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Mixed gaits in small avian terrestrial locomotion


Abstract and Figures

Scientists have historically categorized gaits discretely (e.g. regular gaits such as walking, running). However, previous results suggest that animals such as birds might mix or regularly or stochastically switch between gaits while maintaining a steady locomotor speed. Here, we combined a novel and completely automated large-scale study (over one million frames) on motions of the center of mass in several bird species (quail, oystercatcher, northern lapwing, pigeon, and avocet) with numerical simulations. The birds studied do not strictly prefer walking mechanics at lower speeds or running mechanics at higher speeds. Moreover, our results clearly display that the birds in our study employ mixed gaits (such as one step walking followed by one step using running mechanics) more often than walking and, surprisingly, maybe as often as grounded running. Using a bio-inspired model based on parameters obtained from real quails, we found two types of stable mixed gaits. In the first, both legs exhibit different gait mechanics, whereas in the second, legs gradually alternate from one gait mechanics into the other. Interestingly, mixed gaits parameters mostly overlap those of grounded running. Thus, perturbations or changes in the state induce a switch from grounded running to mixed gaits or vice versa.
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SCIENTIFIC RepoRts | 5:13636 | DOI: 10.1038/srep13636
Mixed gaits in small avian
terrestrial locomotion
Emanuel Andrada1,3, Daniel Haase2, Yefta Sutedja1, John A. Nyakatura3,4,
Brandon M. Kilbourne3,5, Joachim Denzler2, Martin S. Fischer3 & Reinhard Blickhan1
Scientists have historically categorized gaits discretely (e.g. regular gaits such as walking, running).
However, previous results suggest that animals such as birds might mix or regularly or stochastically
switch between gaits while maintaining a steady locomotor speed. Here, we combined a novel and
completely automated large-scale study (over one million frames) on motions of the center of mass
in several bird species (quail, oystercatcher, northern lapwing, pigeon, and avocet) with numerical
simulations. The birds studied do not strictly prefer walking mechanics at lower speeds or running
mechanics at higher speeds. Moreover, our results clearly display that the birds in our study employ
mixed gaits (such as one step walking followed by one step using running mechanics) more often
than walking and, surprisingly, maybe as often as grounded running. Using a bio-inspired model
based on parameters obtained from real quails, we found two types of stable mixed gaits. In the
rst, both legs exhibit dierent gait mechanics, whereas in the second, legs gradually alternate
from one gait mechanics into the other. Interestingly, mixed gaits parameters mostly overlap those
of grounded running. Thus, perturbations or changes in the state induce a switch from grounded
running to mixed gaits or vice versa.
When researchers analyze legged locomotion, they usually categorize discretely regular gaits (i.e. walking
or running) based on the relative contact time of limbs (limb phase and duty factor1) or uctuations
of the mechanical energy at the center of mass (CoM)2,3. e latter categorization is better suited to
discriminate between walking and running (see4 for a deeper discussion on this topic) and served as a
fruitful basis for the development of relative simple models like the inverted pendulum for walking3 or
the spring-mass model for running5. ese relatively simple models for walking and running have greatly
widened our understanding of global principles of locomotion; however, they represent only discrete ide-
alized paradigms. For human locomotion, such discrete changes may apply, but not necessarily for small
animals, as gait transitions have oen been shown to be more gradual in smaller species (e.g.4,6–8). In
particular, smooth gait changes were described for small bird terrestrial locomotion (e.g.6–11). Contrarily,
the existence of hybrid gaits (both legs exhibit a combination of two regular gaits in one stride, e.g. “pen-
dular run12) or mixed gaits (legs display dierent gait dynamics, i.e. one step with walking mechanics is
followed by one step with running mechanics or vice versa at a relatively constant speed) during bipedal
locomotion has received little attention. Scientists usually focus on the investigation of a regular gait and
expect that deviations are due to unsteady locomotion. For example, most of the theoretical work on
bipedal locomotion is focused on one-cycle periodic gaits, and likely avoid unintentionally ‘limping’ or
‘hybrid gaits’ (e.g.5,13–15).
e discussion about hybrid gaits emerged aer numerical energetic optimizations of another simple
model (point-mass and telescopic leg) predicted such a gait during locomotion at intermediate speeds
utilizing long step-lengths, which was termed a ‘pendular run12. More recently, Usherwood16 found hints
1Science of Motion, Friedrich-Schiller University of Jena, Germany. 2Computer Vision Group, Friedrich-Schiller
University of Jena, Germany. 3Institut für Spezielle Zoologie und Evolutionsbiologie mit Phyletischem Museum,
Friedrich-Schiller University of Jena, Germany. 4AG Morphologie und Formengeschichte, Bild Wissen Gestaltung:
ein interdisziplinäres Labor, Institut für Biologie, Humboldt University Berlin, Germany. 5College for Life Sciences,
Wissenschaftskolleg zu Berlin, Berlin, Germany. Correspondence and requests for materials should be addressed
to E.A. (email:
Received: 03 March 2015
Accepted: 30 July 2015
Published: 03 September 2015
SCIENTIFIC RepoRts | 5:13636 | DOI: 10.1038/srep13636
of pendular running in the terrestrial locomotion of pheasants and guineafowl by analyzing their CoM
motions derived from forceplate measurements. Given that the inverted pendulum2 is almost 40 years
old and that the spring-mass model5 is almost 30 years old, it seems fair to wonder to what degree the
walking and running paradigms inuenced and still inuence the selection and analysis of strides in
animal locomotion? is question is of importance not only in regard of avian terrestrial locomotion,
but also to terrestrial locomotion in other tetrapod groups.
It is generally accepted that birds walk at the lowest speeds, however, exceptions such as sparrows exist
(see also text below). At moderate speeds, small birds usually prefer a running gait without aerial phases,
which was termed grounded running15,17,18. eoretically during grounded running, potential (Ep) and
kinetic (Ek) energy of the CoM change nearly in phase (bouncing mechanics), and, consequently, a high
congruity occurs between both energy patterns (%congruity as a measure for CoM energy pattern see19).
In contrast, the vaulting motion of the CoM observed in walking produces EP and EK patterns that uc-
tuate out-of-phase (low congruity). However, zero congruity is not expected for compliant walking13. In
small birds, the shi between vaulting and bouncing mechanics is said to be gradual, rarely approaching
the ideal scenarios (e.g.,7,10). If this is the case, as speed increases, one can expect that %congruity values
will cross a value of 50, which is usually dened as a boundary between walking-like and running-like
gaits (e.g.7,19,20). In this ‘transition zone, small uctuations, as birds experience on a treadmill or face in
irregular natural environments, might produce %congruity shis to either walking or running mechan-
ics. Two eects can be expected: i) in some trials running occurs at a slower speed than walking in
another trial and/or ii) mixed gaits emerge.
In the present paper, we combined a large-scale study (over one million frames) on the uctuations
of the CoM’s mechanical energy in several bird species (quail, oystercatcher, northern lapwing, pigeon,
and avocet) during treadmill locomotion, which was performed in a completely automated way, with
numerical simulations, in order to address two main points.
First, we examined whether the transition between vaulting (i.e. walking) and bouncing (i.e. running)
mechanics correlates with speed, without human inuence introduced via manual digitizing and sub-
jective choice of strides for analysis. Even though globally a trend towards increasing %congruity with
higher speeds was observed in recent investigations, at lower speeds, some birds, such as lapwings7 and
tinamous10, do not always seem to prefer walking mechanics. In contrast, quail18 and the much larger
ostrich17 seem to rely on CoM’s mechanics indicative of walking during slow locomotion.
Second, we asked whether mixed gaits exist at the boundary between walking and grounded run-
ning. Within a range of relative speeds (Froude numbers of approximately 0.5 ~ 0.6), it is frequently
observed that both walking and grounded running gaits occur in birds7,17,18. In addition, it was found
that virtual leg stiness (computed from the ground reaction forces and the length change between the
CoM and foot contact point) remain at values close to 6 during quail walking, grounded running and
running when normalized by body mass and leg-length18. By combining experimental data on quail
and simulations, Andrada and colleagues21 showed that pronograde locomotion maximizes the advan-
tages of grounded running. Moreover, they found that in order to obtain walking gaits, the eective leg,
dened as the length between the hip and foot contact point, must be less sti but more damped than a
leg tuned for running. us, they speculated that in the quail there must occur a shi to an increasing
role of elastic tissues during running as also observed in running turkeys and running humans22,23. It is
therefore conceivable that during the transition between walking and grounded running, model related
leg parameters such as leg stiness or leg damping should be suitable for both gaits, thus facilitating a
potential emergence of mixed gaits.
To address these questions, we analyzed X-ray recordings on a large quantitative scale using the
algorithms developed by Haase and colleagues24. e methodology permits an automatic tracking of
the CoM. In addition, foot contacts and aerial phases were also detected through automation. en we
determined for each step the percentage of congruity to dierentiate vaulting from bouncing mechanics.
Finally, to test whether mixed gaits are part of the repertoire of the dynamics of pronograde bipedal
locomotion, and not just a treadmill artifact, we explored numerically, based on parameters derived
from quail (cf.21), the existence of periodic mixed gaits within the overlap zone of walking, grounded
running and running by using a simple model called Pronograde Virtual Pivot Point (PVPP;21). In sim-
ulations both legs have same basic eective leg parameters such as leg length (l0), leg stiness (k), and
leg damping (c).
Congruity of CoM mechanics. In general no correlation between %congruity and speed was
observed. However, some dierences among species can be established based on the scatter plots.
