Pygmy locomotion

Relating cardiorespiratory responses to work rate during incremental ramp exercise on treadmill in children and adolescents: sex and age differences

PURPOSE

Evaluation of cardiopulmonary exercise testing (CPET) slopes such as [Formula: see text] (cardiac/skeletal muscle function) and [Formula: see text] (O2 delivery/utilization), using treadmill protocols is limited because the difficulties in measuring the total work rate ([Formula: see text]). To overcome this limitation, we proposed a new method in quantifying [Formula: see text] to determine CPET slopes.

METHODS

CPET's were performed by healthy patients, (n = 674, 9-18 year) 300 female (F) and 374 male (M), using an incremental ramp protocol on a treadmill. For this protocol, a quantitative relationship based on biomechanical principles of human locomotion, was used to quantify the [Formula: see text] of the subject. CPET slopes were determined by linear regression of the data recorded until the gas exchange threshold occurred.

RESULTS

The method to estimate [Formula: see text] was substantiated by verifying that: [Formula: see text] for treadmill exercise corresponded to an efficiency of muscular work similar to that of cycle ergometer; [Formula: see text] (mL min-1 W-1) was invariant with age and greater in M than F older than 12 years old (13-14 years: 9.6 ± 1.5(F) vs. 10.5 ± 1.8(M); 15-16 years: 9.7 ± 1.7(F) vs. 10.6 ± 2.2(M); 17-18 years: 9.6 ± 1.7(F) vs. 11.0 ± 2.3(M), p < 0.05); similar to cycle ergometer exercise, [Formula: see text] was inversely related to body weight (BW) (r = 0.71) or [Formula: see text] (r = 0.66) and [Formula: see text] was not related to BW (r = - 0.01), but had a weak relationship with [Formula: see text] (r = 0.28).

CONCLUSION

The proposed approach can be used to estimate [Formula: see text] and quantify CPET slopes derived from incremental ramp protocols at submaximal exercise intensities using the treadmill, like the cycle ergometer, to infer cardiovascular and metabolic function in both healthy and diseased states.

The loss of the 'pelvic step' in human evolution

Human bipedalism entails relatively short strides compared with facultatively bipedal primates. Unique non-sagittal-plane motions associated with bipedalism may account for part of this discrepancy. Pelvic rotation anteriorly translates the hip, contributing to bipedal stride length (i.e. the 'pelvic step'). Facultative bipedalism in non-human primates entails much larger pelvic rotation than in humans, suggesting that a larger pelvic step may contribute to their relatively longer strides. We collected data on the pelvic step in bipedal chimpanzees and over a wide speed range of human walking. At matched dimensionless speeds, humans have 26.7% shorter dimensionless strides, and a pelvic step 5.4 times smaller than bipedal chimpanzees. Differences in pelvic rotation explain 31.8% of the difference in dimensionless stride length between the two species. We suggest that relative stride lengths and the pelvic step have been significantly reduced throughout the course of hominin evolution.

Whole-body and segmental analysis of body composition in adult males with achondroplasia using dual X-ray absorptiometry

Achondroplasia is a condition characterized by a genetic mutation affecting long bone endplate development. Current data suggests that the bone mineral content (BMC) and bone mineral density (BMD) of achondroplasic populations are below age matched individuals of average stature (controls). Due to the disproportionate limb-to-torso length compared to controls however, the lower BMC and BMD may be nullified when appropriately presented. The aim of this study was to measure whole-body and segmental body composition in adult males with achondroplasia (N = 10, 22 ±3 yrs), present data relative to whole-body and whole-limb values and compare all values to age matched controls (N = 17, 22 ±2 yrs). Dual X-ray absorptiometry (DEXA) was used to measure the in vivo mass of the whole-body and 15 segments, from which BMD, BMC, fat free mass (FFM) and body fat mass were measured. BMC of lumbar vertebrae (L1-4) was also measured and presented as a volumetric BMD (BMDVOL). The achondroplasic group had less BMC, BMD and FFM, and more body fat mass than controls as a whole-body measure. The lower achondroplasic BMC and BMD was somewhat nullified when presented relative to whole-body and whole-limb values respectively. There was no difference in lumbar BMDVOL between groups. Whole-body BMD measures presented the achondroplasic group as 'osteopenic'. When relative to whole-limb measures however, achondroplasic BMD descriptions were normal. Further work is needed to create a body composition database for achondroplasic population's, or for clinicians to present achondroplasic body composition values relative to the whole-limb.

