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    Variations in muscle activity and exerted torque during temporary blood flow restriction in healthy individuals
    (2021) Gizzi, Leonardo; Yavuz, Utku Ş.; Hillerkuss, Dominic; Geri, Tommaso; Gneiting, Elena; Domeier, Franziska; Schmitt, Syn; Röhrle, Oliver
    Recent studies suggest that transitory blood flow restriction (BFR) may improve the outcomes of training from anatomical (hypertrophy) and neural control perspectives. Whilst the chronic consequences of BFR on local metabolism and tissue adaptation have been extensively investigated, its acute effects on motor control are not yet fully understood. In this study, we compared the neuromechanical effects of continuous BFR against non-restricted circulation (atmospheric pressure-AP), during isometric elbow flexions. BFR was achieved applying external pressure either between systolic and diastolic (lower pressure-LP) or 1.3 times the systolic pressure (higher pressure-HP). Three levels of torque (15, 30, and 50% of the maximal voluntary contraction-MVC) were combined with the three levels of pressure for a total of 9 (randomized) test cases. Each condition was repeated 3 times. The protocol was administered to 12 healthy young adults. Neuromechanical measurements (torque and high-density electromyography-HDEMG) and reported discomfort were used to investigate the response of the central nervous system to BFR. The investigated variables were: root mean square (RMS), and area under the curve in the frequency domain-for the torque, and average RMS, median frequency and average muscle fibres conduction velocity-for the EMG. The discomfort caused by BFR was exacerbated by the level of torque and accumulated over time. The torque RMS value did not change across conditions and repetitions. Its spectral content, however, revealed a decrease in power at the tremor band (alpha-band, 5-15 Hz) which was enhanced by the level of pressure and the repetition number. The EMG amplitude showed no differences whilst the median frequency and the conduction velocity decreased over time and across trials, but only for the highest levels of torque and pressure. Taken together, our results show strong yet transitory effects of BFR that are compatible with a motor neuron pool inhibition caused by increased activity of type III and IV afferences, and a decreased activity of spindle afferents. We speculate that a compensation of the central drive may be necessary to maintain the mechanical output unchanged, despite disturbances in the afferent volley to the motor neuron pool.
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    Comparative sensitivity analysis of muscle activation dynamics
    (2015) Rockenfeller, Robert; Günther, Michael; Schmitt, Syn; Götz, Thomas
    We 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.
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    Editorial - somatosensory integration in human movement : perspectives for neuromechanics, modelling and rehabilitation
    (2021) Gizzi, Leonardo; Vujaklija, Ivan; Sartori, Massimo; Röhrle, Oliver; Severini, Giacomo
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    Modeling the chemoelectromechanical behavior of skeletal muscle using the parallel open-source software library OpenCMISS
    (2013) Heidlauf, Thomas; Röhrle, Oliver
    An extensible, flexible, multiscale and multiphysics model for non-isometric skeletal muscle behavior is presented. The skeletal muscle chemoelectromechanical model is based on a bottom-up approach modeling the entire excitation-contraction pathway by strongly coupling a detailed biophysical model of a half-sarcomere to the propagation of action potentials along skeletal muscle fibers, and linking cellular parameters to a transversely isotropic continuum-mechanical constitutive equation describing the overall mechanical behavior of skeletal muscle tissue. Since the multiscale model exhibits separable time scales, a special emphasis is placed on employing computationally efficient staggered solution schemes. Further, the implementation builds on the open-source software library OpenCMISS and uses state-ofthe-art parallelization techniques taking advantage of the unique anatomical fiber architecture of skeletal muscles. OpenCMISS utilizes standardized data structures for geometrical aspects (FieldML) and cellular models (CellML). Both standards are designed to allow for a maximum on flexibility, reproducibility, and extensibility. The results demonstrate the model´s capability of simulating different aspects of non-isometric muscle contraction and to efficiently simulate the chemoelectromechanical behavior in complex skeletal muscles such as the tibialis anterior muscle.
