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N Trayanova

Publications and source records attributed to N Trayanova.

At least 37 records · Page 2Linked to original sources
PubMed1991

Modification of a cylindrical bidomain model for cardiac tissue.

Previous models based on a cylindrical bidomain assumed either that the ratio of intracellular and interstitial conductivities in the principal directions were the same or that there was no radial variation in potential (i.e., a planar front, delta Vm/delta rho = 0). This paper presents a formulation and the expressions for the intracellular, interstitial, extracellular, and transmembrane potentials arising from nonplanar propagation along a cylindrical bundle of cardiac tissue represented as a bidomain with arbitrary anisotropy. For unequal anisotropy, the transmembrane current depends not only on the local change of the transmembrane potential but also on the nature of the transmembrane potential throughout the volume.

Animals↗
PubMed1991

Spatio-temporal characteristics of SEP to tibial nerve stimulation.

Source derivation techniques have recently been applied to analyse the spatial distribution of brain potentials. Somatosensory evoked potentials (SEPs) to tibial nerve stimulation recorded at 8 sites were analysed by using 2 source derivation techniques: Laplacian and criterion, presented by Kossev et al. (1988). First SEP recorded as a function of time were averaged and thus their basic components P39, N49, P58 were enhanced. In most of the subjects these components had maximal amplitudes at Ez rather than Cz. These sites were taken as nodes and the source derivation techniques were applied for all SEP components. Spatial derivatives (potential gradients) between adjacent leads were also computed. The current density at the nodes for different time points of SEP was obtained using Laplacian technique. For the chosen electrodes places and subjects it was found that the maximal source density did not correspond always to the SEP peak amplitudes. According to the criterion used it might be supposed that the generators of P39, N49 and P58 were located close to the scalp surface. Because of the significant individual variety of the results obtained more research is needed for choosing the appropriate scalp sites and for the contribution of the base line when measuring the SEP amplitudes.

Adult↗
PubMed1990

A planar slab bidomain model for cardiac tissue.

A fully three-dimensional model of the ventricular or atrial free wall will involve a planar geometry of finite thickness. The governing equations for the interstitial and extracellular potential of a planar slab of cardiac tissue comprised of parallel fibers undergoing uniform plane-wave activation are presented. A comparison with a bidomain of cylindrical geometry with the same half-thickness shows that the potentials in the planar bidomain (as a function of depth) approach core-conductor behavior more quickly.

Animals↗
PubMed1990

Extracellular potentials and currents of a single active fiber in a restricted volume conductor.

Based on mathematical expressions governing the electric field, the extracellular potentials generated by a single active fiber in a restricted circular cylindrical volume conductor are evaluated. This paper examines the effect of the extent of the volume conductor, with radius b, on the extracellular potentials at different field points. For values of b less than 1.5 times the fiber radius, the extracellular potentials in the volume conductor are always the core conductor potentials, independent of the shape and amplitude of the transmembrane potential. For b greater than a critical radius (a value that depends on the transmembrane potential waveform), the extracellular potentials at and near the membrane are the same as if the volume conductor were unbounded. Near the boundary with the insulator, the amplitude of the extracellular potentials is equal to the core conductor amplitude, although the potentials are much broader than the core conductor potential.

Action Potentials↗
PubMed1990

Electrotonic potentials of myelinated nerve fibers.

The extracellular electrotonic potentials of a single myelinated nerve fiber in a volume conductor of infinite extent were studied. The spatial distribution of the transmembrane electrotonic potential was obtained by integrating the system of differential equations constituting the model of the activation of a myelinated nerve fiber. The stimulus was step-like. The present investigation was concerned with the steady-state conditions only. The spatial distribution of the extracellular potentials at various radial distances in the conducting medium was calculated using the line source model. Up to a certain radial distance the discontinuous structure of the myelinated fiber is reflected in the oscillatory nature of the extracellular potentials, while further in the volume conductor the potentials are smooth. The magnitude of the radial decline of the extracellular potentials were compared for myelinated fibers of various internodal distances.

Evoked Potentials, Somatosensory↗
PubMed1990

Equivalent sources for the extracellular potentials of single fibers and bundles.

