Models of central pattern generators for quadruped locomotion II. Secondary gaits

We continue the analysis of the network of symmetrically coupled cells modeling central pattern generators (CPG) for quadruped locomotion proposed by Golubitsky, Stewart, Buono and Collins by studying secondary gaits. Secondary gaits are modeled by output signals from the CPG where each cell emits one of two different output signals along with exact phase shifts. Examples of secondary gaits are transverse gallop, rotary gallop, and canter. We classify secondary gaits that bifurcate when the Poincaré map of a primary gait has a real eigenvalue crossing the unit circle. In particular, we show that periodic solutions modeling transverse gallop and rotary gallop bifurcate from primary gaits. Moreover, we find gaits from period-doubling bifurcations and analyze plausible footfall patterns. Numerical simulations are performed using the Morris-Lecar equations as cell dynamics.     

Gaits of Japanese macaques (Macaca fuscata) on a horizontal ladder and arboreal stability

Most primates use diagonal sequence (DS), diagonal couplets (DC) gaits when they walk or run quadrupedally, and it has been suggested that DSDC gaits contribute to stability in their natural arboreal habitats compared to other symmetrical gaits. However, this postulate is based solely on studies of primate gaits using continuous terrestrial and arboreal substrates. A particular species may select suitable gaits according to the substrate properties. Here, we analyzed the gaits of Japanese macaques moving on a horizontal ladder with rung intervals ranging from 0.40 to 0.80 m to elucidate the relative advantages of each observed form of gait. The rung arrangement forced our macaques to choose either diagonal coupling or DS gaits. One macaque consistently used diagonal coupling (i.e., DSDC and LSDC gaits) across narrow and intermediate rung intervals, whereas the other macaque used DS gaits (i.e., DSDC and DSLC gaits). At wider rung intervals, both macaques shifted to a two‐one sequence (TOS), which is characterized by two nearly simultaneous touchdowns of both forelimbs and one touchdown of each hind limb in a stride. The transition to the TOS sequence increased the duration of support on multiple limbs, but always included periods of a whole‐body aerial phase. These results suggest that Japanese macaques prefer DSDC gaits, because the diagonal coupling and DS contribute separately to stability on complex supports compared to the lateral coupling and lateral sequence. We also postulate that stability triggers the transition from symmetrical gaits to the TOS sequence. Am J Phys Anthropol, 2009. © 2008 Wiley‐Liss, Inc.     

Stability, limb coordination and substrate type: the ecorelevance of gait sequence pattern in primates

The coordination of limb movements during mammalian locomotion has been well documented in the literature. Most mammals use lateral sequence (LS) gaits, in which a forelimb follows an ipsilateral hind limb during the stride cycle. Primates, however, tend to utilize diagonal sequence (DS) gaits, whereby a contralateral forelimb follows a given hind limb during the stride cycle. A number of scenarios have been offered to explain why primates favor DS gaits, most of them relating to the use of the arboreal habitat and, in particular, the exploitation of a terminal branch niche. Yet to date, there is surprisingly little evidence to support the advantage of DS gaits for negotiating different aspects of the terminal branch environment. Nonetheless, it is apparent that primates possess unique morphologies and a higher than typically recognized degree of flexibility in gait sequence pattern, both of which likely offer advantages for moving upon discontinuous and unstable terminal branches. This paper reviews potential explanations for the use of DS gaits in primates and considers mechanisms by which gait sequence may be altered during different types of arboreal challenges.     

Contribution to the analysis of gaits: practical elements to complement the Hildebrand method

This paper suggests three additions to the Hildebrand method for gait-pattern specification. The first allows an extension of this method by the use of the forelimb as reference. Thus, dataset could be gathered indifferently from fore or hindlimbs cycles to identify a symmetrical gait or compare gaits of diverse species. On the basis of Hildebrand's definitions, the second suggestion permits to check the proportion of symmetrical and asymmetrical gaits adopted by different individuals of one or different species. The third addition makes a graphical clear-cut between four basic modes of gallops: rotary, transverse, half-bound and bound. These additions will facilitate extensive data comparison either to evaluate the range of variation within a single species or to specify the preferred gaits in diverse species.     

