Universität Stuttgart
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Item Open Access Comparative sensitivity analysis of muscle activation dynamics(2015) Rockenfeller, Robert; Günther, Michael; Schmitt, Syn; Götz, ThomasWe mathematically compared two models of mammalian striated muscle activation dynamics proposed by Hatze and Zajac. Both models are representative for a broad variety of biomechanical models formulated as ordinary differential equations (ODEs). These models incorporate parameters that directly represent known physiological properties. Other parameters have been introduced to reproduce empirical observations. We used sensitivity analysis to investigate the influence of model parameters on the ODE solutions. In addition, we expanded an existing approach to treating initial conditions as parameters and to calculating second- order sensitivities. Furthermore, we used a global sensitivity analysis approach to include finite ranges of parameter values. Hence, a theoretician striving for model reduction could use the method for identifying particularly low sensitivities to detect superfluous parameters. An experimenter could use it for identifying particularly high sensitivities to improve parameter estimation. Hatze’s nonlinear model incorporates some parameters to which activation dynamics is clearly more sensitive than to any parameter in Zajac’s linear model. Other than Zajac’s model, Hatze’s model can, however, reproduce measured shifts in optimal muscle length with varied muscle activity. Accordingly we extracted a specific parameter set for Hatze’s model that combines best with a particular muscle force-length relation.Item Open Access Cross-bridge mechanics estimated from skeletal muscles’ work-loop responses to impacts in legged locomotion(2021) Christensen, Kasper B.; Günther, Michael; Schmitt, Syn; Siebert, TobiasLegged locomotion has evolved as the most common form of terrestrial locomotion. When the leg makes contact with a solid surface, muscles absorb some of the shock-wave accelerations (impacts) that propagate through the body. We built a custom-made frame to which we fixated a rat (Rattus norvegicus, Wistar) muscle (m. gastrocnemius medialis and lateralis: GAS) for emulating an impact. We found that the fibre material of the muscle dissipates between 3.5 and 23μJ ranging from fresh, fully active to passive muscle material, respectively. Accordingly, the corresponding dissipated energy in a half-sarcomere ranges between 10.4 and 68zJ, respectively. At maximum activity, a single cross-bridge would, thus, dissipate 0.6% of the mechanical work available per ATP split per impact, and up to 16% energy in common, submaximal, activities. We also found the cross-bridge stiffness as low as 2.2pNnm-1, which can be explained by the Coulomb-actuating cross-bridge part dominating the sarcomere stiffness. Results of the study provide a deeper understanding of contractile dynamics during early ground contact in bouncy gait.Item Open Access Implementation and validation of the extended Hill-type muscle model with robust routing capabilities in LS-DYNA for active human body models(2017) Kleinbach, Christian; Martynenko, Oleksandr; Promies, Janik; Häufle, Daniel F. B.; Fehr, Jörg; Schmitt, SynIn the state of the art finite element AHBMs for car crash analysis in the LS-DYNA software material named *MAT_MUSCLE (*MAT_156) is used for active muscles modeling. It has three elements in parallel configuration, which has several major drawbacks: restraint approximation of the physical reality, complicated parameterization and absence of the integrated activation dynamics. This study presents implementation of the extended four element Hill-type muscle model with serial damping and eccentric force-velocity relation including Ca2+ dependent activation dynamics and internal method for physiological muscle routing.Item Open Access On laterally perturbed human stance: experiment, model, and control(2018) Suissa, Dan; Günther, Michael; Shapiro, Amir; Melzer, Itshak; Schmitt, SynItem Open Access Theoretical hill-type muscle and stability : numerical model and application(2013) Schmitt, Syn; Günther, Michael; Rupp, Tille; Bayer, Alexandra; Häufle, Daniel F. B.The construction of artificial muscles is one of the most challenging developments in today's biomedical science. The application of artificial muscles is focused both on the construction of orthotics and prosthetics for rehabilitation and prevention purposes and on building humanoid walking machines for robotics research. Research in biomechanics tries to explain the functioning and design of real biological muscles and therefore lays the fundament for the development of functional artificial muscles. Recently, the hyperbolic Hill-type force-velocity relation was derived from simple mechanical components. In this contribution, this theoretical yet biomechanical model is transferred to a numerical model and applied for presenting a proof-of-concept of a functional artificial muscle. Additionally, this validated theoretical model is used to determine force-velocity relations of different animal species that are based on the literature data from biological experiments. Moreover, it is shown that an antagonistic muscle actuator can help in stabilising a single inverted pendulum model in favour of a control approach using a linear torque generator.Item Open Access Muscle wobbling mass dynamics : eigenfrequency dependencies on activity, impact strength, and ground material(2023) Christensen, Kasper B.; Günther, Michael; Schmitt, Syn; Siebert, TobiasIn legged locomotion, muscles undergo damped oscillations in response to the leg contacting the ground (an impact). How muscle oscillates varies depending on the impact situation. We used a custom-made frame in which we clamped an isolated rat muscle ( M. gastrocnemius medialis and lateralis : GAS) and dropped it from three different heights and onto two different ground materials. In fully activated GAS, the dominant eigenfrequencies were 163 Hz, 265 Hz, and 399 Hz, which were signficantly higher (p < 0.05) compared to the dominant eigenfrequencies in passive GAS: 139 Hz, 215 Hz, and 286 Hz. In general, neither changing the falling height nor ground material led to any significant eigenfrequency changes in active nor passive GAS, respectively. To trace the eigenfrequency values back to GAS stiffness values, we developed a 3DoF model. The model-predicted GAS muscle eigenfrequencies matched well with the experimental values and deviated by - 3.8%, 9.0%, and 4.3% from the passive GAS eigenfrequencies and by - 1.8%, 13.3%, and - 1.5% from the active GAS eigenfrequencies. Differences between the frequencies found for active and passive muscle impact situations are dominantly due to the attachment of myosin heads to actin.