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.     

Joint axes of rotation and body segment parameters of pig limbs

To enable a quantification of net joint moments and joint reaction forces, indicators of joint loading, this study aimed to locate the mediolateral joint axes of rotation and establish the body segment parameters of the limbs of pigs (Sus scrofa). To locate the joint axes of rotation the scapulohumeral, humeroradial, carpal complex, metacarpophalangeal, coxofemoral, femorotibial, tarsal, and metatarsophalangeal joints from 12 carcasses were studied. The joints were photographed in three positions, bisecting lines drawn at fixed landmarks with their intersection marking the joint axes of rotation. The body segment parameters, i.e. the segment mass, center of mass and moment of inertia were measured on the humerus, radius/ulna, metacarpus, forepastern, foretoe, femur, tibia, metatarsus, hindpastern, and hindtoe segments from five carcasses. The segments were weighed, and their center of mass was found by balancing them. The moments of inertia of the humerus, radius/ulna, femur and tibia were found by rotating the segments. The moments of inertia of the remaining segments were calculated. Generally, the joint axes of rotation were near the attachment site of the lateral collateral ligaments. The forelimb, with segments taken as one, was significantly lighter and shorter than the hindlimb (P < 0.001). In all segments the center of mass was located 31 to 50% distal to the proximal segment end. The segment mass decreased with distance from the trunk, as did the segment moment of inertia. The results may serve as reference on the location of the joint axes of rotation and on the body segment parameters for inverse dynamic modeling of pigs.     

Changes in segment inertia proportions between 4 and 20 years

Growth between 4 and 20 yr produces an increase in body mass and a redistribution of that mass throughout the body. It is the purpose of this investigation to describe changes in the segment mass, radius to the mass centre and radius of gyration for a sample of males, 4-20 yr and the potential effects of these changes on joint reaction forces and moments. The data were collected annually over 9 yr in a mixed longitudinal study completed in 1985. Elliptical zones 2 cm wide were used to model the 16 segments of the body. From these and reported segment densities, mass, the coordinates of the mass centre and the principal moments of inertia were determined for the segments and the body. The parameters reported are the inertia parameters suitable for a sagittal planar analysis with the head and neck considered one segment and values given for other fused segments. The accuracy of the method was judged against the total body mass, and other accuracy estimates from the literature were examined. The parameters are presented as proportions of total mass or segment length. It is clear from the polynomial regressions that there is a substantial redistribution of the mass between segments and this is consistent with the principles of cephalo-caudal and distal-to-proximal development. The proportions for radius and radius of gyration indicate that mass redistribution within segments is comparatively small. The parameters for a 6 yr-old were compared to the parameters expected at 18, 24 and 54 yr and substantial differences noted.(ABSTRACT TRUNCATED AT 250 WORDS)     

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.     

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.     

A sensitivity analysis method for the body segment inertial parameters based on ground reaction and joint moment regressor matrices

This paper presents a method allowing a simple and efficient sensitivity analysis of dynamics parameters of complex whole-body human model. The proposed method is based on the ground reaction and joint moment regressor matrices, developed initially in robotics system identification theory, and involved in the equations of motion of the human body. The regressor matrices are linear relatively to the segment inertial parameters allowing us to use simple sensitivity analysis methods. The sensitivity analysis method was applied over gait dynamics and kinematics data of nine subjects and with a 15 segments 3D model of the locomotor apparatus. According to the proposed sensitivity indices, 76 segments inertial parameters out the 150 of the mechanical model were considered as not influent for gait. The main findings were that the segment masses were influent and that, at the exception of the trunk, moment of inertia were not influent for the computation of the ground reaction forces and moments and the joint moments. The same method also shows numerically that at least 90% of the lower-limb joint moments during the stance phase can be estimated only from a force-plate and kinematics data without knowing any of the segment inertial parameters.     

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.     

Assessment of the mass,length, center of mass,and principal moment of inertia of body segments in adult males of the brown anole (Anolis sagrei) and green,or carolina,anole (Anolis carolinensis)

This study provides a morphometric data set of body segments that are biomechanically relevant for locomotion in two ecomorphs of adult male anoles, namely, the trunk‐ground Anolis sagrei and the trunk‐crown Anolis carolinensis. For each species, 10 segments were characterized, and for each segment, length, mass, location of the center of mass, and radius of gyration were measured or calculated, respectively. The radii of gyration were computed from the moments of inertia by using the double swing pendulum method. The trunk‐ground A. sagrei has relatively longer and stockier hindlimbs and forelimbs with smaller body than A. carolinensis. These differences between the two ecomorphs demonstrated a clear relationship between morphology and performance, particularly in the context of predator avoidance behavior, such as running or jumping in A. sagrei and crypsis in A. carolinensis. Our results provide new perspectives on the mechanism of adaptive radiation as the limbs of the two species appear to scale via linear factors and, therefore, may also provide explanations for the mechanism of evolutionary changes of structures within an ecological context. J. Morphol., 2012. © 2012 Wiley Periodicals, Inc.     

