Goats decrease hindlimb stiffness when walking over compliant surfaces.

Leg stiffness, commonly estimated as the 'compression' of a defined leg element in response to a load, has long been used to characterize terrestrial locomotion. This study investigated how goats adjust the stiffness of their hindlimbs to accommodate surfaces of different stiffness. Goats provide a compelling animal model for studying leg stiffness modulation, because they skillfully ambulate over a range of substrates that vary in compliance. To investigate the adjustments that goats make when walking over such substrates, ground reaction forces and three-dimensional trajectories of hindlimb markers were recorded as goats walked on rigid, rubber and foam surfaces. Net joint moments, power and work at the hip, knee, ankle and metatarsophalangeal joints were estimated throughout stance via inverse dynamics. Hindlimb stiffness was estimated from plots of total leg force versus total leg length, and individual joint stiffness was estimated from plots of joint moment versus joint angle. Our results support the hypothesis that goats modulate hindlimb stiffness in response to surface stiffness; specifically, hindlimb stiffness decreased on the more compliant surfaces (P<0.002). Estimates of joint stiffness identified hip and ankle muscles as the primary drivers of these adjustments. When humans run on compliant surfaces, they generally increase leg stiffness to preserve their center-of-mass mechanics. We did not estimate center-of-mass mechanics in this study; nevertheless, our estimates of hindlimb stiffness suggest that goats exhibit a different behavior. This study offers new insight into mechanisms that allow quadrupeds to modulate their gait mechanics when walking on surfaces of variable compliance.

The human iliotibial band is specialized for elastic energy storage compared with the chimp fascia lata.

This study examines whether the human iliotibial band (ITB) is specialized for elastic energy storage relative to the chimpanzee fascia lata (FL). To quantify the energy storage potential of these structures, we created computer models of human and chimpanzee lower limbs based on detailed anatomical dissections. We characterized the geometry and force-length properties of the FL, tensor fascia lata (TFL) and gluteus maximus (GMax) in four chimpanzee cadavers based on measurements of muscle architecture and moment arms about the hip and knee. We used the chimp model to estimate the forces and corresponding strains in the chimp FL during bipedal walking, and compared these data with analogous estimates from a model of the human ITB, accounting for differences in body mass and lower extremity posture. We estimate that the human ITB stores 15- to 20-times more elastic energy per unit body mass and stride than the chimp FL during bipedal walking. Because chimps walk with persistent hip flexion, the TFL and portions of GMax that insert on the FL undergo smaller excursions (origin to insertion) than muscles that insert on the human ITB. Also, because a smaller fraction of GMax inserts on the chimp FL than on the human ITB, and thus its mass-normalized physiological cross-sectional area is about three times less in chimps, the chimp FL probably transmits smaller muscle forces. These data provide new evidence that the human ITB is anatomically derived compared with the chimp FL and potentially contributes to locomotor economy during bipedal locomotion.

Modulation of joint moments and work in the goat hindlimb with locomotor speed and surface grade.

Goats and other quadrupeds must modulate the work output of their muscles to accommodate the changing mechanical demands associated with locomotion in their natural environments. This study examined which hindlimb joint moments goats use to generate and absorb mechanical energy on level and sloped surfaces over a range of locomotor speeds. Ground reaction forces and the three-dimensional locations of joint markers were recorded as goats walked, trotted and galloped over 0, +15 and -15 deg sloped surfaces. Net joint moments, powers and work were estimated at the goats' hip, knee, ankle and metatarsophalangeal joints throughout the stance phase via inverse dynamics calculations. Differences in locomotor speed on the level, inclined and declined surfaces were characterized and accounted for by fitting regression equations to the joint moment, power and work data plotted versus non-dimensionalized speed. During level locomotion, the net work generated by moments at each of the hindlimb joints was small (less than 0.1 J kg(-1) body mass) and did not vary substantially with gait or locomotor speed. During uphill running, by contrast, mechanical energy was generated at the hip, knee and ankle, and the net work at each of these joints increased dramatically with speed (P<0.05). The greatest increases in positive joint work occurred at the hip and ankle. During downhill running, mechanical energy was decreased in two main ways: goats generated larger knee extension moments in the first half of stance, absorbing energy as the knee flexed, and goats generated smaller ankle extension moments in the second half of stance, delivering less energy. The goats' hip extension moment in mid-stance was also diminished, contributing to the decrease in energy. These analyses offer new insight into quadrupedal locomotion, clarifying how the moments generated by hindlimb muscles modulate mechanical energy at different locomotor speeds and grades, as needed to accommodate the demands of variable terrain.

