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.     

Measurement of body segment mass,center of gravity,and determination of moments of inertia by double pendulum in Lemur fulvus

The collection of data on physical parameters of body segments is a preliminary critical step in studying the biomechanics of locomotion. Little data on nonhuman body segment parameters has been published. The lack of standardization of techniques for data collection and presentation has made the comparative use of these data difficult and at times impossible. This study offers an approach for collecting data on center of gravity and moments of inertia for standardized body segments. The double swing pendulum approach is proposed as a solution for difficulties previously encountered in calculating moments of inertia for body segments. A format for prompting a computer to perform these calculations is offered, and the resulting segment mass data for Lemur fulvus is presented.     

Adjustments to McConville et al. and Young et al. body segment inertial parameters

Body segment inertial parameters (BSIPs) are important data in biomechanics. They are usually estimated from predictive equations reported in the literature. However, most of the predictive equations are ambiguously applicable in the conventional 3D segment coordinate systems (SCSs). Also, the predictive equations reported in the literature all include two assumptions: the centre of mass and the proximal and distal endpoints are assumed to be aligned, and the inertia tensor is assumed to be principal in the segment axes. These predictive equations, restraining both position of the centre of mass and orientation of the principal axes of inertia, become restrictive when computing 3D inverse dynamics, when analyzing the influence of BSIP estimations on joint forces and moments and when evaluating personalized 3D BSIPs obtained from medical imaging. In the current study, the extensive data from McConville et al. (1980. Anthropometric relationships of body and body segment moments of inertia. AFAMRL-TR-80-119, Aerospace Medical Research Laboratory, Wright-Patterson Air Force Base, Dayton, Ohio) and from Young et al. (1983. Anthropometric and mass distribution characteristics of the adults female. Technical Report AFAMRL-TR-80-119, FAA Civil Aeromedical Institute, Oklaoma City, Oklaoma) are adjusted in order to correspond to joint centres and to conventional segment axes. In this way, scaling equations are obtained for both males and females that provide BSIPs which are directly applicable in the conventional SCSs and do not restrain the position of the centre of mass and the orientation of the principal axes. These adjusted scaling equations may be useful for researchers who wish to use appropriate 3D BSIPs for posture and movement analysis.     

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)     

A point cluster method for in vivo motion analysis: applied to a study of knee kinematics.

A new method for deriving limb segment motion from markers placed on the skin is described. The method provides a basis for determining the artifact associated with nonrigid body movement of points placed on the skin. The method is based on a cluster of points uniformly distributed on the limb segment. Each point is assigned an arbitrary mass. The center of mass and the inertia tensor of this cluster of points are calculated. The eigenvalues and eigenvectors of the inertia tensor are used to define a coordinate system in the cluster as well as to provide a basis for evaluating non-rigid body movement. The eigenvalues of the inertia tensor remain invariant if the segment is behaving as a rigid body, thereby providing a basis for determining variations for nonrigid body movement. The method was tested in a simulation model where systematic and random errors were introduced into a fixed cluster of points. The simulation demonstrated that the error due to nonrigid body movement could be substantially reduced. The method was also evaluated in a group of ten normal subjects during walking. The results for knee rotation and translation obtained from the point cluster method compared favorably to results previously obtained from normal subjects with intra-cortical pins placed into the femur and tibia. The resulting methodology described in this paper provides a unique approach to the measurement of in vivo motion using skin-based marker systems.     

Automatic determination of anatomical coordinate systems for three-dimensional bone models of the isolated human knee

The combination of three-dimensional (3-D) models with dual fluoroscopy is increasingly popular for evaluating joint function in vivo. Applying these modalities to study knee motion with high accuracy requires reliable anatomical coordinate systems (ACSs) for the femur and tibia. Therefore, a robust method for creating ACSs from 3-D models of the femur and tibia is required. We present and evaluate an automated method for constructing ACSs for the distal femur and proximal tibia based solely on 3-D bone models. The algorithm requires no observer interactions and uses model cross-sectional area, center of mass, principal axes of inertia, and cylindrical surface fitting to construct the ACSs. The algorithm was applied to the femur and tibia of 10 (unpaired) human cadaveric knees. Due to the automated nature of the algorithm, the within specimen variability is zero for a given bone model. The algorithm’s repeatability was evaluated by calculating variability in ACS location and orientation across specimens. Differences in ACS location and orientation between specimens were low (<1.5 mm and <2.5°). Variability arose primarily from natural anatomical and morphological differences between specimens. The presented algorithm provides an alternative method for automatically determining subject-specific ACSs from the distal femur and proximal tibia.     