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.     

An efficient probabilistic methodology for incorporating uncertainty in body segment parameters and anatomical landmarks in joint loadings estimated from inverse dynamics

Inverse dynamics is a standard approach for estimating joint loadings in the lower extremity from kinematic and ground reaction data for use in clinical and research gait studies. Variability in estimating body segment parameters and uncertainty in defining anatomical landmarks have the potential to impact predicted joint loading. This study demonstrates the application of efficient probabilistic methods to quantify the effect of uncertainty in these parameters and landmarks on joint loading in an inverse-dynamics model, and identifies the relative importance of the parameters and landmarks to the predicted joint loading. The inverse-dynamics analysis used a benchmark data set of lower-extremity kinematics and ground reaction data during the stance phase of gait to predict the three-dimensional intersegmental forces and moments. The probabilistic analysis predicted the 1-99 percentile ranges of intersegmental forces and moments at the hip, knee, and ankle. Variabilities, in forces and moments of up to 56% and 156% of the mean values were predicted based on coefficients of variation less than 0.20 for the body segment parameters and standard deviations of 2 mm for the anatomical landmarks. Sensitivity factors identified the important parameters for the specific joint and component directions. Anatomical landmarks affected moments to a larger extent than body segment parameters. Additionally, for forces, anatomical landmarks had a larger effect than body segment parameters, with the exception of segment masses, which were important to the proximal-distal joint forces. The probabilistic modeling approach predicted the range of possible joint loading, which has implications in gait studies, clinical assessments, and implant design evaluations.     

Predictive regression modeling of body segment parameters using individual-based anthropometric measurements

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 (Merrill et al., 2017). Estimated errors in the prediction of BSPs can be as large as 40%, depending on age, and the prediction method employed (Durkin and Dowling, 2003). Thus, more accurate and representative segment parameter inputs are required for attempting to predict modeling outputs such as joint contact forces, muscle forces, and injury risk in individuals. This study aims to provide statistical models for predicting torso, thigh, shank, upper arm, and forearm segment parameters in working adults using whole body dual energy x-ray absorptiometry (DXA) scan data along with a set of anthropometric measurements. The statistical models were developed on a training data set, and independently validated on a separate test data set. The predicted BSPs in validation data were, on average, within 5% of the actual in vivo DXA-based BSPs, while previously developed predictions (de Leva, 1996) had average errors of up to 60%, indicating that the new models greatly increase the accuracy in predicting segment parameters. These final developed models can be used for calculating representative BSPs in individuals for use in modeling applications dependent on these parameters.     

A 3D Generic Inverse Dynamic Method using Wrench Notation and Quaternion Algebra

In the literature, conventional 3D inverse dynamic models are limited in three aspects related to inverse dynamic notation, body segment parameters and kinematic formalism. First, conventional notation yields separate computations of the forces and moments with successive coordinate system transformations. Secondly, the way conventional body segment parameters are defined is based on the assumption that the inertia tensor is principal and the centre of mass is located between the proximal and distal ends. Thirdly, the conventional kinematic formalism uses Euler or Cardanic angles that are sequence-dependent and suffer from singularities.

In order to overcome these limitations, this paper presents a new generic method for inverse dynamics. This generic method is based on wrench notation for inverse dynamics, a general definition of body segment parameters and quaternion algebra for the kinematic formalism.     

A rigid body model of the forearm

In this article the forearm, with its complex, continuous motion of masses during pronation/supination, was approximated by a rigid body model consisting of a radial segment rotating around an ulnar segment. The method used to obtain the model parameters is based on three-dimensional voxel data that include velocity information. We propose a criterion that allows the voxels to be attributed to either of the two segments. It is based on the notion that the rotational kinetic energy determined from the voxel data equals the kinetic energy of the rigid body model. To obtain a three-dimensional smoothing we further propose a parameterization of the shape of both segments. These shapes can then be used to determine the dynamic integrals of the segments, i.e. mass, center of mass, and inertia. Using this approach we determined all model parameters for a human forearm from three series of MRI scans in a supinated, a pronated, and an intermediate position. In the appendix, a procedure is described that allows the dynamic quantities to be scaled homogeneously without recalculation of the integrals. Thus, this article provides all essential parameters required for three-dimensional dynamic simulations of general movements of the forearm.     

Evolution of larval segment position across 12 Drosophila species*

Many developmental traits that are critical to the survival of the organism are also robust. These robust traits are resistant to phenotypic change in the face of variation. This presents a challenge to evolution. In this article, we asked whether and how a well-established robust trait, Drosophila segment patterning, changed over the evolutionary history of the genus. We compared segment position scaled to body length at the first-instar larval stage among 12 Drosophila species. We found that relative segment position has changed many times across the phylogeny. Changes were frequent, but primarily small in magnitude. Phylogenetic analysis demonstrated that rates of change in segment position are variable along the Drosophila phylogenetic tree, and that these changes can occur in short evolutionary timescales. Correlation between position shifts of segments decreased as the distance between two segments increased, suggesting local control of segment position. The posterior-most abdominal segment showed the highest magnitude of change on average, had the highest rate of evolution between species, and appeared to be evolving more independently as compared to the rest of the segments. This segment was exceptionally elongated in the cactophilic species in our dataset, raising questions as to whether this change may be adaptive.     

