Self-consistent model of a pulsed air discharge excited by surface waves

A complete self-consistent electrodynamic model of a pulsed gas discharge excited by surface waves is developed. The model allows one to calculate both the initial phase of the discharge front propagation and the parameters of the produced plasma. The spatiotemporal evolution of the electromagnetic field and plasma parameters at the discharge front is investigated for the first time. It is shown that discharge propagation is mainly governed by a breakdown wave in an inhomogeneous electric field at the leading edge of the ionization front. It is found that the effect of the electric field enhancement in the plasma resonance region significantly affects the velocity of the breakdown wave. The results of calculations agree well with experimental data.     

Experimental validation of a time-domain-based wave propagation model of blood flow in viscoelastic vessels

Time-domain-based one-dimensional wave propagation models of the arterial system are preferable over one-dimensional wave propagation models in the frequency domain since the latter neglect the non-linear convection forces present in the physiological situation, especially when the vessel is tapered. Moreover, one-dimensional wave propagation models of the arterial system can be used to provide boundary conditions for fully three-dimensional fluid-structure interaction computations that are usually defined in the time domain. In this study, a time-domain-based one-dimensional wave propagation model in a cross-sectional area, flow and pressure (A,q,p)-formulation is developed. Using this formulation, a constitutive law that includes viscoelasticity based on the mechanical behaviour of a Kelvin body, is introduced. The resulting pressure and flow waves travelling through a straight and tapered vessel are compared to experimental data obtained from measurements in an in vitro setup. The model presented shows to be well suited to predict wave propagation through these straight and tapered vessels with viscoelastic wall properties and hereto can serve as a time-domain-based method to model wave propagation in the human arterial system.     

Observation and Investigation of “Reverse Breakdown” in a Discharge Tube

A discharge operating in a 80-cm-long discharge tube with an inner diameter of 15 mm, filled with a 3 : 1 neon–argon mixture at a pressure of 1 Torr, was investigated experimentally. Square voltage pulses with a period of 1 s were supplied to one of the tube electrodes, the second electrode being ungrounded. The initial stage of breakdown—the primary breakdown between the high-voltage (active) electrode and the tube wall, accompanied by the propagation of the prebreakdown ionization wave—was the same as in the conventional scheme with a grounded low-voltage electrode. Since the discharge gap was not closed, the discharge was not ignited. An essentially new effect was observed after the end of the voltage pulse. After a certain time interval, voltage spikes of opposite polarity, the amplitude and shape of which were close to those observed during the primary breakdown, appeared in the voltage and current waveforms of the active electrode. Simultaneously, a radiation pulse from the region adjacent to the active electrode was observed and an ionization wave began to propagate toward the second electrode. This work is dedicated to investigating this effect (which was named “reverse breakdown”) and analyzing its mechanism. A conclusion is made on the similarity of this phenomenon to the processes occurring in atmospheric-pressure dielectric barrier discharges.     

Dynamics of Breakdown in a Low-Pressure Argon–Mercury Mixture in a Long Discharge Tube

Breakdown dynamics in the course of glow discharge ignition in a long discharge tube (80 cm in length and 25 mm in diameter) filled with argon at a pressure of 3–4 Torr and mercury vapor at room temperature was studied experimentally. Rectangular voltage pulses with amplitudes from 1 to 2.5 kV were applied to the tube anode, the cathode being grounded. Complex electrical and optical measurements of the breakdown dynamics were carried out. Breakdown begins with a primary discharge between the anode and the tube wall. In this stage, a jump in the anode current and a sharp decrease in the anode voltage are observed and prebreakdown ionization wave arises near the anode. The cathode current appears only after the ionization wave reaches the cathode. The wave propagation velocity was measured at different points along the tube axis. The wave emission spectrum contains Hg, Ar, and Ar⁺ lines. The intensities of these lines measured at a fixed point exhibit very different time behaviors. The effect of the tube shielding on the breakdown characteristics was examined. It is found that, at a sufficiently narrow gap between the shield and the tube, this effect can be substantial.     

