High-frequency vibrations e.g., induced by legs impacting with the ground during terrestrial locomotion can provoke damage within tendons even leading to ruptures. So far, macroscopic Hill-type muscle models do not account for the observed high-frequency damping at low-amplitudes. Therefore, former studies proposed that protective damping might be explained by modelling the contractile machinery of the muscles in more detail, i.e., taking the microscopic processes of the actin-myosin coupling into account. In contrast, this study formulates an alternative hypothesis: low but significant damping of the passive material in series to the contractile machinery--e.g., tendons, aponeuroses, titin--may well suffice to damp these hazardous vibrations. Thereto, we measured the contraction dynamics of a piglet muscle-tendon complex (MTC) in three contraction modes at varying loads and muscle-tendon lengths. We simulated all three respective load situations on a computer: a Hill-type muscle model including a contractile element (CE) and each an elastic element in parallel (PEE) and in series (SEE) to the CE pulled on a loading mass. By comparing the model to the measured output of the MTC, we extracted a consistent set of muscle parameters. We varied the model by introducing either linear damping in parallel or in series to the CE leading to accordant re-formulations of the contraction dynamics of the CE. The comparison of the three cases (no additional damping, parallel damping, serial damping) revealed that serial damping at a physiological magnitude suffices to explain damping of high-frequency vibrations of low amplitudes. The simulation demonstrates that any undamped serial structure within the MTC enforces SEE-load eigenoscillations. Consequently, damping must be spread all over the MTC, i.e., rather has to be de-localised than localised within just the active muscle material. Additionally, due to suppressed eigenoscillations Hill-type muscle models taking into account serial damping are numerically more efficient when used in macroscopic biomechanical neuro-musculo-skeletal models.
By following the common definition of forward-dynamics simulations, i.e. predicting movement based on (neural) muscle activity, this work describes, for the first time, a forward-dynamics simulation framework of a musculoskeletal system, in which all components are represented as continuous, three-dimensional, volumetric objects. Within this framework, the mechanical behaviour of the entire muscle-tendon complex is modelled as a nonlinear hyperelastic material undergoing finite deformations. The feasibility and the full potential of the proposed forward-dynamics simulation framework is demonstrated on a two-muscle, three-dimensional, continuum-mechanical model of the upper limb. The musculoskeletal model consists of three bones, i.e. humerus, ulna, and radius, an one-degree-of-freedom elbow joint, and an antagonistic muscle pair, i.e. the biceps and triceps brachii, and takes into consideration the contact between the skeletal muscles and the humerus. Numerical studies have shown that the proposed upper limb model is capable of predicting realistic moment arms and muscle forces for the entire range of activation and motion. Within the limitations of the model, the presented simulations provide, for the first time, insights into existing contact forces and their influence on the muscle fibre stretch. Based on the presented simulations, the overall change in fibre stretch is typically less than 3%, despite the fact that the contact forces reach up to 71% of the exerted muscle force. Movement-predicting simulations are achieved by minimising a nonlinear moment equilibrium equation. Based on the forward-dynamics simulation approach, an iterative solution procedures for position-driven (inverse dynamics) and force-driven scenarios have been proposed accordingly. Applying these methodologies to time-dependent scenarios demonstrates that the proposed methods can be linked to state-of-the-art control algorithms predicting time-dependent muscle activation levels based on principles of forward dynamics.
Determining the internal dynamics of the human spine's biological structure is one essential step that allows enhanced understanding of spinal degeneration processes. The unavailability of internal load figures in other methods highlights the importance of the forward dynamics approach as the most powerful approach to examine the internal degeneration of spinal structures. Consequently, a forward dynamics full-body model of the human body with a detailed lumbar spine is introduced. The aim was to determine the internal dynamics and the contribution of different spinal structures to loading. The multi-body model consists of the lower extremities, two feet, shanks and thighs, the pelvis, five lumbar vertebrae, and a lumped upper body including the head and both arms. All segments are modelled as rigid bodies. 202 muscles (legs, back, abdomen) are included as Hill-type elements. 58 nonlinear force elements are included to represent all spinal ligaments. The lumbar intervertebral discs were modelled nonlinearly. As results, internal kinematics, muscle forces, and internal loads for each biological structure are presented. A comparison between the nonlinear (new, enhanced modelling approach) and linear (standard modelling approach, bushing) modelling approaches of the intervertebral disc is presented. The model is available to all researchers as ready-to-use C/C++ code within our in-house multi-body simulation code demoa with all relevant binaries included.