The Oxygen Consumption and Metabolic Cost of Walking and Running in Adults With Achondroplasia

The disproportionate body mass and leg length of Achondroplasic individuals may affect their net oxygen consumption (V͘O₂) and metabolic cost (C) when walking at running compared to those of average stature (controls). The aim of this study was to measure submaximal V͘O₂ and C during a range of set walking speeds (SWS; 0.56 – 1.94 m⋅s^-1, increment 0.28 m⋅s^-1), set running speeds (SRS; 1.67 – 3.33 m⋅s^-1, increment 0.28 m⋅s^-1) and a self-selected walking speed (SSW). V͘O₂ and C was scaled to total body mass (TBM) and fat free mass (FFM) while gait speed was scaled to leg length using Froude’s number (Fr). Achondroplasic V͘O_2TBM and V͘O_2FFM were on average 29 and 35% greater during SWS (P < 0.05) and 12 and 18% higher during SRS (P < 0.05) than controls, respectively. Achondroplasic C_TBM and C_FFM were 29 and 33% greater during SWS (P < 0.05) and 12 and 18% greater during SRS (P < 0.05) than controls, respectively. There was no difference in SSW V͘O_2TBM or V͘O_2FFM between groups (P > 0.05), but C_TBM and C_FFM at SSW were 23 and 29% higher (P < 0.05) in the Achondroplasic group compared to controls, respectively. V͘O_2TBM and V͘O_2FFM correlated with Fr for both groups (r = 0.984 – 0.999, P < 0.05). Leg length accounted for the majority of the higher V͘O_2TBM and V͘O_2FFM in the Achondroplasic group, but further work is required to explain the higher Achondroplasic C_TBM and C_FFM at all speeds compared to controls.

New and Noteworthy: There is a leftward shift of oxygen consumption scaled to total body mass and fat free mass in Achondroplasic adults when walking and running. This is nullified when talking into account leg length. However, despite these scalars, Achondroplasic individuals have a higher walking and metabolic cost compared to age matched non-Achondroplasic individuals, suggesting biomechanical differences between the groups.

Human Locomotion in Hypogravity: From Basic Research to Clinical Applications

We have considerable knowledge about the mechanisms underlying compensation of Earth gravity during locomotion, a knowledge obtained from physiological, biomechanical, modeling, developmental, comparative, and paleoanthropological studies. By contrast, we know much less about locomotion and movement in general under sustained hypogravity. This lack of information poses a serious problem for human space exploration. In a near future humans will walk again on the Moon and for the first time on Mars. It would be important to predict how they will move around, since we know that locomotion and mobility in general may be jeopardized in hypogravity, especially when landing after a prolonged weightlessness of the space flight. The combination of muscle weakness, of wearing a cumbersome spacesuit, and of maladaptive patterns of locomotion in hypogravity significantly increase the risk of falls and injuries. Much of what we currently know about locomotion in hypogravity derives from the video archives of the Apollo missions on the Moon, the experiments performed with parabolic flight or with body weight support on Earth, and the theoretical models. These are the topics of our review, along with the issue of the application of simulated hypogravity in rehabilitation to help patients with deambulation problems. We consider several issues that are common to the field of space science and clinical rehabilitation: the general principles governing locomotion in hypogravity, the methods used to reduce gravity effects on locomotion, the extent to which the resulting behavior is comparable across different methods, the important non-linearities of several locomotor parameters as a function of the gravity reduction, the need to use multiple methods to obtain reliable results, and the need to tailor the methods individually based on the physiology and medical history of each person.

The mechanical function of the tibialis posterior muscle and its tendon during locomotion

The tibialis posterior (TP) muscle is believed to provide mediolateral stability of the subtalar joint during the stance phase of walking as it actively lengthens to resist pronation at foot contact and then actively shortens later in stance to contribute to supination. Because of its anatomical structure of short muscle fibres and long series elastic tissue, we hypothesised that TP would be a strong candidate for energy storage and return. We investigated the potential elastic function of the TP muscle and tendon through simultaneous measurements of muscle fascicle length (ultrasound), muscle tendon unit length (musculoskeletal modelling) and muscle activation (intramuscular electromyography). In early stance, TP fascicles actively shortened as the entire muscle-tendon unit lengthened, resulting in the absorption of energy through stretch of the series elastic tissue. Energy stored in the tendinous tissue from early stance was maintained during mid-stance, although a small amount of energy may have been absorbed via minimal shortening in the series elastic elements and lengthening of TP fascicles. A significant amount of shortening occurred in both the fascicles and muscle-tendon unit in late stance, as the activation of TP decreased and power was generated. The majority of the shortening was attributable to shortening of the tendinous tissue. We conclude that the tendinous tissue of TP serves two primary functions during walking: 1) to buffer the stretch of its fascicles during early stance and 2) to enhance the efficiency of the TP through absorption and return of elastic strain energy.

