Froude number corrections in anthropological studies

Cross slope gait biomechanics for individuals with and without a unilateral transtibial amputation

BACKGROUND

This research was conducted to better understand compensatory strategies during cross-slope walking for adults with and without a unilateral transtibial amputation.

METHODS

Fourteen individuals with unilateral transtibial amputation and 14 individuals with no lower limb amputation participated in this study. Motion and force data were captured while participants walked on a treadmill in a virtual reality environment for level and ± 5° cross slopes. Temporal-spatial parameters, kinematics (ankle, knee, hip, pelvis, trunk), and ground reaction forces were examined.

FINDINGS

Compared to level, participants had similar step width but slightly longer steps for top-cross-slope and slightly shorter steps for bottom-cross-slope. Top-cross-slope required a more flexed limb with ankle eversion, and bottom-cross-slope required a more extended limb with ankle inversion. Participants had similar lateral pelvis and trunk motion for all walking conditions, but slightly more anterior trunk lean for top cross-slope with more anterior trunk lean observed for individuals with a lower limb amputation than without lower limb amputation. Participants with a lower limb amputation compensated for limited prosthetic ankle-foot dorsiflexion on the top-cross-slope by increasing prosthetic side hip flexion, reducing intact ankle/knee flexion, and increasing intact push-off force.

INTERPRETATION

Gait adaptations during cross-slope walking were primarily in the lower extremities and were largely similar for those with and without a transtibial amputation. The information presented in this paper provides a better understanding of gait strategies adopted during cross-slope walking and can guide researchers and industry in prosthetic development.

Scaling of linear anthropometric dimensions in living humans

OBJECTIVES

Some previous studies suggest that humans do not conform to geometric similarity (isometry) in anthropometric dimensions of the upper and lower limbs. Researchers often rely on a single statistical approach to the study of scaling patterns, and it is unclear whether these methods produce similar results and are equally robust. This study used one bivariate and one multivariate method to examine how linear anthropometric dimensions scale in a sample of adult humans.

MATERIALS AND METHODS

Motion capture marker data from 104 adults of varying height and mass were used to calculate anthropometric dimensions. We analyzed scaling patterns in pooled and separate sexes with two methods: (1) bivariate log-log regression and (2) multivariate principal component analysis (PCA). We calculated 95% highest density/confidence intervals for each method and defined positive/negative allometry as estimates lying outside those intervals.

RESULTS

Results identified isometric scaling of the upper arm, thigh, and shoulder, positive allometry of the forearm and shank, and negative allometry of the pelvis in the pooled sample using both statistical methods. Patterns of allometry in the pooled sample were similar between methods but differed in magnitude. Sex-specific results differed in both pattern and magnitude between log-log regression and PCA. Only one measurement (shoulder width) departed from isometry in the sex-specific log-log regressions.

DISCUSSION

Our findings suggest that especially in sex-specific analyses, the pattern and magnitude of allometry are sensitive to statistical methodology. When body mass was selected as the size variable, most human linear anthropometric dimensions in this sample scaled isometrically and were therefore geometrically similar within sexes.

Quantifying intralimb coordination of terrestrial ungulates with Fourier coefficient affine superimposition

Many phenomena related to motor behaviour in animals are spatially and temporally periodic, making them accessible for transformation to the frequency domain via Fourier Series. Although this has been applied previously, it had not been noticed that the characteristic arrangement of Fourier coefficients in their complex-valued representation resembles landmarks in geometric morphometrics. We define a superimposition procedure in the frequency domain, which removes affine differences (mean, amplitude, phase) to reveal and compare the shape of periodic kinematic measures. This procedure is conceptually linked to dynamic similarity, which can thereby be assessed on the level of individual limb elements. We demonstrate how to make intralimb coordination accessible for large-scale, quantitative analyses. By applying this to a dataset from terrestrial ungulates, dominant patterns in forelimb coordination during walking are identified. This analysis shows that typical strides of these animals differ mostly in how much the limbs are lifted in the presence or absence of obstructive substrate features. This is shown to be independent of morphological features. Besides revealing fundamental characteristics of ungulate locomotion, we argue that the suggested method is generally suitable for the large-scale quantitative assessment of coordination and dynamics in periodic locomotor phenomena.

