Simulation of gait and gait initiation associated with body oscillating behavior in the gravity environment on the Moon, Mars and Phobos

 A double-inverted pendulum model of body oscillations in the frontal plane during stepping [Brenière and Ribreau (1998) Biol Cybern 79: 337–345] proposed an equivalent model for studying the body oscillating behavior induced by step frequency in the form of: (1) a kinetic body parameter, the natural body frequency (NBF), which contains gravity and which is invariable for humans, (2) a parametric function of frequency, whose parameter is the NBF, which explicates the amplitude ratio of center of mass to center of foot pressure oscillation, and (3) a function of frequency which simulates the equivalent torque necessary for the control of the head-arms-trunk segment oscillations. Here, this equivalent model is used to simulate the duration of gait initiation, i.e., the duration necessary to initiate and execute the first step of gait in subgravity, as well as to calculate the step frequencies that would impose the same minimum and maximum amplitudes of the oscillating responses of the body center of mass, whatever the gravity value. In particular, this simulation is tested under the subgravity conditions of the Moon, Mars, and Phobos, where gravity is 1/6, 3/8, and 1/1600 times that on the Earth, respectively. More generally, the simulation allows us to establish and discuss the conditions for gait adaptability that result from the biomechanical constraints particular to each gravity system. Received: 15 February 1999 / Accepted in revised form: 9 October 2000     

Determination of equivalent amounts of kinetic energy, work, and heat energy in the human body

The goal of this study is determine the mechanical equivalent of heat and the functional capacity of metabolism of walking at a slow pace (velocity = 4022m/hour, length of a step=75cm, energy utilization of a 70 kg person is 200kcal/hour). 50 healthy physicians were chosen randomly, and up and down motion of the body were determined as 6cm while stepping. Based on these, the heat equivalent is 37.5kcal/hour for horizontal motion and 52.7kcal/hour for 6cm up-and-down bobbing motions of body, and the functional capacity of metabolism is at least 45% ([37.5+52.7]/200=45%) for slow walking state, that this capacity is twofold more than earlier information. Muscle converts kinetic energy (work) to heat via friction, and heat sources of the body, and the concepts of thermogenesis and the functional capacity of metabolism should be revised.     

Head bobbing and the body movement of little egrets (<Emphasis Type="Italic">Egretta garzetta</Emphasis>) during walking

Although previous studies have indicated that head bobbing of birds is an optokinetic movement, head bobbing can also be controlled by some biomechanical constraints when it occurs during walking. In the present study, the head bobbing, center of gravity, and body movements of little egrets (Egretta garzetta) during walking were examined by determination of the position of the center of gravity using carcasses and by motion analysis of video films of wild egrets during walking. The results showed that the hold phase occurs while the center of gravity is over the supporting foot during the single support phase. In addition, the peak speed of neck extension was coincident with the peak speed of the center of gravity. These movements are similar to those of pigeons, and suggest the presence of biomechanical constraints on the pattern of head bobbing and body movements during walking.     

Independent metabolic costs of supporting body weight and accelerating body mass during walking.

The metabolic cost of walking is determined by many mechanical tasks, but the individual contribution of each task remains unclear. We hypothesized that the force generated to support body weight and the work performed to redirect and accelerate body mass each individually incur a significant metabolic cost during normal walking. To test our hypothesis, we measured changes in metabolic rate in response to combinations of simulated reduced gravity and added loading. We found that reducing body weight by simulating reduced gravity modestly decreased net metabolic rate. By calculating the metabolic cost per Newton of reduced body weight, we deduced that generating force to support body weight comprises approximately 28% of the metabolic cost of normal walking. Similar to previous loading studies, we found that adding both weight and mass increased net metabolic rate in more than direct proportion to load. However, when we added mass alone by using a combination of simulated reduced gravity and added load, net metabolic rate increased about one-half as much as when we added both weight and mass. By calculating the cost per kilogram of added mass, we deduced that the work performed on the center of mass comprises approximately 45% of the metabolic cost of normal walking. Our findings support the hypothesis that force and work each incur a significant metabolic cost. Specifically, the cost of performing work to redirect and accelerate the center of mass is almost twice as great as the cost of generating force to support body weight.     

