A Physiologically Based, Multi-Scale Model of Skeletal Muscle Structure and Function

Röhrle, Oliver; Davidson, John B.; Pullan, Andrew J.

doi:10.3389/fphys.2012.00358

Cited by 82 publications

(90 citation statements)

References 63 publications

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“…The bipennate muscle fibre directions are based on DT-MRI data [42]. The geometry of the muscle without the fat/skin tissue has previously been used in [18,36,43]. To reduce complexity and computational time, only 2700 muscle fibres are considered that are grouped into 10 MUs.…”

Section: Tibialis Anteriormentioning

confidence: 99%

Predicting electromyographic signals under realistic conditions using a multiscale chemo–electro–mechanical finite element model

2015

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One contribution of 11 to a theme issue 'Multiscale modelling in biomechanics: theoretical, computational and translational challenges'. This paper presents a novel multiscale finite element-based framework for modelling electromyographic (EMG) signals. The framework combines (i) a biophysical description of the excitation-contraction coupling at the half-sarcomere level, (ii) a model of the action potential (AP) propagation along muscle fibres, (iii) a continuum-mechanical formulation of force generation and deformation of the muscle, and (iv) a model for predicting the intramuscular and surface EMG. Owing to the biophysical description of the half-sarcomere, the model inherently accounts for physiological properties of skeletal muscle. To demonstrate this, the influence of membrane fatigue on the EMG signal during sustained contractions is investigated. During a stimulation period of 500 ms at 100 Hz, the predicted EMG amplitude decreases by 40% and the AP propagation velocity decreases by 15%. Further, the model can take into account contraction-induced deformations of the muscle. This is demonstrated by simulating fixed-length contractions of an idealized geometry and a model of the human tibialis anterior muscle (TA). The model of the TA furthermore demonstrates that the proposed finite element model is capable of simulating realistic geometries, complex fibre architectures, and can include different types of heterogeneities. In addition, the TA model accounts for a distributed innervation zone, different fibre types and appeals to motor unit discharge times that are based on a biophysical description of the a motor neurons.

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Section: Tibialis Anteriormentioning

confidence: 99%

Predicting electromyographic signals under realistic conditions using a multiscale chemo–electro–mechanical finite element model

2015

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“…To decrease the computational effort for solving (4), projection-based model order reduction techniques are applied. Here, the reduced basis is obtained by means of a proper orthogonal decomposition (POD).…”

Section: Methodsmentioning

confidence: 99%

“…The nonlinear constitutive equation used in this work follows the general setup of [3,4]. Therein, muscle tissue, is modelled as hyperelastic, homogeneous, transversely isotropic and incompressible material.…”

Section: Skeletal Muscle Modelmentioning

confidence: 99%

“…Additionally, this governing equation is subject to an incompressibility constraint equation, which restricts the set of admissible states, to ensure that no volumetric change occurs. With F being the deformation gradient and J := detF the Jacobian or volume ratio, the incompressibility constraint readsThe nonlinear constitutive equation used in this work follows the general setup of [3,4]. Therein, muscle tissue, is modelled as hyperelastic, homogeneous, transversely isotropic and incompressible material.…”

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confidence: 99%

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Model order reduction of dynamic skeletal muscle models