The Motion of Body Center of Mass During Walking: A Review Oriented to Clinical Applications

Human walking is usually conceived as the cyclic rotation of the limbs. The goal of lower-limb movements, however, is the forward translation of the body system, which can be mechanically represented by its center of mass (CoM). Lower limbs act as struts of an inverted pendulum, allowing minimization of muscle work, from infancy to old age. The plantar flexors of the trailing limbs have been identified as the main engines of CoM propulsion. Motion of the CoM can be investigated through refined techniques, but research has been focused on the fields of human and animal physiology rather than clinical medicine. Alterations in CoM motion could reveal motor impairments that are not detectable by clinical observation. The study of the three-dimensional trajectory of the CoM motion represents a clinical frontier. After adjusting for displacement due to the average forward speed, the trajectory assumes a figure-eight shape (dubbed the “bow-tie”) with a perimeter about 18 cm long. Its lateral size decreases with walking velocity, thus ensuring dynamic stability. Lateral redirection appears as a critical phase of the step, requiring precise muscle sequencing. The shape and size of the “bow-tie” as functions of dynamically equivalent velocities do not change from child to adulthood, despite anatomical growth. The trajectory of the CoM thus appears to be a promising summary index of both balance and the neural maturation of walking. In asymmetric gaits, the affected lower limb avoids muscle work by pivoting almost passively, but extra work is required from the unaffected side during the next step, in order to keep the body system in motion. Generally, the average work to transport the CoM across a stride remains normal. In more demanding conditions, such as walking faster or uphill, the affected limb can actually provide more work; however, the unaffected limb also provides more work and asymmetry between the steps persists. This learned or acquired asymmetry is a formerly unsuspected challenge to rehabilitation attempts to restore symmetry. Techniques of selective loading of the affected side, which include constraining the motion of the unaffected limb or forcing the use of the affected limb on split-belt treadmills which impose a different velocity and power to either limb, are now under scrutiny.

Humans, geometric similarity and the Froude number: is ''reasonably close'' really close enough?

Understanding locomotor energetics is imperative, because energy expended during locomotion, a requisite feature of primate subsistence, is lost to reproduction. Although metabolic energy expenditure can only be measured in extant species, using the equations of motion to calculate mechanical energy expenditure offers unlimited opportunities to explore energy expenditure, particularly in extinct species on which empirical experimentation is impossible. Variability, either within or between groups, can manifest as changes in size and/or shape. Isometric scaling (or geometric similarity) requires that all dimensions change equally among all individuals, a condition that will not be met in naturally developing populations. The Froude number (Fr), with lower limb (or hindlimb) length as the characteristic length, has been used to compensate for differences in size, but does not account for differences in shape.To determine whether or not shape matters at the intraspecific level, we used a mechanical model that had properties that mimic human variation in shape. We varied crural index and limb segment circumferences (and consequently, mass and inertial parameters) among nine populations that included 19 individuals that were of different size. Our goal in the current work is to understand whether shape variation changes mechanical energy sufficiently enough to make shape a critical factor in mechanical and metabolic energy assessments.Our results reaffirm that size does not affect mass-specific mechanical cost of transport (Alexander and Jayes, 1983) among geometrically similar individuals walking at equal Fr. The known shape differences among modern humans, however, produce sufficiently large differences in internal and external work to account for much of the observed variation in metabolic energy expenditure, if mechanical energy is correlated with metabolic energy. Any species or other group that exhibits shape differences should be affected similarly to that which we establish for humans. Unfortunately, we currently do not have a simple method to control or adjust for size-shape differences in individuals that are not geometrically similar, although musculoskeletal modeling is a viable, and promising, alternative. In mouse-to-elephant comparisons, size differences could represent the largest source of morphological variation, and isometric scaling factors such as Fr can compensate for much of the variability. Within species, however, shape differences may dominate morphological variation and Fr is not designed to compensate for shape differences. In other words, those shape differences that are "reasonably close" at the mouse-to-elephant level may become grossly different for within-species energetic comparisons.

