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Register a new userOn propagation of waves in pressurized fiber-reinforced hyperelastic tubes based on a reduced model
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A refined dynamic finite-strain shell theory for incompressible hyperelastic materials was developed by the authors recently. In this paper, we first derive the associated linearized incremental theory, and then use it to investigate wave propagation in a fiber-reinforced hyperelastic tube that is subjected to an axial pre-stretch and internal pressure. We obtain the dispersion relations for both axisymmetric and non-axisymmetric waves and discuss their accuracy by comparing them with the exact dispersion relations. The bending effect is also examined by comparing the dispersion curves based on the present theory and membrane theory, respectively. It is shown that the present theory is more accurate than the membrane theory in studying wave propagation and the bending effect plays an important role in some wave modes for relatively large wavenumbers. The effects of the pressure, axial pre-stretch and fiber angle on the dispersion relations are displayed. These results provide a theoretical foundation for wave propagation in arteries, which can be used to determine arterial properties.
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In the emerging field of 3D bioprinting, cell damage due to large deformations is considered a main cause for cell death and loss of functionality inside the printed construct. Those deformations, in turn, strongly depend on the mechano-elastic response of the cell to the hydrodynamic stresses experienced during printing. In this work, we present a numerical model to simulate the deformation of biological cells in arbitrary three-dimensional flows. We consider cells as an elastic continuum according to the hyperelastic Mooney-Rivlin model. We then employ force calculations on a tetrahedralized volume mesh. To calibrate our model, we perform a series of FluidFM(R) compression experiments with REF52 cells demonstrating that all three parameters of the Mooney-Rivlin model are required for a good description of the experimental data at very large deformations up to 80%. In addition, we validate the model by comparing to previous AFM experiments on bovine endothelial cells and artificial hydrogel particles. To investigate cell deformation in flow, we incorporate our model into Lattice Boltzmann simulations via an Immersed-Boundary algorithm. In linear shear flows, our model shows excellent agreement with analytical calculations and previous simulation data.
Soft materials can be designed with a functionally graded (FG) property for specific applications. In this paper, we analyze the axisymmetric guided wave propagation in a pressurized FG elastomeric hollow cylinder. The cylinder is subjected to a combined action of axial pre-stretch and pressure difference applied to the inner and outer cylindrical surfaces. We consider both torsional waves and longitudinal waves propagating in the FG cylinder made of incompressible isotropic elastomer, which is characterized by the Mooney-Rivlin strain energy function but with the material parameters varying with the radial coordinate in an affine way. The pressure difference generates an inhomogeneous deformation field in the FG cylinder, which dramatically complicates the superimposed wave problem described by the small-on-large theory. A particularly efficient approach is hence employed which combines the state-space formalism for the incremental wave motion with the approximate laminate or multi-layer technique. Dispersion relations for the two types of axisymmetric guided waves are then derived analytically. The accuracy and convergence of the proposed approach is validated numerically. The effects of the pressure difference, material gradient, and axial pre-stretch on both the torsional and the longitudinal wave propagation characteristics are discussed in detail through numerical examples. It is found that the frequency of axisymmetric waves depends nonlinearly on the pressure difference and the material gradient, and an increase in the material gradient enhances the capability of the pressure difference to adjust the wave behavior in the FG cylinder.
It is suggested that the propagation of the action potential is accompanied by an axoplasmic pressure pulse propagating in the axoplasm along the axon length. The pressure pulse stretch-modulates voltage-gated Na (Nav) channels embedded in the axon membrane, causing their accelerated activation and inactivation and increasing peak channel conductance. As a result, the action potential propagates due to mechano-electrical activation of Nav channels by straggling ionic currents and the axoplasmic pressure pulse. The velocity of such propagation is higher than in the classical purely electrical Nav activation mechanism, and it may be close to the velocity of propagation of pressure pulses in the axoplasm. Extracellular Ca ions influxing during the voltage spike, or Ca ions released from intracellular stores, may trigger a mechanism that generates and augments the pressure pulse, thus opposing its viscous decay. The model can potentially explain a number of phenomena that are not contained within the purely electrical Hodgkin-Huxley-type framework: the Meyer-Overton rule for the effectiveness of anesthetics, as well as various mechanical, optical and thermodynamic phenomena accompanying the action potential. It is shown that the velocity of propagation of axoplasmic pressure pulses is close to the measured velocity of the nerve impulse, both in absolute magnitude and in dependence on axon diameter, degree of myelination and temperature.
Many systems such as critical infrastructure exhibit a modular structure with many links within the modules and few links between them. One approach to increase the robustness of these systems is to reinforce a fraction of the nodes in each module, so that the reinforced nodes provide additional needed sources for themselves as well as for their nearby neighborhood. Since reinforcing a node can be an expensive task, the efficiency of the decentralization process by reinforced nodes is vital. In our study we analyze a new model which combines both above mentioned features of real complex systems - modularity and reinforced nodes. Using tools from percolation theory, we derived an analytical solution for any partition of reinforced nodes; between nodes which have links that connect them to other modules (inter-nodes) and nodes which have connections only within their modules (intra-nodes). Among our results, we find that near the critical percolation point ($papprox p_c$) the robustness is greatly affected by the distribution. In particular, we find a partition of reinforced nodes which yields an optimal robustness and we show that the optimal partition remains constant for high average degrees.
Transcription is the first step of gene expression, in which a particular segment of DNA is copied to RNA by the enzyme RNA polymerase (RNAP). Despite many details of the complex interactions between DNA and RNA synthesis disclosed experimentally, much of physical behavior of transcription remains largely unknown. Understanding torsional mechanics of DNA and RNAP together with its nascent RNA and RNA-bound proteins in transcription maybe the first step towards deciphering the mechanism of gene expression. In this study, based on the balance between viscous drag on RNA synthesis and torque resulted from untranscribed supercoiled DNA template, a simple model is presented to describe mechanical properties of transcription. With this model, the rotation and supercoiling density of the untranscribed DNA template are discussed in detail. Two particular cases of transcription are considered, transcription with constant velocity and transcription with torque dependent velocity. Our results show that, during the initial stage of transcription, rotation originated from the transcribed part of DNA template is mainly released by the rotation of RNAP synthesis. During the intermediate stage, the rotation is usually released by both the supercoiling of the untranscribed part of DNA template and the rotation of RNAP synthesis, with proportion depending on the friction coefficient in environment and the length of nascent RNA. However, with the approaching to the upper limit of twisting of the untranscribed DNA template, the rotation resulted from transcription will then be mainly released by the rotation of RNAP synthesis.
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