The metabolic and mechanical costs of step time asymmetry in walking

Animals use both pendular and elastic mechanisms to minimize energy expenditure during terrestrial locomotion. Elastic gaits can be either bilaterally symmetric (e.g. run and trot) or asymmetric (e.g. skip, canter and gallop), yet only symmetric pendular gaits (e.g. walk) are observed in nature. Does minimizing metabolic and mechanical power constrain pendular gaits to temporal symmetry? We measured rates of metabolic energy expenditure and calculated mechanical power production while healthy humans walked symmetrically and asymmetrically at a range of step and stride times. We found that walking with a 42 per cent step time asymmetry required 80 per cent (2.5 W kg⁻¹) more metabolic power than preferred symmetric gait. Positive mechanical power production increased by 64 per cent (approx. 0.24 W kg⁻¹), paralleling the increases we observed in metabolic power. We found that when walking asymmetrically, subjects absorbed more power during double support than during symmetric walking and compensated by increasing power production during single support. Overall, we identify inherent metabolic and mechanical costs to gait asymmetry and find that symmetry is optimal in healthy human walking.     

Footfall dynamics for racewalkers and runners barefoot on compliant surfaces

The main purpose of this study is to investigate the role of footfall surface compliance on the physical parameters affecting barefoot racewalkers and runners. These parameters are identified using a new inverted pendulum body model with a forward moving foot pivot. Model correlations of footfall loads measured for four compliant surface mats showed leg–foot compression stiffness for both gaits were in the range of 10.8–12.9 kN/m, with the initial stiffness spikes in the range of 6.5–52 kN/m. The average leg damping factor was about 0.6% for racewalkers and 6% for runners. For both gaits there was negative leg damping just prior to foot lift-off. Compared to the peak reactions for the rigid surface, a mat of intermediate compliance (1020 kN/m) was effective in reducing the runners’ peak reaction spikes by as much as 17%.     

Gait selection and the ontogeny of quadrupedal walking in squirrel monkeys (Saimiri boliviensis)

Locomotor researchers have long known that adult primates employ a unique footfall sequence during walking. Most mammals use lateral sequence (LS) gaits, in which hind foot touchdowns are followed by ipsilateral forefoot touchdowns. In contrast, most quadrupedal primates use diagonal sequence (DS) gaits, in which hind foot touchdowns are followed by contralateral forefoot touchdowns. However, gait selection in immature primates is more variable, with infants and juveniles frequently using LS gaits either exclusively or in addition to DS gaits. I explored the developmental bases for this phenomenon by examining the ontogeny of gait selection in juvenile squirrel monkeys walking on flat and simulated arboreal substrates (i.e., a raised pole). Although DS gaits predominated throughout development, the juvenile squirrel monkeys nonetheless utilized LS gaits in one-third of the ground strides and in one-sixth of pole strides. Multiple logistic regression analyses showed that gait selection within the juvenile squirrel monkey sample was not significantly associated with either age or body mass per se, arguing against the oft-cited argument that general neuromuscular maturation is responsible for ontogenetic changes in preferred footfall sequence. Rather, lower level biomechanical variables, specifically the position of the whole-body center of mass and the potential for interference between ipsilateral fore and hindlimbs, best explained variation in footfall patterns. Overall, results demonstrate the promise of developmental studies of growth and locomotor development to serve as "natural laboratories" in which to explore how variability in morphology is, or is not, associated with variability in locomotor behavior.     