Biomechanical analysis of movement strategies in human forward trunk bending. I. Modeling

 Two behavioral goals are achieved simultaneously during forward trunk bending in humans: the bending movement per se and equilibrium maintenance. The objective of the present study was to understand how the two goals are achieved by using a biomechanical model of this task. Since keeping the center of pressure inside the support area is a crucial condition for equilibrium maintenance during the movement, we decided to model an extreme case, called “optimal bending”, in which the movement is performed without any center of pressure displacement at all, as if standing on an extremely narrow support. The “optimal bending” is used as a reference in the analysis of experimental data in a companion paper. The study is based on a three-joint (ankle, knee, and hip) model of the human body and is performed in terms of “eigenmovements”, i.e., the movements along eigenvectors of the motion equation. They are termed “ankle”, “hip”, and “knee” eigenmovements according to the dominant joint that provides the largest contribution to the corresponding eigenmovement. The advantage of the eigenmovement approach is the presentation of the coupled system of dynamic equations in the form of three independent motion equations. Each of these equations is equivalent to the motion equation for an inverted pendulum. Optimal bending is constructed as a superposition of two (hip and ankle) eigenmovements. The hip eigenmovement contributes the most to the movement kinematics, whereas the contributions of both eigenmovements into the movement dynamics are comparable. The ankle eigenmovement moves the center of gravity forward and compensates for the backward center of gravity shift that is provoked by trunk bending as a result of dynamic interactions between body segments. An important characteristic of the optimal bending is the timing of the onset of each eigenmovement: the ankle eigenmovement onset precedes that of the hip eigenmovement. Without an earlier onset of the ankle eigenmovement, forward bending on the extremely narrow support results in falling backward. This modeling approach suggests that during trunk bending, two motion units – the hip and ankle eigenmovements – are responsible for the movement and for equilibrium maintenance, respectively. Received: 1 July 1999 / Accepted in revised form: 23 October 2000     

Energetics of walking and running: insights from simulated reduced-gravity experiments.

On Earth, a person uses about one-half as much energy to walk a mile as to run a mile. On another planet with lower gravity, would walking still be more economical than running? When people carry weights while they walk or run, energetic cost increases in proportion to the added load. It would seem to follow that if gravity were reduced, energetic cost would decrease in proportion to body weight in both gaits. However, we find that under simulated reduced gravity, the rate of energy consumption decreases in proportion to body weight during running but not during walking. When gravity is reduced by 75%, the rate of energy consumption is reduced by 72% during running but only by 33% during walking. Because reducing gravity decreases the energetic cost much more for running than for walking, walking is not the cheapest way to travel a mile at low levels of gravity. These results suggest that the link between the mechanics of locomotion and energetic cost is fundamentally different for walking and for running.     

Maximum walking speed and lower limb length in hominids

In 1984, Helene (Am. J. Physics 52:656) and Alexander (Am. Scientist 72:348–354) presented equations which purported to explain how lower limb length limited maximum walking speed in humans. The equations were based on a simplified model of human walking in which the center of mass (CoM) “vaults” over the supporting leg. Increasing walking speed by increasing stride frequency or stride length would increase the upward acceleration of the CoM in the first half of stance phase, to the point that it would be greater than the downward pull of gravity, and the individual would become airborne. This constitutes running by most definitions. While these models ignored various mechanical factors, such as knee flexion during midstance, that reduce the vertical movement of the CoM, the general idea is plausible inasmuch as the CoM of the body does oscillate vertically with each step. One hypothesis tested here is whether it is indeed the interaction between the pull of gravity and the individual's own upward acceleration that determines at what speed (or cadence) he changes from walking to running. Another hypothesis considered is that increased lower limb length (L) was selected for in early hominids, because of the locomotor advantages of longer lower limbs. Results indicate, however, that while L was clearly related to maximum possible walking speed, it was not an important factor in determining maximum “comfortable” walking speed. These and other results from the recent literature suggest that increased lower limb length provided no selective advantage in locomotion, and other explanations should be sought. © 1996 Wiley-Liss, Inc.     