Gait Transitions in Human Infants: Coping with Extremes of Treadmill Speed

Spinal pattern generators in quadrupedal animals can coordinate different forms of locomotion, like trotting or galloping, by altering coordination between the limbs (interlimb coordination). In the human system, infants have been used to study the subcortical control of gait, since the cerebral cortex and corticospinal tract are immature early in life. Like other animals, human infants can modify interlimb coordination to jump or step. Do human infants possess functional neuronal circuitry necessary to modify coordination within a limb (intralimb coordination) in order to generate distinct forms of alternating bipedal gait, such as walking and running? We monitored twenty-eight infants (7–12 months) stepping on a treadmill at speeds ranging between 0.06–2.36 m/s, and seventeen adults (22–47 years) walking or running at speeds spanning the walk-to-run transition. Six of the adults were tested with body weight support to mimic the conditions of infant stepping. We found that infants could accommodate a wide range of speeds by altering stride length and frequency, similar to adults. Moreover, as the treadmill speed increased, we observed periods of flight during which neither foot was in ground contact in infants and in adults. However, while adults modified other aspects of intralimb coordination and the mechanics of progression to transition to a running gait, infants did not make comparable changes. The lack of evidence for distinct walking and running patterns in infants suggests that the expression of different functional, alternating gait patterns in humans may require neuromuscular maturation and a period of learning post-independent walking.

Architecture and functional ecology of the human gastrocnemius muscle-tendon unit

The gastrocnemius muscle-tendon unit (MTU) is central to human locomotion. Structural variation in the human gastrocnemius MTU is predicted to affect the efficiency of locomotion, a concept most often explored in the context of performance activities. For example, stiffness of the Achilles tendon varies among individuals with different histories of competitive running. Such a finding highlights the functional variation of individuals and raises the possibility of similar variation between populations, perhaps in response to specific ecological or environmental demands. Researchers often assume minimal variation in human populations, or that industrialized populations represent the human species as well as any other. Yet rainforest hunter-gatherers, which often express the human pygmy phenotype, contradict such assumptions. Indeed, the human pygmy phenotype is a potential model system for exploring the range of ecomorphological variation in the architecture of human hindlimb muscles, a concept we review here.

Estimation of quasi-stiffness of the human hip in the stance phase of walking

This work presents a framework for selection of subject-specific quasi-stiffness of hip orthoses and exoskeletons, and other devices that are intended to emulate the biological performance of this joint during walking. The hip joint exhibits linear moment-angular excursion behavior in both the extension and flexion stages of the resilient loading-unloading phase that consists of terminal stance and initial swing phases. Here, we establish statistical models that can closely estimate the slope of linear fits to the moment-angle graph of the hip in this phase, termed as the quasi-stiffness of the hip. Employing an inverse dynamics analysis, we identify a series of parameters that can capture the nearly linear hip quasi-stiffnesses in the resilient loading phase. We then employ regression analysis on experimental moment-angle data of 216 gait trials across 26 human adults walking over a wide range of gait speeds (0.75-2.63 m/s) to obtain a set of general-form statistical models that estimate the hip quasi-stiffnesses using body weight and height, gait speed, and hip excursion. We show that the general-form models can closely estimate the hip quasi-stiffness in the extension (R(2) = 92%) and flexion portions (R(2) = 89%) of the resilient loading phase of the gait. We further simplify the general-form models and present a set of stature-based models that can estimate the hip quasi-stiffness for the preferred gait speed using only body weight and height with an average error of 27% for the extension stage and 37% for the flexion stage.

Estimation of quasi-stiffness of the human knee in the stance phase of walking

Biomechanical data characterizing the quasi-stiffness of lower-limb joints during human locomotion is limited. Understanding joint stiffness is critical for evaluating gait function and designing devices such as prostheses and orthoses intended to emulate biological properties of human legs. The knee joint moment-angle relationship is approximately linear in the flexion and extension stages of stance, exhibiting nearly constant stiffnesses, known as the quasi-stiffnesses of each stage. Using a generalized inverse dynamics analysis approach, we identify the key independent variables needed to predict knee quasi-stiffness during walking, including gait speed, knee excursion, and subject height and weight. Then, based on the identified key variables, we used experimental walking data for 136 conditions (speeds of 0.75-2.63 m/s) across 14 subjects to obtain best fit linear regressions for a set of general models, which were further simplified for the optimal gait speed. We found R(2) > 86% for the most general models of knee quasi-stiffnesses for the flexion and extension stages of stance. With only subject height and weight, we could predict knee quasi-stiffness for preferred walking speed with average error of 9% with only one outlier. These results provide a useful framework and foundation for selecting subject-specific stiffness for prosthetic and exoskeletal devices designed to emulate biological knee function during walking.

