This paper describes the dynamics of circus movement around a fixed obstacle, using a one-dimensional continuous and uniform ring model of cardiac tissue to simulate sustained reentry. The membrane ionic current is simulated by a modified Beeler-Reuter formulation in which the kinetics of the fast sodium current were updated using more recent voltage-clamp data. Changes in the ring length are used to modify the dynamics of reentry. Reentry is stable if the ring length (X) exceeds a critical value (Xcrit) and complete block occurs if X is below a minimum (Xmin). Irregular sustained reentry is observed at intermediate ring lengths, as a narrow range of aperiodic reentry near Xcrit, and a larger range of quasi-periodic reentry at shorter ring lengths. The basic pattern of irregular reentry is an alternation between long and short cycle length, action potential duration (APD), diastolic interval (DIA), wavelength, and excitable gap. In aperiodic reentry cycle length variations are small, APD and DIA fluctuations are of medium amplitude, and conduction velocity over the whole pathway is essentially constant during successive turns. Much larger fluctuations in these various quantities occur during quasi-periodic reentry, and they increase in size as X approaches Xmin. The complexity of quasi-periodic reentry patterns is related to three factors: the slope of the APD versus DIA relation, which is greater than 1, the existence of a zone of slow conduction on the ring when the excitable gap becomes quite short, and the occurrence of triggered waves of secondary repolarization and excitability recovery. In the present model, quasi-periodic reentry with triggered secondary recovery covers most of the range of ring lengths, giving rise to sustained irregular reentry. There is very close agreement between our simulation results and experimental data obtained on rings of cardiac tissue.

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PubMedDate not supplied

Simulation of two-dimensional anisotropic cardiac reentry: effects of the wavelength on the reentry characteristics.

A two-dimensional sheet model was used to study the dynamics of reentry around a zone of functional block. The sheet is a set of parallel, continuous, and uniform cables, transversely interconnected by a brick-wall arrangement of fixed resistors. In accord with experimental observations on cardiac tissue, longitudinal propagation is continuous, whereas transverse propagation exhibits discontinuous features. The width and length of the sheet are 1.5 and 5 cm, respectively, and the anisotropy ratio is fixed at approximately 4:1. The membrane model is a modified Beeler-Reuter formulation incorporating faster sodium current dynamics. We fixed the basic wavelength and action potential duration of the propagating impulse by dividing the time constants of the secondary inward current by an integer K. Reentry was initiated by a standard cross-shock protocol, and the rotating activity appeared as curling patterns around the point of junction (the q-point) of the activation (A) and recovery (R) fronts. The curling R front always precedes the A front and is separated from it by the excitable gap. In addition, the R front is occasionally shifted abruptly through a merging with a slow-moving triggered secondary recovery front that is dissociated from the A front and q-point. Sustained irregular reentry associated with substantial excitable gap variations was simulated with short wavelengths (K = 8 and K = 4). Unsustained reentry was obtained with a longer wavelength (K = 2), leading to a breakup of the q-point locus and the triggering of new activation fronts.

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PubMedDate not supplied

Simulation of propagation along an isolated skeletal muscle fiber in an isotropic volume conductor.

This paper describes a model of the frog skeletal muscle fiber that includes the effects of the transverse tubular system (T system) on propagation. Uniform propagation on an isolated fiber suspended in Ringer's solution or in air is simulated by placing the cylindrical fiber model in a concentric three-dimensional isotropic volume conductor. The current through the T system outlets at the sarcolemmal surface is comparable in magnitude to the sarcolemmal current density, but is of opposite polarity. When it is added to the sarcolemmal current, the resulting triphasic waveform has a 100% increase in the leading positive peak, a 50% reduction in the negative peak, and more than 60% reduction in the trailing positive peak. As a result the tubular output current causes a reduction in the conduction velocity, a decrease in the maximum rate of rise of the action potential. and an important modification of the extracellular potential. Compared to an isolated fiber in a large volume of Ringer's solution, uniform propagation within a 2-micron-thick volume conductor annulus is slowed down from 1.92 to 0.72 m/s, and the extracellular potential is increased from 1 to 108 mV peak to peak, in agreement with published experimental measurements.

