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W Krassowska

Publications and source records attributed to W Krassowska.

30 records · Page 2Linked to original sources
PubMed1990

Potential distribution in three-dimensional periodic myocardium--Part I: Solution with two-scale asymptotic analysis.

The use of two-scale asymptotic analysis allows development of a model of the steady-state potential distribution in three-dimensional cardiac muscle preserving the underlying cellular network. The myocardium is modeled as a periodic structure consisting of cylindrical cells embedded in extracellular fluid and connected by longitudinal and side junctions. The method is applicable to cardiac muscle of arbitrary extent since the periodicity of the tissue is dealt with analytically, and thus numerical computations require no more resources than a continuous volume conductor problem. The asymptotic analysis approach reveals that the potential in a periodic myocardium consists of two components. The large-scale component provides the baseline for the total solution and can be determined from the anisotropic monodomain model associated with the original periodic problem. The method provides the formula for calculating the conductivity of the equivalent monodomain model on the basis of cell geometry and conductivity distribution in the cardiac tissue. The small-scale component reflects the periodicity of the underlying structure and oscillates with periods determined by the dimensions of cardiac cells. The magnitude of these oscillations depends upon the gradient of the large-scale component. During stimulation with extracellular electrodes, the small-scale component determines both the shape and the magnitude of the transmembrane potential, while the influence of the large-scale component is negligible. Hence, the small-scale component merits closer attention in pacing and defibrillation studies, especially since the model based on two-scale asymptotic analysis provides an effective means of its computation.

Electric Stimulation↗
PubMed1990

Potential distribution in three-dimensional periodic myocardium--Part II: Application to extracellular stimulation.

Modeling potential distribution in the myocardium treated as a periodic structure implies that activation from high-current stimulation with extracellular electrodes is caused by the spatially oscillating components of the transmembrane potential. This hypothesis is tested by comparing the results of the model with experimental data. The conductivity, fiber orientation, the extent of the region, the location of the pacing site, and the stimulus strength determined from experiments are components of the model used to predict the distributions of potential, potential gradient, and the transmembrane potential throughout the region. Next, assuming that a specific value of the transmembrane potential is necessary and sufficient to activate fully repolarized myocardium, the model provides an analytical relation between large-scale field parameters, such as gradient and current density, and small-scale parameters, such as transmembrane potential. This relation is used to express the stimulation threshold in terms of gradient or current density components and to explain its dependence upon fiber orientation. The concept of stimulation threshold is generalized to three dimensions, and an excitability surface is constructed, which for cardiac muscle is approximately conical in shape. The numerical values of transmembrane potential and stimulation thresholds calculated using asymptotic analysis are in agreement with the results of animal experiments, confirming the validity of this approach to study the electrophysiology of periodic cardiac muscle.

Animals↗
PubMed1989

Modelling the periodicity of cardiac muscle.

The intractable problem of modelling cardiac muscle of arbitrary extent while preserving cellular structure has been solved using an analytical rather than numerical approach with a method called two-scale asymptotic analysis. In this method, the myocardium was modelled as a collection of bundles arranged periodically in space and connected by junctions, and the distribution of the steady-state potential and current density was determined. The potential both along and across fibers was found to contain a distinct periodic component that determines the transmembrane potential. The magnitude of the transmembrane potential depends on the gradient of applied potential, the dimensions of the bundles, and their internal conductivity. Current flows primarily in the extracellular space, and the extracellular pathway also determines the apparent conductivity of cardiac muscle.

Electric Conductivity↗
PubMed1988

Transmural activations and stimulus potentials in three-dimensional anisotropic canine myocardium.

Epicardial and endocardial pacing are widely used, yet little is known about the three-dimensional distribution of potentials generated by the pacing stimulus or the spread of activation from these pacing sites. In six open-chest dogs, simultaneous recordings were made from 120 transmural electrodes in 40 plunge electrodes within a 35 X 20 X 5-mm portion of the right ventricular outflow tract during epicardial and endocardial pacing at a strength of twice diastolic threshold and at 1 mA. The magnitude of extracellular potentials generated by the stimulus and the activation times were compared in regions proximal (less than 10-12 mm) and distal to the pacing site. Local fiber orientation was histologically determined at each recording electrode. For endocardial pacing, endocardial potentials were larger than epicardial potentials only in the proximal region (p less than 0.001); while in the distal region, epicardial potentials were larger (p less than 0.001), and endocardial activation occurred earlier than epicardial activation for both regions (p less than 0.001). For epicardial pacing, epicardial potentials were larger than endocardial potentials in both regions (p less than 0.001), and epicardial activation occurred earlier only in the proximal region (p less than 0.02), while endocardial activation occurred before epicardial activation in the distal region (p less than 0.01). In planes of recording electrodes parallel to the epicardium and endocardium, the initial isochrones were elliptical with the major axes of the ellipses along the mean fiber orientation between the pacing site and recording plane rather than along the local fiber orientation in the recording plane. Thus, the ellipses in each plane rotated with respect to each other so that in three dimensions the activation front was helicoid, yet the twist of the helix was less than that of the corresponding transmural rotation of fibers. For pacing from the right ventricular outflow tract, we conclude that beyond 10-12 mm from endocardial and epicardial pacing sites epicardial stimulus potentials in both cases are larger than endocardial potentials because of resistivity differences inside and outside the heart wall and activation in both cases is primarily endocardial to epicardial because of rapid endocardial conduction, and we conclude that the initial spread of activation is helicoid and determined by transmural fiber direction.

