A dynamic similarity hypothesis for the gaits of quadrupedal mammals

The dynamic similarity hypothesis postulates that different mammals move in a dynamically similar fashion whenever they travel at speeds that give them equal values of a dimensionless parameter, the Froude number. Thus, given information about one species, it could be possible to predict for others relationships between size, speed and features of gait such as stride length, duty factor, the phase relationships of the feet and the patterns of force exerted on the ground.
Data for a diverse sample of mammals have been used to test the hypothesis. It is found to be tenable in many cases when comparisons are confined to quadrupedal mammals of the type described by Jenkins (1971) as "cursorial". Most mammals of mass greater than 5 kg are of this type. Although the hypothesis applies less successfully to comparisons between cursorial and non-cursorial mammals it is shown to be a reasonable approximation even for such comparisons and for comparisons between quadrupedal mammals and bipedal mammals and birds.     

Modela-r as a Froude and Strouhal dimensionless numbers combination for dynamic similarity in running

The aim of this study was to test the hypothesis that running at fixed fractions of Froude (Nfr) and Strouhal (Str) dimensionless numbers combinations induce dynamic similarity between humans of different sizes. Nineteen subjects ran in three experimental conditions, (i) constant speed, (ii) similar speed (Nfr) and (iii) similar speed and similar step frequency (Nfr and Str combination). In addition to anthropometric data, temporal, kinematic and kinetic parameters were assessed at each stage to measure dynamic similarity informed by dimensional scale factors and by the decrease of dimensionless mechanical parameter variability. Over a total of 54 dynamic parameters, dynamic similarity from scale factors was met for 16 (mean r=0.51), 32 (mean r=0.49) and 52 (mean r=0.60) parameters in the first, the second and the third experimental conditions, respectively. The variability of the dimensionless preceding parameters was lower in the third condition than in the others. This study shows that the combination of Nfr and Str, computed from the dimensionless energy ratio at the center of gravity (Modela-r) ensures dynamic similarity between different-sized subjects. The relevance of using similar experimental conditions to compare mechanical dimensionless parameters is also proved and will highlight the study of running techniques, or equipment, and will allow the identification of abnormal and pathogenic running patterns. Modela-r may be adapted to study other abilities requiring bounces in human or animal locomotion or to conduct investigations in comparative biomechanics.     

Validity of the MarkWiiR for kinematic analysis during walking and running gaits

The aim of this study was to validate the MarkWiiR (MW) captured by the Nintendo Wii-Remote (100-Hz) to assess active marker displacement by comparison with 2D video analysis. Ten participants were tested on a treadmill at different walking (1<6 km · h⁻¹) and running (10<13 km · h⁻¹) speeds. During the test, the active marker for MW and a passive marker for video analysis were recorded simultaneously with the two devices. The displacement of the marker on the two axes (x-y) was computed using two different programs, Kinovea 0.8.15 and CoreMeter, for the camera and MW, respectively. Pearson correlation was acceptable (x-axis r≥0.734 and y-axis r≥0.684), and Bland–Altman plots of the walking speeds showed an average error of 0.24±0.52% and 1.5±0.91% for the x- and y-axis, respectively. The difference of running speeds showed average errors of 0.67±0.33% and 1.26±0.33% for the x- and y-axes, respectively. These results demonstrate that the two measures are similar from both the x- and the y-axis perspective. In conclusion, these findings suggest that the MarkWiiR is a valid and reliable tool to assess the kinematics of an active marker during walking and running gaits.     

Symmetrical and asymmetrical gaits in the mouse: patterns to increase velocity

The gaits of the adult SWISS mice during treadmill locomotion at velocities ranging from 15 to 85 cm s^–1 have been analysed using a high-speed video camera combined with cinefluoroscopic equipment. The sequences of locomotion were analysed to determine the various space and time parameters of limb kinematics. We found that velocity adjustments are accounted for differently by the stride frequency and the stride length if the animal showed a symmetrical or an asymmetrical gait. In symmetrical gaits, the increase of velocity is provided by an equal increase in the stride length and the stride frequency. In asymmetrical gaits, the increase in velocity is mainly assured by an increase in the stride frequency in velocities ranging from 15 to 29 cm s^–1. Above 68 cm s^–1, velocity increase is achieved by stride length increase. In velocities ranging from 29 to 68 cm s^–1, the contribution of both variables is equal as in symmetrical gaits. Both stance time and swing time shortening contributed to the increase of the stride frequency in both gaits, though with a major contribution from stance time decrease. The pattern of locomotion obtained in a normal mouse should be used as a template for studying locomotor control deficits after lesions or in different mutations affecting the nervous system.     