The effect of branch diameter on primate gait sequence pattern

Most mammals use lateral sequence gaits during quadrupedal locomotion, a pattern characterized by the touchdown of a forelimb directly following the ipsilateral hind limb in a given stride cycle. Primates, however, tend to use diagonal sequence (DS) gaits, whereby it is the touchdown of a contralateral forelimb that follows that of a given hind limb most closely in time. A number of scenarios have been offered to explain why primates favor DS gaits, most of them relating to the use of the arboreal habitat and, in particular, the exploitation of a narrow branch niche. This experimental study explores the potential explanation for the use of DS gaits by examining the relationship between branch diameter and gait patterns in 360 strides collected from six species of quadrupedal strepsirrhine primates on broad and narrow diameter supports. Gait sequence is quantified using limb phase, or the percentage of time during a stride cycle that a forelimb touchdown follows an ipsilateral hind limb touchdown. Although Loris, Nycticebus and Eulemur rubriventer individuals in this study did exhibit significantly lower locomotor velocities on narrower supports (P<0.01 in all three species), analyses of covariance showed no significant differences in limb phase values between broad and narrow diameter supports. Hence, results indicate surprisingly little evidence to suggest that alterations in gait sequence pattern provide a specific advantage for negotiating narrow supports.     

The biomechanics of skipping gaits: a third locomotion paradigm?

Skipping, a gait children display when they are about four- to five-years-old, is revealed to be more than a behavioural peculiarity. By means of metabolic and biomechanical measurements at several speeds, the relevance of skipping is shown to extend from links between bipedal and quadrupedal locomotion (namely galloping) to understanding why it could be a gait of choice in low-gravity conditions, and to some aspects of locomotion evolution (ground reaction forces of skipping seem to originate from pushing the walking gait to unnaturally high speeds). When the time-courses of mechanical energy and the horizontal ground reaction force are considered, a different locomotion paradigm emerges, enabling us to separate, among the bouncing gaits, the trot from the gallop (quadrupeds) and running from skipping (bipeds). The simultaneous use of pendulum-like and elastic mechanisms in skipping gaits, as shown by the energy curve analysis, helps us to understand the low cost of transport of galloping quadrupeds.     

The effects of natural substrate discontinuities on the quadrupedal gait kinematics of free‐ranging Saimiri sciureus

Wild primates encounter complex matrices of substrates that differ in size, orientation, height, and compliance, and often move on multiple, discontinuous substrates within a single bout of locomotion. Our current understanding of primate gait is limited by artificial laboratory settings in which primate quadrupedal gait has primarily been studied. This study analyzes wild Saimiri sciureus (common squirrel monkey) gait on discontinuous substrates to capture the realistic effects of the complex arboreal habitat on walking kinematics. We collected high‐speed video footage at Tiputini Biodiversity Station, Ecuador between August and October 2017. Overall, the squirrel monkeys used more asymmetrical walking gaits than symmetrical gaits, and specifically asymmetrical lateral sequence walking gaits when moving across discontinuous substrates. When individuals used symmetrical gaits, they used diagonal sequence gaits more than lateral sequence gaits. In addition, individuals were more likely to change their footfall sequence during strides on discontinuous substrates. Squirrel monkeys increased the time lag between touchdowns both of ipsilaterally paired limbs (pair lag) and of the paired forelimbs (forelimb lag) when walking across discontinuous substrates compared to continuous substrates. Results indicate that gait flexibility and the ability to alter footfall patterns during quadrupedal walking may be critical for primates to safely move in their complex arboreal habitats. Notably, wild squirrel monkey quadrupedalism is diverse and flexible with high proportions of asymmetrical walking. Studying kinematics in the wild is critical for understanding the complexity of primate quadrupedalism.     