Estimation of quasi-stiffness and propulsive work of the human ankle in the stance phase of walking

Characterizing the quasi-stiffness and work of lower extremity joints is critical for evaluating human locomotion and designing assistive devices such as prostheses and orthoses intended to emulate the biological behavior of human legs. This work aims to establish statistical models that allow us to predict the ankle quasi-stiffness and net mechanical work for adults walking on level ground. During the stance phase of walking, the ankle joint propels the body through three distinctive phases of nearly constant stiffness known as the quasi-stiffness of each phase. Using a generic equation for the ankle moment obtained through an inverse dynamics analysis, we identify key independent parameters needed to predict ankle quasi-stiffness and propulsive work and also the functional form of each correlation. These parameters include gait speed, ankle excursion, and subject height and weight. Based on the identified form of the correlation and key variables, we applied linear regression on experimental walking data for 216 gait trials across 26 subjects (speeds from 0.75–2.63 m/s) to obtain statistical models of varying complexity. The most general forms of the statistical models include all the key parameters and have an R² of 75% to 81% in the prediction of the ankle quasi-stiffnesses and propulsive work. The most specific models include only subject height and weight and could predict the ankle quasi-stiffnesses and work for optimal walking speed with average error of 13% to 30%. We discuss how these models provide a useful framework and foundation for designing subject- and gait-specific prosthetic and exoskeletal devices designed to emulate biological ankle function during level ground walking.

Cooperative breeding and maternal energy expenditure among Aka foragers

OBJECTIVES

Previous research among foragers and theory suggests that nonmaternal caregivers offer essential assistance, which supports female reproduction and the costs associated with lengthy child development. Mothers' face trade-offs in energy allocation between work and childcare, particularly when mothers have an infant. These trade-offs likely have crucial impacts on the pace of reproduction and child health. Caregivers can help mothers with childcare or they can reduce a mother's nonchildcare workload. If caregivers assist mothers by substituting childcare, then maternal energy expenditure (EE) in other work activities should increase. If caregivers assist mothers by substituting labor, then maternal EE in work activities should decrease when caregivers are present.

METHODS

Utilizing detailed, quantitative behavioral observations and EE data, we test these propositions with data from 28 Aka forager mothers with children <35 months old. We isolate paternal, grandmaternal, and other caregiver effects on maternal EE and childcare in multivariate analyses.

RESULTS

Our results show that caregivers (largely grandmothers) significantly reduce mothers' work EE by as much 216 kcal across a 9-hour observation period, while fathers and juveniles appear to increase maternal EE. Direct childcare from grandmothers decreases maternal direct care by about one-to-one indicating a labor substitution. Direct childcare from fathers decreases maternal care by almost 4 to 1, resulting in a net reduction of total direct care from all caregivers.

CONCLUSIONS

Our results indicate that there are multiple pathways by which helpers offset maternal work/childcare trade-offs.

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.

Optimal walking speed following changes in limb geometry

The principle of dynamic similarity states that the optimal walking speeds of geometrically similar animals are independent of size when speed is normalized to the dimensionless Froude number (Fr). Furthermore, various studies have shown similar dimensionless optimal speed (Fr ∼0.25) for animals with quite different limb geometries. Here, we wondered whether the optimal walking speed of humans depends solely on total limb length or whether limb segment proportions play an essential role. If optimal walking speed solely depends on the limb length then, when subjects walk on stilts, they should consume less metabolic energy at a faster optimal speed than when they walk without stilts. To test this prediction, we compared kinematics, electromyographic activity and oxygen consumption in adults walking on a treadmill at different speeds with and without articulated stilts that artificially elongated the shank segment by 40 cm. Walking on stilts involved a non-linear reorganization of kinematic and electromyography patterns. In particular, we found a significant increase in the alternating activity of proximal flexors-extensors during the swing phase, despite significantly shorter normalized stride lengths. The minimal metabolic cost per unit distance walked with stilts occurred at roughly the same absolute speed, corresponding to a lower Fr number (Fr ∼0.17) than in normal walking (Fr ∼0.25). These findings are consistent with an important role of limb geometry optimization and kinematic coordination strategies in minimizing the energy expenditure of human walking.

Evolution of the human pygmy phenotype

Small human body size, or the 'pygmy' phenotype, is characteristic of certain African, Southeast Asian and South American populations. The convergent evolution of this phenotype, and its strong association with tropical rainforests, have motivated adaptive hypotheses that stress the advantages of small size for coping with food limitation, warm, humid conditions and dense forest undergrowth. Most recently, a life-history model has been used to suggest that the human pygmy phenotype is a consequence of early growth cessation that evolved to facilitate early reproductive onset amid conditions of high adult mortality. As we discuss here, these adaptive scenarios are not mutually exclusive and should be evaluated in consort. Findings from this area of research are expected to inform interpretations of diversity in the hominin fossil record, including the purported small-bodied species Homo floresiensis.

