Component inertia modeling of segmental wobbling and rigid masses

A modification to an existing mathematical model is described, which permits the determination of subject-specific inertia parameters for wobbling and rigid masses of female body segments. The model comprises segment-specific soft tissue, bone, and lung components. A total of 59 geometric solids (40 soft tissue, 17 bone, 2 lung) were used to represent the body components. Ninety-five anthropometric measurements were collected from 7 female participants and were used to develop and evaluate the model. The success of the model is evaluated using predicted mass and mass distribution. The overall absolute accuracy in predicted whole body mass was better than 3.0%, with a maximum error of 4.9%. The appropriateness of the cadaver-based density values used in the model is addressed and the accuracy of the component inertia model in relation to uniform density models is discussed. The model offers a novel approach for determining component inertia parameters, which have been used successfully in a wobbling mass model to produce realistic kinetic analyses of drop-landings.     

The appropriate use of regression equations for the estimation of segmental inertia parameters

Linear regression equations are commonly used in conjunction with experimental data to provide linear relationships between quantities which are dimensionally distinct. In many cases theoretical relationships between such quantities are known and can be used as a basis for non-linear regression equations. This study compares linear and non-linear approaches for estimating the segmental moments of inertia from anthropometric measurements using the data of Chandler et al. [Chandler et al. (1975) Investigation of inertial properties of the human body. AMRL Technical Report 74-137, Wright Patterson Air Force Base. OH.] Right limb data were used to derive the equations while left limb data were used as a cross-validation sample to evaluate the inertia estimates calculated from the equations. For the limb segments the standard error estimates had average values of 21% for the linear equations and 13% for the non-linear equations. Data on a 10 yr-old boy was used to compare the two approaches outside the sample range. The mean percentage residuals were 286% for the linear equations and 20% for the non-linear equations. A set of non-linear equations is provided.     

Identification and experimental validation of damping ratios of different human body segments through anthropometric vibratory model in standing posture

A 15 degrees of freedom lumped parameter vibratory model of human body is developed, for vertical mode vibrations, using anthropometric data of the 50th percentile US male. The mass and stiffness of various segments are determined from the elastic modulii of bones and tissues and from the anthropometric data available, assuming the shape of all the segments is ellipsoidal. The damping ratio of each segment is estimated on the basis of the physical structure of the body in a particular posture. Damping constants of various segments are calculated from these damping ratios. The human body is modeled as a linear spring-mass-damper system. The optimal values of the damping ratios of the body segments are estimated, for the 15 degrees of freedom model of the 50th percentile US male, by comparing the response of the model with the experimental response. Formulating a similar vibratory model of the 50th percentile Indian male and comparing the frequency response of the model with the experimental response of the same group of subjects validate the modeling procedure. A range of damping ratios has been considered to develop a vibratory model, which can predict the vertical harmonic response of the human body.     

A new geometric-based model to accurately estimate arm and leg inertial estimates

Segment estimates of mass, center of mass and moment of inertia are required input parameters to analyze the forces and moments acting across the joints. The objectives of this study were to propose a new geometric model for limb segments, to evaluate it against criterion values obtained from DXA, and to compare its performance to five other popular models. Twenty five female and 24 male college students participated in the study. For the criterion measures, the participants underwent a whole body DXA scan, and estimates for segment mass, center of mass location, and moment of inertia (frontal plane) were directly computed from the DXA mass units. For the new model, the volume was determined from two standing frontal and sagittal photographs. Each segment was modeled as a stack of slices, the sections of which were ellipses if they are not adjoining another segment and sectioned ellipses if they were adjoining another segment (e.g. upper arm and trunk). Length of axes of the ellipses was obtained from the photographs. In addition, a sex-specific, non-uniform density function was developed for each segment. A series of anthropometric measurements were also taken by directly following the definitions provided of the different body segment models tested, and the same parameters determined for each model. Comparison of models showed that estimates from the new model were consistently closer to the DXA criterion than those from the other models, with an error of less than 5% for mass and moment of inertia and less than about 6% for center of mass location.     

