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Skeletal muscle tissue has a highly complex and heterogeneous structure comprising several physical length scales. In the simplest model of muscle tissue, it can be represented as a one dimensional nonlinear spring in the direction of muscle fibres. However, at the finest level, muscle tissue includes a complex network of collagen fibres, actin and myosin proteins, and other cellular materials. This study shall derive an intermediate physical model which encapsulates the major contributions of the muscle components to the elastic response apart from activation-related along-fibre responses. The micro-mechanical factors in skeletal muscle tissue (eg. connective tissue, fluid, and fibres) can be homogenized into one material aggregate that will capture the behaviour of the combination of material components. In order to do this, the corresponding volume fractions for each type of material need to be determined by comparing the stress-strain relationship for a volume containing each material. This results in a model that accounts for the micro-mechanical features found in muscle and can therefore be used to analyze effects of neuro-muscular diseases such as cerebral palsy or muscular dystrophies. The purpose of this study is to construct a model of muscle tissue that, through choosing the correct material parameters based on experimental data, will accurately capture the mechanical behaviour of whole muscle. This model is then used to look at the impacts of the bulk modulus and material parameters on muscle deformation and strain energy-density distributions. [ABSTRACT FROM AUTHOR]

Hill-type muscle models are widely used within the field of biomechanics to predict and understand muscle behaviour, and are often essential where muscle forces cannot be directly measured. However, these models have limited accuracy, particularly during cyclic contractions at the submaximal levels of activation that typically occur during locomotion. To address this issue, recent studies have incorporated effects into Hill-type models that are oftentimes neglected, such as size-dependent, history-dependent, and activation-dependent effects. However, the contribution of these effects on muscle performance has yet to be evaluated under common contractile conditions that reflect the range of activations, strains, and strain rates that occur in vivo. The purpose of this study was to develop a modelling framework to evaluate modifications to Hill-type muscle models when they contract in cyclic loops that are typical of locomotor muscle function. Here we present a modelling framework composed of a damped harmonic oscillator in series with a Hill-type muscle actuator that consists of a contractile element and parallel elastic element. The intrinsic force-length and force-velocity properties are described using Bezier curves where we present a system to relate physiological parameters to the control points for these curves. The muscle-oscillator system can be geometrically scaled while preserving dynamic and kinematic similarity to investigate the muscle size effects while controlling for the dynamics of the harmonic oscillator. The model is driven by time-varying muscle activations that cause the muscle to cyclically contract and drive the dynamics of the harmonic oscillator. Thus, this framework provides a platform to test current and future Hill-type model formulations and explore factors affecting muscle performance in muscles of different sizes under a range of cyclic contractile conditions. [ABSTRACT FROM AUTHOR]

Background: Osteoclasts, cells responsible for bone resorption, contribute to the development of degenerative, metabolic and neoplastic bone diseases, which are often characterized by persistent changes in bone microenvironment. We aimed to investigate the dynamics of osteoclast formation and death in cultures that considerably exceeded the length of standard protocol and to design a mathematical model describing osteoclastogenesis. Methodology/Principal Findings: RAW 264.7 monocytic cells fuse to form multinucleated osteoclasts upon treatment with pro-resorptive cytokine RANKL. We have found that in long-term experiments (15-26 days), the dynamics of changes in osteoclast numbers was remarkably complex and qualitatively variable in different experiments. Whereas 19 of 46 experiments exhibited single peak of osteoclast formation, in 27 experiments we observed development of successive waves of osteoclast formation and death. Periodic changes in osteoclast numbers were confirmed in long-term cultures of mouse bone marrow cells treated with M-CSF and RANKL. Because the dynamics of changes in osteoclast numbers was found to be largely independent of monocytes, a two-species model of ordinary differential equations describing the changes in osteoclasts and monocytes was ineffective in recapitulating the oscillations in osteoclast numbers. Following experimental observation that medium collected from mature osteoclasts inhibited osteoclastogenesis in fresh cultures, we introduced a third variable, factor f, to describe osteoclast-derived inhibitor. This model allowed us to simulate the oscillatory changes in osteoclasts, which were coupled to oscillatory changes in the factor f, whereas monocytes changed exponentially. Importantly, to achieve the experimentally observed oscillations with increasing amplitude, we also had to assume that osteoclast presence stimulates osteoclast formation. Conclusions/Significance: This study identifies the critical role for osteoclast autocrine regulation in controlling long-term dynamic of osteoclast formation and death and describes the complementary roles for negative and positive feedback mediators in determining the sharp dynamics of activation and inactivation of osteoclasts. [ABSTRACT FROM AUTHOR]