We recorded trials from avocets that met the criteria for analysis at speed between 0.14 ms1 and
1.77 ms1. Despite this speed range, avocets seem to prefer the transition zone of % congruity values
ranging between 40% and 70% (Fig. 1). No aerial phases were observed at speeds below 1.2 ms1. At
speeds above 1.2 ms1, only two individuals ran without aerial phases, but still exhibited in 29% of steps
%congruity values lower than 50. In this speed interval, 3 individuals ran with aerial phases in just 16%
of the steps. When generally comparing one step with the subsequent step (Table1 and Fig.2), ~52%
of these pairs of steps exhibited solely running mechanics in both steps, ~8% solely walking mechanics
walking in both steps, and ~40% mixed walking and running mechanics between steps. Most of the aerial
SCIENTIFIC RepoRts | 5:13636 | DOI: 10.1038/srep13636
phases where observed in the area of two consecutive running steps. Individual dierences are signicant
due to one individual which used relatively more walking and less bouncing mechanics during trials
(Table1). e variation observed among the other three individuals is random.
Northern lapwings displayed a pattern similar to avocets, but with slightly enhanced dispersion of
the data. ey moved at speeds ranging from 0.06 ms1 to 1.75 ms1. Northern lapwings did not incor-
porate aerial phases at speeds lower than 1.0 ms1. At speeds above 1 ms1 they used aerial phases in
23% of the steps, but in 39% of the steps %congruity was still lower than 50 (Fig.1). When comparing
consecutive steps in general, ~40% of them exhibited running mechanics in both steps, ~44% a mixture
of walking and running, and ~16% walking in both steps (Fig.2). As observed for the avocets, individual
dierences are signicant due to one individual (B67), which used relatively more frequently walking
and less bouncing mechanics (Table1). e variation observed among the other three individuals is due
to chance.
Oystercatchers and pigeons displayed a similar pattern in their scatter plots, though in dierent
speeds ranges (oystercatchers: 0.13 ms1 to 2.3 ms1; pigeons: 0.07 ms1 to .81 ms1). Both species exhib-
ited intermediate %congruity values (between 40 and 70) at lower speeds, followed by a greater disper-
sion at intermediate and high speeds. We did not record aerial phase running in oystercatchers at speeds
below 1.4 ms1. At speeds ranging between 1 ms1 and 1.4 ms1, oystercatcher exhibited in 31% of the
steps %congruity values lower than 50. At speeds higher than 1.4 ms1, they used aerial phases in 23%
of the steps, and vaulting mechanics in 40% steps. When comparing one step with the subsequent one,
32% of them exhibited running mechanics in both steps, ~53% a mixture of walking and running, and
~15% walking in both steps. e variation observed between individuals is random (Table1).
Pigeons moving on the treadmill did not exhibit aerial phases. At speeds higher than 0.4 ms1, pigeons
still showed in 36% of the steps %congruity values lower than 50%. %. When comparing one step with
the following step, on average ~31% of them exhibited running mechanics in both steps, ~53% a mixture
of walking and running, and ~16% walking in both steps. Individual dierences are signicant due to one
individual (200), which used relatively more walking and less grounded running during trials (Table1).
e variation observed among the other three individuals is random.
0 1 2
0 1 2
0 1 2
norther lapwings
0 0.5 1
0 0.5 1
0.82 1.650.76 1.52 ~0.5 ~1
treadmill speed
0.88 1.77 0.48 0.96
treadmill speed
Figure 1. %Congruity of CoM mechanics related to treadmill and dimensionless speed (
). %congruity
values lower up to 50 are oen related to vaulting mechanics, while those larger than 50 are interpreted as
bouncing mechanics. Each point represent a step. Red points indicates that aerial phases occurred.
SCIENTIFIC RepoRts | 5:13636 | DOI: 10.1038/srep13636
We collected data from quails locomoting at speeds ranging from 0.15 ms1 to 0.85 ms1. Most of the
collected data was at speeds lower than 0.6 m s1. Similar to the pigeons, the quail did not exhibit aerial
phases within that speed range. At speeds higher than 0.4 ms1, quail exhibited only in 14% of the steps
%congruity values lower than 50%. When comparing one step with its following one, ~29% of them
exhibited running mechanics in both steps, ~55% a mixture of walking and running, and ~16% walking
in both steps. e variation observed between individuals is only due to chance (Table1).
Simulations. We simulated quail locomotion using the minimalistic PVPP model and parameters
introduced in21. Results presented below are stable simulations. Stable walking, grounded running, and
running were already presented in21. Here, we add results for mixed gaits. In simulations, we found two
dierent types of mixed gaits, and an apparently mixed gait. In the preferred–leg mixed gait, one leg
exclusively exhibits walking mechanics and the other only running mechanics (Fig.3). In alternating
mixed gait, both legs gradually shi, out of phase, between walking and running mechanics. An appar-
ently mixed gait converges very slowly to grounded running, thus aer small perturbations, the gait
seems to be mixed (even aer 100 simulated steps, Fig.3, k = 100 Nm1, magenta).
Mixed gaits in simulations using walking-like parameters. Using parameters obtained from walking quail
such as eective leg stiness and damping, average speed of locomotion (see methods), simulations
yielded mixed gaits at speeds ranging from 0.17 ms1 to 0.65 ms1.
Mass (g)
Total steps i
vs i + 1v (%) b (%) m (%) p-value
Vanellus vanellus
B65+ 169.8 103 11 42 47
p = 0,003
p = 0,582+
B67 184.9 195 24 29 47
B76+ 163.2 150 13 45 42
B100+ 163.6 158 15 46 39
Haematopus ostralegus
5769 (1) 450.0 118 14 31 55
p = 0,487
5769 (4) 490.0 22 15 26 59
3970 (5) 433.3 391 17 37 46
3970 (7) 455.0 208 13 34 53
Recurvirostra avosetta
Orange+ 285.0 192 5 59 36
p = 0,034
p = 0,439+
Silber+ 348.0 193 8 53 39
Green+ 358.0 66 3 53 44
Wei ß 344.0 266 10 44 46
Coturnix coturnix
1 220 41 27 24 49
p = 0.662
2 202 67 10 33 57
5 204 63 17 26 57
8 202 29 14 31 55
9 225 49 14 30 56
Columba livia
437+ 582 108 9 35 56
p = 0,000
p = 0,32+
200 472 90 32 18 50
233+ 519 249 12 40 48
727+ 577 158 12 31 57
Table 1. Individual data. Body mass for individual study animals, total number of steps analyzed per
individual, percentage of occurrence of vaulting mechanics (v), bouncing mechanics (b), and mixed gaits
(m), and p-value chi^2 test. For pigeon, avocets, and northern lapwings is the p-value computed signicant
due to the variation of one individual (bold). e variation of the other 3 individuals (marked with+ ) among
these species is due to chance (see p+).
SCIENTIFIC RepoRts | 5:13636 | DOI: 10.1038/srep13636
e mixed gait domain is a long, inclined volume that comprises almost the whole range of VPP
heights (Fig.3 le, cyan volume with black mesh). For lower VPP height, damping values are the highest
and decrease with increasing VPP height. e domain also stretched from mean trunk angles between
120° and 135°. Interestingly, the mixed gaits domain is located far from parameters that induce the model
to exhibit walking. e latter were observed at a more prone trunk position. Mixed gaits made up 5%
of the total solutions.
Mixed gaits in simulations using bouncing-like parameters. Using parameters obtained from bouncing-like
quail gaits (see methods and table1), mixed gaits existed in ve small separated volumes (Fig.3 right,
cyan volumes with black mesh). e largest one is located at damping values exceeding 6.5 Nsm1 with
relatively shallow trunk angles between 112° and 120° and VPP heights up to 0.03 m. Again, mixed gait
domains are located far from parameters which induce the model to exhibit walking. Using bouncing-like
parameters, mixed gaits made up only 2% of the total solutions.
Independent of parameters being walking- or bouncing-like, the mixed gait produces an imbalance in
the GRFs. In Fig.4A we present a comparison between the GRF obtained for grounded running and for
preferred-leg mixed gait with identical model parameters though diering leg compression. During this
mixed gait, the peak of the GRF measured in the grounded running leg increased by 54% while maxi-
mal value of the vertical GRF in the vaulting leg decreased by the same value. Both gaits oscillate about
similar system energy (SEgr ~ 0.246 J; SEm ~ 0.248 J); however the dimensionless specic cost of transport
is about 20% higher for mixed gait (CoTgr = 0.211, CoTm = 0.254).
We asked whether small birds predominantly use vaulting mechanics at lower speeds, and bouncing
mechanics at the higher speeds. Alternatively, small avian locomotion is less discrete and permit the
0 50 100
%congruity step i+1
%congruity step i
0 50 100
%congruity step i
0 50 10
%congruity step i
0 50 100
northern lapwings
%congruity step i+1
%congruity step i
0 50 100
%congruity step i
0 50 10
%congruity step i
Figure 2. Values of %Congruity in step i vs. step i + 1. Quadrant I and IV depict mixed gaits. In I
%congruity shis from walking values in step i to values representing running mechanics in step i + 1. e
inverse occurs in IV. II and III portray regular gaits of running and walking mechanics, respectively. Red
points indicates that aerial phases occurred. For individual/marker type correspondence see Table1. Bottom
right shows a single trial from individual “3970(7)” comprised of 23 steps at 2.1 m s1. Note that it combines
mixed gaits, grounded running, running (red), and walking. Arabic numbers indicate step sequence.