In vitro assessment of a motion-based optimization method for locating the talocrural and subtalar joint axes

The locations of the joint axes of the ankle complex vary considerably between subjects, yet no noninvasive method with demonstrated accuracy exists for locating these axes. The moments of muscle and ground reaction forces about the joint axes are dependent on axis locations, making knowledge of these locations critical to accurate musculoskeletal modeling of the foot and ankle. The accuracy of a computational optimization method that fits a two-revolute model to measured motion was assessed using computer-generated data, a two-revolute mechanical linkage, and three lower-leg cadaver specimens. Motions were applied to cadaver specimens under axial load while bone-mounted markers attached to the tibia, talus, and calcaneus were tracked using a video-based motion analysis system. Estimates of the talocrural and subtalar axis locations were computed from motions of the calcaneus relative to the tibia using the optimization method. These axes were compared to mean helical axes computed directly from tibia, talus, and calcaneus motions. The optimization method performed well when the motions were computer-generated or measured in the mechanical linkage, with angular differences between optimization and mean helical axes ranging from 1 deg to 5 deg. In the cadaver specimens, however, these differences exceeded 20 deg. Optimization methods that locate the anatomical joint axes of the ankle complex by fitting two revolute joints to measured tibia-calcaneus motions may be limited because of problems arising from non-revolute behavior.     

Evaluation of a 3D object registration method for analysis of humeral kinematics

In 3D image-based studies of joint kinematics, 3D registration methods should be automatic, insensitive to segmentation inconsistencies and use coordinate systems that have clinically relevant orientations and locations because this is important for analyzing rotation angles and translation directions. We developed and evaluated a registration method, which is based on the cylindrical geometry of the humerus shaft and an analysis of the inertia moments of the humerus head, in order to consistently and automatically orient the humerus coordinate system according to its anatomy. Registration techniques must be thoroughly evaluated. In this study we used a well-detectable marker as reference, from which coordinate system determination errors of a 3D object could be measured. This allowed us to quantify by means of unique error analysis the translational and rotational errors in terms of how much and about/along which humeral axis errors occurred. The evaluation experiments were performed using virtual rotations of 3D humeral binary image, a humerus model and a 3D image of a volunteer's shoulder. They indicated that the humeral coordinate system determination errors primarily originated from segmentation inconsistencies, which influenced mostly the humeral transverse axes orientation. The error analysis revealed that the developed registration method reduced the effect of manual segmentation inconsistencies on the orientation of the humeral transverse axes up to 37%, in comparison to the commonly used inertia registration.     

Anterior cruciate ligament injury induced by internal tibial torsion or tibiofemoral compression

The knee is one of the most frequently injured joints in the human body. Approximately 91% of ACL injuries occur during sporting activities, usually from a non-contact event. The most common kinetic scenarios related with ACL injuries are internal twisting of the tibia relative to the femur or combined torque and compression during a hard landing. The hypothesis of this study was that the magnitudes and types of motion observed after ACL rupture would significantly change from the relative joint displacements present just before ACL injury. Compression or torsion experiments were conducted on 7 pairs of knee joints with repetitive tests at increasing intensity until catastrophic failure. ACL injury was documented in all cases at 5.4±2 kN of TF compression or 33±13 Nm of internal tibial torque. The femur displaced posteriorly relative to the tibia in pre-failure and with a higher magnitude in failure tests under both loading conditions. In compression experiments there was internal rotation of the tibia in pre-failure tests, but external rotation of the tibia after the ACL failed. In torsion experiments, failure occurred at 58±19° of internal tibial rotation, and valgus rotation of the femur increased significantly after ACL injury. These new data show that the joint motions can vary in magnitude and direction before and after failure of the ACL. Video-based studies consistently document external rotation of the tibia combined with valgus knee bending as the mechanism of ACL injury although these motions could be occurring after ACL rupture.     

Scaling of the appendicular skeleton of the giraffe (Giraffa camelopardalis)

Giraffes have remarkably long and slender limb bones, but it is unknown how they grow with regard to body mass, sex, and neck length. In this study, we measured the length, mediolateral (ML) diameter, craniocaudal (CC) diameter and circumference of the humerus, radius, metacarpus, femur, tibia, and metatarsus in 10 fetuses, 21 females, and 23 males of known body masses. Allometric exponents were determined and compared. We found the average bone length increased from 340 ± 50 mm at birth to 700 ± 120 mm at maturity, while average diameters increased from 30 ± 3 to 70 ± 11 mm. Fetal bones increased with positive allometry in length (relative to body mass) and in diameter (relative to body mass and length). In postnatal giraffes bone lengths and diameters increased iso‐ or negatively allometric relative to increases in body mass, except for the humerus CC diameter which increased with positive allometry. Humerus circumference also increased with positive allometry, that of the radius and tibia isometrically and the femur and metapodials with negative allometry. Relative to increases in bone length, both the humerus and femur widened with positive allometry. In the distal limb bones, ML diameters increased isometrically (radius, metacarpus) or positively allometric (tibia, metatarsus) while the corresponding CC widths increased with negative allometry and isometrically, respectively. Except for the humerus and femur, exponents were not significantly different between corresponding front and hind limb segments. We concluded that the patterns of bone growth in males and females are identical. In fetuses, the growth of the appendicular skeleton is faster than it is after birth which is a pattern opposite to that reported for the neck. Allometric exponents seemed unremarkable compared to the few species described previously, and pointed to the importance of neck elongation rather than leg elongation during evolution. Nevertheless, the front limb bones and especially the humerus may show adaptation to behaviors such as drinking posture. J. Morphol. 276:503–516, 2015. © 2014 Wiley Periodicals, Inc.     