The extracellular field generated by the activity of a single fiber or a bundle of fibers can be considered as arising from equivalent sources distributed in the intracellular space. These equivalent sources can be single or double layer disks. An evaluation of the source density for each single fiber or a fiber in a bundle requires a knowledge of the intracellular and extracellular (interstitial for the bundles) potentials on both sides of the fiber membrane. This can be avoided by substituting the exact expressions for the fields in terms of the transmembrane potential. Such a calculation is rather straight forward for a single fiber, however, for a bundle of tightly packed and numerous fibers it would be easier if the discrete structure is replaced by a bi-domain in which the intracellular and interstitial spaces are considered continua, superimposed in space, separated everywhere by a membrane and characterized by macroscopic conductivities.

Animals↗
PubMed1989

Extracellular potentials of a single myelinated nerve fiber in an unbounded volume conductor.

The extracellular potentials of a single myelinated nerve fiber in an unbounded volume conductor were studied. The spatial distribution of the transmembrane potential was obtained by integrating the system of partial differential equations characterizing the electric processes in the active myelinated nerve fiber. The spatial distribution of the extracellular potentials at various radial distances in the volume conductor were calculated using the line source model. Up to a certain radial distance (500 microns) the discontinuity of the action potential propagation is reflected in the extracellular potentials, while further in the volume conductor the potentials are smooth. The effect of the fiber diameter and the internodal distance on the volume conductor potentials as well as the changes in the magnitude of the extracellular potential (in the time domain) between two adjacent nodes at various radial distances were studied. The radial decline of the peak-to-peak amplitude of the extracellular potential depends on the radial coordinate r of the field point and increases with the increase of r.

Animals↗
PubMed1989

Separation of the sodium and potassium currents from an action potential of a single active fiber.

A method for calculation of the sodium and potassium currents of an active fiber is presented. The method includes the determination of the transmembrane ionic current, the sodium Nernst potential and the sodium conductivity as well. The method was illustrated by using an action potential of a single striated frog muscle fiber. The derivatives of the experimentally recorded action potential, necessary for calculation of the ionic current, were obtained by means of Fourier transform.

Action Potentials↗
PubMed1988

Potential and current distributions in a cylindrical bundle of cardiac tissue.

The intracellular and interstitial potentials associated with each cell or fiber in multicellular preparations carrying a uniformly propagating wave are important for characterizing the electrophysiological behavior of the preparation and in particular, for evaluating the source contributed by each fiber. The aforementioned potentials depend on a number of factors including the conductivities characterizing the intracellular, interstitial, and extracellular domains, the thickness of the tissue, and the distance (depth) of the field point from the surface of the tissue. A model study is presented describing the extracellular and interstitial potential distribution and current flow in a cylindrical bundle of cardiac muscle arising from a planar wavefront. For simplicity, the bundle is considered as a bidomain. Using typical values of conductivity, the results show that the intracellular and interstitial potential of fibers near the center of a very large bundle (greater than 10 mm) may be approximated by the potentials of a single fiber surrounded by a limited extracellular space (a fiber in oil), hence justifying a core-conductor model. For smaller bundles, the peak interstitial potential is less than that predicted by the core-conductor model but still large enough to affect the overall source strength. The magnitude of the source strength is greatest for fibers lying near the center of the bundle and diminishes sharply for fibers within 50 microns of the surface.

Animals↗
PubMed1988

Comparison of the different variants of the current source density analysis methods in neurophysiological studies.

Computer calculations and theoretical studies of different variants of current-source density analysis (CSDA) for neurophysological studies were carried out. The different variants of the method are compared by estimating equiweight surfaces and equiweight lines in particular planes. The decrease in the distance between the different points of measurement has been found to result in more selective presentation of the neuronal activity. It is shown that this distance cannot be very small--50 micron seems a reasonable limit. Bidimensional and especially unidimensional CSD-analysis produces considerable volumes with negative weights, these weights being rather high in absolute value. Errors in the interpretation of the results are possible, such as incorrect calculation of the current density and even erroneous determination of its sign.

Mathematics↗
PubMed1988

A method for calculation the extracellular potentials from experimentally recorded intracellular potentials of a single muscle fibers.

A method for calculation the extracellular potentials from experimentally recorded intracellular potentials of single muscle fibers is proposed. The method is based on the use of Fourier transform technique. The extracellular potentials of single frog muscle fibers in homogeneous unbounded volume conductor at different temperature are calculated. An analytical approximation of the intracellular action potential (including the afterpotential) is proposed. By the use of this approximation the capability of the method is studied.

Action Potentials↗
PubMed1987

Extracellular potential field of unmyelinated active axons.

