Electromechanical coupling of waves in nerve fibres

The propagation of an action potential (AP) in a nerve fibre is accompanied by mechanical and thermal effects. In this paper, an attempt is made to build up a mathematical model which couples the AP with a possible pressure wave (PW) in the axoplasm and waves in the nerve fibre wall (longitudinal—LW and transverse—TW) made of a lipid bilayer (biomembrane). A system of differential equations includes the governing equations of single waves with coupling forces between them. The single equations are kept as simple as possible in order to carry out the proof of concept. An assumption based on earlier studies is made that the coupling forces depend on changes (the gradient, time derivative) of the voltage. In addition, it is assumed that the transverse displacement of the biomembrane can be calculated from the gradient of the LW in the biomembrane. The computational simulation is focused to determining the influence of possible coupling forces on the emergence of mechanical waves from the AP. As a result, an ensemble of waves (AP, PW, LW, TW) emerges. The further experiments should verify assumptions about coupling forces.     

Generation of auroral kilometric radiation by a finite-size source in a dipole magnetic field

Generation, amplification, and propagation of auroral kilometric radiation in a narrow three-dimensional plasma cavity in which a weakly relativistic electron beam propagates is studied in the geometrical optics approximation. It is shown that the waves that start with a group velocity directed earthward and have optimal relation between the wave vector components determining the linear growth rate and the wave residence time inside the amplification region undergo the largest amplification. Taking into account the longitudinal velocity of fast electrons results in the shift of the instability domain toward wave vectors directed to the Earth and leads to a change in the dispersion relation, due to which favorable conditions are created for the generation of waves with frequencies above the cutoff frequency for the cold background plasma at the wave generation altitude. The amplification factor for these waves is lower than for waves that have the same wave vectors but are excited by the electron beams with lower velocities along the magnetic field. For waves excited at frequencies below the cutoff frequency of the background plasma at the generation altitude, the amplification factor increases with increasing longitudinal electron velocity, because these waves reside for a longer time in the amplification region.     

Anisotropic propagation of Ca2+ waves in isolated cardiomyocytes.

Digital imaging microscopy of fluor-3 fluorescence was used to study the propagation of intracellular Ca2+ waves in isolated adult rat cardiomyocytes from 17 to 37 degrees C. Ca2+ waves spread in both transverse and longitudinal direction of a myocyte. Transverse propagation was pronounced in waves starting from a focus at the edge of a myocyte and in waves following an irregular, curved path (spiral waves). For the former type of waves, propagation velocities were determined. Both transverse and longitudinal wave components propagated at constant velocity ranging from 30 to 125 micron/s. Myocytes were anisotropic with respect to wave propagation: waves propagated faster in the longitudinal than in the transverse direction. The ratio between longitudinal and transverse velocity increased from 1.30 at 17 degrees C to 1.55 at 37 degrees C. Apparent activation energies for transverse and longitudinal wave propagation were estimated to be -20 kJ/mol, suggesting that these processes are limited by diffusion of Ca2+. Direction-dependent propagation velocities are interpreted to result from the highly ordered structure of the myocytes, especially from the anisotropic arrangement of diffusion obstacles such as myofilaments and mitochondria.     

Effect of parametric resonance on the formation of waves with a broad multiharmonic spectrum during the development of two-stream instability

A cubically nonlinear multiharmonic theory of two-stream instability in a two-velocity relativistic electron beam is constructed with allowance for parametric resonance between harmonics of longitudinal waves of different types, as well as between wave harmonics of the same type. The effect of these two kinds of parametric resonance interaction on the development of two-stream instability is investigated. It is shown that parametric resonance between different types of longitudinal waves excited in a two-velocity beam can substantially affect the development of physical processes in the system under study. It is proposed to use parametric resonance between longitudinal waves of different types to form waves with a prescribed broad multiharmonic spectrum.     

