Circulation of excitation waves in a model medium containing unexcitable obstacles

Serial semithin optical sections were used for 3D reconstruction of rat ventricular tissue. At histological resolution, older animals (18 months) were found to have regions of fibrous connective tissue not observed in young animals (2 months). The 3D data were used in mathematical modeling of excitation wave propagation in a medium containing such obstacles. The values of conductance, medium excitation threshold, and pulse repetition rate were determined whereat the model predicts rhythm disorders caused by circulation of the excitation wave.     

Traveling waves in a piecewise-linear reaction-diffusion model of excitable medium

One-dimensional autowaves (traveling waves) in excitable medium described by a piecewise-linear reaction-diffusion system have been investigated. Two main types of wave have been considered: a single pulse and a periodic sequence of pulses (wave trains). In a two-component system, oscillations are due to the second component of the reaction-diffusion system, while in a one-component system, they are caused by external periodic excitation (forcing). Using semianalytical solutions for the wave profile, the shape and velocity of autowaves have been found. It is shown that the dispersion relation for oscillating sequences of pulses has an anomalous character.     

Surface waves on the boundary of a conducting medium and their excitation by a relativistic electron beam

Excitation of surface waves by a relativistic electron beam propagating over a conducting cylindrical medium (metal or highly ionized plasma) is investigated theoretically. Dispersion relations describing the linear interaction of surface electromagnetic waves with a monoenergetic electron beam are derived, and the growth rates and spatial amplification factors of excited waves are determined. Condition for the nonlinear trapping of the beam electrons by a surface wave is used to determine the maximum amplitude of the excited wave and the optimal radiator length. The electric field of a surface wave excited by an electron beam is estimated for a particular case.     

The rotation of autowaves as a result of their penetration through a system of unexcitable obstacles. A mechanism of arrhythmias associated with aging

The dependence of the frequency of occurrence of excitation vortices rotating around unexcitable obstacles on the size and the number of the obstacles and also on the medium excitation threshold was studied. It was shown that the vortex formation takes place in a wide range of the model parameter values. The assumption was formulated that the mechanism of formation of excitation vortices under study underlies the increase in the heart arrhythmias associated with aging.     

Critical scale of propagation influences dynamics of waves in a model of excitable medium

Background  

Duration and speed of propagation of the pulse are essential factors for stability of excitation waves. We explore the propagation of excitation waves resulting from periodic stimulation of an excitable cable to determine the minimal stable pulse duration in a rate-dependent modification of a Chernyak-Starobin-Cohen reaction-diffusion model.     

Evolution of spiral and scroll waves of excitation in a mathematical model of ischaemic border zone

Abnormal electrical activity from the boundaries of ischemic cardiac tissue is recognized as one of the major causes in generation of ischemia-reperfusion arrhythmias. Here we present theoretical analysis of the waves of electrical activity that can rise on the boundary of cardiac cell network upon its recovery from ischaemia-like conditions. The main factors included in our analysis are macroscopic gradients of the cell-to-cell coupling and cell excitability and microscopic heterogeneity of individual cells. The interplay between these factors allows one to explain how spirals form, drift together with the moving boundary, get transiently pinned to local inhomogeneities, and finally penetrate into the bulk of the well-coupled tissue where they reach macroscopic scale. The asymptotic theory of the drift of spiral and scroll waves based on response functions provides explanation of the drifts involved in this mechanism, with the exception of effects due to the discreteness of cardiac tissue. In particular, this asymptotic theory allows an extrapolation of 2D events into 3D, which has shown that cells within the border zone can give rise to 3D analogues of spirals, the scroll waves. When and if such scroll waves escape into a better coupled tissue, they are likely to collapse due to the positive filament tension. However, our simulations have shown that such collapse of newly generated scrolls is not inevitable and that under certain conditions filament tension becomes negative, leading to scroll filaments to expand and multiply leading to a fibrillation-like state within small areas of cardiac tissue.     

