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.     

Effects of the Racket Polar Moment of Inertia on Dominant Upper Limb Joint Moments during Tennis Serve

This study examined the effect of the polar moment of inertia of a tennis racket on upper limb loading in the serve. Eight amateur competition tennis players performed two sets of 10 serves using two rackets identical in mass, position of center of mass and moments of inertia other than the polar moment of inertia (0.00152 vs 0.00197 kg.m²). An eight-camera motion analysis system collected the 3D trajectories of 16 markers, located on the thorax, upper limbs and racket, from which shoulder, elbow and wrist net joint moments and powers were computed using inverse dynamics. During the cocking phase, increased racket polar moment of inertia was associated with significant increases in the peak shoulder extension and abduction moments, as well the peak elbow extension, valgus and supination moments. During the forward swing phase, peak wrist extension and radial deviation moments significantly increased with polar moment of inertia. During the follow-through phase, the peak shoulder adduction, elbow pronation and wrist external rotation moments displayed a significant inverse relationship with polar moment of inertia. During the forward swing, the magnitudes of negative joint power at the elbow and wrist were significantly larger when players served using the racket with a higher polar moment of inertia. Although a larger polar of inertia allows players to better tolerate off-center impacts, it also appears to place additional loads on the upper extremity when serving and may therefore increase injury risk in tennis players.     

Biomechanical study of the programming of anticipatory postural adjustments associated with voluntary movement

The present research concerns anticipatory postural adjustments (APA), with the purpose of determining whether they are preprogrammed and of specifying their biomechanical finality. The experimental situation allowed us to distinguish between the voluntary movement itself (an upper limb elevation) and the postural adjustments associated with it. To this aim, the upper limb kinematics, evaluated from an accelerometer fixed at wrist level, were compared to the whole body dynamics, recorded by means of a force platform. Movements, executed in series of five, were studied according to three conditions: bilateral flexions (BF) and unilateral flexions (UF), with (IUF) and without (OUF) an additional inertia, of the stretched upper limb(s). Six right handed adults were tested twice. Results showed that the ground reaction resultant forces as well as the ground reaction resultant moment about the vertical axis presented reproducible variations before and after the onset of upper limb acceleration. The biomechanical organization of APA corresponded, for the three experimental conditions, to an upward and forward acceleration of the body center of gravity, and also, for UF, to a resultant moment directed towards the contralateral side. The duration of APA varied with the characteristics of the forthcoming voluntary movement, increasing significantly from BF to OUF and from OUF to IUF. It is concluded that APA correspond to dynamic phenomena which are centrally preprogrammed. The inertia forces associated with APA may, when the time comes, balance the inertia forces due to the movement of the mobile limb therefore counteracting the disturbance to postural equilibrium.(ABSTRACT TRUNCATED AT 250 WORDS)     

儿童的惯性－惯量特征及其生长

本文应用排水法得到儿童肢体沿长轴的体积分布函数。根据关于人类肢体体积－质量的假定,肢体的质心、转动惯量及旋转半径等动力学常数可由前述的体积分布函数中求出。本文结果显示,部分力学参数与儿童的生长有着密切的联系,并受到性别的影响。因此,这些参数可以用来作为儿童的生长指标。以往数据的离散性表明,无论从系统上或技术上,这一领域都有许多工作要做。     

儿童的惯性－惯量特征及其生长

本文应用排水法得到儿童肢体沿长轴的体积分布函数。根据关于人类肢体体积－质量的假定，肢体的质心、转动惯量及旋转半径等动力学常数可由前述的体积分布函数中求出。本文结果显示，部分力学参数与儿童的生长有着密切的联系，并受到性别的影响。因此，这些参数可以用来作为儿童的生长指标。以往数据的离散性表明，无论从系统上或技术上，这一领域都有许多工作要做。     

Post-hatching growth and development of the pectoral and pelvic limbs in the black noddy, Anous minutus

The black tern (Anous minutus) uses a semi-precocial growth strategy. Terrestrial locomotor capacity occurs soon after hatching, but pectoral limb development is delayed and flight is not possible until about post-hatching day 50. A growth series (hatchlings to fledglings) was used to explore how limb musculoskeletal development varied with body mass. In the pelvic limb, bone lengths scaled isometrically or with negative allometry. Gastrocnemius muscle mass and the failure load and stiffness of the tibiotarsus scaled isometrically. In the pectoral limb, pectoralis and supracoracoideus muscle masses increased with strong positive allometry that was mirrored by increases in wing bone strength and stiffness. Bending strength (sigma(ult)) and modulus (E) remained fairly constant throughout development to fledging for all limb bones. The moment of inertia (I) scaled with negative allometry for the tibiotarsus and with strong positive allometry in the wing bones. Differences in sigma(ult) and E of the tibiotarsus between pre-fledged chicks and adults was due, primarily, to increases in bone density rather than increases in the moment of inertia of the skeletal elements, whereas sigma(ult) of wing bones was a function of increases in both bone density and I. Early development of functional pelvic limbs in tree-nesting birds is relatively unusual, and presumably reflects a familial trait that does not appear to compromise breeding success in this species.     