The Dissipation and Dispersion of Small Waves in Arteries and Veins with Viscoelastic Wall Properties

Theoretical and experimental evidence suggests that the dissipation of high frequency pressure waves in blood vessels is caused primarily by the viscoelastic behavior of the vessel wall. In this theoretical analysis the vessels are considered as fluid-filled circular cylindrical shells whose walls have isotropic and homogeneous viscoelastic properties and are subjected to an initial axial stretch and a transmural pressure. If the wall material is incompressible and behaves as a Voigt solid in shear, the results predict a decrease in wave amplitude per wavelength which is essentially independent of frequency over a wide range. This finding is in qualitative agreement with recent experiments on anesthetized dogs. A parametric study also shows a great sensitivity of the dissipation to changes in transmural pressure and axial stretch. Axisymmetric waves are only mildly dispersive, while all nonaxisymmetric waves are highly dispersive and exhibit much stronger damping per wavelength at low frequencies than do axisymmetric waves.     

On the propagation of a wave front in viscoelastic arteries

In formulating a mathematical model of the arterial system, the one-dimensional flow approximation yields realistic pressure and flow pulses in the proximal as well as in the distal regions of a simulated arterial conduit, provided that the viscoelastic damping induced by the vessel wall is properly taken into account. Models which are based on a purely elastic formulation of the arterial wall properties are known to produce shocklike transitions in the propagating pulses which are not observed in man under physiological conditions. The viscoelastic damping characteristics are such that they are expected to reduce the tendency of shock formation in the model. In order to analyze this phenomenon, the propagation of first and second-order pressure waves is calculated with the aid of a wave front expansion, and criteria for the formation of shocks are derived. The application of the results to the human arterial system show that shock waves are not to be expected under normal conditions, while in case of a pathologically increased pressure rise at the root of the aorta, shocklike transitions may develop in the periphery. In particular, it is shown that second-order waves never lead to shock formation in finite time for the class of initial conditions and mechanical wave guides which are of interest in the mammalian circulation.     

Nonlinear muscles, passive viscoelasticity and body taper conspire to create neuromechanical phase lags in anguilliform swimmers

Locomotion provides superb examples of cooperation among neuromuscular systems, environmental reaction forces, and sensory feedback. As part of a program to understand the neuromechanics of locomotion, here we construct a model of anguilliform (eel-like) swimming in slender fishes. Building on a continuum mechanical representation of the body as an viscoelastic rod, actuated by a traveling wave of preferred curvature and subject to hydrodynamic reaction forces, we incorporate a new version of a calcium release and muscle force model, fitted to data from the lamprey Ichthyomyzon unicuspis, that interactively generates the curvature wave. We use the model to investigate the source of the difference in speeds observed between electromyographic waves of muscle activation and mechanical waves of body curvature, concluding that it is due to a combination of passive viscoelastic and geometric properties of the body and active muscle properties. Moreover, we find that nonlinear force dependence on muscle length and shortening velocity may reduce the work done by the swimming muscles in steady swimming.     

Pressure wave propagation in fluid-filled co-axial elastic tubes. Part 1: Basic theory

Our work is motivated by ideas about the pathogenesis of syringomyelia. This is a serious disease characterized by the appearance of longitudinal cavities within the spinal cord. Its causes are unknown, but pressure propagation is probably implicated. We have developed an inviscid theory for the propagation of pressure waves in co-axial, fluid-filled, elastic tubes. This is intended as a simple model of the intraspinal cerebrospinal-fluid system. Our approach is based on the classic theory for the propagation of longitudinal waves in single, fluid-filled, elastic tubes. We show that for small-amplitude waves the governing equations reduce to the classic wave equation. The wave speed is found to be a strong function of the ratio of the tubes' cross-sectional areas. It is found that the leading edge of a transmural pressure pulse tends to generate compressive waves with converging wave fronts. Consequently, the leading edge of the pressure pulse steepens to form a shock-like elastic jump. A weakly nonlinear theory is developed for such an elastic jump.     

