In the present paper, a new concept for the modelling of skeletal muscles is proposed. An important aspect is the fact that the concept is micromechanically motivated. At the level of the contractile muscle fibres we incorporate the behaviour of the smallest possible unit, the so-called sarcomere, also known as microbiological engine. The contractile fibres (active part of the material) are surrounded by a soft tissue network (passive part of the material). One fundamental advantage of micromechanical approaches in general is the fact that the number of material parameters can be noticeably reduced and the remaining parameters can be usually interpreted physically. The chosen modelling strategy enables the efficient transport of the known information about physiological processes in the fibre to the 3D macroscopic level where, e.g. the dependence of muscle contraction on the stimulus rate is studied. The paper closes with investigations of quasistatic as well as dynamic simulation applied on idealised and non-idealised muscle geometries.
Skeletal muscle responds to passive overstretch through sarcomerogenesis, the creation and serial deposition of new sarcomere units. Sarcomerogenesis is critical to muscle function: It gradually re-positions the muscle back into its optimal operating regime. Animal models of immobilization, limb lengthening, and tendon transfer have provided significant insight into muscle adaptation in vivo. Yet, to date, there is no mathematical model that allows us to predict how skeletal muscle adapts to mechanical stretch in silico. Here we propose a novel mechanistic model for chronic longitudinal muscle growth in response to passive mechanical stretch. We characterize growth through a single scalar-valued internal variable, the serial sarcomere number. Sarcomerogenesis, the evolution of this variable, is driven by the elastic mechanical stretch. To analyze realistic three-dimensional muscle geometries, we embed our model into a nonlinear finite element framework. In a chronic limb lengthening study with a muscle stretch of 1.14, the model predicts an acute sarcomere lengthening from 3.09m to 3.51m, and a chronic gradual return to the initial sarcomere length within two weeks. Compared to the experiment, the acute model error was 0.00% by design of the model; the chronic model error was 2.13%, which lies within the rage of the experimental standard deviation. Our model explains, from a mechanistic point of view, why gradual multi-step muscle lengthening is less invasive than single-step lengthening. It also explains regional variations in sarcomere length, shorter close to and longer away from the muscle-tendon interface. Once calibrated with a richer data set, our model may help surgeons to prevent muscle overstretch and make informed decisions about optimal stretch increments, stretch timing, and stretch amplitudes. We anticipate our study to open new avenues in orthopedic and reconstructive surgery and enhance treatment for patients with ill proportioned limbs, tendon lengthening, tendon transfer, tendon tear, and chronically retracted muscles.
In recent years, the advances in microbiology show that biofilms are structurally complex, dynamic and adaptable systems including attributes of multicellular organisms and miscellaneous ecosystems. One may distinguish between beneficial and harmful biofilms appearing in daily life as well as various industrial processes. In order to advance the growth of the former or prevent the latter type of biofilm, a detailed understanding of its properties is indispensable. Besides microbiological aspects, this concerns the determination of mechanical characteristics, which provides the basis for material modelling. In the present paper the existing experimental methods that have been proposed since the 1980s are reviewed and critically discussed with respect to their usefulness and applicability to develop numerical modelling approaches.
The vastly increasing number of neuro-muscular simulation studies (with increasing numbers of muscles used per simulation) is in sharp contrast to a narrow database of necessary muscle parameters. Simulation results depend heavily on rough parameter estimates often obtained by scaling of one muscle parameter set. However, in vivo muscles differ in their individual properties and architecture. Here we provide a comprehensive dataset of dynamic (n = 6 per muscle) and geometric (three-dimensional architecture, n = 3 per muscle) muscle properties of the rabbit calf muscles gastrocnemius, plantaris, and soleus. For completeness we provide the dynamic muscle properties for further important shank muscles (flexor digitorum longus, extensor digitorum longus, and tibialis anterior; n = 1 per muscle). Maximum shortening velocity (normalized to optimal fiber length) of the gastrocnemius is about twice that of soleus, while plantaris showed an intermediate value. The force-velocity relation is similar for gastrocnemius and plantaris but is much more bent for the soleus. Although the muscles vary greatly in their three-dimensional architecture their mean pennation angle and normalized force-length relationships are almost similar. Forces of the muscles were enhanced in the isometric phase following stretching and were depressed following shortening compared to the corresponding isometric forces. While the enhancement was independent of the ramp velocity, the depression was inversely related to the ramp velocity. The lowest effect strength for soleus supports the idea that these effects adapt to muscle function. The careful acquisition of typical dynamical parameters (e.g. force-length and force-velocity relations, force elongation relations of passive components), enhancement and depression effects, and 3D muscle architecture of calf muscles provides valuable comprehensive datasets for e.g. simulations with neuro-muscular models, development of more realistic muscle models, or simulation of muscle packages.
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