Finite element modeling of impulsive excitation and shear wave propagation in an incompressible,transversely isotropic medium

Elastic properties of materials can be measured by observing shear wave propagation following localized, impulsive excitations and relating the propagation velocity to a model of the material. However, characterization of anisotropic materials is difficult because of the number of elasticity constants in the material model and the complex dependence of propagation velocity relative to the excitation axis, material symmetries, and propagation directions. In this study, we develop a model of wave propagation following impulsive excitation in an incompressible, transversely isotropic (TI) material such as muscle. Wave motion is described in terms of three propagation modes identified by their polarization relative to the material symmetry axis and propagation direction. Phase velocities for these propagation modes are expressed in terms of five elasticity constants needed to describe a general TI material, and also in terms of three constants after the application of two constraints that hold in the limit of an incompressible material. Group propagation velocities are derived from the phase velocities to describe the propagation of wave packets away from the excitation region following localized excitation. The theoretical model is compared to the results of finite element (FE) simulations performed using a nearly incompressible material model with the five elasticity constants chosen to preserve the essential properties of the material in the incompressible limit. Propagation velocities calculated from the FE displacement data show complex structure that agrees quantitatively with the theoretical model and demonstrates the possibility of measuring all three elasticity constants needed to characterize an incompressible, TI material.     

On the roles of Ca2+ diffusion, Ca2+ buffers, and the endoplasmic reticulum in IP3-induced Ca2+ waves.

We have investigated the effects of Ca2+ diffusion, mobile and stationary Ca2+ buffers in the cytosol, and Ca2+ handling by the endoplasmic reticulum on inositol 1,4,5-trisphosphate-induced Ca2+ wave propagation. Rapid equilibration of free and bound Ca2+ is used to describe Ca2+ sequestration by buffers in both the cytosol and endoplasmic reticulum (ER) lumen. Cytosolic Ca2+ regulation is based on a kinetic model of the inositol 1,4,5-trisphosphate (IP3) receptor of De Young and Keizer that includes activation and inhibition of the IP3 receptor Ca2+ channel in the ER membrane and SERCA Ca2+ pumps in the ER. Diffusion of Ca2+ in the cytosol and the ER and the breakdown and diffusion of IP3 are also included in our calculations. Although Ca2+ diffusion is severely limited because of buffering, when conditions are chosen just below the threshold for Ca2+ oscillations, a pulse of IP3 or Ca2+ results in a solitary trigger wave that requires diffusion of Ca2+ for its propagation. In the oscillatory regime repetitive wave trains are observed, but for this type of wave neither the wave shape nor the speed is strongly dependent on the diffusion of Ca2+. Local phase differences lead to waves that are predominately kinematic in nature, so that the wave speed (c) is related to the wavelength (lambda) and the period of the oscillations (tau) approximately by the formula c = lambda/tau. The period is determined by features that control the oscillations, including [IP3] and pump activity, which are related to recent experiments. Both solitary waves and wave trains are accompanied by a Ca2+ depletion wave in the ER lumen, similar to that observed in cortical preparations from sea urchin eggs. We explore the effect of endogenous and exogenous Ca2+ buffers on wave speed and wave shape, which can be explained in terms of three distinct effects of buffering, and show that exogenous buffers or Ca2+ dyes can have considerable influence on the amplitude and width of the waves.     

Quality factor of a plasma waveguide and contraction of laser-induced breakdown waves in gases

A previously developed plasma-waveguide model of a long laser spark in atmospheric-pressure gases is used to describe the evolution of a plasma waveguide produced in the course of electric breakdown and to analyze energy dissipation in it. The requirements are formulated for the plasma density profile to be steep enough in order that the threshold conditions for electric breakdown can be satisfied, and the conditions are determined under which the distortion of the plasma density profile can lead to a decrease in the diameter of the breakdown wave.     

Wave speed in excitable random networks with spatially constrained connections

Very fast oscillations (VFO) in neocortex are widely observed before epileptic seizures, and there is growing evidence that they are caused by networks of pyramidal neurons connected by gap junctions between their axons. We are motivated by the spatio-temporal waves of activity recorded using electrocorticography (ECoG), and study the speed of activity propagation through a network of neurons axonally coupled by gap junctions. We simulate wave propagation by excitable cellular automata (CA) on random (Erdös-Rényi) networks of special type, with spatially constrained connections. From the cellular automaton model, we derive a mean field theory to predict wave propagation. The governing equation resolved by the Fisher-Kolmogorov PDE fails to describe wave speed. A new (hyperbolic) PDE is suggested, which provides adequate wave speed that saturates with network degree , in agreement with intuitive expectations and CA simulations. We further show that the maximum length of connection is a much better predictor of the wave speed than the mean length. When tested in networks with various degree distributions, wave speeds are found to strongly depend on the ratio of network moments rather than on mean degree , which is explained by general network theory. The wave speeds are strikingly similar in a diverse set of networks, including regular, Poisson, exponential and power law distributions, supporting our theory for various network topologies. Our results suggest practical predictions for networks of electrically coupled neurons, and our mean field method can be readily applied for a wide class of similar problems, such as spread of epidemics through spatial networks.     