Theory of nonlinear space charge waves in neutralized electron flows: Gas-dynamic approach

The problem of the structure and dynamics of nonlinear longitudinal space charge waves in an electron flow that is treated as a gas and is described by an adiabatic equation of state with an arbitrary adiabatic index is solved exactly, and the solution obtained is examined in detail. The isothermal case is considered separately. It is shown that the waves in question can occur in the form of a fast or a slow space charge wave. The boundary values of the velocity and amplitude of these waves are obtained. The effect of the finite transverse dimensions of the electron flow on the structure of the wave and its dynamics is investigated.     

Feasibility of using bernstein modes for current drive in toroidal devices

The feasibility of using Bernstein modes for producing electron cyclotron current drive in toroidal devices is examined. It is shown that the negative role of trapped particles may reduce upon increasing the longitudinal slowing-down factor of waves. Numerical geometrical-optics calculations of the propagation and absorption of waves were performed for the scheme in which radiation is launched from the low-field side as an ordinary wave, linearly converted into an extraordinary wave, and finally converted into Bernstein mode. An analysis is performed for medium-sized toroidal devices. Based on numerical simulation, the parameters determining the efficiency of current drive, namely, the characteristic values of the resonant energies and the longitudinal slowing-down factor of waves in the region where most of the microwave power dissipates, are found.     

Wave Propagation through a Viscous Incompressible Fluid Contained in an Initially Stressed Elastic Tube

To have a better understanding of the flow of blood in arteries a theoretical analysis of the pressure wave propagation through a viscous incompressible fluid contained in an initially stressed tube is considered. The fluid is assumed to be Newtonian. The tube is taken to be elastic and isotropic. The analysis is restricted to tubes with thin walls and to waves whose wavelengths are very large compared with the radius of the tube. It is further assumed that the amplitude of the pressure disturbance is sufficiently small so that nonlinear terms of the inertia of the fluid are negligible compared with linear ones. Both circumferential and longitudinal initial stresses are considered; however, their origins are not specified. Initial stresses enter equations as independent parameters. A frequency equation, which is quadratic in the square of the propagation velocity is obtained. Two out of four roots of this equation give the velocity of propagation of two distinct outgoing waves. The remaining two roots represent incoming waves corresponding to the first two waves. One of the waves propagates more slowly than the other. As the circumferential and/or longitudinal stress of the wall increases, the velocity of propagation and transmission per wavelength of the slower wave decreases. The response of the fast wave to a change in the initial stress is on the opposite direction.     

Axonal Transport, Deposition, and Metabolic Turnover of Glycoproteins in the Rat Optic Pathway

Abstract: Following intraocular injection of [³H]fucose in the rat, radioactive glycoproteins are rapidly transported to the nerve terminals in at least two waves, one with a peak at 8 h and a second with a peak at about a week. The molecular weight distribution of radioactive peptides in ach transport wave as determined by gel electrophoresis in buffers containing sodium dodecyl sulfate is very similar. Most of the many glycopeptides in the first wave of rapid transport pass through the optic tract in unison (apparent half-life of about 15 h) and are preferentially destined for the nerve endings. However, two proteins of apparent M. W. 28,000 and 49,000 are preferentially retained in the axons. The remaining proteins, after reaching the nerve endings (superior colliculus), decay with apparent half-lives ranging from 17 to 34 h. During the second wave a large amount of the 28,000 and 49,000 M. W. peptides are again preferentially retained in the axons. The remaining proteins, on reaching the nerve endings, decay with apparent half-lives ranging from 5 to 9 days. Subcellular fractionation of the superior colliculus supports the hypothesis that the 49,000 and 28,000 M. W. peptides are the predominantly labeled glycoproteins present in myelinated axons (representing over 50% of the radioactive glycoproteins 7 days following injection), although they are probably also present in membranes of the nerve endings. A comparison with glycoprotein transport in other tracts (geniculocortical and nigrostriatal tracts) suggests that glycoprotein transport in these pathways has many similarities to glycoprotein transport in the retinal ganglion cells, and that the optic system is a good general model for axonal transport in the CNS.     