Lateral sequence walking in infant Papio cynocephalus: implications for the evolution of diagonal sequence walking in primates

One of the most distinctive aspects of primate quadrupedal walking is the use of diagonal sequence footfalls in combination with diagonal-couplets interlimb timing. Numerous hypotheses have been offered to explain why primates might have evolved this type of gait, yet this important question remains unresolved. Because infant primates use a wider variety of quadrupedal gaits than do adults, they provide a natural experiment with which to test hypotheses about the evolution of unique aspects of primate quadrupedalism. In this study, we present kinematic data on two infant baboons (Papio cynocephalus) in order to test the recent hypothesis that diagonal sequence, diagonal couplets walking might have evolved in primates because their limb positioning provides stability in a small branch environment (Cartmill et al. [2002] Zool J Linn Soc 136:401-420). To assess hindlimb position at the moment of forelimb touchdown, we measured hindlimb angular excursion and ankle position for 84 walking strides, across three different types of gaits (diagonal sequence, diagonal couplets (DSDC); lateral sequence lateral couplets (LSLC); and lateral sequence diagonal couplets (LSDC)). Results indicate that if a forelimb were to contact an unstable substrate, LSLC walking provides as much, and perhaps more, stability when compared to DSDC walking. Therefore, it appears that this moment in a stride was unlikely to be a particularly important selective factor in the evolution of DSDC walking. Further insight into this issue will likely be gained by observations of primate quadrupedalism in natural environments, where the use of lateral sequence gaits might be more common than currently known.     

Gait choice in desert-living black-backed jackals

Gait selection is a strategy used by quadrupeds to meet the demands of locomotion under variable environmental conditions. The movement of black-backed jackals Canis mesomelas within a desert area was investigated. The usage and distribution of gaits in three distinct desert environments in the Namib Desert, Namibia, were analysed. The areas were chosen based on topographical differences: a bare, a featureless sand plain in an interdune valley, a large sand dune and a narrow dune valley with clumped plant growth. Fresh jackal tracks were recorded by GPS once a week for 1 year. Gait types, gait segment lengths and the rate of switches between gaits were analysed. Trot was the most frequently used gait in all areas, followed by walk and the two types of gallop. Jackals used faster gaits, with the lowest number of gait switches in the interdune plain. Movements on the sand dune were characterized by shorter gait segment lengths and frequent gait changes. In the dune valley, movements were slower and the rate of gait changes was intermediate between the other two areas. The strongest influence on gait choice and on gait changes was found to be the terrain topography, mainly the grade. Gait and track choice can be seen as a dynamic adaptation to a demanding environment like the Namib Desert.     

Origins of primate locomotion: gait mechanics of the woolly opossum

The locomotion of primates differs from that of other mammals in three fundamental ways. During quadrupedal walking, primates use diagonal sequence gaits, protract their arms more at forelimb touchdown, and experience lower vertical substrate reaction forces on their forelimbs relative to their hindlimbs. It is widely held that the unusual walking gaits of primates represent a basal adaptation for movement on thin, flexible branches and reflect a major change in the functional role of the forelimb. However, little data on nonprimate arboreal mammals exist to test this notion. To that end, we examined the gait mechanics of the woolly opossum (Caluromys philander), a marsupial convergent with small-bodied prosimians in ecology, behavior, and morphology. Data on the footfall sequence, relative arm protraction, and peak vertical substrate reaction forces were obtained from videotapes and force records for three adult woolly opossums walking quadrupedally on a wooden runway and a thin pole. For all steps recorded on both substrates, woolly opossums always used diagonal sequence walking gaits, protracted their arms beyond 90 degrees relative to horizontal body axis, and experienced peak vertical substrate reaction forces on forelimbs that were significantly lower than on hindlimbs. The woolly opossum is the first nonprimate mammal to show locomotor mechanics that are identical to those of primates. This case of convergence between primates and a committed fine-branch, arboreal marsupial strongly implies that the earliest primates evolved gait specializations for fine-branch locomotion, which reflect important changes in forelimb function.     

Gaits of monkeys and horses: A methodological critique

In a previous paper it was shown that the traditional methodology used to analyze quadrupedal gaits is inadequate when applied to the gaits of monkeys. The traditional methods were modified for use with the monkey sample (Prost, '65). Was the modification a general improvement of the traditional approach or was it dictated by peculiarities of monkey locomotion? The traditional analysis receives its support primarily from its usefulness in handling horse gaits. If it can be shown that the modified methods improve the analysis for horses, then it can be claimed that the system is not a special case designed uniquely for use with monkeys. Motion pictures were taken of an American Saddle Bred, five-gaited horse performing several classic gaits. The films were analyzed using the modified methods developed to analyze monkey gaits. The analysis was superior to the traditional approach. All of the organizing principles which structure horse gaits were found to be identical to those which structure monkey gaits.     