SCIENTIFIC RepoRts | 5:13636 | DOI: 10.1038/srep13636
existence of mixed gaits such as those in which one step with walking mechanics is followed by one step
running mechanics or vice versa at relative constant speed. To test this with reasonable degree of gen-
erality, we conducted an automated large-scale study on CoM movements in a limited number of rela-
tively small, phylogenetically and morphologically diverse species of neognath birds (quail, oystercatcher,
northern lapwing, pigeon, and avocet), using a recently published methodology24.To complement the
experimental data, we also modelled gaits at the transitions between walking, grounded running, and
running based on parameters derived from live quail (cf.21). Still, further studies including data from
paleognath birds, i.e., tinamous and ratitites, will be necessary to test the broader generality of the results
presented here.
Our experimental results show no clear correlation between %congruity and speed. is suggests that
at least the birds studied do not strictly prefer walking mechanics at lower speeds or running mechanics
at higher speeds. Moreover, our results clearly display that the birds in our study engage mixed gaits more
oen than walking and, surprisingly, maybe more/as oen than/as grounded running (Table1, Fig.2). In
general, our statistics show that a bird displaying a walking step on the treadmill only had a chance of ca.
15% to repeat walking in the subsequent step. In contrast, if it exhibits a bouncing step, the probability
to exhibit again a bouncing step rises to ca. 40%. us, for large sequences, as shown in Fig.2, there is a
high chance to see combinations of dierent gaits. Accordingly, we found only in shorter video sequences
(5 to 10 steps) singular gaits such as walking, grounded running or mixed gaits (see Fig. S2).
Recent studies have already shown that some small to medium sized avian species such as lapwings or
tinamous do not always exhibit walking mechanics at lower speeds7,10,11. Other studies have shown that
grounded running may be the most frequently used gait in avian locomotion11,15,18. ese experimental
observations might not be entirely explained by a more compliant leg in small birds. It has been shown
that in mammals, leg stiness scales as the two-third power of body mass25,26, regardless of whether this
is quantied using a virtual leg dened as the length between the CoM and foot contact point or using
the eective leg. In other words, leg stiness is independent of body mass when normalized by body
mass and leg-length27. us, more probably, birds engage running-like or mixed gait mechanics oen
because of their pronograde trunk orientation. Andrada and colleagues recently showed through numer-
ical simulations with the PVPP model that most of the stable solutions obtained using quail parameters
are indeed grounded running21. ese results and those presented here add a functional criterion, namely
the need for stability, to the frequently observed occurrence of grounded running and, as demonstrated
in the current study, mixed gaits.
%congruity step i
%congruity step i+1
%congruity step i
%congruity step i+1
Figure 3. Fields of stable locomotion for walking-like (le) and bouncing-like (right) parameters
(see methods). Grounded running (gr), running (r), walking (w), mixed (m), and apparently mixed
(a-m). Mixed gaits are: (a) preferred-leg mixed gait, a combination of one step walking and one step
grounded running, or (b) alternating mixed gait, the legs alternate gradually between walking and running
mechanics(i.e. while one leg changes from walking to grounded running, the contralateral leg changes in the
opposite way). Apparently mixed gaits converge to grounded running aer ca. 1000 steps. Subplots display
congruity changes between one step and the next for two examples of alternating mixed gaits. For every
simulation, both legs have same leg parameters, such as length at touch-down l0, stiness k, and damping c.
SCIENTIFIC RepoRts | 5:13636 | DOI: 10.1038/srep13636
A clear separation between vaulting and bouncing mechanics can be useful to describe human loco-
motion. However, birds show a greater dispersion in the %congruity values. One explanation for these
ndings may lie in the pronograde trunk position in birds. Together, trunk, neck, and head make more
than 80% of the total mass of an individual, and have a relative motion with respect to the leg (the trunk
oscillates about the hip) so that leg compression and releases do not necessary oscillate in phase with
trunk rotation10,20,28,29. Such a phase shi may vary based on the relation between the inertia of the trunk,
the torque in the hip joint, and viscoelastic properties in the leg. It follows, that dierent anatomies may
favor diverse relationships between potential and kinetic energy. Taking a closer look at the scatter plots,
hints of species-related dierences become evident. Northern lapwings and especially avocets, move
mostly at %congruity values between 40 and 70 independently of speed, and choose bouncing gaits as
oen as mixed gaits if not more frequently. Such a locomotion may be distinctive for birds with relatively
long legs and svelte bodies. e rather bulky pigeon and oystercatcher displayed a dierent pattern.
%congruity values mostly indicate bouncing mechanics at lower speeds. Interestingly, as speed increased,
the dispersion of the %congruity values increased, and even at higher speeds (see Fig.1), they exhibited
vaulting mechanics in ca. 40% of the steps. Quail are predominantly terrestrial birds; however, they did
not show a clear trend towards vaulting or bouncing during locomotion on the treadmill. Quail, pigeon
and oystercatcher seem to employ mixed gaits more frequently than bouncing gaits.
e scarcity of the red points in Fig.1 indicate that running with aerial phases represent a rare event
in our experiments. In our dataset, quail and pigeon did not use aerial phases. Here, the fact that they
CoM's vertical position [m]
CoM's vertical position [m]
CoM's vertical position [m]
Figure 4. Switching between preferred-leg mixed gait and grounded running. In the overlapping
zones of Fig.3, two limit cycles exist for the same model parameters. (A) Model ground reaction forces
(grounded running dashed lines, mixed gait solid line). (B) Step down simulation, grounded running
(black) and preferred-leg mixed gait (cyan). In the simulations presented here model parameters are equal.
During unperturbed locomotion (B, before vertical grey line), just the leg compression decides whether
the gait converges to grounded running (y0 = 0.088) or to a mixed one (y0 = 0.074). e %congruity
values aer 50 steps are: grounded running (leg 1 = leg2 = 89); mixed (leg1 (A, red solid line) = 31.6, leg2
(A, black solid line) = 84.2). Aer step up (D) or step down (B) perturbation, both gaits converge to the
same preferred-leg mixed gait; however, if the gait is mixed before the step-down perturbation, aer the
perturbation it converges much faster to the xed point. Aer step-up-step-down perturbation (C, 20% leg
length), grounded running converges to preferred-leg mixed and preferred-leg mixed to grounded running.
Parameters: Ψ0 = 140°, rVPP = 0.07 m, k = 100 Nm1, and c = 2.9 Nsm1, φ
0 = 50.
SCIENTIFIC RepoRts | 5:13636 | DOI: 10.1038/srep13636
moved at dimensionless speeds (
) lower than 1 may explain the absence of aerial phases. Our quail
subjects were mostly not cooperative to locomote at speeds higher than 0.7 m s1. Aerial phases were
nonexistent or rare in former quail treadmill and trackway studies11,18.
Our results suggest that mixed gaits are a ubiquitous feature in neognath avian locomotion. erefore,
it is reasonable to analyze numerically the existence of mixed gaits with input data of one species. e
PVPP model incorporates three key features of bird locomotion: (i) the pronograde trunk, (ii) asymmet-
ric compliant leg behavior along the leg axis, modelled as a parallel spring-damper system, and (iii) a
xed aperture angle as a leg alignment strategy. All three features were inferred from in vivo experiments
involving quail (for more details see21). By simulating quail gaits using the minimalistic PVPP model in
conjunction with parameters obtained through experiments with live quail, we were able to nd dier-
ent stable mixed-gaits: i) “preferred-leg mixed gait, in which one step walking is followed by one step
grounded running or vice versa, or ii) “alternating mixed gait”, in which a gradual shi from one gait
mechanics into the other, occurring out of phase for each leg. ese two types of mixed gaits emerged
with both legs having same leg length (l0), stiness (k), and damping (c) parameters. Interestingly, no
matter whether leg parameters are vaulting or bouncing like, the parameter spaces belonging to mixed
gaits are not located close to the boundaries between walking and grounded running, but rather at the
boundaries between grounded running and running (Fig. 3). is should not be understood only in
terms of speed, which is a state of the model. In fact, in contrast to12,16, our model found mixed gaits in a
wide range of middle to higher speeds. In agreement with the model predictions, both mixed gaits can be
observed in the experimental data. An example of preferred-leg mixed gait is shown in the ESM Fig. S2,
while the example presented in Fig.2 can be understood as an alternating mixed gait (cp. Fig.3).
Our simulation ndings may explain the remarkable dispersion in the %congruity values observed
in our experimental data. Recall that mixed gaits parameters mostly overlap those of grounded running
(Fig. 3). is means that in the overlapping zones, for the same combination of parameters, two limit
cycles may exist (two stable periodic solutions). In those cases, simply changes in a state variable such as
leg compression or perturbations in CoM height may induce grounded running to change to mixed gaits
or vice versa. One example is presented in Fig.4. ere, both solutions exhibit similar system energy, but
the management of the energy-ow among legs and trunk vary. In addition, the subplots in Fig.3 reveal
that if birds engage alternating mixed gaits, the same gait will be categorized either as mixed, grounded
running, or even walking, depending only on the moment of the observation.
To what degree locomotion on normal ground vs. treadmills diers among avian species is a question
that remains unresolved. Our results discussed here are not free from the issue of potential treadmill
artifacts in the data (i.e. birds not moving normally due to the substrate moving beneath them). On the
other hand, locomotion across tracks is frequently unsteady and limited to freely selected speed ranges
and a few number of observed steps. Nevertheless, simulations support to a certain degree that mixed
gaits are part of the dynamics of pronograde bipedal locomotion and not just a treadmill artifact.
However, our model predicts mixed gaits for only 5% of the solutions when using walking-like param-
eters and only 2% when using bouncing-like parameters, while the measured birds employ it in a large
percentage of their strides. We think there are some possibilities to explain this paradox: a) birds might
use very frequently a combination of leg parameters that are close to the attraction zone of mixed gaits,
b) locomoting without visual ow might represent a disturbance to the animal enforcing such mixed gait
patterns due to the relation between trunk motions and head bobbing20,29, or c) our simple 2D model,
which has identical leg parameters and lacks of medio-lateral motions, fails in showing the complete
solution space for mixed gaits. To investigate possibility ‘b,’ experiments with projected environments
moving matched to the treadmills speed would be helpful.