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PubMedDate not supplied

Propagation on a central fiber surrounded by inactive fibers in a multifibered bundle model.

We studied uniform propagation on a central active fiber surrounded by inactive fibers in a multifibered bundle model lying in a large volume conductor. The behavior of a fully active bundle is considered in a companion paper. The bundle is formed by concentric layers of small cylindrical fibers (radius 5 microns), with a uniform minimum distance (d) between any two adjacent fibers, to yield a bundle radius of about 72 microns. Individual fibers are identical continuous cables of excitable membrane based on a modified Beeler-Reuter model. The intracellular volume fraction (fi) increases to a maximum of about 90% as d is reduced and remains unchanged for d < 0.01 micron. In the range of d < 0.01 micron, the central fiber is effectively shielded from external effects by the first concentric layer of inactive fibers, and a large capacitive load current flows across the surrounding inactive membranes. In addition, the fiber proximity produces a circumferentially nonuniform current density (proximity effect) that is equivalent to an increased average longitudinal interstitial resistance. The conduction velocity is reduced as d becomes smaller in the range of d < 0.1 micron, the interstitial potential becomes larger, and both the maximum rate of rise and time constant of the foot of the upstroke are increased. On the other hand, for d > 0.1 micron, there are negligible changes in the shape of the upstroke, and the behavior of the central fiber is close to that of a uniform cable in a restricted volume conductor. For d larger than about 1.2 microns, the active fiber environment is close to an unbounded isotropic volume conductor.

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PubMedDate not supplied

Interactions between adjacent fibers in a cardiac muscle bundle.

A strand of cardiac muscle was modeled as a small bundle of individual fibers surrounded by a large volume conductor. The bundle is a uniform assembly of small identical cylindrical fibers, arranged as a series of concentric layers, and its behavior is examined in the presence (coupled bundle) or absence (uncoupled bundle) of transverse resistive coupling between adjacent fibers. Individual fibers are continuous cables of excitable membrane, with circumferential segmentation into 12 equal patches to make the membrane potential changes dependent upon the local interstitial potential. The minimum spacing (d) between adjacent fibers is used to modify the interstitial microstructural organization and the intracellular volume fraction (fi). When d is small enough (d < 0.01 micron), fi remains unchanged at its maximum of about 90%, the interstitial potential is large, the transverse interstitial resistance is high, and the proximity effect arising from the close juxtaposition of adjacent fibers is important. A surface fiber of the uncoupled bundle exhibits little sensitivity to changes in the interstitial microstructure, owing to the dominant influence of the external volume conductor, whereas the central fiber shows a large decrease in velocity, substantial waveshape modifications, and a large increase in interstitial potential as d is reduced. In the coupled bundle, all fibers adopt the same velocity during uniform propagation, owing to the strong transverse resistive coupling; when d is reduced in the range of d < 0.01 micron, the velocity and interstitial potential changes are less pronounced than in the uncoupled bundle. When d is large enough (d > 0.01 micron), the bundle behavior (coupled and uncoupled) approaches that obtained with a bidomain formulation.

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PubMedDate not supplied

Simulation of propagation in a bundle of skeletal muscle fibers: modulation effects of passive fibers.

Computer simulations are used to study passive fiber modulation of propagation in a tightly packed bundle of frog skeletal muscle fibers (uniform fiber radius of 50 microns). With T = 20 degrees C and a uniform nominal interstitial cleft width d = 0.35 microns, about 92% of the active fiber source current (Ima) enters the passive tissue as a radial load current (Iep) while the rest flows longitudinally in the cleft between the active and adjacent passive fibers. The conduction velocity of 1.32 m/s was about 30% lower than on an isolated fiber in a Ringer bath, in close agreement with experimental results. The peak-to-peak interstitial potential (phi epp) at the active fiber surface was 38 mV, compared to 1.3 mV for the isolated fiber. A uniform increase of d from 0.35 to 1.2 microns decreased phi epp from 38 to 25 mV, increased the velocity from 1.32 to 1.54 m/s, and decreased the maximum rate of rise of the action potential upstroke (Vmax) from 512 to 503 V/s. Increasing the phase angle of the passive fiber membrane impedence (Zm) increases the phase delay between lma and lep thereby increasing phi epp which in turn slows down propagation and increases V max.

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