Influence of body segments' parameters estimation models on inverse dynamics solutions during gait

The purpose of the present study was to examine the influence of anthropometric data on joint kinetics during gait. We particularly focused on the sensitivity of inverse dynamics solutions to the use of models for body segment parameters (BSP) estimation. Six often used estimation models were selected to provide BSP values for the three segments of the lower limb. Kinematics and dynamics were sampled from seven subjects performing barefoot gait at three different speeds. Joint kinetics were estimated with the bottom-up method using BSP values derived from each estimation model as anthropometric inputs. The BSP estimates were highly sensitive to the model used with deviations ranging from at least 9.73% up to 60%. Maximal variations of peak values for the hip joint flexion/extension moment during the swing phase were 20.11%. Hence, our findings suggest that the influence of BSP cannot be neglected. Observed deviations are especially due to the effect of varying simultaneously the mass, moments of inertia and the center of mass location values, according to the underlying relationship of interdependency linking each component. Considering both the differences found in joint kinetics and the level of accuracy of BSP models, evidence is provided that using multiple regression BSP estimation functions derived from Zatsiorsky and Seluyanov should be recommended to assess joint kinetics.     

The simulation of aerial movement--IV. A computer simulation model

A computer simulation model of human airborne movement is described. The body is modelled as 11 rigid linked segments with 17 degrees of freedom which are chosen with a view to modelling twisting somersaults. The accuracy of the model is evaluated by comparing the simulation values of the angles describing somersault, tilt and twist with the corresponding values obtained from film data of nine twisting somersaults. The maximum deviations between simulation and film are found to be 0.04 revolutions for somersault, seven degrees for tilt and 0.12 revolutions for twist. It is shown that anthropometric measurement errors, from which segmental inertia parameters are calculated, have a small effect on a simulation, whereas film digitization errors can account for a substantial part of the deviation between simulation and film values.     

A computational model for dynamic analysis of the human gait

Biomechanical models are important tools in the study of human motion. This work proposes a computational model to analyse the dynamics of lower limb motion using a kinematic chain to represent the body segments and rotational joints linked by viscoelastic elements. The model uses anthropometric parameters, ground reaction forces and joint Cardan angles from subjects to analyse lower limb motion during the gait. The model allows evaluating these data in each body plane. Six healthy subjects walked on a treadmill to record the kinematic and kinetic data. In addition, anthropometric parameters were recorded to construct the model. The viscoelastic parameter values were fitted for the model joints (hip, knee and ankle). The proposed model demonstrated that manipulating the viscoelastic parameters between the body segments could fit the amplitudes and frequencies of motion. The data collected in this work have viscoelastic parameter values that follow a normal distribution, indicating that these values are directly related to the gait pattern. To validate the model, we used the values of the joint angles to perform a comparison between the model results and previously published data. The model results show a same pattern and range of values found in the literature for the human gait motion.     

Scaling segmental moments of inertia for individual subjects

The purpose of this investigation was to validate methods of scaling human segmental moments of inertia for the transverse principal axis. Firstly, two methods of scaling Chandler et al.'s (Pamphlets DOT HS-801 430 and AMRL TR-74-137, Wright Patterson Air Force Base, OH, 1975) mean subject data to estimate the segmental moments of inertia were used. Chandler et al.'s data were scaled using body mass and segment length (formula 1) or body mass and standing height (formula 2). These data were then compared with a procedure of using the cadaver whose anthropometric measurements most closely match those of the subject. The difference between the criterion data (Chandler's subject data) and scaled values were plotted on scatter diagrams with confidence limits of p less than 0.05 at d.f. = 17. For procedure 1, 43% of the scaled values were plotted within the confidence limits using formula (2) (mass and standing height), compared with 26% for formula (1) (mass and segment length). Formula (1) markedly underestimated the tallest and heaviest subjects. In procedure 2, only 16% and 21% of the scaled values, using formula (1) and (2), respectively, fell within the confidence limits. Results suggested that scaling formulae approximate the moment of inertia of body segments with only limited accuracy. However, if scaling was to be adopted then mean moment of inertia data from an appropriate data set, using the formula that incorporates subject mass and standing height, gave results closest to the criterion value.     