Finally, the data presented here raises the question of the importance or advantages, for example in
terms of energy or stability, that mixed gaits might oer robotics in transitioning between grounded
running and running or in improving eciency. At rst view, mixed gaits seem to confer disadvantages
in terms of visual cue (cf. discussion in10,20) and leg load, because of the larger CoM vertical ampli-
tudes and GRF imbalance. In addition, our simulations indicate that mixed gaits are less ecient than
grounded running at same system energies. e 20% higher requirement of energy obtained from our
simulations poses new questions about trade-os between metabolic optimality and stability that cannot
be completely resolved in this study. However, if metabolic optimality was the only determining factor,
one might expect that small birds would avoid mixed gaits completely. is expectation was clearly not
supported in our experimental results. One way to mitigate the negative metabolic eects of mixed gaits
might be to limit/reduce the %congruity imbalance between legs (see Supplementary Information Fig. S2).
For small animals the terrain is almost always uneven30, and thus, for some leg settings, mixed gaits
might emerge as the only self-stable way of movement.
e main goals of the study were to determine how the congruity of CoM mechanics correlate with
speed and if small birds really use mixed gaits. In light of this, we used available X-ray videos from the
server of the Institut für Spezielle Zoologie und Evolutionsbiologie in Jena from a range of species across
the avian phylogeny. By sampling a limited number of phylogenetically diverse (we sampled species
from three clades: galliformes, columbiformes, and charadriiformes) and morphologically diverse (we
SCIENTIFIC RepoRts | 5:13636 | DOI: 10.1038/srep13636
included three species of shorebirds with highly diering limb segment proportions), we could reason-
ably discern with a limited sample of just a few species whether shi of %congruity and mixed gaits are
a more ubiquitous feature of small avian terrestrial locomotion and not a peculiarity of isolated species.
Note that our study included only neognath birds, therefore, similar studies on tinamous and ratities
will be necessary for a higher level of generality. e methods reported below describe in general the
experimental setup. For the purposes of this study, we reanalyzed previously recorded data.
Our large scale analysis covers 757 treadmill trials of ve species (common quail: Coturnix coturnix,
Eurasian oystercatcher: Haematopus ostralegus, northern lapwing: Vanellus vanellus, domestic pigeon:
Columba livia, and pied avocet: Recurvirostra avosetta), totalizing 7749 steps and 1,267,320 image frames.
Animals were obtained from local breeders and housed in spacious cages with access to food and water
ad libitum at the Institut für Spezielle Zoologie und Evolutionsbiologie in Jena, Germany. e Committee
for Animal Welfare of the State of uringia, Germany, approved the animal keeping and all experimen-
tal procedures (registry number 02-47/10). Animals were kept and all experiments were carried out in
strict accordance with the approved guidelines.
e treadmill was covered with a tunnel made of Plexiglas so that the animals were not able to
y away from the treadmill. When the treadmill was started the animals usually started to walk on
their own. While walking and running on the treadmill at dierent speeds, high-speed X-ray videos
were recorded from the lateral and ventral projection (fully digital X-ray device Neurostar, Siemens
AG, Erlangen, Germany). Additionally, two standard light cameras were synchronized with the X-ray
camera and lmed from a fronto-lateral and a frontal perspective. All recordings were obtained at a rate
of either 0.5 kHz or 1 kHz. Each frame was taken as a digital image with a resolution of 1,536 × 1,024
pixels (X-ray camera) and 512 × 512 pixels (standard light cameras), respectively. e X-ray source oper-
ated at 40 kV and 95 mA. Prior to analysis all X-ray recordings were undistorted using a freely availa-
ble MATLAB (e MathWorks Inc., Natick, MA, USA) routine ( provided by Brown
University (Providence, USA).
We are aware that locomotion is a 3D phenomenon and that birds do not operate limbs only parasag-
ittally29,31,32. However, for the determination of a gait, it is sucient to use CoM oscillations in the sagittal
plane (e.g.2,3,16,18,33,34). us, for the automatic estimation of CoM position and %congruity we only used
the lateral projection of the available X-ray videos.
Removing background and automated CoM estimation. e method published by Haase and
colleagues24 is able to approximate the position of the CoM without any kind of user interaction, solely
based on the automatic analysis of the images of a given X-ray sequence. e main idea of this approach
is to relate each pixel of an image to the mass of matter it represents. e theoretical basis for this process
is the Beer–Lambert law35,36, which describes the absorption of electromagnetic waves traversing an arbi-
trary material. To resolve ambiguities arising from the fact that only one X-ray view is available (cf.36,37),
this method assumes volumic mass and X-ray absorption coecients to be identical for all materials, but
relative errors caused by this approximation are small for materials encountered in X-ray animal anal-
ysis (namely water, fat, tissue, and bone). As the CoM calculation is solely based on image gray values,
it is crucial to remove all background information from the images. Based on the Beer–Lambert law, a
known background component (e.g. obtained by recording an empty sequence) can be removed from an
image via a pixel-wise division by the background image. However, in many cases such as for previously
recorded datasets, the background is not known and thus has to be estimated from the image sequence
itself. Because this is an ill-posed problem (i.e. an innite set of solutions exists), we regularize the esti-
mation to maximize the information explained by the background. e regularized problem has a unique
solution which can eciently be computed as the pixel-wise maximum overall images of a sequence.
Artifacts in the background estimation may appear when the animal remains relatively static over the
course of an entire sequence, but can easily be corrected using inpainting techniques (e.g.38). For more
detailed derivation and discussion of the algorithm please refer to24. An implementation of the algorithm
can be found for Matlab and C + + free for use under
Automated detection of foot contacts, aerial phases, and visibility of bird. Touch-down
detection: we found that when the pixel values of the leg of every frame are projected onto the x-axis,
the obtained 1D-curve display at TD a maximal bimodality. We measured the bimodality value of the
1D-curve by comparing it to a normal distribution of same mean and variance using histogram inter-
section distance. Frames in which a TD event occurs are then found by identifying all local maxima of
the bimodality score over all frames (Fig.5).
Aerial phase: for each frame of a trial, we computed the minimum distance between the lowest point
of the legs and the bottom of the image. Aerwards, a threshold was used to classify each frame as
“aerial phase” or “stance phase” based on its leg height. For each sequence, the threshold was estimated
automatically in such a way that only frames in which the legs are substantially higher than the median
leg height are classied as “aerial phase” (see Supplementary Information, Fig. S1).
Visibility: to account for cases in which the birds le the eld of view, for every frame of each trial we
computed the number of pixels in which the bird is visible (‘bird-pixels’). % of congruity was computed,
only when the measured number of bird-pixel during all frames of a stance phase was higher than 80%
of the maximal computed number of bird-pixels of the complete trial.
SCIENTIFIC RepoRts | 5:13636 | DOI: 10.1038/srep13636
e algorithms described in this section were implemented in the programming language R and are
freely available to download and use fromgshare.1471629.
Percentage of congruity. To dierentiate vaulting from bouncing gaits, we used %congruity19.
%congruity is the percentage of overall frames making up a step which feature frame-to-frame changes
in Ep and Ek of equal sign. Note that %congruity does not consider the magnitudes of mechanical ener-
gies, and therefore cannot account for the amount of energy conversion or recovery. On the other hand,
this method permits the analysis of CoM dynamics without the need of calibration of the X-ray videos.
Ideally, %congruity would be 100% in a perfect bouncing (running) trial and 0% in an ideal vaulting
(walking) trial. Ep was calculated as
Emgy 1
Figure 5. Touch-down detection for an exemplary quail sequence. e plot in the upper part of the gure
shows the computed bimodality scores for each frame of the sequence. Touch-down is detected at local
maxima of the score (marked by vertical dotted lines). For each frame, the bimodality score is assessed by
(1) projecting the pixel values of the legs onto the x-axis, and (2) using the histogram intersection distance
to compare the resulting distribution to a Gaussian distribution of same mean and variance (red curves).
Examples of this process are shown in the lower part of the gure for ve frames between two touch-down
events. e leg-only images are computed automatically based on a projection of the pixel values onto the
SCIENTIFIC RepoRts | 5:13636 | DOI: 10.1038/srep13636
where m is mass, g is gravitational acceleration, and y is the vertical oscillation of the CoM. Ek was
calculated as
=. (+
Emxy05 2
are the horizontal and vertical velocities, respectively. Note that mechanical energies are
not in SI units.
For the sake of simplicity, we dened a step, as the period between the touch-down of a leg and the
touch-down of the contralateral leg. For computing %congruity we did not include the rst and last steps
of each trial, because they are usually incomplete. en, to avoid erroneous %congruity calculation due
to stumbles or speed changes, we used only steps of a trial which exhibited similar contact times. To
accomplish that, we computed the median of the contact periods of the steps of a trial (in frames). Only
contact periods within ±10% of the median were used for further calculations. Further, we discarded
steps if the step-to-step horizontal variation of the CoM was larger than 20 pixels (approx. 5 mm). en,
we used an elliptic high-pass lter to reduce negative eect of dri (2 Hz cut-o frequency) in the com-
putation of congruity. Finally, we low pass ltered at 100 Hz both coordinates of the CoM.
For selected trials (one walking and one bouncing for each individual), we computed the relative
position of the CoM related to the pelvis and the eective leg length. Eective leg length was com-
puted in SI units. For that purpose, we digitized landmarks corresponding to the hip, distal part of the
tarsometatarsus and tip of the middle toe from both lateral and ventral X-ray views using Winanalyse
(Mikromac, Germany). A calibration object into which metal beads were inserted at known distances
was also recorded in both projections at the end of each recording day. Direct linear transformation
(DLT) was performed in Winanalyse to 3D calibrate the recorded space. Eective leg length was then
computed in Matlab from the sagittal projection of the 3D-coordinates.
