Rheology of crossbridge ensembles

Muscle rheology, or the characterization of a muscle's response to external mechanical perturbations, is crucial to an animal's motor control and locomotive abilities. How the rheology emerges from the ensemble dynamics of microscopic actomyosin crossbridges known to underlie muscle forces is however a longstanding question. Classical descriptions in terms of force-length and force-velocity relationships capture only part of the rheology, namely under steady but not dynamical conditions. Although much is known about the actomyosin machinery, current mathematical models that describe the behavior of a population or an ensemble of crossbridges are plagued by an excess of parameters and computational complexity that limits their usage in large-scale musculoskeletal simulations. In this paper, we examine models of crossbridge dynamics of varying complexity and show that the emergent rheology of an ensemble of crossbridges can be simplified to a few dominant time-constants associated with intrinsic dynamical processes. For Huxley's classical two-state crossbridge model, we derive exact analytical expressions for the emergent ensemble rheology and find that it is characterized by a single time-constant. For more complex models with up to five crossbridge states, we show that at most three time-constants are needed to capture the ensemble rheology. Our results thus yield simplified models comprising of a few time-constants for muscle's bulk rheological response that can be readily used in large-scale simulations without sacrificing the model's interpretability in terms of the underlying actomyosin crossbridge dynamics.

Electromyography Based Validation of a Musculoskeletal Hand Model

Regarding the prevention of injuries and rehabilitation of the human hand, musculoskeletal simulations using an inverse dynamics approach allow for insights of the muscle recruitment and thus acting forces on the hand. Currently, several hand models from various research groups are in use, which are mainly validated by the comparison of numerical and anatomical moment arms. In contrast to this validation and model-building technique by cadaver studies, the aim of the present study is to further validate a recently published hand model [1] by analyzing numerically calculated muscle activities in comparison to experimentally measured electromyographical signals of the muscles. Therefore, the electromyographical signals of 10 hand muscles of five test subjects performing seven different hand movements were measured. The kinematics of these tasks were used as input for the hand model, and the numerical muscle activities were computed. To analyze the relationship between simulated and measured activities, the time difference of the muscle on- and off-set points were calculated, which resulted in a mean on- and off-set time difference of 0.58 s between the experimental data and the model. The largest differences were detected for movements that mainly addressed the wrist. One major issue comparing simulated and measured muscle activities of the hand is cross-talk. Nevertheless, the results show that the hand model fits the experiment quite accurately despite some limitations and is a further step towards patient-specific modelling of the upper extremity.

An Automatic and Simplified Approach to Muscle Path Modelling

The current paper aims at proposing an automatic method to design and adjust simplified muscle paths of a musculoskeletal model. These muscle paths are composed of a limited set of via points and an optimization routine is developed to place these via points on the model in order to fit moment arms and musculotendon lengths input data. The method has been applied to a forearm musculoskeletal model extracted from the literature, using theoretical input data as an example. Results showed that for $75\%$ of the muscle set, the relative root mean square error was under $29.23\%$ for moment arms and of $1.09\%$ for musculotendon lengths with regard to the input data. These results confirm the ability of the method to automatically generate computationally efficient muscle paths for musculoskeletal simulations. Using only via points lowers computational expense compared to paths exhibiting wrapping objects. A proper balance between computational time and anatomical realism should be found to help those models being interpreted by practitioners.

Muscle Force Patterns in Lower Extremity Muscles for Elite Discus Throwers, Javelin Throwers and Shot-Putters – A Case Study

Optimal release variables, as well as the kinematics and kinetics of athletes, are crucial for the maximization of throwing distance in athletics. Mathematical models and simulations allow throwing techniques to be studied. However, muscle force patterns and the contribution of specific muscle groups in athletics throwing events are not well understood and require detailed research. In this study, important variables of the muscle force generated during the javelin, discus and shot put events were determined using OpenSim software. Musculoskeletal simulations were carried out based on kinematic and kinetic data collected using the Vicon system and Kistler plates with the help of nine top Polish athletes (three in each event). OpenSim software was used to calculate muscle forces and joint velocities. For each discipline, it was found that the main muscle groups involved in the throwing movement were better at distinguishing throwers than joint velocities. The contribution of right ankle plantar flexors at the beginning of the final acceleration phase as well as left hip extensors at the end of the final acceleration phase was given special attention. This work provides a better understanding of the techniques used in athletics throws. Musculoskeletal simulations of throwing styles might help coaches analyze the techniques of individual athletes, resulting in better adjustment of training programmes and injury prevention protocols.

Muscle coordination retraining inspired by musculoskeletal simulations: a study on reducing knee loading

Humans typically coordinate their muscles to meet movement objectives like minimizing energy expenditure. In the presence of pathology, new objectives gain importance, like reducing loading in an osteoarthritic joint, but people often do not change their muscle coordination patterns to meet these new objectives. Here we use musculoskeletal simulations to identify simple changes in coordination that can be taught by providing feedback of electromyographic activity to achieve a therapeutic goal—reducing joint loading. Our simulations predicted that changing the relative activation of the redundant ankle plantarflexors could reduce knee contact force during walking, but it was unclear whether humans could re-coordinate redundant muscles during a complex task like walking. With simple biofeedback of electromyographic activity, healthy individuals reduced the ratio of gastrocnemius to soleus muscle activation by 25±15% (p=0.004). The resulting “gastrocnemius avoidance” gait pattern reduced the late-stance peak of simulation-estimated knee contact force by 12±12% (p=0.029). Simulation-informed muscle coordination retraining could be a promising treatment for knee osteoarthritis and a powerful tool for optimizing coordination for a variety of rehabilitation and performance applications.

Lower-limb muscle function is influenced by changing mechanical demands in cycling

Although cycling is often considered a seemingly simple, reciprocal task, muscles must adapt their function to satisfy changes in mechanical demands induced by higher crank torques and faster pedalling cadences. We examined if muscle function was sensitive to these changes in mechanical demands across a wide range of pedalling conditions. We collected experimental data of cycling where crank torque and pedalling cadence were independently varied from 13-44 Nm and 60-140 RPM. These data were used in conjunction with musculoskeletal simulations and a recently developed functional index-based approach to characterise the role of the human lower-limb muscles. We found that in muscles that generate most of the mechanical power and work during cycling, greater crank torque induced shifts towards greater muscle activation, greater positive muscle-tendon unit (MTU) work and a more motor-like function, particularly in the limb extensors. Conversely, with faster pedalling cadence, the same muscles exhibited a phase advance in muscle activity prior to crank top dead centre, which led to greater negative MTU power and work and shifted the muscles to contract with more spring-like behaviour. Our results illustrate the capacity for muscles to adapt their function to satisfy the mechanical demands of the task, even during highly constrained reciprocal tasks such as cycling. Understanding how muscles shift their contractile performance under varied mechanical and environmental demands may inform decisions on how to optimise pedalling performance and to design targeted cycling rehabilitation therapies for muscle-specific injuries or deficits.