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.

Anomalous centre of mass energy fluctuations during treadmill walking in healthy individuals

Motorised treadmills are used to research and rehabilitate gait despite conflicting evidence that treadmill ambulation is equivalent to ground walking. It has been suggested that no mechanical differences should exist between these environments but there is little evidence to support this. During ground walking, the whole body centre of mass (COM) acts like an inverted pendulum recovering energy, thereby reducing the effort of locomotion. The energy recovery has a relationship with speed whereby maximum recovery occurs at intermediate speeds. In order to determine the relationship between energy recovery and speed during treadmill walking, we investigated estimated COM displacement in nine healthy individuals each walking on a treadmill at seven different speeds. In addition, we measured oxygen cost to determine the effort of walking. Our participants formed two distinct groups, those with normal COM energy recovery (N%R) that was similar to ground walking, and those with low COM energy recovery (L%R) that was different from typical ground walking. The low energy recovery in the L%R group was attributed to in-phase potential and kinetic energy fluctuations. Despite the low energy recovery values both groups produced the expected 'U'-shaped oxygen cost speed curve with no significant difference between groups (p<0.05), however, only N%R produced a significant relationship between energy recovery and oxygen cost (p<0.05). Although a useful tool, walking on a treadmill may not be a true representation of ground walking and therefore not the most effective way to research or rehabilitate gait.

Effective limb length and the scaling of locomotor cost in terrestrial animals

Relative to body size, smaller animals use more energy to travel a given distance than larger animals, but the anatomical variable driving this negative allometry remains the subject of debate. Here, I report a simple inverse relationship between effective limb length (i.e. hip height) and the energy cost of transport (COT; J kg–1 m–1)for terrestrial animals. Using published data for a diverse set of terrestrial species including birds, mammals, reptiles and arthropods, I show that between-species differences in locomotor cost are driven by differences in limb length. Notably, there is no independent effect of body mass on cost. Remarkably, effective limb length explains 98% of the observed variance in locomotor cost across a wide range of terrestrial species including mammals,birds, reptiles and arthropods. Variation about the limb-length/COT scaling relationship is attributable to taxonomic differences in limb design, with birds and arthropods exhibiting greater residuals than mammals. Differences in COT between semi-aquatic, generalist and cursorial species also corresponds to differences in leg length between these groups. These results are discussed in light of previous investigations of the limb length and locomotor cost.

Froude number corrections in anthropological studies

The Froude number has been widely used in anthropology to adjust for size differences when comparing gait parameters or other nonmorphological locomotor variables (such as optimal walking speed or speed at gait transitions) among humans, nonhuman primates, and fossil hominins. However, the dynamic similarity hypothesis, which is the theoretical basis for Froude number corrections, was originally developed and tested at much higher taxonomic levels, for which the ranges of variation are much greater than in the intraspecific or intrageneric comparisons typical of anthropological studies. Here we present new experimental data on optimal walking speed and the mass-specific cost of transport at that speed from 19 adult humans walking on a treadmill, and evaluate the predictive power of the dynamic similarity hypothesis in this sample. Contrary to the predictions of the dynamic similarity hypothesis, we found that the mass-specific cost of transport at experimentally measured optimal walking speed and Froude number were not equal across individuals, but retained a significant correlation with body mass. Overall, the effect of lower limb length on optimal walking speed was weak. These results suggest that the Froude number may not be an effective way for anthropologists to correct for size differences across individuals, but more studies are needed. We suggest that researchers first determine whether geometric similarity characterizes their data before making inferences based on the dynamic similarity hypothesis, and then check the consistency of their results with and without Froude number corrections before drawing any firm conclusions.

A new model predicting locomotor cost from limb lengthviaforce production

Notably absent from the existing literature is an explicit biomechanical model linking limb design to the energy cost of locomotion, COL. Here, I present a simple model that predicts the rate of force production necessary to support the body and swing the limb during walking and running as a function of speed, limb length, limb proportion, excursion angle and stride frequency. The estimated rate of force production is then used to predict COL via this model following previous studies that have linked COL to force production. To test this model, oxygen consumption and kinematics were measured in nine human subjects while walking and running on a treadmill at range of speeds. Following the model, limb length, speed, excursion angle and stride frequency were used to predict the rate of force production both to support the body's center of mass and to swing the limb. Model-predicted COL was significantly correlated with observed COL, performing as well or better than contact time and Froude number as a predictor of COL for running and walking, respectively. Furthermore, the model presented here predicts relationships between COL, kinematic variables and body size that are supported by published reduced-gravity experiments and scaling studies. Results suggest the model is useful for predicting COL from anatomical and kinematic variables, and may be useful in intra- and inter-specific studies of locomotor anatomy and performance.