Propagated disturbances of transverse potential gradient in intracellular fibrils as the source of motive forces for longitudinal transport in cells

Summary It is proposed as a working hypothesis that conformational changes propagated like waves along intracellular fibrils (tubules, microtubules, microfilaments) have an electric component,i.e., there are waves of disturbance of electric potential in the fibrils. The paper considers the unavoidable consequences of the wave. The latter is accompanied by local electric field in the boundary layer of cytoplasmic fluid. Both positively and negatively charged particles may be attracted to the fibril in certain regions of the field and, being attracted, the particle may be under the action of longitudinal component of electric force. When the force is strong enough to move the particle with wave velocity, the particle will travel smoothly along the fibril, otherwise the movement will be saltatory or of agitation type. Net electroosmotic flow in one direction in the boundary layer of fluid may be expected when the waves are propagated in series. Turbulent motion of the fluid caused by the waves may provide the basis for activated diffusion. Asymmetry of the wave may account for polar transport of this sort. The electric field transmitted along the fibril across a sieve pore in phloem may facilitate electroosmotically the flow through the pore. Quantitative requirements of the hypothesis that electric field generated by the waves may account for different aspects of longitudinal transport in cells are apparently met.     

Effect of a strong monochromatic electromagnetic wave with circular polarization on one-dimensional wake waves in plasma

A study is made of the excitation of wake waves by a one-dimensional bunch of charged particles in an electron plasma in the presence of an intense monochromatic pump wave with circular polarization. In the main state (in the absence of a bunch), the interaction between a pump wave and a plasma is described by the Maxwell equations and the nonlinear relativistic hydrodynamic equations for a cold plasma. The excitation of linear waves by a one-dimensional bunch is investigated against a cold plasma background. It is shown that, in a certain range of the parameter values of the bunch, pump wave, and plasma, the amplitude of the excited transverse waves grows as the energy of the bunch particles increases until the relativistic factor of the bunch reaches a certain threshold value above which the transverse wave amplitude becomes essentially independent of the bunch particle energy and grows as the intensity and frequency of the pump wave increase. The amplitude and wavelength of the longitudinal field, which is shown to depend weakly on the energy of the bunch particles, grows with increasing the pump wave intensity.     

Energy dissipation and pulse wave attenuation in the canine carotid artery

This paper presents methods for calculating, for a segment of artery in vivo, (1) viscous and viscoelastic energy dissipation as a function of time, and (2) the viscous and viscoelastic components of the frequency-dependent attenuation coefficient. The calculations require measurement of arterial diameter and of intra-arterial pressure and flow-rate at two sites along the vessel. Viscous energy dissipation is calculated from the radius-dependent velocity shear in the lumen given by linear theory from the pressure measurements. The attenuation coefficient for a given harmonic of heart rate is calculated as half the sum of the viscous and viscoelastic components at that frequency of the energy dissipated per unit length by forwardtravelling waves, divided by the forward-wave flow work input to the segment at that frequency. Measurements in canine carotid arteries indicate that wall viscoelasticity contributes relatively little to energy dissipation per cardiac cycle and pulse wave attenuation.     

Generation of auroral kilometric radiation by a finite-size source in a dipole magnetic field. Part II

Propagation and amplification of extraordinary electromagnetic waves in a dipole magnetic field in a narrow 3D plasma cavity in which a weakly relativistic electron beam propagates along the magnetic field in the direction of the gradient of the magnetic field strength is investigated. The domain of wave vectors at the starting point for which the wave amplification factors at the output of the density cavity reach their maximum values is found, and the amplification factor as a function of the wave frequency is determined. It is shown that the longitudinal velocity of fast electrons, which enables generation of waves in a broader frequency range, plays an important role in the formation of the spectrum of the auroral kilometric radiation (AKR). In this case, waves with the largest amplification factors at the output of the cavity have frequencies exceeding the cutoff frequency of the background plasma at the wave generation altitude. The global inhomogeneity of the magnetic field and plasma density, which governs the residence time of the waves in the amplification region, plays a key role in the formation of the AKR spectrum. It is shown that this time is the main factor determining the energy of the waves emerging from the source.     

