Michael T. Butcher

Constrained optimization in human running

SUMMARY Walking humans spontaneously select different speed, frequency and step length combinations, depending on which of these three parameters is specified. This behavior can be explained by constrained optimization of cost of transport (metabolic cost/distance) where cost of transport is seen as the main component of an underlying objective function that is minimized within the limitations of specified constraints. It is then of interest to ask whether or not such results are specific to walking only, or indicate a more general feature of locomotion control. The current study examines running gait selection within the framework of constrained optimization by comparing self-selected running gaits to the gaits predicted by constrained optimization of a cost surface constructed from cost data available in the literature. Normalizing speed and frequency values in the behavioral data by preferred speed and frequency reduced inter-subject variability and made group behavioral trends more visible. Although actual behavior did not coincide exactly with running cost optimization, self-selected gait and predictions from the general human cost surface did agree to within the 95% confidence interval and the region of minimal cost+0.005 ml O2 kg-1 m-1. This was similar to the level of agreement between actual and predicted behavior observed in walking. Thus, there seems to be substantial evidence to suggest that (i) selection of gait parameters in running can largely be predicted using constrained optimization, and (ii) general cost surfaces can be constructed using metabolic data from one group that will largely predict the behavior of other groups.

Architectural specialization of the intrinsic thoracic limb musculature of the American badger (Taxidea taxus)

Evaluation of the relationships between muscle structure and digging function in fossorial species is limited. Badgers and other fossorial specialists are expected to have massive forelimb muscles with long fascicles capable of substantial shortening for high power and applying high out‐force to the substrate. To explore this hypothesis, we quantified muscle architecture in the thoracic limb of the American badger (Taxidea taxus) and estimated the force, power, and joint torque of its intrinsic musculature in relation to the use of scratch‐digging behavior. Architectural properties measured were muscle mass, belly length, fascicle length, pennation angle, and physiological cross‐sectional area. Badgers possess hypertrophied shoulder flexors/humeral retractors, elbow extensors, and digital flexors. The triceps brachii is particularly massive and has long fascicles with little pennation, muscle architecture consistent with substantial shortening capability, and high power. A unique feature of badgers is that, in addition to elbow joint extension, two biarticular heads (long and medial) of the triceps are capable of applying high torques to the shoulder joint to facilitate retraction of the forelimb throughout the power stroke. The massive and complex digital flexors show relatively greater pennation and shorter fascicle lengths than the triceps brachii, as well as compartmentalization of muscle heads to accentuate both force production and range of shortening during flexion of the carpus and digits. Muscles of most functional groups exhibit some degree of specialization for high force production and are important for stabilizing the shoulder, elbow, and carpal joints against high limb forces generated during powerful digging motions. Overall, our findings support the hypothesis and indicate that forelimb muscle architecture is consistent with specializations for scratch‐digging. Quantified muscle properties in the American badger serve as a comparator to evaluate the range of diversity in muscle structure and contractile function that exists in mammals specialized for fossorial habits. J. Morphol. 2013.

A comparative collision-based analysis of human gait

This study compares human walking and running, and places them within the context of other mammalian gaits. We use a collision-based approach to analyse the fundamental dynamics of the centre of mass (CoM) according to three angles derived from the instantaneous force and velocity vectors. These dimensionless angles permit comparisons across gait, species and size. The collision angle Φ, which is equivalent to the dimensionless mechanical cost of transport CoTmech, is found to be three times greater during running than walking of humans. This threefold difference is consistent with previous studies of walking versus trotting of quadrupeds, albeit tends to be greater in the gaits of humans and hopping bipeds than in quadrupeds. Plotting the collision angle Φ together with the angles of the CoM force vector Θ and velocity vector Λ results in the functional grouping of bipedal and quadrupedal gaits according to their CoM dynamics—walking, galloping and ambling are distinguished as separate gaits that employ collision reduction, whereas trotting, running and hopping employ little collision reduction and represent more of a continuum that is influenced by dimensionless speed. Comparable with quadrupedal mammals, collision fraction (the ratio of actual to potential collision) is 0.51 during walking and 0.89 during running, indicating substantial collision reduction during walking, but not running, of humans.