Froude and the contribution of naval architecture to our understanding of bipedal locomotion

It is fascinating to think that the ideas of two 19th century naval architects could offer useful insights for 21st century scientists contemplating the exploration of our planetary system or monitoring the long-term effects of a neurosurgical procedure on gait. The Froude number, defined as Fr = v2/gL, where v is velocity, g is gravitational acceleration and L is a characteristic linear dimension (such as leg length), has found widespread application in the biomechanics of bipedal locomotion. This review of two parameters, Fr and dimensionless velocity beta = (Fr)1/2, that have served as the criterion for dynamic similarity, has been arranged in two parts: (I) historical development, including the contributions by William Froude and his son Edmund, two ship designers who lived more than 130 years ago, the classic insights of D'Arcy Wentworth Thompson who, in his magnum opus On Growth and Form, espoused the connection between mathematics and biology, and the pioneering efforts of Robert McNeill Alexander, who popularised the application of Fr to animal locomotion; and (II) selected applications, including a comparison of walking for people of different heights, exploring the effects of different gravitational fields on human locomotion, establishing the impact of pathology and the benefits of treatment, and understanding the walking patterns of bipedal robots. Although not all applications of Fr to locomotion have been covered, the review offers an important historical context for all researchers of bipedal gait, and extends the idea of dimensionless scaling of gait parameters.

Neuromusculoskeletal computer modeling and simulation of upright, straight-legged, bipedal locomotion of Australopithecus afarensis (A.L. 288-1)

The skeleton of Australopithecus afarensis (A.L. 288-1, better known as "Lucy") is by far the most complete record of locomotor morphology of early hominids currently available. Even though researchers agree that the postcranial skeleton of Lucy shows morphological features indicative of bipedality, only a few studies have investigated Lucy's bipedal locomotion itself. Lucy's energy expenditure during locomotion has been the topic of much speculation, but has not been investigated, except for several estimates derived from experimental data collected on other animals. To gain further insights into how Lucy may have walked, we generated a full three-dimensional (3D) reconstruction and forward-dynamic simulation of upright bipedal locomotion of this ancient human ancestor. Laser-scanned 3D bone geometries were combined with state-of-the-art neuromusculoskeletal modeling and simulation techniques from computational biomechanics. A detailed full 3D neuromusculoskeletal model was developed that encompassed all major bones, joints (10), and muscles (52) of the lower extremity. A model of muscle force and heat production was used to actuate the musculoskeletal system, and to estimate total energy expenditure during locomotion. Neural activation profiles for each of the 52 muscles that produced a single step of locomotion, while at the same time minimizing the energy consumed per meter traveled, were searched through numerical optimization. The numerical optimization resulted in smooth locomotor kinematics, and the predicted energy expenditure was appropriate for upright bipedal walking in an individual of Lucy's body size.

Development of pendulum mechanism and kinematic coordination from the first unsupported steps in toddlers

The inverted pendulum model in which the centre of mass of the body vaults over the stance leg in an arc represents a basic mechanism of bipedal walking. Is the pendulum mechanism innate, or is it learnt through walking experience?We studied eight toddlers (about 1 year old) at their first unsupported steps,18 older children (1.3–13 years old), and ten adults. Two infants were also tested repeatedly over a period of 4 months before the onset of independent walking. Pendulum mechanism was quantified from the kinematics of the greater trochanter, correlation between kinetic and gravitational potential energy of the centre of body mass obtained from the force plate recordings, and percentage of recovery of mechanical energy. In toddlers,these parameters deviated significantly (P&lt;10–5)from those of older children and adults, indicating that the pendulum mechanism is not implemented at the onset of unsupported locomotion. Normalising the speed with the Froude number showed that the percentage of recovery of mechanical energy in children older than 2 years was roughly similar to that of the adults (less than 5% difference), in agreement with previous results. By contrast, the percentage of recovery in toddlers was much lower (by about 50%). Pendulum-like behaviour and fixed coupling of the angular motion of the lower limb segments rapidly co-evolved toward mature values within a few months of independent walking experience. Independent walking experience acts as a functional trigger of the developmental changes,as shown by the observation that gait parameters remained unchanged until the age of the first unsupported steps, and then rapidly matured after that age. The findings suggest that the pendulum mechanism is not an inevitable mechanical consequence of a system of linked segments, but requires active neural control and an appropriate pattern of inter-segmental coordination.

