The Murphy number: how pitch moment of inertia dictates quadrupedal walking and running energetics

Adaptation strategies of Icelandic horses with induced transient hindlimb lameness at walk, trot and tölt

BACKGROUND

Icelandic horses are valued for their additional gaits, but assessing lameness in this breed can be challenging. Pelvic (P) vertical movement asymmetries, differences (D) in minimum (min)/maximum (max) position, are used to quantify impact (PDmin) and push-off (PDmax) hindlimb lameness during the trot, but no established parameters exist for detecting hindlimb lameness in other gaits.

OBJECTIVE

To evaluate temporal stride parameters and upper-body movement asymmetry after transient hindlimb lameness induction in walk, trot and tölt.

STUDY DESIGN

In vivo experiment.

METHODS

Eleven Icelandic horses were measured before and after hindlimb lameness was induced (sole pressure). Vertical movement asymmetry of Head (H)/Pelvis (HDmin/HDmax/PDmin/PDmax) and hip-hike were measured during ridden walk, sitting trot and tölt as well as in-hand walk and trot, using an inertial measurement unit system. Linear mixed models compared sound and lame conditions within each gait, and differences in estimated marginal means (mm) between conditions are presented, with significance set at p < 0.05.

RESULTS

Lameness induction significantly increased PDmin asymmetry in all gaits except walk in-hand: walk (PDminridden: 5.07), trot (PDminhand: 10.72, PDminridden: 9.85) and tölt (PDminridden: 4.88). However, PDmax increased only for trot in-hand (PDmaxhand: 4.80). Hip-hike increased on the lame limb side at trot (hip-hikehand: 20.90, hip-hikeridden: 10.81) and tölt (hip-hikeridden: 4.28).

MAIN LIMITATIONS

Findings need verification in clinically lame Icelandic horses with varying diagnoses and lameness severity.

CONCLUSION

PDmin and hip-hike appear to be effective parameters for detecting mild hoof-associated hindlimb lameness in Icelandic horses when trotting in-hand or ridden. At walk or tölt under saddle, only slight PDmin changes were observed, likely due to lower limb loading in those gaits and the pelvic minimum position associating with different loading stages throughout the stride cycle for walking and running gaits. These findings suggest trot is the preferred gait for assessing mild hindlimb lameness in Icelandic horses.

Muscle-Driven Predictive Physics Simulations of Quadrupedal Locomotion in the Horse

Musculoskeletal simulations can provide insights into the underlying mechanisms that govern animal locomotion. In this study, we describe the development of a new musculoskeletal model of the horse, and to our knowledge present the first fully muscle-driven, predictive simulations of equine locomotion. Our goal was to simulate a model that captures only the gross musculoskeletal structure of a horse, without specialized morphological features. We mostly present simulations acquired using feedforward control, without state feedback ("top-down control"). Without using kinematics or motion capture data as an input, we have simulated a variety of gaits that are commonly used by horses (walk, pace, trot, tölt, and collected gallop). We also found a selection of gaits that are not normally seen in horses (half bound, extended gallop, ambling). Due to the clinical relevance of the trot, we performed a tracking simulation that included empirical joint angle deviations in the cost function. To further demonstrate the flexibility of our model, we also present a simulation acquired using spinal feedback control, where muscle control signals are wholly determined by gait kinematics. Despite simplifications to the musculature, simulated footfalls and ground reaction forces followed empirical patterns. In the tracking simulation, kinematics improved with respect to the fully predictive simulations, and muscle activations showed a reasonable correspondence to electromyographic signals, although we did not predict any anticipatory firing of muscles. When sequentially increasing the target speed, our simulations spontaneously predicted walk-to-run transitions at the empirically determined speed. However, predicted stride lengths were too short over nearly the entire speed range unless explicitly prescribed in the controller, and we also did not recover spontaneous transitions to asymmetric gaits such as galloping. Taken together, our model performed adequately when simulating individual gaits, but our simulation workflow was not able to capture all aspects of gait selection. We point out certain aspects of our workflow that may have caused this, including anatomical simplifications and the use of massless Hill-type actuators. Our model is an extensible, generalized horse model, with considerable scope for adding anatomical complexity. This project is intended as a starting point for continual development of the model and code that we make available in extensible open-source formats.

Muscle-controlled physics simulations of bird locomotion resolve the grounded running paradox

Humans and birds use very different running styles. Unlike humans, birds adopt "grounded running" at intermediate speeds-a running gait where at least one foot always maintains ground contact. Avian grounded running is a paradox: Animals usually minimize locomotor energy expenditure, but birds prefer grounded running despite incurring higher energy costs. Using predictive gait simulations of the emu (Dromaius novaehollandiae), we resolve this paradox by demonstrating that grounded running represents an optimal gait for birds, from both energetics and muscle excitations perspectives. Our virtual experiments decoupled effects of posture and tendon elasticity, biomechanically relevant anatomical features that cannot be isolated in real birds. The avian body plan prevents (near) vertical leg postures, making the running style used by humans impossible. Under this anatomical constraint, grounded running is optimal if the muscles produce the highest forces in crouched postures, as is true in most birds. Shared anatomical features suggest that, as a behavior, avian grounded running first evolved within non-avian dinosaurs.