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.     

A 3D generic inverse dynamic method using wrench notation and quaternion algebra

In the literature, conventional 3D inverse dynamic models are limited in three aspects related to inverse dynamic notation, body segment parameters and kinematic formalism. First, conventional notation yields separate computations of the forces and moments with successive coordinate system transformations. Secondly, the way conventional body segment parameters are defined is based on the assumption that the inertia tensor is principal and the centre of mass is located between the proximal and distal ends. Thirdly, the conventional kinematic formalism uses Euler or Cardanic angles that are sequence-dependent and suffer from singularities. In order to overcome these limitations, this paper presents a new generic method for inverse dynamics. This generic method is based on wrench notation for inverse dynamics, a general definition of body segment parameters and quaternion algebra for the kinematic formalism.     

Quantitative approaches to utilizing mutational analysis and disulfide crosslinking for modeling a transmembrane domain.

The transmembrane domain of chemoreceptor Trg from Escherichia coli contains four transmembrane segments in its native homodimer, two from each subunit. We had previously used mutational analysis and sulfhydryl cross-linking between introduced cysteines to obtain data relevant to the three-dimensional organization of this domain. In the current study we used Fourier analysis to assess these data quantitatively for periodicity along the sequences of the segments. The analyses provided a strong indication of alpha-helical periodicity in the first transmembrane segment and a substantial indication of that periodicity for the second segment. On this basis, we considered both segments as idealized alpha-helices and proceeded to model the transmembrane domain as a unit of four helices. For this modeling, we calculated helical crosslinking moments, parameters analogous to helical hydrophobic moments, as a quantitative way of condensing and utilizing a large body of crosslinking data. Crosslinking moments were used to define the relative separation and orientation of helical pairs, thus creating a quantitatively derived model for the transmembrane domain of Trg. Utilization of Fourier transforms to provide a quantitative indication of periodicity in data from analyses of transmembrane segments, in combination with helical crosslinking moments to position helical pairs should be useful in modeling other transmembrane domains.     

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.     

The effect of perturbing body segment parameters on calculated joint moments and muscle forces during gait

This study examined the effect of body segment parameter (BSP) perturbations on joint moments calculated using an inverse dynamics procedure and muscle forces calculated using computed muscle control (CMC) during gait. BSP (i.e. segment mass, center of mass location (com) and inertia tensor) of the left thigh, shank and foot of a scaled musculoskeletal model were perturbed. These perturbations started from their nominal value and were adjusted to ±40% in steps of 10%, for both individual as well as combined perturbations in BSP. For all perturbations, an inverse dynamics procedure calculated the ankle, knee and hip moments based on an identical inverse kinematics solution. Furthermore, the effect of applying a residual reduction algorithm (RRA) was investigated. Muscle excitations and resulting muscle forces were calculated using CMC. The results show only a limited effect of an individual parameter perturbation on the calculated moments, where the largest effect is found when perturbing the shank com (MS_com,shank, the ratio of absolute difference in torque and relative parameter perturbation, is maximally −7.81 N m for hip flexion moment). The additional influence of perturbing two parameters simultaneously is small (MS_{mass+com,thigh} is maximally 15.2 N m for hip flexion moment). RRA made small changes to the model to increase the dynamic consistency of the simulation (after RRA MS_com,shank is maximally 5.01 N m). CMC results show large differences in muscle forces when BSP are perturbed. These result from the underlying forward integration of the dynamic equations.     

Evaluation of a pictorial method to obtain subject‐specific inertial properties in equine limb segments

Data describing segmental masses and moments of inertia (MOI) of limb segments are required for inverse dynamic calculations. In horses, these values are usually calculated using regression equations that have been developed from a limited number of horses representing a small number of breeds. The objective of the present study was to evaluate the performance of a scaling method and a pictorial method for estimating of the values of segmental masses, lengths, and MOI in the equine limb segments by comparing their output with the standard technique involving direct measurements. Limbs of 30 horses of various breeds and sizes were disarticulated post mortem. Segmental masses, lengths, and MOI were determined using a standard method based on weighing the segments, measuring their length with calipers, and estimating the MOI from the rotational frequency of a trifilar pendulum. The scaling method used a jack‐knifing procedure to avoid the need for two data sets. The pictorial method was based on digitization of two orthogonal photographs to determine segmental volumes, which were combined with published values for average segment densities to determine the inertial parameters. Scaling method and pictorial method provided comparable estimation of segmental messes and lengths, but the scaling method performed better in estimating segmental MOI. The scaling method worked well enough in the majority of horses but there were a few horses in which it was less effective. The pictorial method sometimes showed a bias correctable by regression equations but it may not warrant the additional effort unless for specific cases.