For appropriate comparisons of bipedal locomotion among the ve species, we calculated the dimen-
sionless speed (
), dened as
where v is the treadmill speed, g is the gravitational acceleration, and L is the eective leg length dened
as the mean distance between the hip and the tarsometatarso-phalangeal joints during the stance phase.
Statistics. To analyze whether the variation of the individual gait-preference observed among every
species is due to chance we used the Chi-square test (PASW Statistics for Windows, Version 18.0. Chicago:
SPSS Inc.; asymptotic method for expected frequencies above 5, exact method for frequencies below 5).
Numerical model. e sagittal plane PVPP model21 consists of a rigid body of mass m with a moment
of inertia J connected at the hip to two massless legs modeled as parallel spring-damper elements
(Fig.6B). e trunk can pivot freely about the hip axis. e CoM of the model is located at a distance
rh from the hip at an inclination θ from the vertical (Fig.6B). e location of the VPP is given by the
distance rVPP from the CoM and the inclination
from the body axis (Fig.6B). e equations of motion
=− +()
VPPx y00
where Fx and Fy are respectively the sum of the horizontal and vertical components of the GRF of the
legs, g is gravitational acceleration,
, and
are the horizontal, vertical, and rotational CoM accelera-
tions, respectively. e GRF is calculated to point towards the given VPP.
We use the same two gait categories of initial parameters used by Andrada and colleagues (2014),
which is based on the parameters obtained from vaulting and bouncing gaits of live quail: (i) walking-like,
with k = 75 Nm1, φ
0 = 45°, and horizontal initial velocity vx0 = 0.4 ms1, and (ii) bouncing-like with
k = 100 Nm1, φ
0 = 50°, and vx0 = 0.6 ms1. Just as in the experiments with living animals, we relied on
%congruity to discriminate vaulting from bouncing, and then distinguished running from grounded
running by checking for aerial phases (i.e., when no leg has contact to the ground). A rigorous analysis
of stability was not the aim of this paper. Also following our previous work21, we dened stability as the
ability to cope with undetected perturbations of the ground level. Finally to compare eciency between
gaits, we used the dimensionless specic cost of transport, CoT = energy used/(weight x distance trave-
led) (7) (see ESM for more explanations on stability and CoT).
SCIENTIFIC RepoRts | 5:13636 | DOI: 10.1038/srep13636
1. Hildebrand, M. Symmetrical gaits of horses. Science 150, 701–708 (1965).
2. Cavagna, G. A., Heglund, N. C. & Taylor, C. . Mechanical wor in terrestrial locomotion: two basic mechanisms for minimizing
energy expenditure. Am J Physiol 233, 243–261 (1977).
3. Cavagna, G. A., ys, H. & Zamboni, A. e sources of external wor in level waling and running. J Physiol 262, 639–657
4. Binevicius, A. . & eilly, S. M. Correlation of symmetrical gaits and whole body mechanics: debuning myths in locomotor
biodynamics. J Exp Zool Part A: Comparative Experimental Biology 305, 923–934 (2006).
5. Blichan, . e spring-mass model for running and hopping. J Biomech 22, 1217–1227, doi: 10.1016/0021-9290(89)90224-8
6. Gatesy, S. M. & Biewener, A. A. Bipedal locomotion: eects of speed, size and limb posture in birds and humans. J Zool 224,
127–147, doi: 10.1111/j.1469-7998.1991.tb04794.x (1991).
7. Nyaatura, J. A., Andrada, E., Grimm, N., Weise, H. & Fischer, M. S. inematics and Center of Mass Mechanics During
Terrestrial Locomotion in Northern Lapwings (Vanellus vanellus, Charadriiformes). J Exp Zool Part A: Ecological Genetics and
Physiology 317, 580–594, doi: 10.1002/jez.1750 (2012).
8. Schmidt, A. & Binevicius, A. . Structured variability of steady-speed locomotion in rats. J Exp Biol 217, 1402–1406 (2014).
9. Abourachid, A. & enous, S. Bipedal locomotion in ratites (Paleognatiform): examples of cursorial birds. Ibis 142, 538–549, doi:
10.1111/j.1474-919X.2000.tb04455.x (2000).
10. Hancoc, J. A., Stevens, N. A. & Binevicius, A. . Whole-body mechanics and inematics of terrestrial locomotion in the
Elegant-crested Tinamou. Eudromia elegans. Ibis 149, 605–614 (2007).
11. Stoessel, A. & Fischer, M. S. Comparative intralimb coordination in avian bipedal locomotion. J Exp Biol 215, 4055–4069, doi:
10.1242/jeb.070458 (2012).
12. Srinivasan, M. & uina, A. Computer optimization of a minimal biped model discovers waling and running. Nature 439, 72–75
13. Geyer, H., Seyfarth, A. & Blichan, . Compliant leg behaviour explains basic dynamics of waling and running. Proc. . Soc. B
273, 2861–2867, doi: 10.1098/rspb.2006.3637 (2006).
14. Shen, Z. H. & Seipel, J. E. A fundamental mechanism of legged locomotion with hip torque and leg damping. Bioinspiration &
Biomimetics 7, 046010 (2012).
15. Andrada, E., ode, C. & Blichan, . Grounded running in quails: simulations indicate benets of observed xed aperture angle
between legs before touch-down. J eor Biol 335, 97–107 (2013).
16. Usherwood, J. . Inverted pendular running: a novel gait predicted by computer optimization is found between wal and run in
birds. Biol Lett 6, 765–768 (2010).
17. ubenson, J., Heliams, D. B., Lloyd, D. G. & Fournier, P. A. Gait selection in the ostrich: mechanical and metabolic characteristics
of waling and running with and without an aerial phase. Proc. . Soc. Lond. B 271, 1091–1099, doi: 10.1098/rspb.2004.2702
18. Andrada, E., Nyaatura, J. A., Bergmann, F. & Blichan, . Adjustments of global and local hindlimb properties during terrestrial
locomotion of the common quail (Coturnix coturnix). J Exp Biol 216, 3906–3916 (2013).
19. Ahn, A. N., Furrow, E. & Biewener, A. A. Waling and running in the red-legged running frog, assina maculata. J Exp Biol
207, 399–410, doi: 10.1242/jeb.00761 (2004).
20. Nyaatura, J. & Andrada, E. On vision in birds: coordination of head-bobbing and gait stabilises vertical head position in quail.
Front Zool 11, 27 (2014).
21. Andrada, E., ode, C., Sutedja, Y., Nyaatura, J. A. & Blichan, . Trun orientation causes asymmetries in leg function in small
bird terrestrial locomotion. Proc. . Soc. B 281, doi: 10.1098/rspb.2014.1405 (2014).
Figure 6. Bird and PVPP model. To obtain the necessary parameters for the PVPP model, synchronous
X-ray videography and force measurements data from21 were used. (A) Lateral X-ray projection of a quail
during stepping on two forceplates. Schematic drawing superimposed onto X-ray still image depicting
experimental data analyzed for developing the model VPP, GRFs, eective legs (segments hip-CoP1, hip-
CoP2), aperture angle between eective legs at touch-down φ
0, trunk angle θ, angle between eective leg,
and GRF β. (B) Minimalistic quail model using a VPP for postural control, and asymmetric leg behavior
modeled as parallel spring and damper. τ hip torque, ψ
0 angle between trunk and VPP, α angle between
ground and eective leg, k leg stiness, c leg damping, l0 rest length at touchdown, rh distance hip-CoM,
rVPP distance CoM-VPP. Parameters k, c, l0 were optimized to best t the measured force-eective leg length
relationship during stance in the quail (see text and21 for further explanations).
SCIENTIFIC RepoRts | 5:13636 | DOI: 10.1038/srep13636
22. oberts, T. J., Marsh, . L., Weyand, P. G. & Taylor, C. . Muscular force in running tureys: the economy of minimizing wor.
Science 275, 1113–1115 (1997).
23. Farris, D. J. & Sawici, G. S. Human medial gastrocnemius force–velocity behavior shis with locomotion speed and gait. Proc.
Natl. Acad. Sci. U.S.A. 109, 977–982 (2012).
24. Haase, D., Andrada, E., Nyaatura, J. A., ilbourne, B. M. & Denzler, J. Automated approximation of center of mass position in
X-ray sequences of animal locomotion. J Biomech 46, 2082–2086 (2013).
25. Farley, C. T., Glasheen, J. & McMahon, T. A. unning springs: speed and animal size. J Exp Biol 185, 71–86 (1993).
26. Lee, D. V., Isaacs, M. ., Higgins, T. E., Biewener, A. A. & McGowan, C. P. Scaling of the Spring in the Leg during Bouncing
Gaits of Mammals. ICB 54, 1099–1108, doi: 10.1093/icb/icu114 (2014).
27. Blichan, . & Full, . J. Similarity in multilegged locomotion: Bouncing lie a monopode. J Comp Physiol A 173, 509–517, doi:
10.1007/bf00197760 (1993).
28. Hancoc, J. A., Stevens, N. J. & Binevicius, A. . Elegant-crested Tinamous Eudromia elegans do not synchronize head and leg
movements during head-bobbing. Ibis 156, 198–208 (2014).
29. Abourachid, A. et al. Bird terrestrial locomotion as revealed by 3D inematics. Zoology 114, 360–368, doi: 10.1016/j.
zool.2011.07.002 (2011).