Recruitment of faster motor units is associated with greater rates of fascicle strain and rapid changes in muscle force during locomotion.

Animals modulate the power output needed for different locomotor tasks by changing muscle forces and fascicle strain rates. To generate the necessary forces, appropriate motor units must be recruited. Faster motor units have faster activation-deactivation rates than slower motor units, and they contract at higher strain rates; therefore, recruitment of faster motor units may be advantageous for tasks that involve rapid movements or high rates of work. This study identified motor unit recruitment patterns in the gastrocnemii muscles of goats and examined whether faster motor units are recruited when locomotor speed is increased. The study also examined whether locomotor tasks that elicit faster (or slower) motor units are associated with increased (or decreased) in vivo tendon forces, force rise and relaxation rates, fascicle strains and/or strain rates. Electromyography (EMG), sonomicrometry and muscle-tendon force data were collected from the lateral and medial gastrocnemius muscles of goats during level walking, trotting and galloping and during inclined walking and trotting. EMG signals were analyzed using wavelet and principal component analyses to quantify changes in the EMG frequency spectra across the different locomotor conditions. Fascicle strain and strain rate were calculated from the sonomicrometric data, and force rise and relaxation rates were determined from the tendon force data. The results of this study showed that faster motor units were recruited as goats increased their locomotor speeds from level walking to galloping. Slow inclined walking elicited EMG intensities similar to those of fast level galloping but different EMG frequency spectra, indicating that recruitment of the different motor unit types depended, in part, on characteristics of the task. For the locomotor tasks and muscles analyzed here, recruitment patterns were generally associated with in vivo fascicle strain rates, EMG intensity and tendon force. Together, these data provide new evidence that changes in motor unit recruitment have an underlying mechanical basis, at least for certain locomotor tasks.

Crouched postures reduce the capacity of muscles to extend the hip and knee during the single-limb stance phase of gait.

Many children with cerebral palsy walk in a crouch gait that progressively worsens over time, decreasing walking efficiency and leading to joint degeneration. This study examined the effect of crouched postures on the capacity of muscles to extend the hip and knee joints and the joint flexions induced by gravity during the single-limb stance phase of gait. We first characterized representative mild, moderate, and severe crouch gait kinematics based on a large group of subjects with cerebral palsy (N=316). We then used a three-dimensional model of the musculoskeletal system and its associated equations of motion to determine the effect of these crouched gait postures on (1) the capacity of individual muscles to extend the hip and knee joints, which we defined as the angular accelerations of the joints, towards extension, that resulted from applying a 1N muscle force to the model, and (2) the angular acceleration of the joints induced by gravity. Our analysis showed that the capacities of almost all the major hip and knee extensors were markedly reduced in a crouched gait posture, with the exception of the hamstrings muscle group, whose extension capacity was maintained in a crouched posture. Crouch gait also increased the flexion accelerations induced by gravity at the hip and knee throughout single-limb stance. These findings help explain the increased energy requirements and progressive nature of crouch gait in patients with cerebral palsy.

Importance of preswing rectus femoris activity in stiff-knee gait.