Nonresonant excitation of surface waves by a normal electric field

A study is made of nonresonant parametric excitation of surface waves by a spatially uniform, time-dependent electric pump field directed perpendicular to a plane plasma-dielectric interface. A set of equations is derived that describes the dynamics of surface wave excitation. Expression for the growth rate in the linear stage of instability is obtained, and the threshold amplitude of the external electric field above which the parametric instability can occur is found. The spectrum of the excited waves is analyzed. Published in Russian in Fizika Plazmy, 2006, Vol. 32, No. 11, pp. 994–998. The article was translated by the author.     

Group-wise growth of Streptomyces in a medium containing streptomycin

Summary We have described the observation that Streptomyces griseus colonies grow group-wise on agar media containing streptomycin. We have found that this phenomenon is due to a substance (s) produced by germinating Str. griseus spores in media containing streptomycin, and this substance made the neighbouring spores more tolerant to increasing streptomycin concentrations. The substance is produced specifically by Str. griseus strains. The substance has probably a great molecular size, is thermolabile, not a nucleic acid and the applied enzymes did not inactivate it. Some investigated enzyme-poisons did not influence either its production or its effect on Str. griseus spores. We succeeded in carrying over the substance into liquid phase and separate it from the producing culture and this enables us to furterh purification and investigation of the substance.     

Traveling waves in a chemotactic model

A model for chemotaxis in a bacteria-substrate mixture introduced by Keller and Segel, which is described by nonlinear partial differential equations, is studied analytically. The existence of traveling waves is shown for the system in which the substrate diffusion is taken into account and the chemotactic coefficient is greater than the motility one, and the instability of traveling waves is discussed.     

Electric field perturbations of spiral waves attached to millimeter-size obstacles

Reentrant spiral waves can become pinned to small anatomical obstacles in the heart and lead to monomorphic ventricular tachycardia that can degenerate into polymorphic tachycardia and ventricular fibrillation. Electric field-induced secondary source stimulation can excite directly at the obstacle, and may provide a means to terminate the pinned wave or inhibit the transition to more complex arrhythmia. We used confluent monolayers of neonatal rat ventricular myocytes to investigate the use of low intensity electric field stimulation to perturb the spiral wave. A hole 2-4 mm in diameter was created in the center to pin the spiral wave. Monolayers were stained with voltage-sensitive dye di-4-ANEPPS and mapped at 253 sites. Spiral waves were initiated that attached to the hole (n = 10 monolayers). Electric field pulses 1-s in duration were delivered with increasing strength (0.5-5 V/cm) until the wave terminated after detaching from the hole. At subdetachment intensities, cycle length increased with field strength, was sustained for the duration of the pulse, and returned to its original value after termination of the pulse. Mechanistically, conduction velocity near the wave tip decreased with field strength in the region of depolarization at the obstacle. In summary, electric fields cause strength-dependent slowing or detachment of pinned spiral waves. Our results suggest a means to decelerate tachycardia that may help to prevent wave degeneration.     

Resonant excitation of counterpropagating surface waves at a Langmuir wave decay

A study is made of the resonant excitation of surface waves via the decay of a Langmuir wave propagating perpendicularly to a plasma-dielectric interface. The excitation dynamics in the initial stage of decay instability is studied, expressions for the growth rates are obtained, and the threshold amplitude of the Langmuir wave above which parametric instability occurs is found. Published in Russian in Fizika Plazmy, 2007, Vol. 33, No. 4, pp. 346–351. The article was translated by the author.     

Propagation of excitation in a model of neural system

The study of the characteristic statistical properties of neural systems, which was started in a previous paper, is continued here. The initial value problem for the kinetic equations describing the systems is solved in the one-dimensional case under particular conditions. To handle this problem use is made of certain techniques previously introduced by Landau and later improved by Backus and Turski in the context of the study of oscillations in a linearized plasma. The result is used for the discussion of a very simple neural system.     