Post-hatching growth and development of the pectoral and pelvic limbs in the black noddy, Anous minutus.

The black tern (Anous minutus) uses a semi-precocial growth strategy. Terrestrial locomotor capacity occurs soon after hatching, but pectoral limb development is delayed and flight is not possible until about post-hatching day 50. A growth series (hatchlings to fledglings) was used to explore how limb musculoskeletal development varied with body mass. In the pelvic limb, bone lengths scaled isometrically or with negative allometry. Gastrocnemius muscle mass and the failure load and stiffness of the tibiotarsus scaled isometrically. In the pectoral limb, pectoralis and supracoracoideus muscle masses increased with strong positive allometry that was mirrored by increases in wing bone strength and stiffness. Bending strength (sigma(ult)) and modulus (E) remained fairly constant throughout development to fledging for all limb bones. The moment of inertia (I) scaled with negative allometry for the tibiotarsus and with strong positive allometry in the wing bones. Differences in sigma(ult) and E of the tibiotarsus between pre-fledged chicks and adults was due, primarily, to increases in bone density rather than increases in the moment of inertia of the skeletal elements, whereas sigma(ult) of wing bones was a function of increases in both bone density and I. Early development of functional pelvic limbs in tree-nesting birds is relatively unusual, and presumably reflects a familial trait that does not appear to compromise breeding success in this species.     

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.     

Scale Effects between Body Size and Limb Design in Quadrupedal Mammals

Recently the metabolic cost of swinging the limbs has been found to be much greater than previously thought, raising the possibility that limb rotational inertia influences the energetics of locomotion. Larger mammals have a lower mass-specific cost of transport than smaller mammals. The scaling of the mass-specific cost of transport is partly explained by decreasing stride frequency with increasing body size; however, it is unknown if limb rotational inertia also influences the mass-specific cost of transport. Limb length and inertial properties – limb mass, center of mass (COM) position, moment of inertia, radius of gyration, and natural frequency – were measured in 44 species of terrestrial mammals, spanning eight taxonomic orders. Limb length increases disproportionately with body mass via positive allometry (length ∝ body mass^0.40); the positive allometry of limb length may help explain the scaling of the metabolic cost of transport. When scaled against body mass, forelimb inertial properties, apart from mass, scale with positive allometry. Fore- and hindlimb mass scale according to geometric similarity (limb mass ∝ body mass^1.0), as do the remaining hindlimb inertial properties. The positive allometry of limb length is largely the result of absolute differences in limb inertial properties between mammalian subgroups. Though likely detrimental to locomotor costs in large mammals, scale effects in limb inertial properties appear to be concomitant with scale effects in sensorimotor control and locomotor ability in terrestrial mammals. Across mammals, the forelimb''s potential for angular acceleration scales according to geometric similarity, whereas the hindlimb''s potential for angular acceleration scales with positive allometry.     

The area moment of inertia of the tibia: A risk factor for stress fractures

In a prospective study of stress fractures among Israeli infantry recruits, the area moment of inertia of the tibia was found to have a statistically significant correlation with the incidence of tibial, femoral and total stress fractures. Recruits with "low" area moments of inertia of the tibia were found to have higher stress fracture morbidity than those with "high" area moments of inertia. The best correlation was obtained when the area moment of inertia was calculated about the AP axis of bending at a cross-sectional level corresponding to the narrowest tibial width on lateral X-rays, a point which is at the distal quarter of the tibia. This finding indicates that bending forces about the approximate AP axis are an important causal factor for tibial and many other stress fractures. The bone's bending strength, or ability to resist bending moments, as measured by the area moment of inertia, helps determine risk to stress fracture.     