Stiff-knee gait is characterized by diminished and delayed knee flexion during swing. Rectus femoris transfer surgery, a common treatment for stiff-knee gait, is often recommended when a patient exhibits prolonged activity of the rectus femoris muscle during swing. Treatment outcomes are inconsistent, in part, due to limited understanding of the biomechanical factors contributing to stiff-knee gait. This study used a combination of gait analysis and dynamic simulation to examine how activity of the rectus femoris during swing, and prior to swing, contribute to knee flexion. A group of muscle-actuated dynamic simulations was created that accurately reproduced the gait dynamics of ten subjects with stiff-knee gait. These simulations were used to examine the effects of rectus femoris activity on knee motion by eliminating rectus femoris activity during preswing and separately during early swing. The increase in peak knee flexion by eliminating rectus femoris activity during preswing (7.5+/-3.1 degrees ) was significantly greater on average (paired t-test, p=0.035) than during early swing (4.7+/-3.6 degrees ). These results suggest that preswing rectus femoris activity is at least as influential as early swing activity in limiting the knee flexion of persons with stiff-knee gait. In evaluating rectus femoris activity for treatment of stiff-knee gait, preswing as well as early swing activity should be examined.

Does a two-element muscle model offer advantages when estimating ankle plantar flexor forces during human cycling?

Traditional Hill-type muscle models, parameterized using high-quality experimental data, are often "too weak" to reproduce the joint torques generated by healthy adults during rapid, high force tasks. This study investigated whether the failure of these models to account for different types of motor units contributes to this apparent weakness; if so, muscle-driven simulations may rely on excessively high muscle excitations to generate a given force. We ran a series of forward simulations that reproduced measured ankle mechanics during cycling at five cadences ranging from 60 to 140 RPM. We generated both "nominal" simulations, in which an abstract ankle model was actuated by a 1-element Hill-type plantar flexor with a single contractile element (CE), and "test" simulations, in which the same model was actuated by a 2-element plantar flexor with two CEs that accounted for the force-generating properties of slower and faster motor units. We varied the total excitation applied to the 2-element plantar flexor between 60 and 105% of the excitation from each nominal simulation, and we varied the amount distributed to each CE between 0 and 100% of the total. Within this test space, we identified the excitation level and distribution, at each cadence, that best reproduced the plantar flexor forces generated in the nominal simulations. Our comparisons revealed that the 2-element model required substantially less total excitation than the 1-element model to generate comparable forces, especially at higher cadences. For instance, at 140 RPM, the required excitation was reduced by 23%. These results suggest that a 2-element model, in which contractile properties are "tuned" to represent slower and faster motor units, can increase the apparent strength and perhaps improve the fidelity of simulations of tasks with varying mechanical demands.

Contributions of muscles to terminal-swing knee motions vary with walking speed.

Many children with cerebral palsy walk with diminished knee extension during terminal swing, at speeds much slower than unimpaired children. Treatment of these gait abnormalities is challenging because the factors that extend the knee during normal walking, over a range of speeds, are not well understood. This study analyzed a series of three-dimensional, muscle-driven dynamic simulations to determine whether the relative contributions of individual muscles and other factors to angular motions of the swing-limb knee vary with walking speed. Simulations were developed that reproduced the measured gait dynamics of seven unimpaired children walking at self-selected, fast, slow, and very slow speeds (7 subjects x 4 speeds=28 simulations). In mid-swing, muscles on the stance limb made the largest net contribution to extension of the swing-limb knee at all speeds examined. The stance-limb hip abductors, in particular, accelerated the pelvis upward, inducing reaction forces at the swing-limb hip that powerfully extended the knee. Velocity-related forces (i.e., Coriolis and centrifugal forces) also contributed to knee extension in mid-swing, though these contributions were diminished at slower speeds. In terminal swing, the hip flexors and other muscles on the swing-limb decelerated knee extension at the subjects' self-selected, slow, and very slow speeds, but had only a minimal net effect on knee motions at the fastest speeds. Muscles on the stance limb helped brake knee extension at the subjects' fastest speeds, but induced a net knee extension acceleration at the slowest speeds. These data--which show that the contributions of muscular and velocity-related forces to terminal-swing knee motions vary systematically with walking speed--emphasize the need for speed-matched control subjects when attempting to determine the causes of a patient's abnormal gait.

Muscular coordination of knee motion during the terminal-swing phase of normal gait.