Effects of low-pass filter combinations on lower extremity joint moments in distance running

Inverse dynamics is a standard tool in biomechanics, which requires low-pass filtering of external force and kinematic signals. Unmatched filtering procedures are reported to affect joint moment amplitudes in high impact movements, like landing or cutting, but are also common in the analysis of distance running. We analyzed the effects of cut-off frequencies in 94 rearfoot runners at a speed of 3.5 m/s. Additionally, we investigated whether the evaluation of footwear interventions is affected by the choice of cut-off frequencies. We performed 3D inverse dynamics for the hip, knee and ankle joints using different low-pass filter cut-off frequency combinations for a recursive fourth-order Butterworth filter. We observed fluctuations of joint moment curves in the first half of stance, which were most pronounced for the most unmatched cut-off frequency combination (kinematics: 10 Hz; ground reaction forces (GRFs): 100 Hz) and for more proximal joints. Peak sagittal plane hip joint moments were altered by 94% on average. We observed a change in the ranking of subjects based on joint moment amplitude. We found significant (p < 0.001) footwear by cut-off frequency combination interaction effects for most peak joint moments. These findings highlight the importance of cut-off frequency choice in the analysis of joint moments and the assessment of footwear interventions in distance running. Based on our results, we propose to use matched cut-off frequencies around 20 Hz in order to avoid large artificial fluctuations in joint moment curves while at the same time avoiding a severe removal of physiological high-frequency signal content from the GRF signals.     

Accuracy of non-differential GPS for the determination of speed over ground

Accurate determination of speed is important in many studies of human and animal locomotion. Some global positioning system (GPS) receivers can data log instantaneous speed. The speed accuracy of these systems is, however, unclear with manufacturers reporting velocity accuracies of 0.1–0.2 ms⁻¹. This study set out to trial non-differential GPS as a means of determining speed under real-life conditions.

A bicycle was ridden around a running track and a custom-made bicycle speedometer was calibrated. Additional experiments were performed around circular tracks of known circumference and along a straight road. Instantaneous speed was determined simultaneously by the custom speedometer and a data logging helmet-mounted GPS receiver. GPS speed was compared to speedometer speed. The effect on speed accuracy of satellite number; changing satellite geometry, achieved through shielding the GPS antenna; speed; horizontal dilution of precision and cyclist position on a straight or a bend, was evaluated. The relative contribution of each variable to overall speed accuracy was determined by ANOVA. The speed determined by the GPS receiver was within 0.2 ms⁻¹ of the true speed measured for 45% of the values with a further 19% lying within 0.4 ms⁻¹ (n=5060). The accuracy of speed determination was preserved even when the positional data were degraded due to poor satellite number or geometry. GPS data loggers are therefore accurate for the determination of speed over-ground in biomechanical and energetic studies performed on relatively straight courses. Errors increase on circular paths, especially those with small radii of curvature, due to a tendency to underestimate speed.     

The evolutionary transition to sideways-walking gaits in brachyurans was accompanied by a reduction in the number of motor neurons innervating proximal leg musculature

The forwards-walking portly crab, Libinia emarginata is an ancient brachyuran. Its phylogenetic position and behavioral repertoire make it an excellent candidate to reveal the adaptations, which were required for brachyuran crabs to complete their transition to sideways-walking from their forwards-walking ancestors. Previously we showed that in common with other forwards-walking (but distantly related) crustaceans, L. emarginata relies more heavily on its more numerous proximal musculature to propel itself forward than its sideways-walking closer relatives. We investigated if the proximal musculature of L. emarginata is innervated by a greater number of motor neurons than that of sideways-walking brachyurans. We found the distal musculature of spider crabs is innervated by a highly conserved number of motor neurons. However, innervation of its proximal musculature is more numerous than in closely-related (sideways-walking) species, resembling in number and morphology those described for forwards-walking crustaceans. We propose that transition from forward- to sideways-walking in crustaceans involved a decreased role for the proximal leg in favor of the more distal merus–carpus joint.     