30. Fischer, M. S. & Witte, H. Legs evolved only at the end! Phil. Trans. . Soc. A 365, 185–198 (2007).
31. ubenson, J., Lloyd, D. G., Heliams, D. B., Besier, T. F. & Fournier, P. A. Adaptations for economical bipedal running: the eect
of limb structure on three-dimensional joint mechanics. J. . Soc. Interface 8, 740–755, doi: 10.1098/rsif.2010.0466 (2010).
32. ambic, . E., oberts, T. J. & Gatesy, S. M. Long-axis rotation: a missing degree of freedom in avian bipedal locomotion. J Exp
Biol 217, 2770–2782, doi: 10.1242/jeb.101428 (2014).
33. Heglund, N. C., Cavagna, G. A. & Taylor, C. . Energetics and mechanics of terrestrial locomotion. III. Energy changes of the
centre of mass as a function of speed and body size in birds and mammals. J Exp Biol 97, 41–56 (1982).
34. Daley, M. A., Usherwood, J. ., Felix, G. & Biewener, A. A. unning over rough terrain: guinea fowl maintain dynamic stability
despite a large unexpected change in substrate height. J Exp Biol 209, 171–187, doi: 10.1242/jeb.01986 (2006).
35. a, A. C. & Slaney, M. Principles of computerized tomographic imaging. (Society for Industrial and Applied Mathematics, 2001).
36. Buzug, T. M. Computed tomography: from photon statistics to modern cone-beam CT. (Springer, 2008).
37. Tuy, H. . An inversion formula for cone-beam reconstruction. SIAM Journal on Applied Mathematics 43, 546–552 (1983).
38. Bertalmio, M., Bertozzi, A. L. & Sapiro, G. Navier–Stoes, uid dynamics,and image and video inpainting. In: Proceedings of the
IEEE Conference on Computer Vision and Pattern ecognition (CVP), auai, HI, USA. pp.355–362. IEEE, doi: 10.1109/
cvpr.2001.990497 (2001, 12 8-14)
Rommy Petersohn, Ingrid Weiß, Henriette Weise, Nadine Grimm, Irina Mischewski and Itziar Candeal
helped with X-ray data acquisition. Silvia V. Lehmann generated the data basis and computed relative
position of CoMs. is research was supported by DFG (German Research Council) grants Bl 236/22-
1/3, Fi 410/15-1/3, De 735/8-1/3.
Author Contributions
E.A., B.M.K., D.H., J.A.N, J.D., M.S.F. and R.B. conceived the study; B.M.K. and J.A.N. conducted the
experiments; D.H. developed the tracking algorithms, E.A. analysed the experimental data; E.A. and Y.S.
conducted simulations, and E.A. draed the manuscript. All authors contributed to the interpretation of
the results and revised the manuscript.
Additional Information
Supplementary information accompanies this paper at
Competing nancial interests: e authors declare no competing nancial interests.
How to cite this article: Andrada, E. et al. Mixed gaits in small avian terrestrial locomotion. Sci. Rep.
5, 13636; doi: 10.1038/srep13636 (2015).
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... Kinetic data were collected from 55 tetrapod species (Fig. 2). All data collection protocols were approved by the relevant IACUCs and followed previously published methods (Andrada et al., 2015;Bishop et al., 2018;Butcher and Blob, 2008;Granatosky, 2018;Granatosky and Schmitt, 2019;Granatosky et al., 2016Granatosky et al., , 2018bMcElroy et al., 2014;Nyakatura et al., 2014;Nyakatura et al., 2019;Schmitt, 1999;Schmitt and Hanna, 2004;, so are only summarized below. Limb loading data collected from common quails (Coturnix coturnix) by Andrada and colleagues (2014a) were downloaded from the Dryad Digital Repository (Andrada et al., 2014b). ...
... Substrate type was chosen based on the most commonly used substrate in the wild. A small sub-section of the runway or pole was instrumented with Kistler force plates (models 9317B or 9281B; Kistler Instrument Corp., Amherst, NY, USA), an AMTI multi-axis force plate (MC3A-100, AMTI, Watertown, MA, USA) or custom-made force platforms (K&N Scientific, Guilford, VT, USA; and Bertec Corp., Columbus, OH, USA) (Andrada et al., 2014a(Andrada et al., , 2015Bishop et al., 2018;Butcher and Blob, 2008;Granatosky, 2018;Granatosky et al., 2016Granatosky et al., , 2018bMcElroy et al., 2014;Nyakatura et al., 2019;Schmitt, 1999;Schmitt and Hanna, 2004;. Force plate output was sampled at 500-12,000 Hz, imported, summed and processed using BioWare™ v.5.1 software, and then filtered (lowpass Fourier, 60 Hz) and analyzed in MATLAB (MathWorks, Natick, MA, USA). ...
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Comparative analyses of locomotion in tetrapods reveal two patterns of stride cycle variability. Tachymetabolic tetrapods (birds and mammals) have lower inter-cycle variation in stride duration than bradymetabolic tetrapods (amphibians, lizards, turtles, and crocodilians). This pattern has been linked to the fact that birds and mammals share enlarged cerebella, relatively enlarged and heavily myelinated Ia afferents, and γ-motoneurons to their muscle spindles. Tachymetabolic tetrapod lineages also both possess an encapsulated Golgi tendon morphology, thought to provide more spatially precise information on muscle tension. The functional consequence of this derived Golgi tendon morphology has never been tested. We hypothesized that one advantage of precise information on muscle tension would be lower and more predictable limb bone stresses, achieved in tachymetabolic tetrapods by having less variable substrate reaction forces than bradymetabolic tetrapods. To test this hypothesis, we analyzed hindlimb substrate reaction forces during locomotion of 55 tetrapod species in a phylogenetic comparative framework. Variation in species-means of limb loading magnitude and timing confirm that, for most of the variables analyzed, variance in hindlimb loading and timing is significantly lower in species with encapsulated versus unencapsulated Golgi tendon organs. These findings suggest that maintaining predictable limb loading provides a selective advantage for birds and mammals by allowing for energy-savings during locomotion, lower limb bone safety factors, and quicker recovery from perturbations. The importance of variation in other biomechanical variables in explaining these patterns, such as posture, effective mechanical advantage, and center-of-mass mechanics, remains to be clarified.
... Similarly, several bipeds use an intermediate gait, termed grounded running by Andrada et al. [4], that shares the characteristics of the spring-mass model of running during stance, but is deprived of a t f [4,5]. ...
... Similarly, several bipeds use an intermediate gait, termed grounded running by Andrada et al. [4], that shares the characteristics of the spring-mass model of running during stance, but is deprived of a t f [4,5]. ...
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Runners were classified using two different methods based on their spontaneous running form: (1) subjectively using the V®score from the Volodalen® scale, leading to terrestrial and aerial groups; and (2) objectively using the duty factor (DF), leading to high (DFhigh) and low (DFlow) DF groups. This study aimed to compare these two classification schemes. Eighty-nine runners were divided in two groups using the V®score (VOL groups) and were also ranked according to their DF. They ran on a treadmill at 12 km·h−1 with simultaneous recording of running kinematics, using a three-dimensional motion capture system. DF was computed from data as the ratio of ground contact time to stride time. The agreement (95% confidence interval) between VOL and DF groups was 79.8% (69.9%, 87.6%), with relatively high sensitivity (81.6% (68.0%, 91.2%)) and specificity (77.5% (61.6%, 89.2%)). Our results suggest that the DF and V®score reflect similar constructs and lead to similar subgroupings of spontaneous running form (aerial runners if DF < 27.6% and terrestrial runners if DF > 28.8% at 12 km·h−1). These results suggest that DF could be a useful objective measure to monitor real-time changes in spontaneous running form using wearable technology. As a forward-looking statement, spontaneous changes in running form during racing or training could assist in identifying fatigue or changes in environmental conditions, allowing for a better understanding of runners.
... Variations in VPP height were observed in studies on humans walking with different trunk inclinations (Müller et al., 2017), in humans walking and running over visible and camouflaged curbs (Vielemeyer et al., 2019;Drama et al., 2020), and in simulation studies (Lee et al., 2017;Schreff et al., 2023) added to that hypothesis. On the other hand, simulations and experimental studies on birds showed that VPP control in combination with a pronograde trunk stabilizes both trunk and overall locomotion (Andrada et al., 2014;Andrada et al., 2015a;Müller et al., 2017). These findings indicate that the overall body plan influences the stabilizing effect of a VPP. ...
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Dogs ( Canis familiaris ) prefer the walk at lower speeds and the more economical trot at speeds ranging from 0.5 Fr up to 3 Fr. Important works have helped to understand these gaits at the levels of the center of mass, joint mechanics, and muscular control. However, less is known about the global dynamics for limbs and if these are gait or breed-specific. For walk and trot, we analyzed dogs’ global dynamics, based on motion capture and single leg kinetic data, recorded from treadmill locomotion of French Bulldog ( N = 4), Whippet ( N = 5), Malinois ( N = 4), and Beagle ( N = 5). Dogs’ pelvic and thoracic axial leg functions combined compliance with leg lengthening. Thoracic limbs were stiffer than the pelvic limbs and absorbed energy in the scapulothoracic joint. Dogs’ ground reaction forces (GRF) formed two virtual pivot points (VPP) during walk and trot each. One emerged for the thoracic (fore) limbs (VPP TL ) and is roughly located above and caudally to the scapulothoracic joint. The second is located roughly above and cranially to the hip joint (VPP PL ). The positions of VPPs and the patterns of the limbs’ axial and tangential projections of the GRF were gaits but not always breeds-related. When they existed, breed-related changes were mainly exposed by the French Bulldog. During trot, positions of the VPPs tended to be closer to the hip joint or the scapulothoracic joint, and variability between and within breeds lessened compared to walk. In some dogs, VPP PL was located below the pelvis during trot. Further analyses revealed that leg length and not breed may better explain differences in the vertical position of VPP TL or the horizontal position of VPP PL . The vertical position of VPP PL was only influenced by gait, while the horizontal position of VPP TL was not breed or gait-related. Accordingly, torque profiles in the scapulothoracic joint were likely between breeds while hip torque profiles were size-related. In dogs, gait and leg length are likely the main VPPs positions’ predictors. Thus, variations of VPP positions may follow a reduction of limb work. Stability issues need to be addressed in further studies.