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.     

Are fixed limb inertial models valid for dynamic simulations of human movement?

During human movement, muscle activation and limb movement result in subtle changes in muscle mass distribution. Muscle mass redistribution can affect limb inertial properties and limb dynamics, but it is not currently known to what extent. The objectives of this study were to investigate: (1) how physiological alterations of muscle and tendon length affect limb inertial characteristics, and (2) how such changes affect dynamic simulations of human movement. To achieve these objectives, a digital model of a human leg, custom software, and Software for interactive musculoskeletal modeling were used to simulate mass redistribution of muscle–tendon structures within a limb segment during muscle activation and joint movement. Thigh and shank center of mass and moments of inertia for different muscle activation and joint configurations were determined and compared. Limb inertial parameters representing relaxed muscles and fully active muscles were input into a simulated straight-leg movement to evaluate the effect inertial parameter variations could have on movement simulation results. Muscle activation and limb movement altered limb segment center of mass and moments of inertia by less than 0.04 cm and 1.2%, respectively. These variations in limb inertial properties resulted in less than 0.01% change in maximum angular velocity for a simulated straight-leg hip flexion task. These data demonstrate that, for the digital human leg model considered, assuming static quantities for segment center of masses and moments of inertia in movement simulations appear reasonable and induce minimal errors in simulated movement dynamics.     

Coordination of leg muscles during speed skating

Five speed skaters of elite performance level and six speed skaters of trained level were subjected to an inverse dynamical analysis during speed skating. Push-off forces were registered by means of special skates. Myoelectric activity (EMG) of ten leg muscles and cinematographic data were recorded. Linked segment modelling yielded net joint moments and joint powers. The speed skating technique is characterized by a typical horizontal position of the trunk and a suppression of a plantar flexion during the push-off. This technique, necessary to reduce external friction, constrains the transfer of rotation in joints to translation of the mass center of the body. In spite of constrained push-off, the EMG levels of the leg muscles show a proximo-distal temporal order which to a certain extent is comparable to that previously found in an unconstrained vertical jump. This proximo-distal sequence is also reflected by the time courses of the net moment and net power output in hip, knee and ankle joints. The temporal sequence in activation levels of activated muscles is not different between elite and trained speed skaters. The difference in performance level between these groups obviously has an origin in the ability of the elite speed skaters to realise larger net joint moments. Differences in net joint moments and in kinematics result in a higher power output and a lower air frictional force for the elite than for the trained speed skaters.     

An investigation of the interactions between lower-limb bone morphology,limb inertial properties and limb dynamics

Bone mass and size clearly affect the safety and survival of wild animals as well as human beings, however, little is known about the interactions between bone size and movement dynamics. A modeling approach was used to investigate the hypothesis that increased bone cortical area causes increased limb moments of inertia, decreased lower-limb movement maximum velocities, and increased energy requirements to sustain submaximum lower-limb locomotion movements. Custom software and digital data of a human leg were used to simulate femur, tibia, and fibula cortical bone area increases of 0%, 22%, 50%, and 80%. Limb segment masses, center of mass locations, and moments of inertia in the sagittal plane were calculated for each bone condition. Movement simulations of unloaded running and cycling motions were performed. Linear regression analyses were used to determine the magnitude of the effect cortical area has on limb moment of inertia, velocity, and the internal work required to move the limbs at a given velocity. The thigh and shank moment of inertia increased linearly up to 1.5% and 6.9%, respectively for an 80% increase in cortical area resulting in 1.3% and 2.0% decreases in maximum unloaded cycling and running velocities, respectively, and in 3.0% and 2.9% increases in internal work for the cycling and running motions, respectively. These results support the hypothesis and though small changes in movement speed and energy demands were observed, such changes may have played an important role in animal survival as bones evolved and became less robust.     

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.     