Optimal foot shape for a passive dynamic biped

Passive walking dynamics describe the motion of a biped that is able to "walk" down a shallow slope without any actuation or control. Instead, the walker relies on gravitational and inertial effects to propel itself forward, exhibiting a gait quite similar to that of humans. These purely passive models depend on potential energy to overcome the energy lost when the foot impacts the ground. Previous research has demonstrated that energy loss at heel-strike can vary widely for a given speed, depending on the nature of the collision. The point of foot contact with the ground (relative to the hip) can have a significant effect: semi-circular (round) feet soften the impact, resulting in much smaller losses than point-foot walkers. Collisional losses are also lower if a single impulse is broken up into a series of smaller impulses that gradually redirect the velocity of the center of mass rather than a single abrupt impulse. Using this principle, a model was created where foot-strike occurs over two impulses, "heel-strike" and "toe-strike," representative of the initial impact of the heel and the following impact as the ball of the foot strikes the ground. Having two collisions with the flat-foot model did improve efficiency over the point-foot model. Representation of the flat-foot walker as a rimless wheel helped to explain the optimal flat-foot shape, driven by symmetry of the virtual spoke angles. The optimal long period foot shape of the simple passive walking model was not very representative of the human foot shape, although a reasonably anthropometric foot shape was predicted by the short period solution.     

Evaluating dynamic error of a treadmill and the effect on measured kinetic gait parameters: Implications and possible solutions

The dynamic properties of instrumented treadmills influence the force measurement of the embedded force platform. We investigated these properties using a frequency response function, which evaluates the ratio between the measured and applied forces in the frequency domain. For comparison, the procedure was also performed on the gold-standard ground-embedded force platform. A predictive model of the systematic error of both types of force platform was then developed and tested against different input signals that represent three types of running patterns. Results show that the treadmill structure distorts the measured force signal. We then modified this structure with a simple stiffening frame in an attempt to reduce measurement error. Consequently, the overall absolute error was reduced (−22%), and the error in force-derived metrics was also sufficiently reduced: −68% for average loading rate error and −80% for impact peak error. Our procedure shows how to measure, predict, and reduce systematic dynamic error associated with treadmill-installed force platforms. We suggest this procedure should be implemented to appraise data quality, and frequency response function values should be included in research reports.     

Three-dimensional analysis of horse and human gaits in therapeutic riding

Therapeutic horse riding or hippotherapy is used as an intervention for treating individuals with mental and physical disabilities. Equine-assisted interventions are based on the hypothesis that the movement of the horse's pelvis during horseback riding resembles human ambulation, and thus provides motor and sensory inputs similar to those received during human walking. However, this hypothesis has not been investigated quantitatively and qualitatively. This study aimed to verify the hypothesis by conducting a three-dimensional analysis of the horse's movements while walking and human ambulation. Using four sets of equipments, we analysed the acceleration patterns of walking in 50 healthy humans and 11 horses. In addition, we analysed the exercise intensity by comparing the heart rate, breathing rate, and blood pressure of 127 healthy individuals before and after walking and horse riding. The acceleration data series of the stride phase of horse walking were compared with those of human walking, and the frequencies (in Hz) were analysed by Fast Fourier transform.The acceleration curves of human walking overlapped with those of horse walking, with the frequency band of human walking corresponding with that of horse walking. Exercise intensity, as measured by the heart rate and breathing rate, was not significantly different between horse riding and human walking. The levels of diastolic blood pressure were slightly higher during horse riding than during walking, but were lower during both conditions compared with those in normal conditions (P < 0.01). The present study shows that, although not completely matched, the accelerations of the horse and human walking are comparable quantitatively and qualitatively. Horse riding at a walking gait could generate motor and sensory inputs similar to those produced by human walking, and thus could provide optimum benefits to persons with ambulatory difficulties.     