Functional osteology of the forelimb digging apparatus of badgers

Abstract Badgers (Carnivora, Mustelidae) constitute a nonmonophyletic assemblage of mammals that are characterized by a general similarity of appearance and a broad geographic distribution. A comparative analysis of the forelimb osteology of badgers was performed to assess how observed differences in their scratch-digging behavior are related to variation of forelimb structure. We measured forelimb bone proportions of 87 skeletal specimens and calculated 8 functional indexes that were analyzed using analysis of variance and principal component analysis to identify the osteological correlates of fossorial ability in this clade. The indexes that best characterize forelimb specialization for scratch-digging in badgers are related to a robust humerus, large humeral epicondyles, and a long olecranon process, and these features increase from digger to semifossorial forms. A large scapular area for muscle attachment and a robust ulna also are correlated with fossorial ability. Semifossorial forms are indicated to have greater forelimb muscle mass, increased mechanical advantage of the elbow extensors, and the ability of the elbow extensor and carpal and digital flexor muscles to apply high out-force to the substrate. Digger forms are indicated to have relatively less robust and longer distal limb bones, and lower limb out-force capability. This study reveals that for badgers there is a distinct relationship between the proportions of the forelimb bones and fossorial ability. The indexes tested that relate to mechanical advantage of the elbow extensors and mass and force production capacity of the musculature have the discriminatory ability to distinguish between degrees of forelimb specialization and fossorial ability of badgers.

Locomotor loading mechanics in the hindlimbs of tegu lizards ( Tupinambis merianae ): comparative and evolutionary implications

SUMMARY Skeletal elements are usually able to withstand several times their usual load before they yield, and this ratio is known as the bones safety factor. Limited studies on amphibians and non-avian reptiles have shown that they have much higher limb bone safety factors than birds and mammals. It has been hypothesized that this difference is related to the difference in posture between upright birds and mammals and sprawling ectotherms; however, limb bone loading data from a wider range of sprawling species are needed in order to determine whether the higher safety factors seen in amphibians and non-avian reptiles are ancestral or derived conditions. Tegus (family Teiidae) are an ideal lineage with which to expand sampling of limb bone loading mechanics for sprawling taxa, particularly for lizards, because they are from a different clade than previously sampled iguanas and exhibit different foraging and locomotor habits (actively foraging carnivore versus burst-activity herbivore). We evaluated the mechanics of locomotor loading for the femur of the Argentine black and white tegu (Tupinambus merianae) using three-dimensional measurements of the ground reaction force and hindlimb kinematics, in vivo bone strains and femoral mechanical properties. Peak bending stresses experienced by the femur were low (tensile: 10.4±1.1 MPa; compressive: –17.4±0.9 MPa) and comparable to those in other reptiles, with moderate shear stresses and strains also present. Analyses of peak femoral stresses and strains led to estimated safety factor ranges of 8.8–18.6 in bending and 7.8–17.5 in torsion, both substantially higher than typical for birds and mammals but similar to other sprawling tetrapods. These results broaden the range of reptilian and amphibian taxa in which high femoral safety factors have been evaluated and further indicate a trend for the independent evolution of lower limb bone safety factors in endothermic taxa.

Femoral loading mechanics in the Virginia opossum, Didelphis virginiana: torsion and mediolateral bending in mammalian locomotion