Computer simulation of bend propagation by axoplasmic microtubules

The generation of bending waves by microtubules in squid nerve axoplasm has been modelled using appropriately modified versions of computer programs developed previously for simulation of flagellar bending waves. The results confirm that a constant longitudinal force directed along the axis of the microtubule is sufficient to cause the generation of regular oscillations and propagated bending waves when the forward gliding movement of the microtubule is obstructed. No control mechanism is required to modulate the active force-generating system. In order to obtain bending waves similar to those observed experimentally, it was necessary to use a model for the force-generating system in which the active force decreases with increasing sliding velocity. If the elastic bending resistance of axoplasmic microtubules is similar to that of microtubules in sperm terminal filaments, the longitudinal force per unit length generated by the axoplasmic microtubules must be of the same order of magnitude as the force generated by dynein arms along the doublet microtubules of eukaryotic flagella.     

Direct and indirect innervation of smooth muscle cells of rat stomach,with special reference to the interstitial cells of Cajal

Interstitial cells of Cajal in the circular (ICC-CM) and longitudinal (ICC-LM) muscle layer of the rat gastric antrum and their innervation were studied ultrastructurally. Both ICC-CM and ICC-LM are characterized by many mitochondria, rough and smooth endoplasmic reticulum, caveolae, and formation of gap junctions with each other and with muscle cells, though ICC-LM tend to show more variable cytoplasmic features depending on section profiles. Close contacts between nerve terminals and both ICC-CM and ICC-LM are observed. These possible synaptic structures are characterized by: (1) accumulation of synaptic vesicles in nerve varicosities, (2) a narrow gap (about 20 nm) between pre- and postjunctional membranes, (3) lack of a basal lamina between pre- and postjunctional membranes, and (4) the presence of an electron-dense lining on the inner aspect of prejunctional membranes. Almost the same characteristics are observed between the nerve terminals and the muscle cells of both circular and longitudinal muscle layers of the same specimens. Therefore, we conclude that the smooth muscle cells of both circular and longitudinal layers of the rat antrum are directly and indirectly innervated via ICC. Their functional significance is discussed.     

Transmission characteristics of axial waves in blood vessels

The elastic behavior of blood vessels can be quantitatively examined by measuring the propagation characteristics of waves transmitted by them. In addition, specific information regarding the viscoelastic properties of the vessel wall can be deduced by comparing the observed wave transmission data with theoretical predictions. The relevance of these deductions is directly dependent on the validity of the mathematical model for the mechanical behavior of blood vessels used in the theoretical analysis. Previous experimental investigations of waves in blood vessels have been restricted to pressure waves even though theoretical studies predict three types of waves with distinctly different transmission characteristics. These waves can be distinguished by the dominant displacement component of the vessel wall and are accordingly referred to as radial, axial and circumferential waves. The radial waves are also referred to as pressure waves since they exhibit pronounced pressure fluctuations. For a thorough evaluation of the mathematical models used in the analysis it is necessary to measure also the dispersion and attenuation of the axial and circumferential (torsion) waves.

To this end a method has been developed to determine the phase velocities and damping of sinusoidal axial waves in the carotid artery of anesthetized dogs with the aid of an electro-optical tracking system. For frequencies between 25 and 150 Hz the speed of the axial waves was between 20 and 40 m/sec and generally increased with frequency, while the natural pressure wave travelled at a speed of about 10 m/sec. On the basis of an isotropic wall model the axial wave speed should however be approximately 5 times higher than the pressure wave speed. This discrepancy can be interpreted as an indication for an anisotropic behavior of the carotid wall. The carotid artery appears to be more elastic in the axial than in the circumferential direction.     

Amplification of surface waves in a plasma waveguide by a straight relativistic electron beam in a finite magnetic field

The problem of the excitation of electron waves in a thin-walled annular cold plasma in a cylindrical waveguide by a straight relativistic electron beam in a finite magnetic field is considered. The dispersion properties of a waveguide system with parameters close to the experimental ones are investigated. It is shown that the growth rate of the excited high-frequency plasma wave is comparable to that of the low-frequency wave, which is weakly sensitive to the strength of the longitudinal magnetic field.