Classification accuracy of a single tri-axial accelerometer for training background and experience level in runners

Accelerometers are increasingly used tools for gait analysis, but there remains a lack of research on their application to running and their ability to classify running patterns. The purpose of this study was to conduct an exploratory examination into the capability of a tri-axial accelerometer to classify runners of different training backgrounds and experience levels, according to their 3-dimensional (3D) accelerometer data patterns. Training background was examined with 14 competitive soccer players and 12 experienced marathon runners, and experience level was examined with 16 first-time and the same 12 experienced marathon runners. Discrete variables were extracted from 3D accelerations during a short run using root mean square, wavelet transformation, and autocorrelation procedures. A principal component analysis (PCA) was conducted on all variables, including gait speed to account for covariance. Eight PCs were retained, explaining 88% of the variance in the data. A stepwise discriminant analysis of PCs was used to determine the binary classification accuracy for training background and experience level, with and without the PC of Speed. With Speed, the accelerometer correctly classified 96% of runners for both training background and experience level. Without Speed, the accelerometer correctly classified 85% of runners based on training background, but only 68% based on experience level. These findings suggest that the accelerometer is effective in classifying athletes of different training backgrounds, but is less effective for classifying runners of different experience levels where gait speed is the primary discriminator.     

Effects of support size and orientation on symmetric gaits in free-ranging tamarins of Amazonian Peru: implications for the functional significance of primate gait sequence patterns

The adoption of a specific gait sequence pattern during symmetrical locomotion has been proposed to have been a key advantage for the exploitation of the fine branch niche in early primates. Diverse aspects of primate locomotion have been extensively studied in technically equipped laboratory settings, but evolutionary conclusions derived from these investigations have rarely been verified in wild primates. Bridging the gap from the lab to the field, we conducted an actual performance determination of symmetrical gaits in two free-ranging tamarin species (Saguinus mystax and Saguinus fuscicollis) of Amazonian Peru by analyzing high-speed video recordings of naturally occurring locomotor bouts. Tamarins arguably represent viable models for aspects of early primate locomotion. We tested three specific hypotheses derived from laboratory studies to test for the influence of support size and orientation and to gain further insight into the functional significance of primate gait sequence patterns: (1) The tamarins utilize symmetrical gaits at a higher rate on small supports than on larger ones. (2) During symmetrical locomotion on small supports, diagonal sequences are utilized at a higher rate than on larger supports. (3) On inclines, diagonal sequences are predominantly used and on declines, lateral sequences are predominantly used. Our results corroborated hypotheses 1 and 3. We found no clear support for hypothesis 2. In conclusion, our results add to the notion that primate gait plasticity, rather than uniform adoption of diagonal sequence gaits, enabled early primates to accommodate different support types and effectively exploit the small branch niche.     

A dynamic model of thoracic differentiation for the control of turning in the stick insect

Leg movements of stick insects (Carausius morosus) making turns towards visual targets are examined in detail, and a dynamic model of this behaviour is proposed. Initial results suggest that front legs shape most of the body trajectory, while the middle and hind legs just follow external forces (Rosano H, Webb B, in The control of turning in real and simulated stick insects, vol. 4095, pp 145–156, 2006). However, some limitations of this explanation and dissimilarities in the turning behaviour of the insect and the model were found. A second set of behavioural experiments was made by blocking front tarsi to further investigate the active role of the other legs for the control of turning. The results indicate that it is necessary to have different roles for each pair of legs to replicate insect behaviour. We demonstrate that the rear legs actively rotate the body while the middle legs move sideways tangentially to the hind inner leg. Furthermore, we show that on average the middle inner and hind outer leg contribute to turning while the middle outer leg and hind inner leg oppose body rotation. These behavioural results are incorporated into a 3D dynamic robot simulation. We show that the simulation can now replicate more precisely the turns made by the stick insect. This work was supported by CONACYT México and the European Commission under project FP6-2003-IST2-004690 SPARK.     

A new way of analysing symmetrical and asymmetrical gaits in quadrupeds

This new approach highlights for the first time that all the gaits, symmetrical as well as asymmetrical, correspond to the succession of sequences that start by the movements of the two fore limbs, followed by the movements of the two hind limbs. Inside those sequences, the gaits are identified by the time lag between the movements of the two pairs and by the time lag between the movements of the two feet inside each pair. This approach, by breaking the stride paradigm, gives a new framework to locomotion analysis.     