Inertial characteristics of adolescent male body segments

In response to the presently limited information on body segment inertial characteristics of children and adolescents this investigation estimated the mass, centre of mass and principal moments of inertia of adolescent male body segments. Significant prediction equations based on anthropometric measurements were then sought. Thirteen subjects were measured at 6-monthly intervals for 2.5 yr to provide inertial characteristics for the leg, thigh, lower trunk and upper trunk segments. These characteristics were derived using an elliptical zone modelling technique. Following a correlation analysis, significant prediction equations of segment inertial parameters were derived from five, or fewer, anthropometric measurements. For all cases, more than 84% of the variance in the dependent variable was accounted for with a maximum R2 value of 94% being recorded for the prediction of thigh segment mass. The use of these prediction equations offered accurate and convenient estimates of body segment inertial characteristics within the limitations applicable to all modelling approaches. In contrast to recent studies, these equations accommodated the current morphological status of the subject.     

A 3D interactive method for estimating body segmental parameters in animals: application to the turning and running performance of Tyrannosaurus rex

We developed a method based on interactive B-spline solids for estimating and visualizing biomechanically important parameters for animal body segments. Although the method is most useful for assessing the importance of unknowns in extinct animals, such as body contours, muscle bulk, or inertial parameters, it is also useful for non-invasive measurement of segmental dimensions in extant animals. Points measured directly from bodies or skeletons are digitized and visualized on a computer, and then a B-spline solid is fitted to enclose these points, allowing quantification of segment dimensions. The method is computationally fast enough so that software implementations can interactively deform the shape of body segments (by warping the solid) or adjust the shape quantitatively (e.g., expanding the solid boundary by some percentage or a specific distance beyond measured skeletal coordinates). As the shape changes, the resulting changes in segment mass, center of mass (CM), and moments of inertia can be recomputed immediately. Volumes of reduced or increased density can be embedded to represent lungs, bones, or other structures within the body. The method was validated by reconstructing an ostrich body from a fleshed and defleshed carcass and comparing the estimated dimensions to empirically measured values from the original carcass. We then used the method to calculate the segmental masses, centers of mass, and moments of inertia for an adult Tyrannosaurus rex, with measurements taken directly from a complete skeleton. We compare these results to other estimates, using the model to compute the sensitivities of unknown parameter values based upon 30 different combinations of trunk, lung and air sac, and hindlimb dimensions. The conclusion that T. rex was not an exceptionally fast runner remains strongly supported by our models-the main area of ambiguity for estimating running ability seems to be estimating fascicle lengths, not body dimensions. Additionally, the craniad position of the CM in all of our models reinforces the notion that T. rex did not stand or move with extremely columnar, elephantine limbs. It required some flexion in the limbs to stand still, but how much flexion depends directly on where its CM is assumed to lie. Finally we used our model to test an unsolved problem in dinosaur biomechanics: how fast a huge biped like T. rex could turn. Depending on the assumptions, our whole body model integrated with a musculoskeletal model estimates that turning 45 degrees on one leg could be achieved slowly, in about 1-2s.     

Regression equations to predict segmental moments of inertia from anthropometric measurements: an extension of the data of Chandler et al. (1975)

A set of regression equations was developed to fully utilize the data of Chandler et al. (AMRL Technical Report 74-137, Wright-Patterson Air Force Base, 1975) to estimate segmental moments of inertia in living subjects. Using anthropometric measurements as predictors, moments of inertia can be computed about both transverse and longitudinal axes passing through each segment's center of mass. Symmetry about segment long axes is assumed. Because of the small sample size upon which these equations are based, it is suggested that they be used cautiously, especially to avoid extrapolation to subjects having anthropometric measurements outside the range of sample values.     

Mass, center of mass, and moment of inertia estimates for infant limb segments.

To quantify limb dynamics, accurate estimates are needed of anthropometric inertia parameters (mass, center-of-mass location, and moments of inertia). These estimates, however, are not available for human infants; therefore, the movement dynamics of infants have not been studied extensively. Here, regression equations for the masses, center-of-mass locations, and transverse moments of inertia of upper and lower limb segments (upper arm, forearm, and hand; thigh, leg, and foot) of 0.04 to 1.50 yr old infants are provided. A mathematical model of the human body was used to determine the anthropometric inertia parameters for upper limbs in 44 infants and for lower limbs in 70 infants. Stepwise linear regressions were used to fit the distributions of the anthropometric inertia parameters. The regression equations accounted for significant amounts of the variance (64-98%), and the R2-values compared favorably when our equations were cross-validated. Consequently, these regression equations can provide, for infants of similar ages, reasonable estimates of upper and lower limb anthropometric inertia parameters, suitable for equations of motion in the analysis of limb dynamics in human infants.     