Action Potentials↗
PubMed1988

Extracellular field required for excitation in three-dimensional anisotropic canine myocardium.

It is not known how well potential gradient, current density, and energy correlate with excitation by extracellular stimulation in the in situ heart. Additionally, the influence of fiber orientation and stimulus polarity on the extracellular thresholds for stimulation expressed in terms of these factors has not been assessed. To answer these questions for myocardium in electrical diastole, extracellular excitation thresholds were determined from measurements of stimulus potentials and activation patterns recorded from 120 transmural electrodes in a 35 X 20 X 5-mm region of the right ventricular outflow tract in six open-chest dogs. Extracellular potential gradients, current densities, energies, and their components longitudinal and transverse to the local fiber orientation at each recording site were calculated from the stimulus potentials produced by 3-msec constant-current stimuli. The resulting values in regions directly excited by the stimulus field were compared with the values in regions not directly excited but activated by the spread of wavefronts conducting away from the directly excited region. Magnitudes of 3.66 mA/cm2 for current density, 9.7 microJ/cm3 for energy, and 804 mV/cm for potential gradient yielded minimum misclassifications of 8%, 13%, and 17%, respectively, of sites directly and not directly excited. A linear bivariate combination of the longitudinal (l) and transverse (t) components of the potential gradient yielded 7% misclassification (threshold ratio t/l of 2.88), and linear combination of corresponding current density components yielded 8% misclassification (threshold ratio t/l of 1.04). Anodal and cathodal thresholds were not significantly different (p = 0.39). Potential gradient, current density, and energy strength-duration curves were constructed for pulse durations (D) of 0.2-20 msec. The best fit hyperbolic curve for current density magnitude (Jm) was Jm = 3.97/D + 3.15, where Jm is in mA/cm2, and D is in msec. Thus, for stimulation during electrical diastole 1) both current density magnitude and longitudinal and transverse components of the potential gradient are closely correlated with excitation, 2) the extracellular potential gradient along cardiac cells has a lower threshold than across cells, while current density thresholds along and across cells are similar, 3) anodal and cathodal thresholds are approximately equal for stimuli greater than or equal to 5 mA, and 4) the extracellular potential gradient, current density, and energy excitation thresholds can be expressed by strength-duration equations.

Action Potentials↗
PubMedDate not supplied

Electroporation and shock-induced transmembrane potential in a cardiac fiber during defibrillation strength shocks.

Experimental studies have shown that the magnitude of the shock-induced transmembrane potential (Vm) saturates with increasing electric field strength. This study uses a mathematical model to investigate the effects of electroporation and membrane kinetics on Vm in a cardiac fiber. The model consists of the core conductor equation for a one-dimensional fiber, where excitability is represented by the Luo-Rudy dynamic model (1994-1995) and electroporation is described by a membrane conductance that increases exponentially with Vm squared. For shocks delivered during the plateau of an action potential, the model reproduces the experimentally observed saturation of Vm with a root mean square error of 4.27% and a correlation coefficient of 0.9992. For shocks delivered during diastole, the saturation of Vm is qualitatively reproduced even when the sodium and calcium channels are inactivated. Quantitative replication of the response to diastolic shocks is hindered by the choice of electroporation parameters (optimized for shocks delivered during the plateau) and differences in the membrane kinetics between model and experiment. The complex behavior of Vm during large shocks is due to a combination of electroporation, electrotonus, propagation, and active membrane kinetics. The modeling results imply that the experimentally observed saturation of Vm is due to electroporation of the lipid bilayer.

Action Potentials↗
PubMedDate not supplied

The role of spatial interactions in creating the dispersion of transmembrane potential by premature electric shocks.

Strong electric shocks applied during the refractory period can initiate or terminate cardiac arrhythmias. To elucidate the underlying mechanism, Knisley et al. used rabbit papillary muscle in vitro to scan the refractory period of an action potential with shocks of different strengths. The resulting map of the shock-induced changes in the transmembrane potential (Vm) illustrates the substrate for the creation of rotors. Our study uses computer simulations to reproduce this experimental map. Three models (a space-clamped membrane, a single cell, and a one-dimensional fiber) were used to determine whether the observed map was caused by (i) the intrinsic dynamics of the membrane, (ii) the simultaneous depolarization and hyperpolarization of the opposite ends of each cell, or (iii) spatial interactions involving the whole muscle strand. The results show that the membrane and single cell models cannot reproduce the experimental map. The fiber model reproduces the shock-induced changes in Vm and demonstrates that they are caused by a propagating disturbance, which, depending on the coupling interval and the shock strength, can be a new action potential or an electrotonus and can arrive from the depolarized end or from both depolarized and hyperpolarized ends of the fiber. These results indicate that the induction of rotors in the heart may not be a direct effect of the electric field.

Action Potentials↗