Adaptation strategies of the Icelandic horse with induced forelimb lameness at walk, trot and tölt

BACKGROUND AND OBJECTIVE

Lameness assessment in the gaited Icelandic horse is complex. We aimed to describe their kinematic and temporal adaptation strategies in response to forelimb lameness at walk, trot and tölt.

STUDY DESIGN

In vivo experiment.

METHODS

Ten clinically non-lame Icelandic horses were measured before and after reversible forelimb lameness induction. Upper body and limb kinematics were measured using 11 inertial measurement units mounted on the poll, withers, pelvis (tubera sacrale) and all four limbs and hoofs (Equimoves®, 500 Hz). Horses were measured on a straight line at walk and trot in-hand and at walk, trot and tölt while ridden. Linear mixed models were used to compare baseline and lame conditions (random factor = 'horse'), and results are presented as the difference in estimated marginal means or percentage of change.

RESULTS

Lameness induction significantly (p < 0.05) increased head vertical movement asymmetry at walk (HDmin/HDmaxHAND: 18.8/5.7 mm, HDmin/HDmaxRIDDEN: 9.8/0.3 mm) and trot (HDmin/HDmaxHAND: 18.1/7.8 mm, HDmin/HDmaxRIDDEN: 24.0/9.3 mm). At the tölt, however, HDmin did not change significantly (1.1 mm), but HDmax increased by 11.2 mm (p < 0.05). Furthermore, pelvis vertical movement asymmetry (PDmax) increased by 4.9 mm, sound side dissociation decreased (-8.3%), and sound diagonal dissociation increased (6.5%). Other temporal stride variables were also affected, such as increased stance duration of both forelimbs at walk, tölt and in-hand trot.

MAIN LIMITATIONS

Only one degree of lameness (mild) was induced with an acute lameness model.

CONCLUSIONS

Classical forelimb lameness metrics, such as vertical head and withers movement asymmetry, were less valuable at tölt compared to walk and trot, except for HDmax. Therefore, it is advised to primarily use the walk and trot to detect and quantify forelimb lameness in the Icelandic horse.

Walking-and Running and Jumping-with Dinosaurs and Their Cousins, Viewed Through the Lens of Evolutionary Biomechanics

Archosauria diversified throughout the Triassic Period before experiencing two mass extinctions near its end ∼201 Mya, leaving only the crocodile-lineage (Crocodylomorpha) and bird-lineage (Dinosauria) as survivors; along with the pterosaurian flying reptiles. About 50 years ago, the "locomotor superiority hypothesis" (LSH) proposed that dinosaurs ultimately dominated by the Early Jurassic Period because their locomotion was superior to other archosaurs'. This idea has been debated continuously since, with taxonomic and morphological analyses suggesting dinosaurs were "lucky" rather than surviving due to being biologically superior. However, the LSH has never been tested biomechanically. Here we present integration of experimental data from locomotion in extant archosaurs with inverse and predictive simulations of the same behaviours using musculoskeletal models, showing that we can reliably predict how extant archosaurs walk, run and jump. These simulations have been guiding predictive simulations of extinct archosaurs to estimate how they moved, and we show our progress in that endeavour. The musculoskeletal models used in these simulations can also be used for simpler analyses of form and function such as muscle moment arms, which inform us about more basic biomechanical similarities and differences between archosaurs. Placing all these data into an evolutionary and biomechanical context, we take a fresh look at the LSH as part of a critical review of competing hypotheses for why dinosaurs (and a few other archosaur clades) survived the Late Triassic extinctions. Early dinosaurs had some quantifiable differences in locomotor function and performance vs. some other archosaurs, but other derived dinosaurian features (e.g., metabolic or growth rates, ventilatory abilities) are not necessarily mutually exclusive from the LSH; or maybe even an opportunistic replacement hypothesis; in explaining dinosaurs' success.

Competing Models of Work in Quadrupedal Walking: Center of Mass Work is Insufficient to Explain Stereotypical Gait

The walking gaits of cursorial quadrupedal mammals tend to be highly stereotyped as a four-beat pattern with interspersed periods of double and triple stance, often with double-hump ground reaction force profiles. This pattern has long been associated with high energetic economy, due to low apparent work. However, there are differing ways of approximating the work performed during walking and, consequently, different interpretations of the primary mechanism leading to high economy. A focus on Net Center of Mass (COM) Work led to the claim that quadrupedal walking is efficient because it effectively trades potential and kinetic energy of the COM. Individual Limbs COM Work instead focuses on the ability of the limbs to manage the trajectory of the COM to limit energetic losses to the ground ("collisions"). By focusing on the COM, both these metrics effectively dismiss the importance of rotation of the elongate quadrupedal body. Limb Extension Work considers work required to extend and contract each limb like a strut, and accounts for the work of body pitching. We tested the prescriptive ability of these approximations of work by optimizing them within a quadrupedal model with two approximations of the body as a point-mass or a rigid distributed mass. Perfect potential-kinetic energy exchange of the COM was possible when optimizing Net COM Work, resulting in highly compliant gaits with duty factors close to one, far different than observed mammalian gaits. Optimizing Individual Limbs COM Work resulted in alternating periods of single limb stance. Only the distributed mass model, with Limb Extension Work as the cost, resulted in a solution similar to the stereotypical mammalian gait. These results suggest that maintaining a near-constant limb length, with distributed contacts, are more important mechanisms of economy than either transduction of potential-kinetic energy or COM collision mitigation for quadrupedal walking.