Biomechanical analysis of primate bipedal walking by computer simulation

A computer simulation technique was applied to make clear the mechanical characteristics of primate bipedal walking. A primate body and the walking mechanism were modeled mathematically with a set of dynamic equations. Using a digital computer, the following were calculated from these equations by substituting measured displacements and morphological data of each segment of the primate: the acceleration, joint angle, center of gravity, foot force, joint moment, muscular force, transmitted force at the joint, electric activity of the muscle, generated power by the leg and energy expenditure in walking.The model was evaluated by comparing some of the calculated results with the experimental results such as foot force and electromyographic data, and improved in order to obtain the agreement between them.The level bipedal walking of man, chimpanzee and Japanese monkey and several types of synthesized walking were analyzed from the viewpoint of biomechanics.It is concluded that the bipedal walking of chimpanzee is nearer to that of man than to that of the Japanese monkey because of its propulsive mechanism, but it requires large muscular force for supporting the body weight.     

A double-inverted pendulum model for studying the adaptability of postural control to frequency during human stepping in place

In order to analyze the influence of gravity and body characteristics on the control of center of mass (CM) oscillations in stepping in place, equations of motion in oscillating systems were developed using a double-inverted pendulum model which accounts for both the head-arms-trunk (HAT) segment and the two-legged system. The principal goal of this work is to propose an equivalent model which makes use of the usual anthropometric data for the human body, in order to study the ability of postural control to adapt to the step frequency in this particular paradigm of human gait. This model allows the computation of CM-to-CP amplitude ratios, when the center of foot pressure (CP) oscillates, as a parametric function of the stepping in place frequency, whose parameters are gravity and major body characteristics. Motion analysis from a force plate was used to test the model by comparing experimental and simulated values of variations of the CM-to-CP amplitude ratio in the frontal plane versus the frequency. With data from the literature, the model is used to calculate the intersegmental torque which stabilizes the HAT when the Leg segment is subjected to a harmonic torque with an imposed frequency. Received: 24 February 1997 / Accepted in revised form: 30 June 1998     

An Experimental Analysis of Overcoming Obstacle in Human Walking

In this paper, an experimental analysis of overcoming obstacle in human walking is carried out by means of a motion capture system. In the experiment, the lower body of an adult human is divided into seven segments, and three markers are pasted to each segment with the aim to obtain moving trajectory and to calculate joint variation during walking. Moreover, kinematic data in terms of displacement, velocity and acceleration are acquired as well. In addition, ground reaction forces are measured using force sensors. Based on the experimental results, features of overcoming obstacle in human walking are ana- lyzed. Experimental results show that the reason which leads to smooth walking can be identified as that the human has slight movement in the vertical direction during walking; the reason that human locomotion uses gravity effectively can be identified as that feet rotate around the toe joints during toe-off phase aiming at using gravitational potential energy to provide propulsion for swing phase. Furthermore, both normal walking gait and obstacle overcoming gait are characterized in a form that can provide necessary knowledge and useful databases for the implementation of motion planning and gait planning towards overcoming obstacle for humanoid robots.     

Optimal diving behaviour for foraging in relation to body size

Overall, large animals dive longer and deeper than small animals; however, after the difference in body size is taken into account, smaller divers often tend to make relatively longer dives. Neither physiological nor theoretical explanations have been provided for this paradox. This paper develops an optimal foraging diving model to demonstrate the effect of body size on diving behaviour, and discusses optimal diving behaviour in relation to body size. The general features of the results are: (1) smaller divers should rely more heavily on anaerobic respiration, (2) larger divers should not always make longer dives than smaller divers, and (3) an optimal body size exists for each diving depth. These results explain the relatively greater diving ability observed in smaller divers, and suggest that if the vertical distribution of prey in the water column is patchy, there is opportunity for a population of diving animals to occupy habitat niches related to body size.     

Kinetic analysis of the center of gravity of the human body in normal and pathological gaits

The kinetics of the body's center of gravity during level walking were analyzed in 50 normal subjects and 47 patients. The three-dimensional displacements of the center of gravity were computed by the integration of force plate data. The energy levels and the power requirements of the center of gravity were also calculated, and the average and standard deviation of these variables were determined for normal and pathological gaits. The sex-related variation in normal gait, as suggested by previous force plate studies, was clearly demonstrated in our study. The parameters obtained from the displacements and the energy variations of the center of gravity are considered useful in the evaluation of stability and efficiency for pathological gaits.     

