Friction is an inherent factor in any real physical system, affecting, as it is natural, the dynamics of the entire system. In particular, the computation of friction losses are of special interest because friction factors can not be easily predicted theoretically in an accurate manner. In oscillatory systems friction is studied by two approaches, viscous and dry damping. Viscous damping is usually treated in physics courses due to its relatively easy-to-find analytical solution, whereas dry damping requires piece-wise solutions. This paper studies friction factors affecting a customised experimental platform for electric bikes. We seek to estimate the friction torque and then the coefficient of friction, where the damping of its amplitude will be evaluated. We study the oscillations of two different rolling systems. The first rolling system is a rowlock, and the second is a bicycle wheel axis. In both systems amplitude damping was measured and analysed. The experimental data for each rolling system was obtained by visual information, recording oscillations using a smartphone camera and then analysing it using Tracker, a freeware for video analysis. Results show that both systems behave very close to a dry damped oscillation. The model proposed matches properly the experimental data, and a value for the friction torque and coefficient of friction in both systems was estimated.
Training exercise produces skeletal muscle adaptation: at the organ scale, as anatomical changes; and at the myofiber scale, as mitochondrial and protein type content. The protein content of a myofiber is controlled by the calcineurin-NFATc signaling pathway: exercise triggers the pathway, and its final product is the translocation of dephosphorylated NFATc to the nucleus. Once in the nucleus, NFATc controls the state of the gene program to encode the slow or the fast fiber type characteristics. In the long term, the adaptation of the fiber type characteristics produces a shift in muscle fiber type: an increase in the number of myofibers of the fast type (which means that myofibers of the slow type shift to fast type) is related to force production; and an increase in the number of myofibers of the slow type (myofibers of the fast type shift to slow type) is related to fatigue resistance. These macroscopic features, i.e. force production and fatigue resistance, are the main target of most training protocols; however, little attention is focused on the limitations imposed by the fiber distribution of muscles at the organ scale. Based on the calcineurin-NFATc signaling pathway, we represented an exercise stimulus by a cytosolic calcium signal, and simulated the dynamics of NFATc in the nucleus. In this contribution, we present a dynamical model for the calcineurin-NFATc signaling pathway to describe the time course of dephosphorilated NFATc in the nucleus. We used an experimental report of a continuous stimulation pattern for calibration, and an experimental report of a pulsed stimulation pattern for comparison; we obtained a good agreement between the simulations and the experimental measurements.
Skeletal muscle adaptation is correlated to training exercise by triggering different signaling pathways that target many functions; in particular, the IGF1-AKT pathway controls protein synthesis and degradation. These two functions regulate the adaptation in size and strength of muscles. Computational models for muscle adaptation have focused on: the biochemical description of signaling pathways or the mechanical description of muscle function at organ scale; however, an interrelation between these two models should be considered to understand how an adaptation in muscle size affects the protein synthesis rate. In this research, a dynamical model for the IGF1-AKT signaling pathway is linked to a continuum-mechanical model describing the active and passive mechanical response of a muscle; this model is used to study the impact of the adaptive muscle geometry on the protein synthesis at the fiber scale. This new computational model links the signaling pathway to the mechanical response by introducing a growth tensor, and links the mechanical response to the signaling pathway through the evolution of the protein synthesis rate. The predicted increase in cross sectional area (CSA) due to an 8 weeks training protocol excellently agreed with experimental data. Further, our results show that muscle growth rate decreases, if the correlation between protein synthesis and CSA is negative. The outcome of this study suggests that multi-scale models coupling continuum mechanical properties and molecular functions may improve muscular therapies and training protocols.
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