Talocrural joint in African hominoids: implications for Australopithecus afarensis

Talocrural joints of the African apes, modern humans, and A.L.288-1 are compared in order to investigate ankle function in the Hadar hominids. Comparisons between the hominids and African pongids clearly illustrate the anatomical and mechanical changes that occurred in this joint as a consequence of the evolutionary transition to habitual bipedality. Features which are considered include the obliquity of the distal tibial articular surface, the shape of the talar trochlea, and the location and functional implications of the talocrural axis. In every functionally significant feature examined the A.L.288-1 talocrural joint is fully bipedal. Moreover, the Hadar ankle complex also shows the functional constraints which are necessarily imposed by the adaptation to habitual bipedalism.     

Multi-sensor assessment of dynamic balance during gait in patients with subacute stroke

The capacity to maintain upright balance by minimising upper body oscillations during walking, also referred to as gait stability, has been associated with a decreased risk of fall. Although it is well known that fall is a common complication after stroke, no study considered the role of both trunk and head when assessing gait stability in this population. The primary aim of this study was to propose a multi-sensor protocol to quantify gait stability in patients with subacute stroke using gait quality indices derived from pelvis, sternum, and head accelerations. Second, the association of these indices with the level of walking ability, with traditional clinical scale scores, and with fall events occurring within the six months after patients’ dismissal was investigated. The accelerations corresponding to the three abovementioned body levels were measured using inertial sensors during a 10-Meter Walk Test performed by 45 inpatients and 25 control healthy subjects. A set of indices related to gait stability were estimated and clinical performance scales were administered to each patient. The amplitude of the accelerations, the way it is attenuated/amplified from lower to upper body levels, and the gait symmetry provide valuable information about subject-specific motor strategies, discriminate between different levels of walking ability, and correlate with clinical scales. In conclusion, the proposed multi-sensor protocol could represent a useful tool to quantify gait stability, support clinicians in the identification of patients potentially exposed to a high risk of falling, and assess the effectiveness of rehabilitation protocols in the clinical routine.     

Change in Criteria for USP Dissolution Performance Verification Tests

The US Pharmacopeial Convention has been evaluating its performance verification tests (PVT) for several years. These tests help ensure the integrity of the US Pharmacopeia performance test when a dissolution procedure, as described in General Chapter Dissolution <711>, is relied upon to test a nonsolution orally administered dosage form. One result of the evaluation is a change in the PVT criterion from one based on individual tablet results to one based on the mean and variability of a set of tablets. This paper describes the new PVT and its criterion and how its acceptance limits are derived from results of a collaborative study, explains a two-stage option for the test, and presents operating characteristics.     

Evolving locomotion for a 12-DOF quadruped robot in simulated environments

We demonstrate the power of evolutionary robotics (ER) by comparing to a more traditional approach its performance and cost on the task of simulated robot locomotion. A novel quadruped robot is introduced, the legs of which – each having three non-coplanar degrees of freedom – are very maneuverable. Using a simplistic control architecture and a physics simulation of the robot, gaits are designed both by hand and using a highly parallel evolutionary algorithm (EA). It is found that the EA produces, in a small fraction of the time that takes to design by hand, gaits that travel at two to four times the speed of the hand-designed one. The flexibility of this approach is demonstrated by applying it across a range of differently configured simulators.     

Sampling frequencies and measurement error for linear and temporal gait parameters in primate locomotion

Quantitative analyses of animal motion are increasingly easy to conduct using simple video equipment and relatively inexpensive software packages. With careful use, such analytical tools have the potential to quantify differences in movement between individuals or species and to allow insights into the behavioral consequences of morphological differences between taxa. However, as with any other type of measurement, there are errors associated with kinematic measurements. Because normative kinematic data on human and nonhuman primate locomotion are used to model aspects of gait of fossil hominins, errors in the extant data influence the accuracy of fossil gait reconstructions. The principal goal of this paper is to illustrate the effect of camera speeds (frame rates) on kinematic measurement errors, and to demonstrate how these errors vary with subject size, movement velocity, and sample size. Kinematic data for human walking and running (240 Hz), as well as data for primate quadrupedal walking and running (180 Hz) were used as inputs for a simulation of the measurement errors associated with various linear and temporal kinematic variables. Measurement errors were shown to increase as camera speed, subject body size, and interval duration all decrease, and as movement velocity increases. These results have implications for the methods used to calculate subject velocity and suggest that using a moving marker to measure the linear displacements of the body is preferable to the use of a stationary marker. Finally, while slower camera speeds will always result in higher measurement errors than do faster camera speeds, this effect can be moderated to some extent by collecting sufficiently large samples of data.