In this study, we investigated to which extent Hill-type muscle models can explain the electromechanical delay (EMD). The EMD is a phenomenon that has been well examined in muscle experiments. The EMD is the time lag between a change in muscle stimulation and the subsequent measurable change in muscle force. A variety of processes as, e.g., signal conduction and interaction of contractile and elastic muscle structures contribute to the EMD. The relative contributions of the particular processes have not been fully unveiled so far. Thereto, we simulated isometric muscle contractions using two Hill-type muscle models. Their parameters were extracted from experiments on the cat soleus muscle. In agreement with literature data, predicted EMD values depend on muscle-tendon complex (MTC) length and increase when reducing MTC lengths. The highest EMD values (28 and 27 ms) occur at the lowest MTC length examined (78% of optimal length). Above optimal MTC length, we¯nd EMD saturation (2 ms) in one model. In the other model, the EMD slightly re-increases up to 9 ms at the highest length examined (113% of optimal length). The EMD values predicted by the two models were then compared to EMD values found in the same experiments from which the muscle parameters were extracted. At optimal MTC length, the EMD values, mapping ion release and visco-elastic interactions, predicted by both models (3.5 and 5.5 ms) just partly account for the measured § Corresponding author. value (15.8 ms). The biggest share (about 9 ms) of the remaining 11 ms can be attributed to signal conduction along the nerve and on the muscle surface. Further potential sources of delayed force generation are discussed.
Parallel passive-elastic elements can reduce the energy consumption and torque requirements for motors in powered legged systems. However, the hardware design for such combined actuators is challenged by the need to engage and disengage the parallel elasticity depending on the gait phase. Although clutches in the drive train are often proposed, compact and low cost solutions of clutched parallel elastic actuators have so far not been established. Here we present the design and control of an initial prototype for a parallel elastic actuator. The actuator combines a DC motor with a parallel spring that is engaged and disengaged by a commercially available, compact and low-cost electric clutch. In experiments that mimic the torque and motion patterns of knee extensor muscles in human rebounding tasks we find that the parallel spring in the prototype reduces the energy consumption of the actuator by about 80% and the peak torque requirement for the DC motor by about 66%. In addition, we find that a simple trigger-based control can reliably engage and disengage the electric clutch during the motion, allowing the spring to support the motor in rebound, to remove stored energy from the system as necessary for stopping, and to virtually disappear at the actuator output level. On the other hand, the hardware experiments also reveal that our initial design limits the precision in the torque control, and we propose specific improvements to overcome these limitations.
Computational modeling provides a framework to understand human movement control. For this approach, physiologically motivated and experimentally validated models are required to predict the dynamic interplay of the neuronal controller with the musculoskeletal biophysics. Previous studies show, that an adequate model of arm movements should consider muscle fiber contraction dynamics, parallel and serial elasticities, and activation dynamics. Numerous validated macroscopic model representations of these structures and processes exist. In this study, the influence of these structures and processes on maximum movement velocity of goal-directed arm movements was investigated by varying their mathematical model descriptions. It was found that the movement velocity strongly depends on the pre-activation of the muscles (differences up to 91.6%) and the model representing activation dynamics (differences up to 43.3%). Looking at the influence of the active muscle fibers (contractile element), the simulations reveal that velocities systematically differ depending on the width of the force-length relation (differences up to 17.4%). The series elasticity of the tendon influences the arm velocity up to 7.6%. In conclusion, in fast goal-directed arm movements from an equilibrium position, the modeling of the biophysical muscle properties influences the simulation results. To reliably distinguish between mathematical formulations by experimental validation, the initial muscular activity and the activation dynamics have to be modeled validly, as their influence excels. To this end, further experiments systematically varying the initial muscular activity would be needed.
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