Cellulose production by Gluconacetobacter hansenii in a medium containing ethanol

The addition of 1% (v/v) ethanol to the basal medium inhibited growth of Gluconacetobacter hansenii but decreased the numbers of non-cellulose producing cells. Cellulose production increased 1.7 times to approx. 2.5 g l(-1) and showed a pattern of mixed growth-associated production. Microbial cells produced rigid pellicle-type bacterial cellulose as the shell of a large lump of bacterial cellulose like a static culture. The inoculum cultivated for 3 d maintained cellulose production by the fifth batch.     

High level of sporulation ofMetarhizium anisopliae in a medium containing by-products

Summary Solid-state fermentation of rice bran or rice-bran-husk mixtures byMetarhizium anisopliae proved to be highly successful in spore yield. Optimum sporulation response on bran medium occurred when the initial water activity values ranged from 0.982 to 0.999. When bran was supplemented with 50% rice husk, the spore yield almost doubled, but a narrower initial water activity range (0.997–0.999) was optimum. Under these conditions, spore yields were 5–15 times higher (depending on the strain) than those currently obtained on the basis of rice grain fermentations.     

Regulation of excitation energy transfer in organisms containing phycobilins

The mechanism of excitation energy redistribution (state transition) in organisms containing phycobilins is reviewed. Recent measurements using time-resolved fluorescence spectroscopy in the picosecond range confirm that the state transition in cyanobacteria and red algae is controlled by changes in the kinetics of energy transfer from PS 2 to PS 1 (spillover) rather than by physical dislocation of the phycobilisome and reassociation between the two photosystems (mobile antenna model). Contrary to the analogous situation in higher plants, there is no compelling evidence for the involvement of a protein phosphorylation event in the rapid time range of the state transition, but a variety of data indicate that a membrane conformational change occurs that might change the relative distance between, and/or orientation of the two photosystems within the thylakoid. The state transition is most probably initiated by the redox state of the intersystem electron transport chain, and the conversion to state 1 is driven by coupled PS1 cyclic electron transport. The cryptomonads also undergo wavelength dependent changes in excitation energy distribution by a mechanism very similar to that observed in the red algae and cyanobacteria. However, the changes in energy distribution in this group are most likely related to a photoprotection mechanism for PS2 rather than to a state transition.Abbreviations APC allophycocyanin - EF exoplasmic face - PE phycoerythrin - PC phycocyanin - PF protoplasmic face - LHC light harvesting chlorophyll a/b protein - PBS phycobilisome - LD linear dichroism - RC reaction center     

Existence of excitation waves for a collection of cardiomyocytes electrically coupled to fibroblasts

We consider mathematical models of a collection of cardiomyocytes (myocardial tissue) coupled to a varying number of fibroblasts. Our aim is to understand how conductivity (δ) and fibroblast density (η) affect the stability of the collection. We provide mathematical and computational arguments indicating that there is a region of instability in the η-δ space. Mathematical arguments, based on a simplified model of the coupled myocyte-fibroblast system, show that for certain parameter choices, a stationary solution cannot exist. Numerical experiments (1D, 2D) are based on a recently developed model of electro-chemical coupling between a human atrial myocyte and a number of associated atrial fibroblasts. The numerical experiments demonstrate that there is a region of instability of the form observed in the simplified model analysis.     

Traveling waves in a model of influenza A drift

Between major pandemics, the influenza A virus changes its antigenic properties by accumulating point mutations (drift) mainly in the RNA genes that code for the surface proteins hemagglutinin (HA) and neuraminidase (NA). The successful strain (variant) that will cause the next epidemic is selected from a reduced number of progenies that possess relatively high transmissibility and the ability to escape from the immune surveillance of the host. In this paper, we analyse a one-dimensional model of influenza A drift (Z. Angew. Math. Mech. 76 (2) (1996) 421) that generalizes the classical SIR model by including mutation as a diffusion process in a phenotype space of variants. The model exhibits traveling wave solutions with an asymptotic wave speed that matches well those obtained from numerical simulations. As exact solutions for these waves are not available, asymptotic estimates for the amplitudes of infected and recovered classes are provided through an exponential approximation based on the smallness of the diffusion constant. Through this approximation, we find simple scaling properties to several parameters of relevance to the epidemiology of the disease.