Energetics, Locomotion, and Female Reproduction: Implications for Human Evolution

In our reconstructions of human evolution, a few key questions consistently rise to the surface. These questions tend to revolve around how the morphology of previous hominin species would have allowed them to gain access to resources during key life-history events, particularly gestation and lactation. Here the data surrounding the interactions between these key issues are assessed, making particular notes of recent advances in the fields of energetics and biomechanics as they relate to locomotion during reproduction. Reconstructions of body mass, lower limb length, and pelvic breadth suggest diverse mobility strategies for different hominin species and may offer some clues about the demographic shifts occurring in the late Pleistocene.

Kinematics of quadrupedal locomotion in sugar gliders (Petaurus breviceps): effects of age and substrate size

Arboreal mammals face unique challenges to locomotor stability. This is particularly true with respect to juveniles, who must navigate substrates similar to those traversed by adults, despite a reduced body size and neuromuscular immaturity. Kinematic differences exhibited by juveniles and adults on a given arboreal substrate could therefore be due to differences in body size relative to substrate size, to differences in neuromuscular development, or to both. We tested the effects of relative body size and age on quadrupedal kinematics in a small arboreal marsupial (the sugar glider, Petaurus breviceps; body mass range of our sample 33-97 g). Juvenile and adult P. breviceps were filmed moving across a flat board and three poles 2.5, 1.0 and 0.5 cm in diameter. Sugar gliders (regardless of age or relative speed) responded to relative decreases in substrate diameter with kinematic adjustments that promote stability; they increased duty factor, increased the average number of supporting limbs during a stride, increased relative stride length and decreased relative stride frequency. Limb phase increased when moving from the flat board to the poles, but not among poles. Compared with adults, juveniles (regardless of relative body size or speed) used lower limb phases, more pronounced limb flexion, and enhanced stability with higher duty factors and a higher average number of supporting limbs during a stride. We conclude that although substrate variation in an arboreal environment presents similar challenges to all individuals, regardless of age or absolute body size, neuromuscular immaturity confers unique problems to growing animals, requiring kinematic compensation.

Comparative intralimb coordination in avian bipedal locomotion

Analyses of how intralimb coordination during locomotion varies within and across different taxa are necessary for understanding the morphological and neurological basis for locomotion in general. Previous findings suggest that intralimb proportions are the major source of kinematic variation that governs intralimb coordination across taxa. Also, independence of kinematics from habitat preference and phylogenetic position has been suggested for mammals. This leads to the hypothesis that among equally-sized bird species exhibiting equal limb proportions similar kinematics can be observed. To test this hypothesis, the bipedal locomotion of two distantly related ground-dwelling bird species (Eudromia elegans and Coturnix coturnix) and of a less terrestrial species (Corvus monedula) was investigated by means of a biplanar high-speed x-ray videographic analysis. Birds were exhibiting similar intralimb proportions and were filmed over a broad range of speed while moving on a treadmill. Joint- and limb element angles, as well as pelvic rotations, were quantified. Regarding fore-aft motions of the limb joints and elements, a congruent pattern of intralimb coordination was observed among all experimental species. The sample of species suggests that it is largely independent of their habitat preference and systematic position and it seems to be related to demands for coping with an irregular terrain with a minimum of necessary control. Hence, the initial hypothesis was confirmed. However, this congruence is not found when looking at medio-lateral limb motions and pelvic rotations, showing distinct differences between ground-dwellers (e.g., largely restricted to a parasagittal plane) and Corvus (e.g., an increased mobility of the hip joint).