A multiscale approach for modelling wave propagation in an arterial segment

A mathematical model of blood flow through an arterial vessel is presented and the wave propagation in it is studied numerically. Based on the assumption of long wavelength and small amplitude of the pressure waves, a quasi-one-dimensional (1D) differential model is adopted. It describes the non-linear fluid-wall interaction and includes wall deformation in both radial and axial directions. The 1D model is coupled with a six compartment lumped parameter model, which accounts for the global circulatory features and provides boundary conditions. The differential equations are first linearized to investigate the nature of the propagation phenomena. The full non-linear equations are then approximated with a numerical finite difference method on a staggered grid. Some numerical simulations show the characteristics of the wave propagation. The dependence of the flow, of the wall deformation and of the wave velocity on the elasticity parameter has been highlighted. The importance of the axial deformation is evidenced by its variation in correspondence of the pressure peaks. The wave disturbances consequent to a local stiffening of the vessel and to a compliance jump due to prosthetic implantations are finally studied.     

A new model for nuclear envelope breakdown

Nuclear envelope breakdown was investigated during meiotic maturation of starfish oocytes. Fluorescent 70-kDa dextran entry, as monitored by confocal microscopy, consists of two phases, a slow uniform increase and then a massive wave. From quantitative analysis of the first phase of dextran entry, and from imaging of green fluorescent protein chimeras, we conclude that nuclear pore disassembly begins several minutes before nuclear envelope breakdown. The best fit for the second phase of entry is with a spreading disruption of the membrane permeability barrier determined by three-dimensional computer simulations of diffusion. We propose a new model for the mechanism of nuclear envelope breakdown in which disassembly of the nuclear pores leads to a fenestration of the nuclear envelope double membrane.     

Determination of viscoelastic moduli of arteries

A model for the arterial wall, motivated by wave propagation findings, is developed. The wall is taken to be a viscoelastic, orthotropic, prestressed shell which is materially characterized at any prestress level by ten incremental moduli. By using the momentum equations and the wave propagation characteristics for three axisymmetric modes, the ten moduli are found in terms of the three wave speeds, the three attenuation coefficients and the prestresses.     

Near field effect on elasticity measurement for cartilage-bone structure using Lamb wave method

Background

Cartilage elasticity changes with cartilage degeneration. Hence, cartilage elasticity detection might be an alternative to traditional imaging methods for the early diagnosis of osteoarthritis. Based on the wave propagation measurement, Shear wave elastography (SWE) become an emerging non-invasive elasticity detection method. The wave propagation model, which is affected by tissue shapes, is crucial for elasticity estimating in SWE. However, wave propagation model for cartilage was unclear.

Methods

This study aimed to establish a wave propagation model for the cartilage-bone structure. We fabricated a cartilage-bone structure, and studied the elasticity measurement and wave propagation by experimental and numerical Lamb wave method (LWM).

Results

Results indicated the wave propagation model satisfied the lamb wave theory for two-layered structure. Moreover, a near field region, which affects wave speed measurements and whose occurrence can be prevented if the wave frequency is larger than one critical frequency, was observed.

Conclusion

Our findings would provide a theoretical foundation for further application of LWM in elasticity measurement of cartilage in vivo. It can help the application of LWM to the diagnosis of osteoarthritis.

     

A PKC wave follows the calcium wave after activation of Xenopus eggs

Calcium waves are well-known hallmarks of egg activation that trigger resumption of the cell cycle and development of the embryo. These waves rapidly and efficiently assure that activation signals are transmitted to all regions of the egg. Although the mechanism by which the calcium wave propagates across an egg as large as that of Xenopus is not known, two models prevail. One model is a wave of calcium-induced calcium release (CICR) and the other is propagation by inositol-induced calcium release (IICR). IICR requires a wave of phosphatidylinositol 4,5-bisphosphate (PIP2) hydrolysis, generating two second messengers, IP3, which then releases calcium and DAG, which activates protein kinase C (PKC). We show here that a wave of PKC-green fluorescent protein travels across the egg immediately following, and at the same velocity as, the calcium wave. This is the first example of a PKC wave in a vertebrate egg and supports the IICR model of wave propagation.     

A three-dimensional model of intercellular calcium signaling in epithelial cells

We have developed a fully three-dimensional (3D) model of calcium signaling in epithelial cells based on a set of reaction diffusion equations that are solved on a large-scale finite-element code in three dimensions. We have explicitly included the cellular compartments including the cell nucleus, cytoplasm, and gap junctions. The model allows for buffering of free Ca2+, calcium-induced calcium release, and the explicit inclusion of mobile buffers. To make quantitative comparisons to experimental results, we used fluorescence microscopy images of cells to generate an accurate mesh describing cell morphology. We found that Ca2+ wave propagation through the tissue is a function of both initial conditions used to start the wave and various geometrical parameters that affect propagation such as gap junction density and distribution, and the presence of nuclei. The exogenous dyes used in experimental imaging also affect wave propagation.     