When and how does steady state gait movement induced from upright posture begin?

The aim of this research was to study when and how the stationary process of gait begins when walking starts from upright posture. The subject initially stood up on a large force plate, then walked. Three conditions of speed (slow, normal, fast) were examined. Five subjects participated in the experiment. A total of 105 trials were performed. The results show that, at the end of the first step, the progression velocity of the center of gravity is not significantly different from the mean progression velocity of gait during the second step of gait and that the time necessary to reach steady state gait from initial posture phase is constant. Furthermore, the frequency of the first step, when compared to published values of the steady state gait frequency, is not significantly different from these frequencies.

It can be concluded that the aim of the gait initiation process is to place the subject in steady-state gait within the first step, in an invariant time which is dependent only on the body segment parameters of each subject.     

Minimizing center of mass vertical movement increases metabolic cost in walking.

A human walker vaults up and over each stance limb like an inverted pendulum. This similarity suggests that the vertical motion of a walker's center of mass reduces metabolic cost by providing a mechanism for pendulum-like mechanical energy exchange. Alternatively, some researchers have hypothesized that minimizing vertical movements of the center of mass during walking minimizes the metabolic cost, and this view remains prevalent in clinical gait analysis. We examined the relationship between vertical movement and metabolic cost by having human subjects walk normally and with minimal center of mass vertical movement ("flat-trajectory walking"). In flat-trajectory walking, subjects reduced center of mass vertical displacement by an average of 69% (P = 0.0001) but consumed approximately twice as much metabolic energy over a range of speeds (0.7-1.8 m/s) (P = 0.0001). In flat-trajectory walking, passive pendulum-like mechanical energy exchange provided only a small portion of the energy required to accelerate the center of mass because gravitational potential energy fluctuated minimally. Thus, despite the smaller vertical movements in flat-trajectory walking, the net external mechanical work needed to move the center of mass was similar in both types of walking (P = 0.73). Subjects walked with more flexed stance limbs in flat-trajectory walking (P < 0.001), and the resultant increase in stance limb force generation likely helped cause the doubling in metabolic cost compared with normal walking. Regardless of the cause, these findings clearly demonstrate that human walkers consume substantially more metabolic energy when they minimize vertical motion.     

Walking in simulated reduced gravity: mechanical energy fluctuations and exchange

Walking humansconserve mechanical and, presumably, metabolic energy with an invertedpendulum-like exchange of gravitational potential energy and horizontalkinetic energy. Walking in simulated reduced gravity involves arelatively high metabolic cost, suggesting that the inverted-pendulummechanism is disrupted because of a mismatch of potential and kineticenergy. We tested this hypothesis by measuring the fluctuations andexchange of mechanical energy of the center of mass at differentcombinations of velocity and simulated reduced gravity. Subjects walkedwith smaller fluctuations in horizontal velocity in lower gravity, suchthat the ratio of horizontal kinetic to gravitational potential energyfluctuations remained constant over a fourfold change in gravity. Theamount of exchange, or percent recovery, at 1.00 m/s was notsignificantly different at 1.00, 0.75, and 0.50 G (average 64.4%),although it decreased to 48% at 0.25 G. As a result, the amount ofwork performed on the center of mass does not explain the relatively high metabolic cost of walking in simulated reduced gravity.

     

Optimal climbing speed explains the evolution of extreme sexual size dimorphism in spiders

Several hypotheses have been put forward to explain the evolution of extreme sexual size dimorphism (SSD). Among them, the gravity hypothesis (GH) explains that extreme SSD has evolved in spiders because smaller males have a mating or survival advantage by climbing faster. However, few studies have supported this hypothesis thus far. Using a wide span of spider body sizes, we show that there is an optimal body size (7.4 mm) for climbing and that extreme SSD evolves only in spiders that: (1) live in high‐habitat patches and (2) in which females are larger than the optimal size. We report that the evidence for the GH across studies depends on whether the body size of individuals expands beyond the optimal climbing size. We also present an ad hoc biomechanical model that shows how the higher stride frequency of small animals predicts an optimal body size for climbing.     