[The effect of similar speed's walking and functional classification of foot contact on variability of the vertical ground reaction force]

INTRODUCTION

The variability of the normal ground reaction force (F(z)) is a restrictive factor for the clinical analyse of kinetics parameters recorded during walking.

OBJECTIVE

The aim of this study is the decrease of the inter-individual variability of the normal ground reaction force: F(z).

MATERIAL AND METHOD

The method tested consists in imposing a similar speed to the subjects during walking tests, then to class foot according to their function: loading or propulsive foot. A group of seven young adults walk at spontaneous speed (VSpon) for the first walking test then at similar speed (Vsim = N(Fr) x square root of (g x li); where N(Fr) is the Froud's number, g is the gravitational acceleration and li is the length of the lower limb) for the second walking test. Two forces platforms register the F(z) of two consecutive steps. The normal ground reaction force and the mean coefficient of variability are retained to test for speed (VSim and VSpon) and functional classification effects.

RESULTS

The CoV of F(z) decreases from 13% to 8% when the subjects walk at similar speed rather than at spontaneously chosen speed. The variability decreases by 1-1.5% when the data are classified according to functional criterion. The inter-individual variability of the F(z) significantly reduces when the tests are performed at similar speed and when the loading or propulsive factors are used for functional classification.

CONCLUSION

The coupling of the methods described must permit to the clinician to constitute a data base which, tainted of less variability, should make easier the detection of pathology affecting the ground reaction force.

Climbing and the daily energy cost of locomotion in wild chimpanzees: implications for hominoid locomotor evolution

As noted by previous researchers, the chimpanzee postcranial anatomy reflects a compromise between the competing demands of arboreal and terrestrial locomotion. In this study, we measured the distance climbed and walked per day in a population of wild chimpanzees and used published equations to calculate the relative daily energy costs. Results were used to test hypotheses regarding the arboreal-terrestrial tradeoff in chimpanzee anatomy, specifically whether arboreal adaptations serve to minimize daily locomotor energy costs by decreasing the energy spent climbing. Our results show that chimpanzees spend approximately ten-times more energy per day on terrestrial travel than on vertical climbing, a figure inconsistent with minimizing energy costs in our model. This suggests non-energetic factors, such as avoiding falls from the canopy, may be the primary forces maintaining energetically costly climbing adaptations. These analyses are relevant to anatomical comparisons with living and extinct hominoids.

The double contact phase in walking children

During walking, when both feet are on the ground (the double contact phase), the legs push against each other, and both positive and negative work are done simultaneously. The work done by one leg on the other (W(int,dc)) is not counted in the classic measurements of the positive muscular work done during walking. Using force platforms, we studied the effect of speed and age (size) on W(int,dc). In adults and in 3-12-year-old children, W(int,dc) (J kg(-1) m(-1)) as a function of speed shows an inverted U-shaped curve, attaining a maximum value that is independent of size but that occurs at higher speeds in larger subjects. Normalising the speed with the Froude number shows that W(int,dc) is maximal at about 0.3 in both children and adults. Differences due to size disappear for the most part when normalised with the Froude number, indicating that these speed-dependent changes are primarily a result of body size changes. At its maximum, W(int,dc) represents more than 40% of W(ext) (the positive work done to move the centre of mass of the body relative to the surroundings) in both children and adults.

Invariant aspects of human locomotion in different gravitational environments

Previous literature showed that walking gait follows the same mechanical paradigm, i.e. the straight/inverted pendulum, regardless the body size, the number of legs, and the amount of gravity acceleration. The Froude number, a dimensionless parameter originally designed to normalize the same (pendulum-like) motion in differently sized subjects, proved to be useful also in the comparison, within the same subject, of walking in heterogravity. In this paper the theory of dynamic similarity is tested by comparing the predictive power of the Froude number in terms of walking speed to previously published data on walking in hypogravity simulators. It is concluded that the Froude number is a good first predictor of the optimal walking speed and of the transition speed between walking and running in different gravitational conditions. According to the Froude number a dynamically similar walking speed on another planet can be calculated as [formula: see text] where V(Earth) is the reference speed on Earth.