Estimation of body composition from bioelectrical impedance of body segments

This study provides values of anthropometric measurements and specific impedance, for a sample of 104 adults. The hypothesis that the body composition can be estimated more accurately from measurements of lengths and impedance values of the body segments than from the whole body was tested. The impedance of upper and lower extremities (arm and leg) and trunk were used to compute estimates of body composition parameters (FFM, FM, %F, TBW, ECW). The results were compared with those estimated by the impedance of the whole body. These comparisons demonstrated that significative differences resulted from body composition obtained by segmental impedance and by the whole body.     

Prehistoric mongoloid dispersals. Edited by Takeru Akazawa and Emöke J. E. Szathmáry. New York: Oxford University Press. 1996. 387 pp. ISBN 0-19-852318-1 $150.00 (cloth)

Studies of the dynamics of locomotor performances depend on knowledge of the distribution of body mass within and between limb segments. However, these data are difficult to derive. Segment mass properties have generally been estimated by modelling limbs as truncated cones, but this approach fails to take into account that some segments are of elliptical, not circular, cross section; and further, the profiles of real segments are generally curved. Thus, they are more appropriately modelled as solids of revolution, described by the rotation in space of convex or concave curves, and the possibility of an elliptical cross section needs to be taken into account. In this project we have set out to develop a general geometric model which can take these factors into account, and permit segment inertial properties to be derived from cadavers by segmentation, and from living individuals using linear external measurements. We present a model which may be described by up to four parameters, depending o the profile and serial cross section (circular or ellipsoidal) of the individual segments. The parameters are obtained from cadavers using a simplified complex-pendulum technique, and from intact specimens by calculation from measurements of segment diameters and lengths. From the parameters, the center of mass, moments of inertia, and radii of gyration may be derived, using simultaneous equations. Inertial properties of the body segments of four Pan troglodytes and a single Pongo were determined, and contrasted to comparable findings for humans. Using our approach, the mass distribution characteristics of any individual or species may be represented by a rigid-link segment model or “android.” If this is made to move according to motion functions derived from a real performance of the individual represented, we show that recordings of resulting ground reaction forces may be quite closely simulated by predictive dynamic modelling. © 1996 Wiley-Liss, Inc.     

Estimation of male and female body segment parameters of the Bulgarian population using a 16-segmental mathematical model

Based on a large-scale anthropometric measurements of 5290 individuals (2435 males and 2855 females) of the Bulgarian population aged between 30 and 40 years, we present 16-segmental 3D geometrical model of the human body of the average Bulgarian male and female and calculate mass, volume, location of the mass center and moments of inertia for all the segments for both genders. This study extends current anthropometrical data pool of Caucasian. Wherever possible, the comparison between our model results and data reported in literature for other Caucasian shows an overall good agreement, thus supporting the validity of the described method.     

Analysis of body segment parameter differences between four human populations and the estimation errors of four popular mathematical models

Calculating the kinetics of motion using inverse or forward dynamics methods requires the use of accurate body segment inertial parameters. The methods available for calculating these body segment parameters (BSPs) have several limitations and a main concern is the applicability of predictive equations to several different populations. This study examined the differences in BSPs between 4 human populations using dual energy x-ray absorptiometry (DEXA), developed linear regression equations to predict mass, center of mass location (CM) and radius of gyration (K) in the frontal plane on 5 body segments and examined the errors produced by using several BSP sources in the literature. Significant population differences were seen in all segments for all populations and all BSPs except hand mass, indicating that population specific BSP predictors are needed. The linear regression equations developed performed best overall when compared to the other sources, yet no one set of predictors performed best for all segments, populations or BSPs. Large errors were seen with all models which were attributed to large individual differences within groups. Equations which account for these differences, including measurements of limb circumferences and breadths may provide better estimations. Geometric models use these parameters, however the models examined in this study did not perform well, possibly due to the assumption of constant density or the use of an overly simple shape. Creating solids which account for density changes or which mimic the mass distribution characteristics of the segment may solve this problem. Otherwise, regression equations specific for populations according to age, gender, race, and morphology may be required to provide accurate estimations of BSPs for use in kinetic equations of motion.     