Convergence of forelimb and hindlimb Natural Pendular Period in baboons (Papio cynocephalus) and its implication for the evolution of primate quadrupedalism

The patterns of muscle mass distribution along the lengths of limbs may have important effects on the mechanics and energetics of quadrupedalism. Specifically, Myers and Steudel (J. Morphol. 234 (1997) 183) have shown that fore- and hindlimb Natural Pendular Periods (NPPs) may affect quadrupedal kinematics and must converge to reduce locomotor energetic costs. This study quantifies patterns of limb mass distribution in a live sample of Papio cynocephalus using limb inertial properties (mass, center of mass, mass moment of inertia, and radius of gyration). These inertial properties are calculated using a geometric modeling technique similar to that of Crompton et al. (Am. J. phys. Anthrop. 99 (1996) 547). The inertial properties in Papio are compared to those of Canis from Myers and Steudel (J. Morphol. 234 (1997) 183). The Papio sample has convergent fore- and hindlimb NPPs. Additionally, these limb NPPs are relatively large compared to those of Canis due to the relatively distally distributed limb mass in the Papio sample (relatively large limb masses, relatively distal centers of mass and radii of gyration, and relatively large limb mass moments of inertia). This relatively distal limb mass appears related to the grasping abilities of their hands and feet. Causal links are explored between limb shape adaptations for grasping hands and feet and the kinematics of primate quadrupedalism. In particular, if primates in general follow Papio's limb mass distribution pattern, then relatively large limb NPPs may lead to the relatively low stride frequencies already documented for primates. The kinematics of primate quadrupedalism appears to have been strongly influenced by both selection for grasping hands and feet and selection for reduced locomotor energetic costs.     

Energetic benefits and adaptations in mammalian limbs: Scale effects and selective pressures

Differences in limb size and shape are fundamental to mammalian morphological diversity; however, their relevance to locomotor costs has long been subject to debate. In particular, it remains unknown if scale effects in whole limb morphology could partially underlie decreasing mass‐specific locomotor costs with increasing limb length. Whole fore‐ and hindlimb inertial properties reflecting limb size and shape—moment of inertia (MOI), mass, mass distribution, and natural frequency—were regressed against limb length for 44 species of quadrupedal mammals. Limb mass, MOI, and center of mass position are negatively allometric, having a strong potential for lowering mass‐specific locomotor costs in large terrestrial mammals. Negative allometry of limb MOI results in a 40% reduction in MOI relative to isometry's prediction for our largest sampled taxa. However, fitting regression residuals to adaptive diversification models reveals that codiversification of limb mass, limb length, and body mass likely results from selection for differing locomotor modes of running, climbing, digging, and swimming. The observed allometric scaling does not result from selection for energetically beneficial whole limb morphology with increasing size. Instead, our data suggest that it is a consequence of differing morphological adaptations and body size distributions among quadrupedal mammals, highlighting the role of differing limb functions in mammalian evolution.     

Differences in lower limb transverse plane joint moments during gait when expressed in two alternative reference frames

When comparing previous studies that have measured the three-dimensional moments acting about the lower limb joints (either external moments or opposing internal joint moments) during able-bodied adult gait, significant variation is apparent in the profiles of the reported transverse plane moments. This variation cannot be explained on the basis of adopted convention (i.e. external versus internal joint moment) or inherent variability in gait strategies. The aim of the current study was to determine whether in fact the frame in which moments are expressed has a dominant effect upon transverse plane moments and thus provides a valid explanation for the observed inconsistency in the literature. Kinematic and ground reaction force data were acquired from nine able-bodied adult subjects walking at a self-selected speed. Three-dimensional hip, knee and ankle joint moments during gait were calculated using a standard inverse dynamics approach. In addition to calculating internal joint moments, the components of the external moment occurring in the transverse plane at each of the lower limb joints were calculated to determine their independent effects. All moments were expressed in both the laboratory frame (LF) as well as the anatomical frame (AF) of the distal segment. With the exception of the ankle rotation moment in the foot AF, lower limb transverse plane joint moments during gait were found to display characteristic profiles that were consistent across subjects. Furthermore, lower limb transverse plane joint moments during gait differed when expressed in the distal segment AF compared to the LF. At the hip, the two alternative reference frames produced near reciprocal joint moment profiles. The components of the external moment revealed that the external ground reaction force moment was primarily responsible for this result. Lower limb transverse plane joint moments during gait were therefore found to be highly sensitive to a change in reference frame. These findings indicate that the different transverse plane joint moment profiles during able-bodied adult gait reported in the literature are likely to be explained on this basis.     