Exploring dynamic similarity in human running using simulated reduced gravity

The Froude number (a ratio of inertial to gravitational forces) predicts the occurrence of dynamic similarity in legged animals over a wide range of sizes and velocities for both walking and running gaits at Earth gravity. This is puzzling because the Froude number ignores elastic forces that are crucial for understanding running gaits. We used simulated reduced gravity as a tool for exploring dynamic similarity in human running. We simulated reduced gravity by applying a nearly constant upward force to the torsos of our subjects while they ran on a treadmill. We found that at equal Froude numbers, achieved through different combinations of velocity and levels of gravity, our subjects did not run in a dynamically similar manner. Thus, the inertial and gravitational forces that comprise the Froude number were not sufficient to characterize running in reduced gravity. Further, two dimensionless numbers that incorporate elastic forces, the Groucho number and the vertical Strouhal number, also failed to predict dynamic similarity in reduced-gravity running. To better understand the separate effects of velocity and gravity, we also studied running mechanics at fixed absolute velocities under different levels of gravity. The effects of velocity and gravity on the requirements of dynamic similarity differed in both magnitude and direction, indicating that there are no two velocity and gravity combinations at which humans will prefer to run in a dynamically similar manner. A comparison of walking and running results demonstrated that reduced gravity had different effects on the mechanics of each gait. This suggests that a single unifying hypothesis for the effects of size, velocity and gravity on both walking and running gaits will not be successful.

Locomotor energetics and leg length in hominid bipedality

Because bipedality is the quintessential characteristic of Hominidae, researchers have compared ancient forms of bipedality with modern human gait since the first clear evidence of bipedal australopithecines was unearthed over 70 years ago. Several researchers have suggested that the australopithecine form of bipedality was transitional between the quadrupedality of the African apes and modern human bipedality and, consequently, inefficient. Other researchers have maintained that australopithecine bipedality was identical to that of Homo. But is it reasonable to require that all forms of hominid bipedality must be the same in order to be optimized? Most attempts to evaluate the locomotor effectiveness of the australopithecines have, unfortunately, assumed that the locomotor anatomy of modern humans is the exemplar of consummate bipedality. Modern human anatomy is, however, the product of selective pressures present in the particular milieu in which Homo arose and it is not necessarily the only, or even the most efficient, bipedal solution possible. In this report, we investigate the locomotion of Australopithecus afarensis, as represented by AL 288-1, using standard mechanical analyses. The osteological anatomy of AL 288-1 and movement profiles derived from modern humans are applied to a dynamic model of a biped, which predicts the mechanical power required by AL 288-1 to walk at various velocities. This same procedure is used with the anatomy of a composite modern woman and a comparison made. We find that AL 288-1 expends less energy than the composite woman when locomoting at walking speeds. This energetic advantage comes, however, at a price: the preferred transition speed (from a walk to a run) of AL 288-1 was lower than that of the composite woman. Consequently, the maximum daily range of AL 288-1 may well have been substantially smaller than that of modern people. The locomotor anatomy of A. afarensis may have been optimized for a particular ecological niche-slow speed foraging-and is neither compromised nor transitional.

The costs of human locomotion: maternal investment in child transport

This article investigates maternal investment in child carrying and presents a method for determining when it is energetically advantageous for a mother to carry her child rather than force her child to walk independently. I calculate maternal and child energy consumption while walking and develop correction factors to facilitate making these energy calculations for young children. In addition, I investigate the effect of maternal burdens in addition to the child and of external nutritional support on energy consumption. Since maternal energy is a finite resource, the "decision" to carry a child or force it to walk independently is especially important. This decision can be predicted from the body mass of the mother and child and the child's age. If the mother provides all of the child's nutrition, then the mother should choose to carry her child only when the energy usage of the mother carrying the child is less than the sum of the energy used when the mother and child walk independently. The critical velocity, when the two expenditures are equal, can then be determined. Several general hypotheses are also addressed. The critical velocity of a 60 kg mother with a 4-year-old child approximately equals the average walking speed of adult humans. For a lighter mother, the critical velocity is reached when her child is 3 years old, while for heavier mother this point is not reached until her child is 6 years old. The effect of burdens in addition to the child's mass is minimal. Nutritional support of the child by agencies other than the mother decreases the age at which the mother should force the child to walk independently. In some cases, especially for the lightest mothers, it is never in the mother's best energetic interest to carry her child.

A model equation for the prediction of mechanical internal work of terrestrial locomotion

By refining a previously published model, a simple equation for the estimation of the mechanical internal work during locomotion is presented. The only input variables are the progression speed, the stride frequency and the duty factor, i.e. the fraction of the stride duration at which a foot is in contact with the ground. The inclusion of this last variable, easily measurable, allows to obtain a single equation for both walking and running. The model predictions have been compared with the mechanical internal work experimentally obtained on humans in several conditions: speeds (range 0.8-3.3 m s(-1)), gaits (walking and running) and gradients (+/-15%). The close match between the two indicates that the model equation can be used whenever a direct measurement of the mechanical internal work is unavailable.