The origins of syringomyelia: numerical models of fluid/structure interactions in the spinal cord

A two-dimensional axi-symmetric numerical model is constructed of the spinal cord, consisting of elastic cord tissue surrounded by aqueous cerebrospinal fluid, in turn surrounded by elastic dura. The geometric and elastic parameters are simplified but of realistic order, compared with existing measurements. A distal reflecting site models scar tissue formed by earlier trauma to the cord, which is commonly associated with syrinx formation. Transients equivalent to both arterial pulsation and percussive coughing are used to excite wave propagation. Propagation is investigated in this model and one with a central canal down the middle of the cord tissue, and in further idealized versions of it, including a model with no cord, one with a rigid cord, one with a rigid dura, and a double-length untapered variant of the rigid-dura model. Analytical predictions for axial and radial wave-speeds in these different situations are compared with, and used to explain, the numerical outcomes. We find that the anatomic circumstances of the spinal cerebrospinal fluid cavity probably do not allow for significant wave steepening phenomena. The results indicate that wave propagation in the real cord is set by the elastic properties of both the cord tissue and the confining dura mater, fat, and bone. The central canal does not influence the wave propagation significantly.     

Identification process based on shear wave propagation within a phantom using finite element modelling and magnetic resonance elastography

Magnetic resonance elastography (MRE), based on shear wave propagation generated by a specific driver, is a non-invasive exam performed in clinical practice to improve the liver diagnosis. The purpose was to develop a finite element (FE) identification method for the mechanical characterisation of phantom mimicking soft tissues investigated with MRE technique. Thus, a 3D FE phantom model, composed of the realistic MRE liver boundary conditions, was developed to simulate the shear wave propagation with the software ABAQUS. The assumptions of homogeneity and elasticity were applied to the FE phantom model. Different ranges of mesh size, density and Poisson's ratio were tested in order to develop the most representative FE phantom model. The simulated wave displacement was visualised with a dynamic implicit analysis. Subsequently, an identification process was performed with a cost function and an optimisation loop provided the optimal elastic properties of the phantom. The present identification process was validated on a phantom model, and the perspective will be to apply this method on abdominal tissues for the set-up of new clinical MRE protocols that could be applied for the follow-up of the effects of treatments.     

The covalent oscillator: A paradigm accounting for the sliding/bending mechanism and wave propagation in cilia and flagella

Summary— In most models of wave propagation in eucaryotic flagella and cilia, a clear distinction is made between the dynein dependent microtubule sliding which represents the oscillatory motor and the bending mechanism which regulates wave propagation. Little is known about the physical elements regulating the latter: in the present model, the bending propagation is postulated to be supported by an open/close cyclic mechanism protease/ligase dependent, which involves transient covalent links between adjacent microtubular doublets; this open/close cycle propagates in register with the powering action of the dynein motor along the exoneme. The implications of the model are discussed in relation to previous data which involve protease/ligase in the axonemal function as well as other data which can be integrated by the proposed model.     

A new automated method of image analysis: comparison of ciliary and flagellar beats

A new automated method of image analysis of sperm flagellar (human) and cilia (Dunaliella) bends is developed. This method permits an automatic determination of the line characterizing the flagellum. Two dynamic parameters are measured: the wave propagation velocity and the wave curvature radius. The data reveal similar patterns in the propagation of the principal and reverse waves between flagelated and ciliated cells. Conversely, differences are seen in principal wave curvature due perhaps to the presence of periaxonemal structures in the flagellum, absent in cilium. The identical patterns of reverse wave curvaturei in both systems may be linked to axonemal limitations.     

Saltatory propagation of Ca2+ waves by Ca2+ sparks.

Punctate releases of Ca2+, called Ca2+ sparks, originate at the regular array of t-tubules in cardiac myocytes and skeletal muscle. During Ca2+ overload sparks serve as sites for the initiation and propagation of Ca2+ waves in myocytes. Computer simulations of spark-mediated waves are performed with model release sites that reproduce the adaptive Ca2+ release observed for the ryanodine receptor. The speed of these waves is proportional to the diffusion constant of Ca2+, D, rather than D, as is true for reaction-diffusion equations in a continuous excitable medium. A simplified "fire-diffuse-fire" model that mimics the properties of Ca2+-induced Ca2+ release (CICR) from isolated sites is used to explain this saltatory mode of wave propagation. Saltatory and continuous wave propagation can be differentiated by the temperature and Ca2+ buffer dependence of wave speed.