... The percentage of congruity (%Congruity), as proposed by Ahn & Biewener (2004) more accurately compares the form of the graphs of two energies and is therefore suggested to reflect the phase relationship better than just comparing local minimum values in the phase calculation (Nyakatura et al., 2012). Andrada et al. (2015) studied quail, oystercatcher, northern lapwing, pigeon, and avocet locomotion gaits using an X-ray camera and treadmill, and their birds neither low-speed walking nor high-speed running. Birds employ mixed gaits (e.g., one-step walking followed by one step using running mechanics) more often than walking. ...
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In this study, the effect of the speed on the webbed foot locomotion of the mallard was analyzed based on a considerable number of reliable indoor test data. Four adult male mallards were selected for analysis, and the locomotion speed of the mallard was controlled using the treadmill at an accurate and adjustable speed. The locomotion pattern of the webbed foot of the mallard at different speeds was recorded using a high-speed camera. The changes in the position and conformation of the webbed foot during locomotion on a treadmill were tracked and analyzed using Simi-Motion kinematics software. The results indicated that the stride length of the mallard increased, and the stance phase duration was shortened with the increase of the speed, whereas the swing phase duration did not vary significantly. The duty factor decreased with the increase of the mallard speed but not drop below to 0.5, because the mallards flew with their wings, or moved backward relative to the treadmill with the further increase of the speed. Using the energy method to further distinguish gait, and through the percentage of congruity analysis, it was found that between 0.73 and 0.93 m/s, the gait experienced a transition from walking to grounded running, with no significant changes in spatiotemporal parameters. At speeds between 0.93 and 1.6 m/s, mallards adopt a grounded running gait. The instantaneous changes of the tarsometatarso-phalangeal joint (TMTPJ) angle and the intertarsal joint (ITJ) angle at touch-down, mid-stance and lift-off concomitant with the change of the speed were examined with the TMTPJ and ITJ angle as the research objects. Moreover, the continuous changes of the joint angles were examined in a complete stride cycle. The result indicated that the increase of the speed will also make the TMTPJ and ITJ angle change ahead of time in a stride cycle, proving the shortened stance phase duration. The ITJ angle changed much more than the TMTPJ. Thus, the above result reveals that the mallard primarily responds with the increase of the speed by adjusting the ITJ, instead of the TMTPJ. The vertical displacement of the toe joint points and the toe joint angle was studied (α joint angle is between the second toe and the third toe; β joint angle is between the third toe and the fourth toe) with a complete stride cycle as the research object. The distal phalanxes of the second, third and fourth toes first contacted the ground, and the proximal phalanx touched the ground in turn during the early stance phase duration of the mallard, as indicated by the result of this study. However, the toes got off the ground in turn from the proximal phalanxes when the mallard foot got off the ground. With the decrease of the interphalangeal α and β joint angles, the foot web tended to be close and rapidly recovered before the next touch-down. The above result reveals that the webbed foot of the mallard is a coupling system that plays a role in the adjustment of speed.
... Birds represent an incredibly speciose and ecomorphologically diverse class of vertebrates, spanning more than four orders of magnitude in body size (from approximately 2 g in Mellisuga helenae to greater than 100 kg in Struthio camelus) and occupying habitats as diverse as the equatorial savannah and the tropical rainforest [1]. Similarly, birds have become highly specialized for various forms of locomotion, including flight, swimming, terrestrial running and arboreal climbing [2][3][4][5][6][7][8][9]. While flight is driven by synchronized movements of the wings, these other forms of locomotion are driven by the hindlimb [10] and may incorporate a stronger role of the retrices (flight feathers of the tail) as opposed to the remiges (flight feathers of the wing). ...
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Birds encompass vast ecomorphological diversity and practise numerous distinct locomotor modes. One oft-cited feature seen in climbing birds is an increase in tail ‘stiffness’, yet it remains unclear to what extent these feathers are altered, and the specific mechanism by which differences in functional performance are attained. We collected a broad taxonomic sample of tail feathers (6525 total, from 774 species representing 21 avian orders and ranging in size from approximately 3 g to greater than 11 kg) and present data on their material properties, cross-sectional geometry and morphometrics. Ordinary and phylogenetic least-squares regressions of each variable versus body mass were conducted to assess scaling relationships and demonstrate that tail-supported climbers exhibit longer tail feathers with a wider rachis base and tip, and a greater second moment of area and maximum bending moment. However, no differences were observed in the material properties of the keratin itself. This suggests that tail-supported arboreal climbing birds of multiple orders have independently adopted similar morphologies. Moreover, these geometric relationships follow the same allometric scaling relationships as seen in the long bones of mammalian limbs, suggesting that the morphology of these developmentally and evolutionarily distinct structures are governed by similar functional constraints of weight support.
... Because of body size variation within and among groups, we adjusted treadmill speed dynamically to the individual preferences and abilities of the mice. This method of motion analysis has been described in detail in several recent publications (e.g., Böttger et al, 2011;Andrada et al, 2015;and Niederschuh et al, 2015) and will be only briefly summarized here. The X-ray system operates with high-speed cameras and a maximum spatial resolution of 1,536 dpi × 1,024 dpi. ...
Rhythmic and patterned locomotion is driven by spinal cord neurons that form neuronal circuits, referred to as central pattern generators (CPGs). Recently, dI6 neurons were suggested to participate in the control of locomotion. The dI6 neurons can be subdivided into three populations, one of which expresses the Wilms tumor suppressor gene Wt1 . However, the role that Wt1 exerts on these cells is not understood. Here, we aimed to identify behavioral changes and cellular alterations in the spinal cord associated with Wt1 deletion. Locomotion analyses of mice with neuron-specific Wt1 deletion revealed that these mice ran slower than controls with a decreased stride frequency and an increased stride length. These mice showed changes in their fore-hindlimb coordination, which were accompanied by a loss of contralateral projections in the spinal cord. Neonates with Wt1 deletion displayed an increase in uncoordinated hindlimb movements and their motor neuron output was arrhythmic with a decreased frequency. The population size of dI6, V0 and V2a neurons in the developing spinal cord of conditional Wt1 mutants was significantly altered. These results show that the development of particular dI6 neurons depends on Wt1 expression and loss of Wt1 is associated with alterations in locomotion.
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Small cursorial birds display remarkable walking skills and can negotiate complex and unstructured terrains with ease. The neuromechanical control strategies necessary to adapt to these challenging terrains are still not well understood. Here, we analyzed the 2D- and 3D pelvic and leg kinematic strategies employed by the common quail to negotiate visible steps (upwards and downwards) of about 10%, and 50% of their leg length. We used biplanar fluoroscopy to accurately describe joint positions in three dimensions and performed semi-automatic landmark localization using deep learning. Quails negotiated the vertical obstacles without major problems and rapidly regained steady-state locomotion. When coping with step upwards, the quail mostly adapted the trailing limb to permit the leading leg to step on the elevated substrate similarly as it did during level locomotion. When negotiated steps downwards, both legs showed significant adaptations. For those small and moderate step heights that did not induce aerial running, the quail kept the kinematic pattern of the distal joints largely unchanged during uneven locomotion, and most changes occurred in proximal joints. The hip regulated leg length, while the distal joints maintained the spring-damped limb patterns. However, to negotiate the largest visible steps, more dramatic kinematic alterations were observed. There all joints contributed to leg lengthening/shortening in the trailing leg, and both the trailing and leading legs stepped more vertically and less abducted. In addition, locomotion speed was decreased. We hypothesize a shift from a dynamic walking program to more goal-directed motions that might be focused on maximizing safety.
The vertebrate Bauplan has undergone a very particular evolution in the class of Aves. Irrespective of the enormous variation in colour, plumage, lifestyle, behaviour and size (living species from 0.010 kg to 150 kg; subfossil in Madagascar and New Zealand still larger – see Table 6.1), birds are rather similar in body structure (Romer-Frick 1966; Bock 1974; Oemichen 1950a, b, c): a compact trunk, long neck (often hidden in the plumage), small head with horny beak and folded front- and powerful hindlimbs. From a stock of small theropods evolved bipedal forms in the Jurassic, some of them with similar postures of the forelimbs and some of them with dermal appendages which look like feathers. The long-tailed Archaeopteryx from the upper Cretaceous (Mayr 2013) was completely covered by feathers and possessed teeth.KeywordsAlternative use of forelimbsBipedalityFlightless birdsGaits on groundLocomotor speedMass distributionHoppingRunningBeakLight-weight headLength of neckHindfeet in swimmingWingsStatics of bodyFlying
Wading behaviours, in which an animal walks while partially submerged in water, are present in a variety of taxa including amphibians, reptiles, mammals, and birds. Despite the ubiquity of wading behaviours, few data are available to evaluate how animals adjust their locomotion to accommodate changes in water depth. Because drag from water might impose additional locomotor costs, wading animals might be expected to raise their feet above the water up to a certain point until such behaviours lead to awkward steps and are abandoned. To test for such mechanisms, we measured drag on models of the limbs of Chilean flamingos (Phoenicopterus chilensis) and measured their limb and body kinematics as they walked and waded through increasing depths of water in a zoo enclosure. Substantial drag was incurred by models of both open- and closed-toed feet, suggesting that flamingos could avoid some locomotor costs by stepping over water, rather than through it, during wading. Step height was highest while wading through intermediate water depths and while wading at a faster speed. Stride length increased with increasing water depth and velocity, and the limb joints generally flexed more while moving through intermediate water depths. However, movements of the head and neck were not strongly correlated with water depth or velocity. Our results show a wide range of kinematic changes that occur to allow wading birds to walk through different water depths, and have implications for better understanding the locomotor strategies employed by semi-aquatic species.