Three Characteristics of Cheetah Galloping Improve Running Performance Through Spinal Movement: A Modeling Study

Cheetahs are the fastest land animal. Their galloping shows three characteristics: small vertical movement of their center of mass, small whole-body pitching movement, and large spine bending movement. We hypothesize that these characteristics lead to enhanced gait performance in cheetahs, including higher gait speed. In this study, we used a simple model with a spine joint and torsional spring, which emulate the body flexibility, to verify our hypothesis from a dynamic perspective. Specifically, we numerically searched periodic solutions and evaluated what extent each solution shows the three characteristics. We then evaluated the gait performance and found that the solutions with the characteristics achieve high performances. This result supports our hypothesis. Furthermore, we revealed the mechanism for the high performances through the dynamics of the spine movement. These findings extend the current understanding of the dynamic mechanisms underlying high-speed locomotion in cheetahs.

Center of Mass Offset Enhances the Selection of Transverse Gallop in High-Speed Running by Horses: A Modeling Study

Horses use the transverse gallop in high-speed running. However, different animals use different gaits, and the gait preference of horses remains largely unclear. Horses have fore-aft asymmetry in their body structure and their center of mass (CoM) is anteriorly located far from the center of the body. Since such a CoM offset affects the running dynamics, we hypothesize that the CoM offset of horses is important in gait selection. In order to verify our hypothesis and clarify the gait selection mechanisms by horses from a dynamic viewpoint, we developed a simple model with CoM offset and investigated its effects on running. Specifically, we numerically obtained periodic solutions and classified these solutions into six types of gaits, including the transverse gallop, based on the footfall pattern. Our results show that the transverse gallop is optimal when the CoM offset is located at the position estimated in horses. Our findings provide useful insight into the gait selection mechanisms in high-speed running of horses.

Estimating Gaits of an Ancient Crocodile-Line Archosaur Through Trajectory Optimization, With Comparison to Fossil Trackways

Fossil trackways provide a glimpse into the behavior of extinct animals. However, while providing information of the trackmaker size, stride, and even speed, the actual gait of the organism can be ambiguous. This is especially true of quadrupedal animals, where disparate gaits can have similar trackway patterns. Here, predictive simulation using trajectory optimization can help distinguish gaits used by trackmakers. First, we demonstrated that a planar, five-link quadrupedal biomechanical model can generate the qualitative trackway patterns made by domestic dogs, although a systematic error emerges in the track phase (relative distance between ipsilateral pes and manus prints). Next, we used trackway dimensions as inputs to a model of Batrachotomus kupferzellensis, a long-limbed, crocodile-line archosaur (clade Pseudosuchia) from the Middle Triassic of Germany. We found energetically optimal gaits and compared their predicted track phases to those of fossil trackways of Isochirotherium and Brachychirotherium. The optimal results agree with trackways at slow speeds but differ at faster speeds. However, all simulations point to a gait transition around a non-dimensional speed of 0.4 and another at 1.0. The trackways likewise exhibit stark differences in the track phase at these speeds. In all cases, including when simulations are constrained to the fossil track phase, the optimal simulations after the first gait transition do not correspond to a trot, as often used by living crocodiles. Instead, they are a diagonal sequence gait similar to the slow tölt of Icelandic horses. This is the first evidence that extinct pseudosuchians may have exhibited different gaits than their modern relatives and of a gait transition in an extinct pseudosuchian. The results of this analysis highlight areas where the models can be improved to generate more reliable predictions for fossil data while also showcasing how simple models can generate insights about the behavior of extinct animals.

Dynamical determinants enabling two different types of flight in cheetah gallop to enhance speed through spine movement

Cheetahs use a galloping gait in their fastest speed range. It has been reported that cheetahs achieve high-speed galloping by performing two types of flight through spine movement (gathered and extended). However, the dynamic factors that enable cheetahs to incorporate two types of flight while galloping remain unclear. To elucidate this issue from a dynamical viewpoint, we developed a simple analytical model. We derived possible periodic solutions with two different flight types (like cheetah galloping), and others with only one flight type (unlike cheetah galloping). The periodic solutions provided two criteria to determine the flight type, related to the position and magnitude of ground reaction forces entering the body. The periodic solutions and criteria were verified using measured cheetah data, and provided a dynamical mechanism by which galloping with two flight types enhances speed. These findings extend current understanding of the dynamical mechanisms underlying high-speed locomotion in cheetahs.