Children with cerebral palsy often walk with diminished knee extension during the terminal-swing phase, resulting in a troublesome "crouched" posture at initial contact and a shortened stride. Treatment of this gait abnormality is challenging because the factors that extend the knee during normal walking are not well understood, and because the potential of individual muscles to limit terminal-swing knee extension is unknown. This study analyzed a series of three-dimensional, muscle-driven dynamic simulations to quantify the angular accelerations of the knee induced by muscles and other factors during swing. Simulations were generated that reproduced the measured gait dynamics and muscle excitation patterns of six typically developing children walking at self-selected speeds. The knee was accelerated toward extension in the simulations by velocity-related forces (i.e., Coriolis and centrifugal forces) and by a number of muscles, notably the vasti in mid-swing (passive), the hip extensors in terminal swing, and the stance-limb hip abductors, which accelerated the pelvis upward. Knee extension was slowed in terminal swing by the stance-limb hip flexors, which accelerated the pelvis backward. The hamstrings decelerated the forward motion of the swing-limb shank, but did not contribute substantially to angular motions of the knee. Based on these data, we hypothesize that the diminished knee extension in terminal swing exhibited by children with cerebral palsy may, in part, be caused by weak hip extensors or by impaired hip muscles on the stance limb that result in abnormal accelerations of the pelvis.

OpenSim: open-source software to create and analyze dynamic simulations of movement.

Dynamic simulations of movement allow one to study neuromuscular coordination, analyze athletic performance, and estimate internal loading of the musculoskeletal system. Simulations can also be used to identify the sources of pathological movement and establish a scientific basis for treatment planning. We have developed a freely available, open-source software system (OpenSim) that lets users develop models of musculoskeletal structures and create dynamic simulations of a wide variety of movements. We are using this system to simulate the dynamics of individuals with pathological gait and to explore the biomechanical effects of treatments. OpenSim provides a platform on which the biomechanics community can build a library of simulations that can be exchanged, tested, analyzed, and improved through a multi-institutional collaboration. Developing software that enables a concerted effort from many investigators poses technical and sociological challenges. Meeting those challenges will accelerate the discovery of principles that govern movement control and improve treatments for individuals with movement pathologies.

Why are Antagonist Muscles Co-activated in My Simulation? A Musculoskeletal Model for Analysing Human Locomotor Tasks.

Existing "off-the-shelf" musculoskeletal models are problematic when simulating movements that involve substantial hip and knee flexion, such as the upstroke of pedalling, because they tend to generate excessive passive fibre force. The goal of this study was to develop a refined musculoskeletal model capable of simulating pedalling and fast running, in addition to walking, which predicts the activation patterns of muscles better than existing models. Specifically, we tested whether the anomalous co-activation of antagonist muscles, commonly observed in simulations, could be resolved if the passive forces generated by the underlying model were diminished. We refined the OpenSim™ model published by Rajagopal et al. (IEEE Trans Biomed Eng 63:1-1, 2016) by increasing the model's range of knee flexion, updating the paths of the knee muscles, and modifying the force-generating properties of eleven muscles. Simulations of pedalling, running and walking based on this model reproduced measured EMG activity better than simulations based on the existing model-even when both models tracked the same subject-specific kinematics. Improvements in the predicted activations were associated with decreases in the net passive moments; for example, the net passive knee moment during the upstroke of pedalling decreased from 36.9 N m (existing model) to 6.3 N m (refined model), resulting in a dramatic decrease in the co-activation of knee flexors. The refined model is available from SimTK.org and is suitable for analysing movements with up to 120° of hip flexion and 140° of knee flexion.

Do the hamstrings operate at increased muscle-tendon lengths and velocities after surgical lengthening?