SUMMARY Studies of limb bone loading in terrestrial mammals have typically found anteroposterior bending to be the primary loading regime, with torsion contributing minimally. However, previous studies have focused on large, cursorial eutherian species in which the limbs are held essentially upright. Recent in vivo strain data from the Virginia opossum (Didelphis virginiana), a marsupial that uses a crouched rather than an upright limb posture, have indicated that its femur experiences appreciable torsion during locomotion as well as strong mediolateral bending. The elevated femoral torsion and strong mediolateral bending observed in D. virginiana might result from external forces such as a medial inclination of the ground reaction force (GRF), internal forces deriving from a crouched limb posture, or a combination of these factors. To evaluate the mechanism underlying the loading regime of opossum femora, we filmed D. virginiana running over a force platform, allowing us to measure the magnitude of the GRF and its three-dimensional orientation relative to the limb, facilitating estimates of limb bone stresses. This three-dimensional analysis also allows evaluations of muscular forces, particularly those of hip adductor muscles, in the appropriate anatomical plane to a greater degree than previous two-dimensional analyses. At peak GRF and stress magnitudes, the GRF is oriented nearly vertically, inducing a strong abductor moment at the hip that is countered by adductor muscles on the medial aspect of the femur that place this surface in compression and induce mediolateral bending, corroborating and explaining loading patterns that were identified in strain analyses. The crouched orientation of the femur during stance in opossums also contributes to levels of femoral torsion as high as those seen in many reptilian taxa. Femoral safety factors were as high as those of non-avian reptiles and greater than those of upright, cursorial mammals, primarily because the load magnitudes experienced by opossums are lower than those of most mammals. Thus, the evolutionary transition from crouched to upright posture in mammalian ancestors may have been accompanied by an increase in limb bone load magnitudes.

Functional Morphology of the Forelimb of the Nine-Banded Armadillo ( Dasypus novemcinctus ): Comparative Perspectives on the Myology of Dasypodidae

The nine-banded armadillo, Dasypus novemcinctus, is a member of the family Dasypodidae, which contains all extant species of armadillos and represents the most diverse group of xenarthran mammals by their speciation, form, and range of scratch-digging ability. This study aims to identify muscle traits that reflect specialization for fossorial habit by observing forelimb structure in D. novemcinctus and comparing it among armadillos using available myological data. A number of informative traits were observed in D. novemcinctus and among Dasypodidae, including the absence of m. rhomboideus profundus, the variable presence of a m. articularis humeri and m. coracobrachialis, two heads of m. triceps brachii with scapular origin, and a lack of muscle mass devoted to antebrachial supination. Muscle mass and myosin heavy chain (MHC) isoform content were also quantified from our forelimb dissections. New osteological indices are additionally calculated and reported for D. novemcinctus. Collectively, the findings emphasize muscle mass and power output for limb retraction and specialization of the distal limb for sustained purchase of soil by strong pronation and carpal/digital flexion. Moreover, the myological traits assessed here provide a valuable resource for interpretation of muscle architecture specializations among digging mammals and future reassessment of armadillo phylogeny.

Muscle architecture and out-force potential of the thoracic limb in the Eastern mole (Scalopus aquaticus).

Moles have modified thoracic limbs with hypertrophied pectoral girdle muscles that allow them to apply remarkably high lateral out‐forces during the power stroke when burrowing. To further understand the high force capabilities of mole forelimbs, architectural properties of the thoracic limb muscles were quantified in the Eastern mole (Scalopus aquaticus). Architectural properties measured included muscle mass, moment arm, belly length, fascicle length, and pennation angle, and these were used to provide estimates of maximum isometric force, joint torque, and power. Measurements of muscle moment arms and limb lever lengths were additionally used to analyze the out‐force contributions of the major pectoral girdle muscles. Most muscles have relatively long fascicles and little‐to‐no pennation. The humeral abductor/rotators as a functional group are massive and are capable of relatively high force, power, and joint torque. Of this group, the bipennate m. teres major is the most massive and has the capacity to produce the highest force and joint torque to abduct and axially rotate the humerus. In general, the distal limb muscles are relatively small, but have the capacity for high force and mechanical work by fascicle shortening. The muscle architectural properties of the elbow extensors (e.g., m. triceps brachii) and carpal flexors (e.g., m. palmaris longus) are consistent with the function of these muscles to augment lateral out‐force application. The humeral abductor/rotators m. latissimus dorsi, m. teres major, m. pectoralis, and m. subscapularis are calculated to contribute 13.9 N to out‐force during the power stroke, and this force is applied in a ‘frontal’ plane causing abduction of the humerus about the sternoclavicular joint. Moles have several specializations of their digging apparatus that greatly enhance the application of out‐force, and these morphological features suggest convergence on limb form and burrowing function between New and Old World moles. J. Morphol. 274:1277–1287, 2013.