Experimental and model investigations were carried out on the extracellular action potentials and potential fields of some unmyelinated axons: the medial and the lateral giant axons of Lumbriscus terrestris and small unmyelinated axons (nerve fibres of group C). Close to the membrane the extracellular action potentials are similar in shape to the second space derivative of the intracellular action potentials--they are triphasic in case of intracellular action potential with depolarization after-potential, having four phases in case of intracellular action potentials with hyperpolarization after-potential. Upon increasing the radial distance, the amplitudes of the different phases of the extracellular action potentials decrease at a different rate, while their maxima are shifted, which results in considerable changes in their shape.

Action Potentials↗
PubMed1987

Optimization of the source derivations from the scalp surface.

The selectivity of source derivations (SD) is computer-calucla ted using different combinations of electrodes and different interelectrode differences, with a view to the optimization of the method. For this purpose, the method described by Nunez and Katznelson (1981) is used to calculate surfaces in the brain tissue from the points of which a single current source will determine the same potential in a given point on the scalp surface. The lines of these surfaces are given for different planes. The calculations show that the selectivity increases with the decrease of the interelectrode distances, as well as when more electrodes are used. With a small number of electrodes for SD and especially when one central and two lateral electrodes are used, there exist brain areas in which the generators cause a potential with opposite sign on the scalp surface.

Electrodes↗
PubMed1986

Influence of the muscle fibre end geometry on the extracellular potentials.

Intra- and extracellular action potentials of isolated frog muscle fibres were recorded at different distances to the end of the fibre. The first and second time derivatives of the intracellular action potentials were also recorded. The intracellular action potentials and their first and second time derivatives were almost the same regardless of the place of recording. With the decrease in the axial distance to the end the extracellular action potentials changed gradually in a complicated manner from a shape similar to the second time derivative into a shape similar to the first time derivative. Extracellular potentials, having two negative maxima, were recorded over the terminal taper part of the fibres. These alterations were simulated by a mathematical model. It was shown that the changes in the shape of the extracellular action potentials around the end of the fibres were mainly due to the existence of the fibre end though a better correspondence of the experimentally recorded and the calculated extracellular action potentials was obtained when the morphology of the fibre end was taken into consideration.

Action Potentials↗
PubMed1986

Motor unit potentials at high muscle activity recorded by selective electrodes.

The selectivity of different kinds of electrodes for recording of single motor unit potentials was theoretically evaluated. A new type of selective "branched", superficial and subcutaneous wire electrodes was described. The discharge of single alpha motoneurons during movements against elastic resistance was investigated studying motor unit potentials in m. biceps brachii and m.interosseus dorsalis l. Depending on the velocity of the movement, the following pattern of discharge was found: 1) At slow velocity the frequency of discharge increased and new motor units were recruited. 2) At higher velocity the frequency of discharge was constant. The muscle force increased only when new motor units were recruited. 3) At very quick ballistic movements the frequency of discharge decreased during the movement.

Adult↗
PubMed1985

Relations between the shapes of different muscle potentials. Experimental and model investigations.

Intracellular muscle action potentials, the corresponding to them extracellular action potentials recorded at short and long radial distances, extraterritorial motor unit potentials, evoked muscle potentials (M-, H- and T-potentials) and averaged potentials of the summated electromyogram were studied experimentally and compared with the calculated potentials. The similarity in the shape of the different muscle potentials and some second-rate differences were explained taking into account the point of recording, the different degree of desynchronization of the summated potentials and some other factors.

Action Potentials↗
PubMedDate not supplied

Influence of anisotropy on local and global measures of potential gradient in computer models of defibrillation.

A heart-torso model including fiber orientation is used to calculate electric field strength in an active-can transvenous defibrillation system and estimate errors due to inadequate description of the anisotropy of the myocardium. Using a minimum potential gradient (5 V/cm) in a critical mass (95%) of the tissue, the estimated defibrillation voltage threshold for a right ventricular transvenous lead placement differs by only 4.5% when using isotropic myocardial conductivity compared to a model with realistic fiber architecture. In addition, pointwise comparisons of the two solutions reveal differences of 10.8% rms in potential gradient strength and 31.6% rms in current density magnitude in the myocardium, resulting in a change in the location of the low gradient regions. These results suggest that if a minimum potential gradient throughout the heart is necessary to avoid reinitiation of fibrillatory wave fronts, then isotropic models are adequate for modeling the electric field in the heart. Alternatively, the model demonstrates the use of physiologically based descriptions of anisotropy and fiber orientation, which will soon allow simulations of shock induced membrane polarization during defibrillation.

Adult↗