基于频谱图像灰度共生矩阵的无损测温方法

本文提出了一种基于哈达玛变换的频谱图像灰度共生矩阵(Hadamard-GLCM)的高强度聚焦超声治疗无损测温方法。利用高强度聚焦超声辐照新鲜离体猪肉组织,获取辐照前后的B超图像的减影图像,采用Hadamard变换对其进行处理,获取频谱图像,将频谱图像的灰度共生矩阵惯性矩作为反应温度变化的信息参数。实验表明:不仅单组数据的Hadamard-GLCM惯性矩(HGMI)和温度能很好的线性拟合,而且多组数据的Hadamard-GLCM惯性矩与温度也成近似的线性关系,而且斜率非常接近,拟合度更接近1,误差小,对温度的分辨能力高,容错能力强,与传统的测温方法相比有着明显的优势,能为HIFU治疗过程中的无损测温提供有效的实时依据。     

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.     

Dynamic analysis of a simplified bone model during the process of fracture healing

The dynamic analysis of fracture healing is tackled numerically by means of a bone model which uses the finite element method. The model is of non-uniform cross-sectional area and moment of inertia. Shear and rotatory inertia are taken into account. Considerable variation of the upper natural frequencies is observed as the healing process progresses. The practical implications, as well as present limitations, of the technique are examined.     

Simple and efficient approach to preparation of molecular drawings

A convenient approach to the preparation of good quality molecular drawings is described. The method is based on transforming the atomic coordinates provided by a conventional crystallographic structure analysis or deduced from a model of a particular molecule, to a suitably weighted molecular inertia system and forming a projection of the molecule down the axis that corresponds to its highest moment of inertia. When implemented in a routine which prepares the input to the program ORTEP, the new method very nearly eliminates trial-and-error procedures from the preparation of a molecular diagram with suitable orientation of the molecule.     

Humeral cross-sectional morphology from 18th century Quebec prisoners of war: Limits to activity reconstruction

This study uses measures of cross-sectional robusticity and asymmetry (based on humeral areal and inertial cross-sectional components) to test a prediction from bone remodeling theory that a physically active 18th century Quebec prisoner of war sample (N = 25) should have more robust and asymmetrical humeri than a nonphysically active 20th century New Mexico suburbanite sample (N = 27). Narrative accounts document that prisoners of war engaged in labor-intensive activities, and these activities were confirmed by observations of osteoarthritis and other pathologies. The suburbanite sample, for the most part, did not engage in such activities. The prisoners had higher levels of pathology than the suburbanites (e.g., 80% vs. 22% osteoarthritis; F = 17.95, P < 0.01). For robusticity, the populations did not differ significantly in total area, cortical area, moment areas of inertia about the mediolateral plane, or polar moment area of inertia. The Quebec prison sample did have significantly higher values for moment areas of inertia about the anteroposterior plane. For asymmetry, the populations did not differ in any values (total area, cortical area, moment areas of inertia about the mediolateral plane, moment areas of inertia about the anteroposterior plane, or polar moment of inertia). Thus, examinations of cross-sectional robusticity and asymmetry failed to conclusively confirm the hypothesis that intensive labor leads to changes in humeral morphology. Possible explanations for the lack of differences are discussed, such as poor diet impeding bone remodeling. Nevertheless, the one significant finding suggests that cross-sectional shape is more useful in reconstructing activity patterns than amount of bone in a cross section. Results from this study join those from other recent investigations to suggest that additional controls are required before cross-sectional differences may be confidently attributed to activity patterns.     

A general model for estimating lower extremity inertial properties of individuals with transtibial amputation

Lower extremity joint moment magnitudes during swing are dependent on the inertial properties of the prosthesis and residual limb of individuals with transtibial amputation (TTA). Often, intact limb inertial properties (INTACT) are used for prosthetic limb values in an inverse dynamics model even though these values overestimate the amputated limb’s inertial properties. The purpose of this study was to use subject-specific (SPECIFIC) measures of prosthesis inertial properties to generate a general model (GENERAL) for estimating TTA prosthesis inertial properties. Subject-specific mass, center of mass, and moment of inertia were determined for the shank and foot segments of the prosthesis (n = 11) using an oscillation technique and reaction board. The GENERAL model was derived from the means of the SPECIFIC model. Mass and segment lengths are required GENERAL model inputs. Comparisons of segment inertial properties and joint moments during walking were made using three inertial models (unique sample; n = 9): (1) SPECIFIC, (2) GENERAL, and (3) INTACT. Prosthetic shank inertial properties were significantly smaller with the SPECIFIC and GENERAL model than the INTACT model, but the SPECIFIC and GENERAL model did not statistically differ. Peak knee and hip joint moments during swing were significantly smaller for the SPECIFIC and GENERAL model compared with the INTACT model and were not significantly different between SPECIFIC and GENERAL models. When subject-specific measures are unavailable, using the GENERAL model produces a better estimate of prosthetic side inertial properties resulting in more accurate joint moment measurements for individuals with TTA than the INTACT model.     

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.