Correlation of muscle function and bone strain in the hindlimb of the river cooter turtle (Pseudemys concinna).

During terrestrial locomotion, limb muscles must generate mechanical work and stabilize joints against the ground reaction force. These demands can require high force production that imposes substantial loads on limb bones. To better understand how muscle contractile function influences patterns of bone loading in terrestrial locomotion, and refine force platform equilibrium models used to estimate limb bone safety factors, we correlated in vivo recordings of femoral strain with muscle activation and strain in a major propulsive hindlimb muscle, flexor tibialis internus (FTI), of a species with a published model of hindlimb force production (river cooter turtles, Pseudemys concinna). Electromyography (EMG) recordings indicate FTI activity prior to footfall that continues through approximately 50% of the stance phase. Large EMG bursts occur just after footfall when the muscle has reached its maximum length and is beginning to actively shorten, concurrent with increasing compressive strain on the anterior femur. The FTI muscle shortens through 35% of stance, with mean fascicle shortening strains reaching 14.0 ± 5.4% resting length (L0). At the time of peak compressive strains on the femur, the muscle fascicles remain active, but fascicles typically lengthen until mid‐stance as the knee extends. Influenced by the activity of the dorsal knee extensor femorotibialis, the FTI muscle continues to passively lengthen simultaneously with knee extension and a shift to tensile axial strain on the anterior femur at approximately 40% of stance. The near coincidence in timing of peak compressive bone strain and peak muscle shortening (5.4 ± 4.1% stance) indicates a close correlation between the action of the hip extensor/knee flexor, FTI, and femoral loading in the cooter hindlimb. In the context of equilibrium models of limb bone loading, these results may help explain differences in safety factor estimates observed between previous force platform and in vivo strain analyses in cooters. J. Morphol. 274:1060–1069, 2013.

Myosin Isoform Fiber Type and Fiber Size in the Tail of the Virginia Opossum (Didelphis virginiana)

Muscle fiber type is a well studied property in limb muscles, however, much less is understood about myosin heavy chain (MHC) isoform expression in caudal muscles of mammalian tails. Didelphid marsupials are an interesting lineage in this context as all species have prehensile tails, but show a range of tail‐function depending on either their arboreal or terrestrial locomotor habits. Differences in prehensility suggest that MHC isoform fiber types may also be different, in that terrestrial opossums may have a large distribution of oxidative fibers for object carrying tasks instead of faster, glycolytic fiber types expected in mammals with long tails. To test this hypothesis, MHC isoform fiber type and their regional distribution (proximal/transitional/distal) were determined in the tail of the Virginia opossum (Didelphis virginiana). Fiber types were determined by a combination of myosin‐ATPase histochemistry, immunohistochemistry, and SDS‐PAGE. Results indicate a predominance of the fast MHC‐2A and ‐2X isoforms in each region of the tail. The presence of two fast isoforms, in addition to the slow MHC‐1 isoform, was confirmed by SDS‐PAGE analysis. The overall MHC isoform fiber type distribution for the tail was: 25% MHC‐1, 71% MHC‐2A/X hybrid, and 4% MHC‐1/2A hybrid. Oxidative MHC‐2A/X isoform fibers were found to be relatively large in cross‐section compared to slow, oxidative MHC‐1 and MHC‐1/2A hybrid fibers. A large percentage of fast MHC‐2A/X hybrids fibers may be suggestive of an evolutionary transition in MHC isoform distribution (fast‐to‐slow fiber type) in the tail musculature of an opossum with primarily a terrestrial locomotor habit and adaptive tail‐function. Anat Rec, 2013.