Thermoregulation and endurance running in extinct hominins: Wheeler's models revisited

Thermoregulation is often cited as a potentially important influence on the evolution of hominins, thanks to a highly influential series of papers in the Journal of Human Evolution in the 1980s and 1990s by Peter Wheeler. These papers developed quantitative modeling of heat balance between different potential hominins and their environment. Here, we return to these models, update them in line with new developments and measurements in animal thermal biology, and modify them to represent a running hominin rather than the stationary form considered previously. In particular, we use our modified Wheeler model to investigate thermoregulatory aspects of the evolution of endurance running ability. Our model suggests that for endurance running to be possible, a hominin would need locomotive efficiency, sweating rates, and areas of hairless skin similar to modern humans. We argue that these restrictions suggest that endurance running may have been possible (from a thermoregulatory viewpoint) for Homo erectus, but is unlikely for any earlier hominins.

Experimentally generated footprints in sand: Analysis and consequences for the interpretation of fossil and forensic footprints

Fossilized footprints contain information about the dynamics of gait, but their interpretation is difficult, as they are the combined result of foot anatomy, gait dynamics, and substrate properties. We explore how footprints are generated in modern humans. Sixteen healthy subjects walked on a solid surface and in a layer of fine-grained sand. In each condition, 3D kinematics of the leg and foot were analyzed for three trials at preferred speed, using an infrared camera system. Additionally, calibrated plantar pressures were recorded. After each trial in sand, the depth of the imprint was measured under specific sites. When walking in sand, subjects showed greater toe clearance during swing and a 7 degrees higher knee yield during stance. Maximal pressure was the most influential factor for footprint depth under the heel. For other foot zones, a combination of factors correlates with imprint depth, with pressure impulse (the pressure-time integral) gaining importance distally, at the metatarsal heads and the hallux. We conclude that footprint topology cannot be related to a single variable, but that different zones of the footprint reflect different aspects of the kinesiology of walking. Therefore, an integrated approach, combining anatomical, kinesiological, and substrate-mechanical insights, is necessary for a correct interpretation.

Modern humans are not (quite) isometric

Allometric relationships are important sources of information for many types of anthropological and biological research. The baseline for all allometric relationships is isometry (or geometric similarity), the principal that shape is invariant of size. Here, we formally test for geometric similarity in modern humans, looking at the maximum lengths of four long bones (humerus, radius, femur, and tibia). We use Jolicoeur's multivariate allometry method to examine globally distributed samples of human populations, both collectively and individually. Results indicate that humans are not geometrically similar, although morphological deviations from isometry are small.

The energetics of human walking: is Froude number (Fr) useful for metabolic comparisons?

Velocity and body mass have well-known influences on the amount of metabolic energy that animals require to walk. This relationship could stem from the fact that both are key variables in calculating the mechanical energy of a system in motion. Other variables, like leg length, are also important in mechanical energy calculations and two mechanical formulations that incorporate leg length, Froude number (Fr) and the LiMb model, have been shown to correlate with human metabolic energy expenditure. Both, however, include velocity as a key variable in their calculations, so we wondered if the correlation might derive solely from their relationship with velocity rather than leg length. Using the energetic data and gait parameters from 24 human adults and 48 children, we tested several variables - velocity (V), V(2), body mass, leg length, Fr and LiMb - to see which combinations best explained the variation in oxygen consumption, a proxy of metabolic energy expenditure. An equation with V(2), body mass and leg length as covariates produced the highest R(2), explaining 88% of the variation when all subjects were combined. No significant differences in the predictive power of velocity, V(2), Fr or LiMb were detected, prompting us to conclude that neither Fr nor LiMb compensate for the effect of leg length. Leg length does influence the energetic expenditure of walking humans, but Fr and LiMb do not appear to adequately reflect that effect. The development of another method to compensate for the effect of leg length on metabolic energy consumption is essential.