Residual stress distribution in rabbit limb bones

The presence of the residual stresses in bone tissue has been noted and the authors have reported that there are residual stresses in bone tissue. The aim of our study is to measure the residual stress distribution in the cortical bone of the extremities of vertebrates and to describe the relationships with the osteon population density. The study used the rabbit limb bones (femur, tibia/fibula, humerus, and radius/ulna) and measured the residual stresses in the bone axial direction at anterior and posterior positions on the cortical surface. The osteons at the sections at the measurement positions were observed by microscopy. As a result, the average stresses at the hindlimb bones and the forelimb bones were 210 and 149 MPa, respectively. In the femur, humerus, and radius/ulna, the residual stresses at the anterior position were larger than those at the posterior position, while in the tibia, the stress at the posterior position was larger than that at the anterior position. Further, in the femur and humerus, the osteon population densities in the anterior positions were larger than those in the posterior positions. In the tibia, the osteon population density in the posterior position was larger than that in the anterior position. Therefore, tensile residual stresses were observed at every measurement position in the rabbit limb bones and the value of residual stress correlated with the osteon population density (r=0.55, P<0.01).     

Changes in segmental inertial properties with age

The purpose of this study was to examine how the limb segment inertial parameters vary across the decades from the 1920s to the 1970s. Sixty-six males participated in this study, ranging in age from 20 to 79 years. Pre-screening ensured that all subjects were healthy. The inertial properties of the segments were determined by modeling each segment as series of geometric solids. A multivariate analysis of variance (ANOVA) revealed statistically significant differences between decade age groups for the upper arm, forearm, shank, and thigh (p<0.01). Subsequent ANOVAs revealed statistically significant differences for all the inertial properties for the upper arm, the center of mass location for the forearm, and segment mass for the thigh. Linear regression lines were fit to the data so that each inertial parameter for each segment could be predicted by subject's age, with the slope of this regression line indicating the trend in the data. These trends were statistically significant for all forearm inertial parameters, thigh mass and longitudinal moment of inertia, and forearm center of mass location. The changes for the thigh, upper arm, and forearm were consistent with the changes, which would accompany a change in muscle mass with aging. Resultant joint moments were computed for a set of gait data using inertial properties reflective of the subjects from the age extremes in the study. The resulting differences in the knee and hip moments, young versus old, were all less than 4.5%.     

Structural adaptations of the femur and humerus to arboreal and terrestrial environments in three species of macaque

One reason to measure cross-sectional structural properties of primate long bones is to define mechanically relevant complexes of traits that describe the adaptation of bone to different biomechanical environments. This can be effectively accomplished when congeneric species having different postural and locomotor behaviors are compared. This paper compares the cross-sectional geometry of the femur and humerus in three behaviorally different macaque species as a basis for defining such patterns. Cross-sectional moments of inertia in the standard anatomical planes were calculated at five locations along the diaphyses of the femur and humerus in Macaca fascicularis, M. nemestrina, and M. mulatta. The data suggest that the "barrel-shaped" femur is associated with behaviors for which long limbs and small body size are an asset. This may be associated with, but is not restricted to, leaping behaviors. The data also suggest that structural rigidity of the femur and humerus is greater per unit body weight in primates that spend significant amounts of time in terrestrial environments than in those that are more restricted to climbing in arboreal environments.     

Cineradiographic study of forelimb movements during quadrupedal walking in the brown lemur (Eulemur fulvus, Primates: Lemuridae)

Movements of forelimb joints and segments during walking in the brown lemur (Eulemur fulvus) were analyzed using cineradiography (150 frames/sec). Metric gait parameters, forelimb kinematics, and intralimb coordination are described. Calculation of contribution of segment displacements to stance propulsion shows that scapular retroversion in a fulcrum near the vertebral border causes more than 60% of propulsion. The contribution by the shoulder joint is 30%, elbow joint 5%, and wrist joint 1%. Correlation analysis was applied to reveal the interdependency between metric and kinematic parameters. Only the effective angular movement of the elbow joint during stance is speed-dependent. Movements of all other forelimb joints and segments are independent of speed and influence, mainly, linear gait parameters (stride length, stance length). Perhaps the most important result is the hitherto unknown and unexpected degree of scapular mobility. Scapular movements consist of ante-/retroversion, adduction/abduction, and scapular rotation about the longitudinal axis. Inside rotation of the scapula (60 degrees -70 degrees ), together with flexion in the shoulder joint, mediates abduction of the humerus, which is not achieved in the shoulder joint, and is therefore strikingly different from humeral abduction in man. Movements of the shoulder joint are restricted to flexion and extension. At touch down, the shoulder joint of the brown lemur is more extended compared to that of other small mammals. The relatively long humerus and forearm, characteristic for primates, are thus effectively converted into stride length. Observed asymmetries in metric and kinematic behavior of the left and right forelimb are caused by an unequal lateral bending of the spinal column.