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Register a new userThe energy of muscle contraction. I. Tissue force and deformation during isometric contractions
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During contraction the energy of muscle tissue increases due to energy from the hydrolysis of ATP. This energy is distributed across the tissue as strain-energy potentials in the contractile elements, strain-energy potential from the 3D deformation of the base-material tissue (containing cellular and ECM effects), energy related to changes in the muscles nearly incompressible volume and external work done at the muscle surface. Thus, energy is redistributed through the muscles tissue as it contracts, with only a component of this energy being used to do mechanical work and develop forces in the muscles line-of-action. Understanding how the strain-energy potentials are redistributed through the muscle tissue will help enlighten why the mechanical performance of whole muscle in its line-of-action does not match the performance that would be expected from the contractile elements alone. Here we demonstrate these physical effects using a 3D muscle model based on the finite element method. The tissue deformations within contracting muscle are large, and so the mechanics of contraction were explained using the principles of continuum mechanics for large deformations. We present simulations of a contracting medial gastrocnemius muscle, showing tissue deformations that mirror observations from MRI-based images. This paper tracks the redistribution of strain-energy potentials through the muscle tissue during isometric contractions, and shows how fibre shortening, pennation angle, transverse bulging and anisotropy in the stress and strain of the muscle tissue are all related to the interaction between the material properties of the muscle and the action of the contractile elements.
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Mechanical characterization of brain tissue has been investigated extensively by various research groups over the past fifty years. These properties are particularly important for modelling Traumatic Brain Injury (TBI). In this research, we present the design and calibration of a High Rate Tension Device (HRTD) capable of performing tests up to a maximum strain rate of 90/s. We use experimental and numerical methods to investigate the effects of inhomogeneous deformation of porcine brain tissue during tension at different specimen thicknesses (4.0-14.0 mm), by performing tension tests at a strain rate of 30/s. One-term Ogden material parameters (mu = 4395.0 Pa, alpha = -2.8) were derived by performing an inverse finite element analysis to model all experimental data. A similar procedure was adopted to determine Youngs modulus (E= 11200 Pa) of the linear elastic regime. Based on this analysis, brain specimens of aspect ratio (diameter/thickness) S < 1.0 are required to minimise the effects of inhomogeneous deformation during tension tests.
In embryonic development, programmed cell shape changes are essential for building functional organs, but in many cases the mechanisms that precisely regulate these changes remain unknown. We propose that fluid-like drag forces generated by the motion of an organ through surrounding tissue could generate changes to its structure that are important for its function. To test this hypothesis, we study the zebrafish left-right organizer, Kupffers vesicle (KV), using experiments and mathematical modeling. During development, monociliated cells that comprise the KV undergo region-specific shape changes along the anterior-posterior axis that are critical for KV function: anterior cells become long and thin, while posterior cells become short and squat. Here, we develop a mathematical vertex-like model for cell shapes, which incorporates both tissue rheology and cell motility, and constrain the model parameters using previously published rheological data for the zebrafish tailbud [Serwane et al.] as well as our own measurements of the KV speed. We find that drag forces due to dynamics of cells surrounding the KV could be sufficient to drive KV cell shape changes during KV development. More broadly, these results suggest that cell shape changes could be driven by dynamic forces not typically considered in models or experiments.
We consider a mathematical model for wound contraction, which is based on solving a momentum balance under the assumptions of isotropy, homogeneity, Hookes Law, infinitesimal strain theory and point forces exerted by cells. However, point forces, described by Dirac Delta distributions lead to a singular solution, which in many cases may cause trouble to finite element methods due to a low degree of regularity. Hence, we consider several alternatives to address point forces, that is, whether to treat the region covered by the cells that exert forces as part of the computational domain or as holes in the computational domain. The formalisms develop into the immersed boundary approach and the hole approach, respectively. Consistency between these approaches is verified in a theoretical setting, but also confirmed computationally. However, the hole approach is much more expensive and complicated for its need of mesh adaptation in the case of migrating cells while it increases the numerical accuracy, which makes it hard to adapt to the multi-cell model. Therefore, for multiple cells, we consider the polygon that is used to approximate the boundary of cells that exert contractile forces. It is found that a low degree of polygons, in particular triangular or square shaped cell boundaries, already give acceptable results in engineering precision, so that it is suitable for the situation with a large amount of cells in the computational domain.
Electromagnetic crimping is a high-velocity joining method to join highly conductive workpieces where a pulsed magnetic field is applied without any working medium or mechanical contact to deform the workpiece. This work explores tube-to-tube joining of Copper outer tube and Stainless steel threaded inner tube using electromagnetic crimping. A non-coupled simulation model is developed for the finite element analysis. ANSYS Maxwell package is used to obtain the magnetic field intensity, which is later converted to pressure using an analytical equation, and this pressure is applied to the two-tube working domain in ANSYS Explicit Dynamics. Numerical simulations are done for different combinations of discharge energies and pitches of the thread to analyse deformation, stress and strain. The converged finite element results are validated using experimental data. The amount of deformation is found to be proportional to discharge energy and the pitch of the thread used. An empirical relation is developed for the deformation as a function of discharge energy and pitch. The relation is able to predict the deformation for other discharge energies, which is later verified with ANSYS simulations.
The main aim of this paper is to solve an inverse source problem for a general nonlinear hyperbolic equation. Combining the quasi-reversibility method and a suitable Carleman weight function, we define a map of which fixed point is the solution to the inverse problem. To find this fixed point, we define a recursive sequence with an arbitrary initial term by the same manner as in the classical proof of the contraction principle. Applying a Carleman estimate, we show that the sequence above converges to the desired solution with the exponential rate. Therefore, our new method can be considered as an analog of the contraction principle. We rigorously study the stability of our method with respect to noise. Numerical examples are presented.
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