Children with crouch gait frequently walk with improved knee extension during the terminal swing and stance phases following hamstrings lengthening surgery; however, the mechanisms responsible for these improvements are unclear. This study tested the hypothesis that surgical lengthening enables the hamstrings of persons with cerebral palsy to operate at longer muscle-tendon lengths or lengthen at faster muscle-tendon velocities during walking. Sixty-nine subjects who had improved knee extension after surgery were retrospectively examined. The muscle-tendon lengths and velocities of the subjects' semimembranosus muscles were estimated by combining kinematic data from gait analysis with a three-dimensional computer model of the lower extremity. Log-linear analyses confirmed that the subjects who walked with abnormally short muscle-tendon lengths and/or slow muscle-tendon velocities preoperatively tended to walk with longer lengths (21 of 29 subjects, p<0.01) or faster velocities (30 of 40 subjects, p<0.01) postoperatively. In these cases, surgical lengthening may have slackened the subjects' tight hamstrings and/or diminished the hamstrings' spastic response to stretch. Other subjects walked with muscle-tendon lengths and velocities that were neither shorter nor slower than normal preoperatively (22 of 69 subjects), and the semimembranosus muscles of most of these subjects did not operate at increased lengths or velocities after surgery; in these cases, the subjects' postsurgical improvements in knee extension may have been unrelated to the hamstrings surgery. Analyses of muscle-tendon lengths and velocities may help to distinguish individuals who have "short" or "spastic" hamstrings from those who do not, and thus may augment conventional methods used to describe patients' neuromusculoskeletal impairments and gait abnormalities.

Kinematic and kinetic factors that correlate with improved knee flexion following treatment for stiff-knee gait.

Stiff-knee gait is a movement abnormality in which knee flexion during swing phase is significantly diminished. This study investigates the relationships between knee flexion velocity at toe-off, joint moments during swing phase and double support, and improvements in stiff-knee gait following rectus femoris transfer surgery in subjects with cerebral palsy. Forty subjects who underwent a rectus femoris transfer were categorized as "stiff" or "not-stiff" preoperatively based on kinematic measures of knee motion during walking. Subjects classified as stiff were further categorized as having "good" or "poor" outcomes based on whether their swing-phase knee flexion improved substantially after surgery. We hypothesized that subjects with stiff-knee gait would exhibit abnormal joint moments in swing phase and/or diminished knee flexion velocity at toe-off, and that subjects with diminished knee flexion velocity at toe-off would exhibit abnormal joint moments during double support. We further hypothesized that subjects classified as having a good outcome would exhibit postoperative improvements in these factors. Subjects classified as stiff tended to exhibit abnormally low knee flexion velocities at toe-off (p<0.001) and excessive knee extension moments during double support (p=0.001). Subjects in the good outcome group on average showed substantial improvement in these factors postoperatively. All eight subjects in this group walked with normal knee flexion velocity at toe-off postoperatively and only two walked with excessive knee extension moments in double support. By contrast, all 10 of the poor outcome subjects walked with low knee flexion velocity at toe-off postoperatively and seven walked with excessive knee extension moments in double support. Our analyses suggest that improvements in stiff-knee gait are associated with sufficient increases in knee flexion velocity at toe-off and corresponding decreases in excessive knee extension moments during double support. Therefore, while stiff-knee gait manifests during the swing phase of the gait cycle, it may be caused by abnormal muscle activity during stance.

The role of estimating muscle-tendon lengths and velocities of the hamstrings in the evaluation and treatment of crouch gait.

Persons with cerebral palsy frequently walk with excessive knee flexion during terminal swing and stance. This gait abnormality is often attributed to "short" or "spastic" hamstrings that restrict knee extension, and is often treated by hamstrings lengthening surgery. At present, the outcomes of these procedures are inconsistent. This study examined whether analyses of the muscle-tendon lengths and lengthening velocities of patients' hamstrings during walking may be helpful when deciding whether a candidate is likely to benefit from hamstrings surgery. One hundred and fifty-two subjects were cross-classified in a series of multi-way contingency tables based on their pre- and postoperative gait kinematics, muscle-tendon lengths, muscle-tendon velocities, and hamstrings surgeries. The lengths and velocities of the subjects' semimembranosus muscles were estimated by combining kinematic data from gait analysis with a three-dimensional computer model of the lower extremity. Log-linear analysis revealed that the subjects who walked with abnormally "short" or "slow" hamstrings preoperatively, and whose hamstrings did not operate at longer lengths or faster velocities postoperatively, were unlikely to walk with improved knee extension after treatment (p < 0.05). Subjects who did not walk with abnormally short or slow hamstrings preoperatively, and whose hamstrings did operate at longer lengths or faster velocities postoperatively, tended to exhibit unimproved or worsened anterior pelvic tilt after treatment (p < 0.05). Examination of the muscle-tendon lengths and velocities allows individuals who walk with abnormally short or slow hamstrings to be distinguished from those who do not, and thus may help to identify patients who are at risk for unsatisfactory postsurgical changes in knee extension or anterior pelvic tilt.