Predicting abundance–body size relationships in functional and taxonomic subsets of food webs

Abundance–body size relationships are widely observed macroecological patterns in complete food webs and in taxonomically or functionally defined subsets of those webs. Observed abundance–body size relationships have frequently been compared with predictions based on the energetic equivalence hypothesis and, more recently, with predictions based on energy availability to different body size classes. Here, we consider the ways in which working with taxonomically or functionally defined subsets of food webs affected the relationship between the predicted and observed scaling of biomass and body mass in sediment dwelling benthic invertebrate communities at three sites in the North Sea. At each site, the energy available to body size classes in the “whole” community (community defined as all animals of 0.03125–32.0 g shell-free wet weight) and in three subsets was predicted from estimates of trophic level based on nitrogen stable isotope analysis. The observed and predicted scalings of biomass and body size were not significantly different for the whole community, and reflected an increase in energy availability with body size. However, the results for subsets showed that energy availability could increase or decrease with body size, and that individuals in the subsets were likely to be competing with individuals outside the subsets for energy. We conclude that the study of abundance–body mass relationships in functionally or taxonomically defined subsets of food webs is unlikely to provide an adequate test of the energetic equivalence hypothesis or other relationships between energy availability and scaling. To consistently and reliably interpret the results of these tests, it is necessary to know about energy availability as a function of body size both within and outside the subset considered.     

Contributions of muscles to mediolateral ground reaction force over a range of walking speeds

Impaired control of mediolateral body motion during walking is an important health concern. Developing treatments to improve mediolateral control is challenging, partly because the mechanisms by which muscles modulate mediolateral ground reaction force (and thereby modulate mediolateral acceleration of the body mass center) during unimpaired walking are poorly understood. To investigate this, we examined mediolateral ground reaction forces in eight unimpaired subjects walking at four speeds and determined the contributions of muscles, gravity, and velocity-related forces to the mediolateral ground reaction force by analyzing muscle-driven simulations of these subjects. During early stance (0-6% gait cycle), peak ground reaction force on the leading foot was directed laterally and increased significantly (p<0.05) with walking speed. During early single support (14-30% gait cycle), peak ground reaction force on the stance foot was directed medially and increased significantly (p<0.01) with speed. Muscles accounted for more than 92% of the mediolateral ground reaction force over all walking speeds, whereas gravity and velocity-related forces made relatively small contributions. Muscles coordinate mediolateral acceleration via an interplay between the medial ground reaction force contributed by the abductors and the lateral ground reaction forces contributed by the knee extensors, plantarflexors, and adductors. Our findings show how muscles that contribute to forward progression and body-weight support also modulate mediolateral acceleration of the body mass center while weight is transferred from one leg to another during double support.     

An estimation of center of gravity from force platform data

A general, dynamic relationship between the data obtained from a force platform, center of gravity of the body on the platform and the time rate of change of moment of momentum of the body about its center of gravity was derived from principles of dynamics for a system of particles. The derived equations are useful for processing and interpreting the force platform data. Displacement and path of center of gravity of human body during standing on one foot and level walking were estimated by using the derived equations. An estimation of the time rate of change of moment of momentum of the body was also obtained. A biomechanical interpretation of point of application of the resultant of ground reactions was presented.     

Optimal patterns of growth and reproduction for perennial plants with persisting or not persisting vegetative parts

Summary Optimal allocation of energy to growth, reproduction and storage was considered for perennial plants differing in the proportion of vegetative structures persisting over winter and/or in the amount of resources which can be relocated to storage before abscission of some organs. It was found that for every mortality level there exists a critical proportion of persistent organs. Below this critical value it is optimal to grow without reproduction for the first years until a characteristic size is reached; afterwards, that size is maintained year after year and all extra resources are devoted to reproduction. Some storage is also necessary to maintain constant size. If the proportion of retained vegetative mass is above the critical value, the optimal strategy is gradual growth to an asymptotic size, with growth and reproduction occurring in several years following maturation. In this case real storage occurs only until maturation is reached, then storage is realized only by energy relocation from the vegetative body. Although the optimal solution changes abruptly qualitatively at a given proportion of resources saved from year to year, further growth of this proportion above the critical level brings about a greater difference between size reached at maturity and final size. The predictions of the model seem to follow the pattern of nature qualitatively.