Mordhorst

Wirtz

Röhrle

2016

Proc Appl Math and Mech

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Forward-dynamics simulations of three-dimensional continuum-mechanical skeletal muscle models are a complex and computationally expensive problem. Considering a fully dynamic modelling framework based on the theory of finite elasticity is challenging as the muscles' mechanical behaviour requires to consider a highly nonlinear, viscoelastic and incompressible material behaviour. The governing equations yield a nonlinear second-order differential algebraic equation (DAE), which represents a challenge to model order reduction (MOR) techniques. This contribution shows the results of the offline phase that could be obtained so far by applying a combination of the proper orthogonal decomposition (POD) and the discrete empirical interpolation method (DEIM). MotivationModelling and simulation of the human movement to predict, for example, joint loading, has been a topic of interest for many years (c.f. [1]). State of the art multi-body models include skeletal muscles as one-dimensional objects, which of course do not properly represent reality. Consequently, more realistic three-dimensional continuum-mechanical skeletal muscle models based on realistic muscle geometries are developed. Such models are able to simulate the muscle deformation and forces due to a stimulation (forward simulations, c.f. [2]). Needless to say, that the continuum-mechanical approach requires substantially more computational effort if compared to the one-dimensional model context. Particularly if multi-muscle systems are considered or within the many-query context, the three-dimensional muscle models become prohibitively expensive. This is where model order reduction (MOR) offers an effective remedy. Skeletal muscle modelThe motion and deformation of a continuous muscle, whose shape corresponds to the reference domain Ω 0 ⊂ R 3 , is described by means of the balance of momentumTherein, ρ 0 is the muscle density, v is the velocity field, P is the first Piola-Kirchhoff stress tensor and B denotes the body forces. Additionally, this governing equation is subject to an incompressibility constraint equation, which restricts the set of admissible states, to ensure that no volumetric change occurs. With F being the deformation gradient and J := detF the Jacobian or volume ratio, the incompressibility constraint readsThe nonlinear constitutive equation used in this work follows the general setup of [3,4]. Therein, muscle tissue, is modelled as hyperelastic, homogeneous, transversely isotropic and incompressible material. Furthermore, owing to the electrically active muscle fibres, the muscle tissue does not only exhibit passive but also active material behaviour. These assumptions yield an additive split of the strain energy function, which is inherited by the first Piola-Kirchhoff stress tensorwith p(X, t) denoting the hydrostatic pressure. Introducing a parameter µ ∈ P ⊂ R p comprising any property of the muscle model that shall be varied and using the finite element method to discretize Equations (1) and (2), leads the following second-order paramet...

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“…Röhrle et al (2012) make major advances in that arena by presenting a multi-scale, finite element model of the human tibialis anterior. Their model has the advantage of allowing simulation of fatigue at the cellular and motor unit levels, and can incorporate altered recruitment patterns of motor units due to central components of fatigue.…”

mentioning

confidence: 99%

Muscle fatigue and muscle weakness: what we know and what we wish we did

2013

Frontiers Research Topics

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This Research Topic on muscle fatigue and muscle weakness presents the latest ideas, arguments, and evidence from investigations at the molecular level to macroscopic observations on whole animals including humans, in an effort to identify critical factors underlying fatigue and weakness in health and disease. Skeletal muscles confer movement to the human body using vast amounts of energy provided through complex metabolic pathways such that whole body mobility and energy balance are largely dictated by muscle activity. Conversely, muscle function reflects overall health status as exercise history and chronic conditions affect either or both muscle quality, including protein and fat content, and muscle mass. In health, muscle fatigue is temporary and recovery occurs rapidly, and recreational or competitive athletes are always pursuing the next best fatigue "fix." However, after inactivity-whether due to lifestyle choices, injury or chronic disease-muscle fatigue may occur prematurely and persist, endangering a person's safety because weakness can lead to falls that may result in loss of independence. Individuals are then trapped in a self-perpetuating, vicious cycle of inactivity, disuse muscle atrophy/weakness, and metabolic disturbance that compounds morbidity (i.e., causing metabolic syndrome, obesity, hypertension, cachexia) and eventually premature death. Such issues transcend many scientific disciplines and it becomes evident that not only recognizing fundamental factors in muscle fatigue and muscle weakness is necessary, but also evaluating their interaction with factors outside of the muscle is essential if we aspire to design better interventions that improve muscle function and thus improve quality of life and life prognosis for the ageing population and chronic disease patients.Fatigue and weakness may stem from changes within myocytes that affect cross-bridge function or Ca 2+ activation, to changes within the circulation or function of the nervous system. Within myocytes, metabolic products of ATP hydrolysis in the cytoplasm such as inorganic phosphate (Pi), protons (H + or pH), and ADP have often been considered as agents that could disrupt force generation at the sarcomere level (Fabiato and Fabiato, 1978;

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A Physiologically Based, Multi-Scale Model of Skeletal Muscle Structure and Function

Cited by 82 publications

References 63 publications

Predicting electromyographic signals under realistic conditions using a multiscale chemo–electro–mechanical finite element model

Predicting electromyographic signals under realistic conditions using a multiscale chemo–electro–mechanical finite element model

Model order reduction of dynamic skeletal muscle models

Muscle fatigue and muscle weakness: what we know and what we wish we did

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