Quantifying Achilles tendon force in vivo from ultrasound images.

This study evaluated a procedure for estimating in vivo Achilles tendon (AT) force from ultrasound images. Two aspects of the procedure were tested: (i) accounting for subject-specific AT stiffness and (ii) accounting for changes in the relative electromyographic (EMG) intensities of the three triceps surae muscles. Ten cyclists pedaled at 80rpm while a comprehensive set of kinematic, kinetic, EMG, and ultrasound data were collected. Subjects were tested at four crank loads, ranging from 14 to 44Nm (115 to 370W). AT forces during cycling were estimated from AT length changes and from AT stiffness, which we derived for each subject from ultrasound data and from plantar flexion torques measured during isometric tests. AT length changes were measured by tracking the muscle-tendon junction of the medial gastrocnemius (MG) relative to its insertion on the calcaneus. Because the relative EMG intensities of the triceps surae muscles varied with load during cycling, we divided subjects׳ measured AT length changes by a scale factor, defined as the square root of the relative EMG intensity of the MG, weighted by the fractional physiological cross-sectional areas of the three muscles, to estimate force. Subjects׳ estimated AT forces during cycling increased with load (p<0.05). On average, peak forces ranged from 920±96N (14Nm, 115W) to 1510±129N (44Nm, 370W). For most subjects, ankle moments derived from the ultrasound-based AT strains were 5-12% less than the net ankle moments calculated from inverse dynamics (r2=0.71±0.28, RMSE=8.1±0.33Nm). Differences in the moments increased substantially when we did not account for changes in the muscles׳ relative EMG intensities with load or, in some subjects, when we used an average stiffness, rather than a subject-specific value. The proposed methods offer a non-invasive approach for studying in vivo muscle-tendon mechanics.

Muscular contributions to hip and knee extension during the single limb stance phase of normal gait: a framework for investigating the causes of crouch gait.

Crouch gait, a troublesome movement abnormality among persons with cerebral palsy, is characterized by excessive flexion of the hips and knees during stance. Treatment of crouch gait is challenging, at present, because the factors that contribute to hip and knee extension during normal gait are not well understood, and because the potential of individual muscles to produce flexion or extension of the joints during stance is unknown. This study analyzed a three-dimensional, muscle-actuated dynamic simulation of walking to quantify the angular accelerations of the hip and knee induced by muscles during normal gait, and to rank the potential of the muscles to alter motions of these joints. Examination of the muscle actions during single limb stance showed that the gluteus maximus, vasti, and soleus make substantial contributions to hip and knee extension during normal gait. Per unit force, the gluteus maximus had greater potential than the vasti to accelerate the knee toward extension. These data suggest that weak hip extensors, knee extensors, or ankle plantar flexors may contribute to crouch gait, and strengthening these muscles--particularly gluteus maximus--may improve hip and knee extension. Abnormal forces generated by the iliopsoas or adductors may also contribute to crouch gait, as our analysis showed that these muscles have the potential to accelerate the hip and knee toward flexion. This work emphasizes the need to consider how muscular forces contribute to multijoint movements when attempting to identify the causes of abnormal gait.

The capacity of the human iliotibial band to store elastic energy during running.