Estimated fat, bone mineral, total body water and cell solids in females of two communities of Punjab, India

The data for the present study consist of 502 Jat-Sikh and 510 Bania females of Punjab (India), ranging in age from 20 to 80 years. The different components of the body i.e. fat, bone mineral, total body water and cell solids have been calculated from anthropometric measurements by applying different equations given by various investigators. While studying age changes in different components of the body, it is the fat component, which has undergone major fluctuations past maturity. It has increased significantly from age-group 20-29 to 40-49 in both Jat-Sikh and Bania females. A significant decrease in fat has been observed from age-group 60-69 to 70 +. The bone minerals have exhibited little changes with age. The total body water and cell solids show a significant increase from age-group 20-29 to 30-39, followed by a decrease in both the communities. The decrease in these two components is statistically significant from age-group 40-49 to 50-59 in Bania females only. While comparing the two communities it has been observed that bone minerals are significantly larger in Jat-Sikh females, and fat is significantly larger in Bania females except in the last two age-groups. The other two components i.e. total body water and cell solids show statistically non-significant differences in the two communities.     

Prediction of body volume by a stepwise linear regression technique

Body volume and 35 anthropometric measurements were obtained from 88 active soldiers using standard techniques. These anthropometric measurements were examined for their possible relationships to body volume using stepwise linear regression analysis. Four measurements (Body weight, anterior thigh skinfold thickness, subscapular skinfold thickness and suprailiac skinfold thickness) accounted for 99.7% of the variation in body volume and the introduction of each of these measurements in the equation was significant. The regression equation for predicting body volume from these 4 anthropometric measurements had a multiple correlation coefficient of 0.9987 (P less than 0.001). Body weight alone was correlated with body volume to the extent of 0.9966. An attempt has therefore been made to develop a multiple linear regression equation without incorporation of body weight in the regression analysis. Nine measurements were selected by stepwise linear regression analysis for predicting body volume. These nine measurements accounted for 97.1% of the variation in body volume. These equations have been validated on another small sample of 22 soldiers. The analysis has also revealed that a direct regression of body density from the anthropometric variables gives more accurate results than when estimated body volumes are utilized for calculating body density.     

Muscle force estimation in clinical gait analysis using AnyBody and OpenSim

A variety of musculoskeletal models are applied in different modelling environments for estimating muscle forces during gait. Influence of different modelling assumptions and approaches on model outputs are still not fully understood, while direct comparisons of standard approaches have been rarely undertaken. This study seeks to compare joint kinematics, joint kinetics and estimated muscle forces of two standard approaches offered in two different modelling environments (AnyBody, OpenSim). It is hypothesised that distinctive differences exist for individual muscles, while summing up synergists show general agreement. Experimental data of 10 healthy participants (28 ± 5 years, 1.72 ± 0.08 m, 69 ± 12 kg) was used for a standard static optimisation muscle force estimation routine in AnyBody and OpenSim while using two gait-specific musculoskeletal models. Statistical parameter mapping paired t-test was used to compare joint angle, moment and muscle force waveforms in Matlab. Results showed differences especially in sagittal ankle and hip angles as well as sagittal knee moments. Differences were also found for some of the muscles, especially of the triceps surae group and the biceps femoris short head, which occur as a result of different anthropometric and anatomical definitions (mass and inertia of segments, muscle properties) and scaling procedures (static vs. dynamic). Understanding these differences and their cause is crucial to operate such modelling environments in a clinical setting. Future research should focus on alternatives to classical generic musculoskeletal models (e.g. implementation of functional calibration tasks), while using experimental data reflecting normal and pathological gait to gain a better understanding of variations and divergent behaviour between approaches.     

Anthropometric characteristics of Indian cycle rickshaw pullers

In India, about 0.86 million people is engaged in pulling cycle rickshaws as occupation. There is no anthropometric data of cycle rickshaw pullers although data is available for Indian population. The objective of the study was to collect anthropometric data of the cycle rickshaw pullers so that these could be utilized for redesigning a cycle rickshaw. Anthropometric data for 34 body measurements were recorded from 880 rickshaw pullers (age 18 to 66 years) of four different places in India. The mean values of different standing heights, different lengths and breadths of cycle rickshaw pullers were significantly lower compared with Indian population. However, there was no significant difference in erect sitting height. The outcome of the research project is beneficial for the manufacturers of cycle rickshaws and similar products well as users of such products, including rickshaw pullers. The manufacturers would be able to use the data for fabricating newer models of cycle rickshaws which would be more compatible for rickshaw pullers as well as passengers.