Bipedal animals have diverse morphologies and advanced locomotion abilities. Terrestrial birds, in particular, display agile, efficient, and robust running motion, in which they exploit the interplay between the body segment masses and moment of inertias. On the other hand, most legged robots are not able to generate such versatile and energy-efficient motion and often disregard trunk movements as a means to enhance their locomotion capabilities. Recent research investigated how trunk motions affect the gait characteristics of humans, but there is a lack of analysis across different bipedal morphologies. To address this issue, we analyze avian running based on a spring-loaded inverted pendulum model with a pronograde (horizontal) trunk. We use a virtual point based control scheme and modify the alignment of the ground reaction forces to assess how our control strategy influences the trunk pitch oscillations and energetics of the locomotion. We derive three potential key strategies to leverage trunk pitch motions that minimize either the energy fluctuations of the center of mass or the work performed by the hip and leg. We suggest how these strategies could be used in legged robotics.
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In contrast to the upright trunk in humans, trunk orientation in most birds is almost horizontal (pronograde). It is conceivable that the orientation of the heavy trunk strongly influences the dynamics of bipedal terrestrial locomotion. Here, we analyse for the first time the effects of a pronograde trunk orientation on leg function and stability during bipedal locomotion. For this, we first inferred the leg function and trunk control strategy applied by a generalized small bird during terrestrial locomotion by analysing synchronously recorded kinematic (three-dimensional X-ray videography) and kinetic (three-dimensional force measurement) quail locomotion data. Then, by simulating quail gaits using a simplistic bioinspired numerical model which made use of parameters obtained in in vivo experiments with real quail, we show that the observed asymmetric leg function (left-skewed ground reaction force and longer leg at touchdown than at lift-off) is necessary for pronograde steady-state locomotion. In addition, steady-state locomotion becomes stable for specific morphological parameters. For quail-like parameters, the most common stable solution is grounded running, a gait preferred by quail and most of the other small birds. We hypothesize that stability of bipedal locomotion is a functional demand that, depending on trunk orientation and centre of mass location, constrains basic hind limb morphology and function, such as leg length, leg stiffness and leg damping.
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Trotting, bipedal running, and especially hopping have long been considered the principal bouncing gaits of legged animals. We use the radial-leg spring constant [Formula: see text] to quantify the stiffness of the physical leg during bouncing gaits. The radial-leg is modeled as an extensible strut between the hip and the ground and [Formula: see text] is determined from the force and deflection of this strut in each instance of stance. A Hookean spring is modeled in-series with a linear actuator and the stiffness of this spring [Formula: see text] is determined by minimizing the work of the actuator while reproducing the measured force-deflection dynamics of an individual leg during trotting or running, and of the paired legs during hopping. Prior studies have estimated leg stiffness using [Formula: see text], a metric that imagines a virtual-leg connected to the center of mass. While [Formula: see text] has been applied extensively in human and comparative biomechanics, we show that [Formula: see text] more accurately models the spring in the leg when actuation is allowed, as is the case in biological and robotic systems. Our allometric analysis of [Formula: see text] in the kangaroo rat, tammar wallaby, dog, goat, and human during hopping, trotting, or running show that [Formula: see text] scales as body mass to the two-third power, which is consistent with the predictions of dynamic similarity and with the scaling of [Formula: see text]. Hence, two-third scaling of locomotor spring constants among mammals is supported by both the radial-leg and virtual-leg models, yet the scaling of [Formula: see text] emerges from work-minimization in the radial-leg model instead of being a defacto result of the ratio of force to length used to compute [Formula: see text]. Another key distinction between the virtual-leg and radial-leg is that [Formula: see text] is substantially greater than [Formula: see text], as indicated by a 30-37% greater scaling coefficient for [Formula: see text]. We also show that the legs of goats are on average twice as stiff as those of dogs of the same mass and that goats increase the stiffness of their legs, in part, by more nearly aligning their distal limb-joints with the ground reaction force vector. This study is the first allometric analysis of leg spring constants in two decades. By means of an independent model, our findings reinforce the two-third scaling of spring constants with body mass, while showing that springs in-series with actuators are stiffer than those predicted by energy-conservative models of the leg.
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Ground-dwelling birds are typically characterized as erect bipeds having hind limbs that operate parasagittally. Consequently, most previous research has emphasized flexion/extension angles and moments as calculated from a lateral perspective. Three-dimensional motion analyses have documented non-planar limb movements, but the skeletal kinematics underlying changes in foot orientation and transverse position remain unclear. In particular, long-axis rotation of the proximal limb segments is extremely difficult to measure with topical markers. Here we present six degree of freedom skeletal kinematic data from maneuvering guineafowl acquired by marker-based XROMM (X-ray Reconstruction of Moving Morphology). Translations and rotations of the hips, knees, ankles, and pelvis were derived from animated bone models using explicit joint coordinate systems. We distinguished sidesteps, sidestep yaws, crossover yaws, sidestep turns, and crossover turns, but birds often performed a sequence of blended partial maneuvers. Long-axis rotation of the femur (up to 38°) modulated the foot's transverse position. Long-axis rotation of the tibiotarsus (up to 65°) also affected medio-lateral positioning, but primarily served to either reorient a swing phase foot or yaw the body about a stance phase foot. Tarsometatarsal long-axis rotation was minimal, as was hip, knee, and ankle abduction/adduction. Despite having superficially hinge-like joints, birds coordinate substantial long-axis rotations of the hips and knees to execute complex 3-D maneuvers while striking a diversity of non-planar poses.
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Head-bobbing in birds is a conspicuous behaviour related to vision comprising a hold phase and a thrust phase. The timing of these phases has been shown in many birds, including quail, to be coordinated with footfall during locomotion. We were interested in the biomechanics behind this phenomenon. During terrestrial locomotion in birds, the trunk is subjected to gait-specific vertical oscillations. Without compensation, these vertical oscillations conflict with the demands of vision (i.e., a vertically stable head position). We tested the hypothesis that the coordination between head-bobbing and trunk movement is a means of reconciling the conflicting demands of vision and locomotion which should thus vary according to gait. Significant differences in the timing of head-bobbing were found between gaits. The thrust phase was initiated just prior to the double support phase in walking (vaulting) trials, whereas in running (bouncing) trials, thrust started around midstance. Altering the timing of head-trunk-coordination in simulations showed that the timing naturally favoured by birds minimizes the vertical displacement of the head. When using a bouncing gait the timing of head bobbing had a compensatory effect on the fluctuation of the potential energy of the bird's centre of mass. The results are consistent with expectations based on the vertical trunk fluctuations observed in biomechanical models of vaulting and bouncing locomotion. The timing of the head-bobbing behaviour naturally favoured by quail benefits vision during vaulting and bouncing gaits and potentially helps reducing the mechanical cost associated with head bobbing when using a bouncing gait.
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This volume provides an overview of X-ray technology and the historical development of modern CT systems. The main focus of the book is a detailed derivation of reconstruction algorithms in 2D and modern 3D cone-beam systems. A thorough analysis of CT artifacts and a discussion of practical issues such as dose considerations give further insight into current CT systems. Although written mainly for graduate students of biomedical engineering, medical physics, medicine (radiology), mathematics, electrical engineering, and physics, practitioners in these fields will also benefit from this book. © 2008 Springer-Verlag Berlin Heidelberg. All rights are reserved.
By examining key locomotor parameters during terrestrial locomotion on a substrate without irregularities, we show that rats frequently accelerate and decelerate between two consecutive steps while maintaining an overall steady-speed and that the touchdown order of contralateral limbs significantly influences those speed adjustments. The latter highly correlates with significant adjustments in relative forelimb protraction at touchdown and hindlimb extension at lift off. We conclude that this remarkable level of variability in limb coordination would clearly be advantageous for the functional flexibility needed during terrestrial locomotion on much more irregular (rough) natural terrain. In addition, its occurrence on a substrate lacking irregularities suggests that much of stable, terrestrial steady-speed locomotion in rats is mechanically controlled.
Head-bobbing is the fore–aft movement of the head relative to the body during terrestrial locomotion in birds. It is considered to be a behaviour that helps to stabilize images on the retina during locomotion, yet some studies have suggested biomechanical links between the movements of the head and legs. This study analysed terrestrial locomotion and head-bobbing in the Elegant-crested Tinamou Eudromia elegans at a range of speeds by synchronously recording high-speed video and ground reaction forces in a laboratory setting. The results indicate that the timing of head and leg movements are dissociated from one another. Nonetheless, head and neck movements do affect stance duration, ground reaction forces and body pitch and, as a result, the movement of the centre of mass in head-bobbing birds. This study does not support the hypothesis that head-bobbing is itself constrained by terrestrial locomotion. Instead, it suggests that visual cues are the primary trigger for head-bobbing in birds, and locomotion is, in turn, constrained by a need for image stabilization and depth perception.
This article reviews Computed Tomography From Photon Statistics to Modern Cone-Beam CT by Thorsten M. Buzug , Berlin-Heidelberg, Germany, 2008. 522 pp. (hardcover). Price: $109.00. ISBN: 9783540394075.