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    A physiology-guided classification of active-stress and active-strain approaches for continuum-mechanical modeling of skeletal muscle tissue
    (2021) Klotz, Thomas; Bleiler, Christian; Röhrle, Oliver
    The well-established sliding filament and cross-bridge theory explain the major biophysical mechanism responsible for a skeletal muscle's active behavior on a cellular level. However, the biomechanical function of skeletal muscles on the tissue scale, which is caused by the complex interplay of muscle fibers and extracellular connective tissue, is much less understood. Mathematical models provide one possibility to investigate physiological hypotheses. Continuum-mechanical models have hereby proven themselves to be very suitable to study the biomechanical behavior of whole muscles or entire limbs. Existing continuum-mechanical skeletal muscle models use either an active-stress or an active-strain approach to phenomenologically describe the mechanical behavior of active contractions. While any macroscopic constitutive model can be judged by it's ability to accurately replicate experimental data, the evaluation of muscle-specific material descriptions is difficult as suitable data is, unfortunately, currently not available. Thus, the discussions become more philosophical rather than following rigid methodological criteria. Within this work, we provide a extensive discussion on the underlying modeling assumptions of both the active-stress and the active-strain approach in the context of existing hypotheses of skeletal muscle physiology. We conclude that the active-stress approach resolves an idealized tissue transmitting active stresses through an independent pathway. In contrast, the active-strain approach reflects an idealized tissue employing an indirect, coupled pathway for active stress transmission. Finally the physiological hypothesis that skeletal muscles exhibit redundant pathways of intramuscular stress transmission represents the basis for considering a mixed-active-stress-active-strain constitutive framework.
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    Symplectic model order reduction with non-orthonormal bases
    (2019) Buchfink, Patrick; Bhatt, Ashish; Haasdonk, Bernard
    Parametric high-fidelity simulations are of interest for a wide range of applications. But the restriction of computational resources renders such models to be inapplicable in a real-time context or in multi-query scenarios. Model order reduction (MOR) is used to tackle this issue. Recently, MOR is extended to preserve specific structures of the model throughout the reduction, e.g. structure-preserving MOR for Hamiltonian systems. This is referred to as symplectic MOR. It is based on the classical projection-based MOR and uses a symplectic reduced order basis (ROB). Such a ROB can be derived in a data-driven manner with the Proper Symplectic Decomposition (PSD) in the form of a minimization problem. Due to the strong nonlinearity of the minimization problem, it is unclear how to efficiently find a global optimum. In our paper, we show that current solution procedures almost exclusively yield suboptimal solutions by restricting to orthonormal ROBs. As new methodological contribution, we propose a new method which eliminates this restriction by generating non-orthonormal ROBs. In the numerical experiments, we examine the different techniques for a classical linear elasticity problem and observe that the non-orthonormal technique proposed in this paper shows superior results with respect to the error introduced by the reduction.
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    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, Syn
    In 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.
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    Tailoring enhanced optical chirality : design principles for chiral plasmonic nanostructures
    (2012) Schäferling, Martin; Dregely, Daniel; Hentschel, Mario; Giessen, Harald
    Electromagnetic fields with strong optical chirality can be formed in the near-field of chiral plasmonic nanostructures. We calculate and visualize the degree of chirality to identify regions with relatively high values. This leads to design principles for a simple utilization of chiral fields. We investigate planar geometries which offer a convenient way to access the designated fields as well as three-dimensional nanostructures which show a very high local optical chirality.
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    A physiologically based, multi-scale model of skeletal muscle structure and function
    (2012) Röhrle, Oliver; Davidson, John B.; Pullan, Andrew J.
    Models of skeletal muscle can be classified as phenomenological or biophysical. Phenomenological models predict the muscle’s response to a specified input based on experimental measurements. Prominent phenomenological models are the Hill-type muscle models, which have been incorporated into rigid-body modeling frameworks, and three-dimensional continuum-mechanical models. Biophysically based models attempt to predict the muscle’s response as emerging from the underlying physiology of the system. In this contribution, the conventional biophysically based modeling methodology is extended to include several structural and functional characteristics of skeletal muscle. The result is a physiologically based, multi-scale skeletal muscle finite element model that is capable of representing detailed, geometrical descriptions of skeletal muscle fibers and their grouping. Together with a well-established model of motor-unit recruitment, the electro-physiological behavior of single muscle fibers within motor units is computed and linked to a continuummechanical constitutive law. The bridging between the cellular level and the organ level has been achieved via a multi-scale constitutive law and homogenization. The effect of homogenization has been investigated by varying the number of embedded skeletal muscle fibers and/or motor units and computing the resulting exerted muscle forces while applying the same excitatory input. All simulations were conducted using an anatomically realistic finite element model of the tibialis anterior muscle. Given the fact that the underlying electro-physiological cellular muscle model is capable of modeling metabolic fatigue effects such as potassium accumulation in the T-tubular space and inorganic phosphate build-up, the proposed framework provides a novel simulation-based way to investigate muscle behavior ranging from motor-unit recruitment to force generation and fatigue.