The human iliotibial band (ITB) is a poorly understood fascial structure that may contribute to energy savings during locomotion. This study evaluated the capacity of the ITB to store and release elastic energy during running, at speeds ranging from 2-5m/s, using a model that characterizes the three-dimensional musculoskeletal geometry of the human lower limb and the force-length properties of the ITB, tensor fascia lata (TFL), and gluteus maximus (GMax). The model was based on detailed analyses of muscle architecture, dissections of 3-D anatomy, and measurements of the muscles' moment arms about the hip and knee in five cadaveric specimens. The model was used, in combination with measured joint kinematics and published EMG recordings, to estimate the forces and corresponding strains in the ITB during running. We found that forces generated by TFL and GMax during running stretch the ITB substantially, resulting in energy storage. Anterior and posterior regions of the ITB muscle-tendon units (MTUs) show distinct length change patterns, in part due to different moment arms at the hip and knee. The posterior ITB MTU likely stores more energy than the anterior ITB MTU because it transmits larger muscle forces. We estimate that the ITB stores about 1J of energy per stride during slow running and 7J during fast running, which represents approximately 14% of the energy stored in the Achilles tendon at a comparable speed. This previously unrecognized mechanism for storing elastic energy may be an adaptation to increase human locomotor economy.

Validation of Hill-type muscle models in relation to neuromuscular recruitment and force-velocity properties: predicting patterns of in vivo muscle force.

We review here the use and reliability of Hill-type muscle models to predict muscle performance under varying conditions, ranging from in situ production of isometric force to in vivo dynamics of muscle length change and force in response to activation. Muscle models are frequently used in musculoskeletal simulations of movement, particularly when applied to studies of human motor performance in which surgically implanted transducers have limited use. Musculoskeletal simulations of different animal species also are being developed to evaluate comparative and evolutionary aspects of locomotor performance. However, such models are rarely validated against direct measures of fascicle strain or recordings of muscle-tendon force. Historically, Hill-type models simplify properties of whole muscle by scaling salient properties of single fibers to whole muscles, typically accounting for a muscle's architecture and series elasticity. Activation of the model's single contractile element (assigned the properties of homogenous fibers) is also simplified and is often based on temporal features of myoelectric (EMG) activation recorded from the muscle. Comparison of standard one-element models with a novel two-element model and with in situ and in vivo measures of EMG, fascicle strain, and force recorded from the gastrocnemius muscles of goats shows that a two-element Hill-type model, which allows independent recruitment of slow and fast units, better predicts temporal patterns of in situ and in vivo force. Recruitment patterns of slow/fast units based on wavelet decomposition of EMG activity in frequency-time space are generally correlated with the intensity spectra of the EMG signals, the strain rates of the fascicles, and the muscle-tendon forces measured in vivo, with faster units linked to greater strain rates and to more rapid forces. Using direct measures of muscle performance to further test Hill-type models, whether traditional or more complex, remains critical for establishing their accuracy and essential for verifying their applicability to scientific and clinical studies of musculoskeletal function.

Accuracy of gastrocnemius muscles forces in walking and running goats predicted by one-element and two-element Hill-type models.

Hill-type models are commonly used to estimate muscle forces during human and animal movement-yet the accuracy of the forces estimated during walking, running, and other tasks remains largely unknown. Further, most Hill-type models assume a single contractile element, despite evidence that faster and slower motor units, which have different activation-deactivation dynamics, may be independently or collectively excited. This study evaluated a novel, two-element Hill-type model with "differential" activation of fast and slow contractile elements. Model performance was assessed using a comprehensive data set (including measures of EMG intensity, fascicle length, and tendon force) collected from the gastrocnemius muscles of goats during locomotor experiments. Muscle forces predicted by the new two-element model were compared to the forces estimated using traditional one-element models and to the forces measured in vivo using tendon buckle transducers. Overall, the two-element model resulted in the best predictions of in vivo gastrocnemius force. The coefficient of determination, r(2), was up to 26.9% higher and the root mean square error, RMSE, was up to 37.4% lower for the two-element model than for the one-element models tested. All models captured salient features of the measured muscle force during walking, trotting, and galloping (r(2)=0.26-0.51), and all exhibited some errors (RMSE=9.63-32.2% of the maximum in vivo force). These comparisons provide important insight into the accuracy of Hill-type models. The results also show that incorporation of fast and slow contractile elements within muscle models can improve estimates of time-varying, whole muscle force during locomotor tasks.