therefore overestimated segment volume.

The results from this study indicate that human limb segment inertial parameters can be estimated with high precision when modeling the body segments as series of geometric solids. The inertial parameters for the foot and hand segments had the lowest precisions; for these segments if measurement precision is considered to be an important factor then precision can be increased by summing repeat measures. There was little difference between inter- and intra-operator precisions, therefore comparison of inertial parameters determined using the same protocol but obtained by different operators is entirely justified, as is having two measurers taking measurements on the same subject to speed the data collection process.

Comparison of the reported accuracies in Cappozzo and Berme (1990) with the precisions from the present study indicate measurement imprecision is a much smaller source of error than error due to lack of accuracy. The present study was not able to assess accuracy, but assessed and reported the precision with which the inertial parameters of human limb segments are estimated, such data has not been reported before.

REFERENCES

Andrews, J.G., and Mish, S.P. J. Biom. 29, 651-654, 1996.

Cappozzo, A. and Berme, N. In Biomechanics of Human Movement, Bertec, 1990.

Dempster, W. WADC Technical Report 55-159, Wright Patterson Air Force Base, Ohio, 1955.

Fleiss, J.L. The Design and Analysis of Clinical Experiments. John Wiley and Sons, 1986

Hatze, H. J. Biom. 13, 833-843, 1980.

Hinrichs, R.N. J. Biom. 18, 621-624, 1985.

Mungiole, M. and Martin, P.E. J. Biom., 23, 1039-1046, 1990.