From Tension to Compression: Asymmetric Mechanical Behaviour of Trabecular Bone's Organic Phase

On multiscale tension-compression asymmetry in skeletal muscle

Skeletal muscle tissue shows a clear asymmetry with regard to the passive stresses under tensile and compressive deformation, referred to as tension-compression asymmetry (TCA). The present study is the first one reporting on TCA at different length scales, associated with muscle tissue and muscle fibres, respectively. This allows for the first time the comparison of TCA between the tissue and one of its individual components, and thus to identify the length scale at which this phenomenon originates. Not only the passive stress-stretch characteristics were recorded, but also the volume changes during the axial tension and compression experiments. The study reveals clear differences in the characteristics of TCA between fibres and tissue. At tissue level TCA increases non-linearly with increasing deformation and the ratio of tensile to compressive stresses at the same magnitude of strain reaches a value of approximately 130 at 13.5% deformation. At fibre level instead it initially drops to a value of 6 and then rises again to a TCA of 14. At a deformation of 13.5%, the tensile stress is about 6 times higher. Thus, TCA is about 22 times more expressed at tissue than fibre scale. Moreover, the analysis of volume changes revealed little compressibility at tissue scale whereas at fibre level, especially under compressive stress, the volume decreases significantly. The data collected in this study suggests that the extracellular matrix has a distinct role in amplifying the TCA, and leads to more incompressible tissue behaviour. STATEMENT OF SIGNIFICANCE: This article analyses and compares for the first time the tension-compression asymmetry (TCA) displayed by skeletal muscle at tissue and fibre scale. In addition, the volume changes of tissue and fibre specimens with application of passive tensile and compressive loads are studied. The study identifies a key role of the extracellular matrix in establishing the mechanical response of skeletal muscle tissue: It contributes significantly to the passive stress, it is responsible for the major part of tissue-scale TCA and, most probably, prevents/balances the volume changes of muscle fibres during deformation. These new results thus shed light on the origin of TCA and provide new information to be used in microstructure-based approaches to model and simulate skeletal muscle tissue.

Time-dependent behaviour of demineralised trabecular bone - Experimental investigation and development of a constitutive model

Trabecular bone is a cellular composite material comprising primarily of mineral and organic phases and its mechanical response to loads is time-dependent. The contribution of the organic phase to the time-dependent behaviour of bone is not yet understood. We investigated the time-dependent response of demineralised trabecular bone through tensile multiple-load-creep-unload-recovery experiments. We found that demineralised trabecular bone's time-dependent response is nonlinearly related to the applied stress levels - it stiffens with increased stress levels. Our results also indicated that the time-dependent behaviour is associated with the original bone volume ratio (BV/TV). Irrecoverable strain exists, even at the low strain levels, but are not associated with BV/TV. Furthermore, we found that the nonlinear viscoelastic model can accurately predict the time-dependent behaviour of the trabecular bone's organic phase, which can be incorporated together with the properties of mineral to generate a composite model of bone. This study will help to provide a better understanding of this natural composite material.

Investigating the passive mechanical behaviour of skeletal muscle fibres: Micromechanical experiments and Bayesian hierarchical modelling

Characterisation of the skeletal muscle's passive properties is a challenging task since its structure is dominated by a highly complex and hierarchical arrangement of fibrous components at different scales. The present work focuses on the micromechanical characterisation of skeletal muscle fibres, which consist of myofibrils, by realising three different deformation states, namely, axial tension, axial compression, and transversal compression. To the best of the authors' knowledge, the present study provides a novel comprehensive data set representing of different deformation states. These data allow for a better understanding of muscle fibre load transfer mechanisms and can be used for meaningful modelling approaches. As the present study shows, axial tension and compression experiments reveal a strong tension-compression asymmetry at fibre level. In comparison to the tissue level, this asymmetric behaviour is more pronounced at the fibre scale, elucidating the load transfer mechanism in muscle tissue and aiding in the development of future modelling strategies. Further, a Bayesian hierarchical modelling approach was used to consider the experimental fluctuations in a parameter identification scheme, leading to more comprehensive parameter distributions that reflect the entire observed experimental uncertainty. STATEMENT OF SIGNIFICANCE: This article examines for the first time the mechanical properties of skeletal muscle fibres under axial tension, axial compression, and transversal compression, leading to a highly comprehensive data set. Moreover, a Bayesian hierarchical modelling concept is presented to identify model parameters in a broad way. The results of the deformation states allow a new and comprehensive understanding of muscle fibres' load transfer mechanisms; one example is the effect of tension-compression asymmetry. On the one hand, the results of this study contribute to the understanding of muscle mechanics and thus to the muscle's functional understanding during daily activity. On the other hand, they are relevant in the fields of skeletal muscle multiscale, constitutive modelling.