Propagation of excitation in surviving neocortical slices

Propagation of excitation was investigated in neocortical guinea-pig slices maintained in vitro. Stimuli were applied at different distances from the chosen neuron. A comparison between latencies of induced spike responses would point to complex structure and configuration of vertically oriented columnar array. Such arrays of relatively synchronously activated neurons have a narrow peak in layer II (of up to 300 µm), a broad central portion in layer V about 600 µm or above), and a narrower base in layer VI (of about 300 µm). Layer-by-layer diversity in excitation propagation was found within the array, moreover.Institute of Biological Physics, Academy of Sciences of the USSR, Pushchino-on-Oka. Translated from Neirofiziologiya, Vol. 22, No. 4, pp. 472–481, July–August, 1990.     

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.     

Current injection into a two-dimensional anisotropic bidomain.

A two-dimensional sheet of anisotropic cardiac tissue is represented with the bidomain model, and the finite element method is used to solve the bidomain equations. When the anisotropy ratios of the intracellular and extracellular spaces are not equal, the injection of current into the tissue induces a transmembrane potential that has a complicated spatial dependence, including adjacent regions of depolarized and hyperpolarized tissue. This behavior may have important implications for the electrical stimulation of cardiac tissue and for defibrillation.     

On the formation of circulating patterns of excitation in anisotropic excitable media

We present a model of excitable media with the feature that it has a vulnerable phase during which a premature current stimulus will result in the formation of a reentrant selfsustained wave of excitation. The model exploits anisotropic coupling of identical cells, and is therefore useful as a model for the myocardium. We give rigorous verification that there is a vulnerable phase, and demonstrate numerically that permanently rotating waves are formed. Finally, it is shown that the direction of fastest propagation in myocardium is not necessarily the direction of highest safety factor, contrary to commonly accepted opinion.     

Propagation of shear waves in muscle tissue

A mathematical model of the propagation of acoustic shear waves in muscle tissue is considered. Muscle is modeled as an incompressible transversely isotropic viscoelastic continuum with quasi-one-dimensional active tension. There are two types of shear waves in an infinite medium. Waves of the second type (transverse) propagate without decay even when myofibril viscosity is taken into account. A problem of standing transverse waves in a rectangular layer was investigated numerically. The values of the problem parameters are found for which one can easily estimate the active tension (or muscle tone) from the characteristics of standing waves. This value is informative for diagnostics of the muscle state.     

Electric and magnetic fields from two-dimensional anisotropic bisyncytia.

Cardiac tissue can be considered macroscopically as a bidomain, anisotropic conductor in which simple depolarization wavefronts produce complex current distributions. Since such distributions may be difficult to measure using electrical techniques, we have developed a mathematical model to determine the feasibility of magnetic localization of these currents. By applying the finite element method to an idealized two-dimensional bisyncytium with anisotropic conductivities, we have calculated the intracellular and extracellular potentials, the current distributions, and the magnetic fields for a circular depolarization wavefront. The calculated magnetic field 1 mm from the tissue is well within the sensitivity of a SQUID magnetometer. Our results show that complex bisyncytial current patterns can be studied magnetically, and these studies should provide valuable insight regarding the electrical anisotropy of cardiac tissue.     

Propagation of shear waves in the muscle tissue

A mathematical model of the propagation of acoustic shear waves in muscle tissue is considered. The muscle is modelled by an incompressible transversely isotropic viscoelastic continuum with quasi-one-dimensional active tension. Two types of shear waves in an infinite medium have been established. The waves of the second type (transverse) propagate without attenuation even when myofibril viscosity is taken into account. A problem of standing transverse waves in a rectangular layer has been investigated numerically. The values of the problem parameters have been found for which the active tension or muscle tonus is easily estimated from the characteristics of standing waves. This value is informative for the diagnosis of muscle state.     

A resistor interpretation of general anisotropic cardiac tissue

This paper describes a spatial discretization scheme for partial differential equation systems that contain anisotropic diffusion. The discretization method uses unstructured finite volumes, or the boxes, that are formed as a secondary geometric structure from an underlying triangular mesh. We show how the discretization can be interpreted as a resistive circuit network, where each resistor is assigned at each edge of the triangular element. The resistor is computed as an anisotropy dependent geometric quantity of the local mesh structure. Finally, we show that under certain conditions, the discretization gives rise to negative resistors that can produce non-physical hyperpolarizations near depolarizing stimuli. We discuss how the proper choice of triangulation (anisotropic Delaunay triangulation) can ensure monotonicity (i.e. all resistors are positive).     

Propagation of Asparagus racemosus through tissue culture

Murashige and Skoog's medium with 2, 4-D and kinetin induced callus in the shoot segments of Asparagus racemosus. Regeneration of shoot buds and clonal multiplication of excised shoots through proliferation of nodal buds could be achieved by the use of IAA and BAP in the medium. Rooting was achieved with half strength MS basal medium plus IBA. Complete plants with cladode, crown and root systems were developed in hormone free medium. The plants were successfully transferred to soil.