The gaits of chelonians: walking techniques for very low speeds

The gaits of three species of chelonians have been studied by filming and by recording the forces the feet exert on the ground. Chelonians could keep their bodies in equilibrium if they walked so as to have at least three feet on the ground at all times, and if the feet moved in appropriate sequence. However, they generally use a gait in which there are at times only two feet on the ground, and they do not maintain equilibrium, but pitch and roll through angular ranges of around 10°. Maintenance of equilibrium would require the feet to exert abruptly changing forces, which they are probably not capable of doing because of the slowness of chelonian muscle. Records of the forces exerted by the feet do not show abrupt changes. It is shown by mathematical modelling that if only slow changes of force are possible, the gaits and force patterns which chelonians use are close to the optimum which minimizes pitching and rolling. Gaits only a little different would be impracticable at low speeds because of excessive pitching and/or rolling. Slow muscle may be more efficient than fast muscle, and can maintain tension more economically.     

Laterality in the gallop gait of horses

Bilateral asymmetry in gallop stride limb contact patterns of four Quarter Horse fillies was documented by high-speed cinematography. Horses were filmed with rider by two cameras simultaneously while galloping along a straightaway. Even though signaled for each gallop lead an equivalent number of times, horses frequently switched leads, selecting the left lead nearly twice as often as the right. Velocities and stride lengths were greater for the left lead than the right, but stride frequencies did not differ between leads. Velocity effects were partitioned out in limb contact data analysis to enable the determination of persistent gallop stride asymmetries. The contact duration for the trailing (right) fore limb on the left lead exceeded the contact duration for the trailing (left) fore limb on the right lead. Selecting the right fore limb as the trailing fore limb may have allowed horses to use it to withstand the greater stresses and caused them to preferentially gallop with the left fore limb leading. Laterality may have an important influence on equine gallop motion patterns and thereby influence athletic performance.     

Symmetrical gaits of dogs in relation to body build

Symmetrical gaits of 37 breeds of dogs were analyzed. Usual walking and trotting gaits resemble those of other carnivores of similar size and conformation. Only certain long-legged dogs pace – usually at the fast walk or slow run. At the moderate walk, long-legged dogs tend to use lateral-couplets gaits, whereas short-legged breeds tend to use single-foot gaits. Many dogs must turn the axis of the body slightly from the line of travel at the trot to prevent interference between fore and hind feet. The relative duration with the ground made by fore and hind feet is discussed, usual support-sequences of the varicus gaits are presented, and the amount of variation is shown.     

Tumour-associated immunoglobulins and host cell infiltration

Summary Using a variety of techniques, we have investigated the possible interrelationship between tumour-associated immunoglobulins and infiltrating host cells. Initial cytological and histological studies revealed that tumour models which normally have a high immunoglobulin content also contained a relatively high proportion of host cells which could bind immunoglobulin by cytophilic processes. Rosette assays on tumour cell suspensions from mice also challenged with SRBC suggested that some of the immunoglobulin present may be non-specifically bound to host cells or synthesized in situ. Evidence that the local production of immunoglobulin could occur was obtained by protein A-PFC analysis of tumour cell suspensions. These studies also revealed that there were many more IgA-secreting cells within tumours than in spleen or lymph nodes. Finally, immunoglobulin analysis on gradient-separated tumour cell suspensions indicated that immunoglobulin was associated with both tumour and host cell-enriched (i.e., Fc-positive) fractions. These observations emphasize that much of the immunoglobulin previously noted in tumour eluates may not be associated with tumour cells as such, but may be bound to or synthesized by infiltrating host lymphoreticular cells.