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W Krassowska

Publications and source records attributed to W Krassowska.

At least 19 recordsLinked to original sources
PubMed1995

Effects of electroporation on transmembrane potential induced by defibrillation shocks.

This study uses a one-dimensional model of cardiac strand to investigate the effects of electroporation on transmembrane potential (Vm) induced by defibrillation shocks. The strand is stimulated at the ends by extracellular electrodes. Its membrane, when exposed to large Vm, increases its conductance in a manner consistent with reversible electrical breakdown. Numerical simulations indicate that Vm increases proportionally to the shock strength only until the ends of the strand electroporate. Beyond this point, further increases in shock strength result in only a minor change in Vm. This arrest in the growth of Vm is caused by pores that develop in the cells immediately adjacent to the electrodes and that shunt part of the stimulating current directly into intracellular space. Consequently, only a fraction of the delivered current, Icr, gives rise to Vm; the current in excess of Icr divides itself proportionally between intra- and extracellular space and does not contribute to macroscopic Vm. Thus, electroporation has a beneficial effect: the formation of pores prevents the development of an excessively high Vm and limits the damage to the tissue. In contrast, electroporation does not affect the "sawtooth" component of Vm that reflects polarization of individual cells by electric field. These results indicate that electroporation does not impair the ability of the shock to reach the distant myocardium and may actually aid defibrillation by reducing nonuniformity of electrical conditions between regions close to the electrodes and in the bulk of tissue.

Algorithms↗
PubMed1995

Choosing the optimal monophasic and biphasic waveforms for ventricular defibrillation.

INTRODUCTION: The truncated exponential waveform from an implantable cardioverter defibrillator can be described by three quantities: the leading edge voltage, the waveform duration, and the waveform time constant (tau s). The goal of this work was to develop and test a mathematical model of defibrillation that predicts the optimal durations for monophasic and the first phase of biphasic waveforms for different tau s values. In 1932, Blair used a parallel resistor-capacitor network as a model of the cell membrane to develop an equation that describes stimulation using square waves. We extended Blair's model of stimulation, using a resistor-capacitor network time constant (tau m), equal to 2.8 msec, to explicitly account for the waveform shape of a truncated exponential waveform. This extended model predicted that for monophasic waveforms with tau s of 1.5 msec, leading edge voltage will be constant for waveforms 2 msec and longer; for tau s of 3 msec, leading edge voltage will be constant for waveforms 3 msec and longer; for tau s of 6 msec, leading edge voltage will be constant for waveforms 4 msec and longer. We hypothesized that the best phase 1 of a biphasic waveform is the best monophasic waveform. Therefore, the optimal first phase of a biphasic waveform for a given tau s is the same as the optimal monophasic waveform. METHODS AND RESULTS: We tested these hypotheses in two animal experiments. Part I: Defibrillation thresholds were determined for monophasic waveforms in eight dogs. For tau s of 1.5 msec, waveforms were truncated at 1, 1.5, 2, 2.5, 3, 4, 5, and 6 msec. For tau s of 3 msec, waveforms were truncated at 1,2,3,4,5,6, and 8 msec. For tau s of 6 msec, waveforms were truncated at 2,3,4,5,6,8, and 10 msec. For waveforms with tau s of 1.5, leading edge voltage was not significantly different for the waveform durations of 1.5 msec and longer. For waveforms with tau s of 3 msec, leading edge voltage was not significantly different for waveform durations of 2 msec and longer. For waveforms with tau s of 6 msec, there was no significant difference in leading edge voltage for the waveforms tested. Part II: Defibrillation thresholds were determined in another eight dogs for the same three tau s values. For each value of tau s, six biphasic waveforms were tested: 1/1, 2/2, 3/3, 4/4, 5/5, and 6/6 msec. For waveforms with tau s of 1.5 msec, leading edge voltage was a minimum for the 2/2 msec waveform. For waveforms with tau s of 3 msec, leading edge voltage was a minimum for the 3/3 msec waveform. For waveforms with tau s of 6 msec, leading edge voltage was a minimum and not significantly different for the 3/3, 4/4, 5/5, and 6/6 msec waveforms. CONCLUSIONS: The model predicts the optimal monophasic duration and the first phase of a biphasic waveform to within 1 msec as tau s varies from 1.5 to 6 msec: for tau s equal to 1.5 msec, the optimal monophasic waveform duration and the optimal first phase of a biphasic waveform is 2 msec, for tau s equal to 3.0 msec, the optimal duration is 3 msec, and for tau s equal to 6 msec, the optimal duration is 4 msec. For both monophasic and biphasic waveforms, optimal waveform duration shortens as the waveform time constant shortens.

Animals↗
PubMed1994

Response of a single cell to an external electric field.

The response of a cell to an external electric field is investigated using dimensional analysis and singular perturbation. The results demonstrate that the response of a cell is a two-stage process consisting of the initial polarization that proceeds with the cellular time constant (< 1 microseconds), and of the actual change of physiological state that proceeds with the membrane time constant (several milliseconds). The second stage is governed by an ordinary differential equation similar to that of a space-clamped membrane patch but formulated in terms of intracellular rather than transmembrane potential. Therefore, it is meaningful to analyze the physiological state and the dynamics of a cell as a whole instead of the physiological states and the dynamics of the underlying membrane patches. This theoretical result is illustrated with an example of an excitation of a cylindrical cell by a transverse electric field.

Action Potentials↗
PubMed1994

Effective boundary conditions for syncytial tissues.

This study derives effective boundary conditions for potentials and currents on the interface between syncytial tissue and a surrounding volume conductor. The derivation is based on an idealized representation of the syncytium as a network of interconnected cells arranged periodically in space. The microscopic model of an interface assumes that the extracellular fluid is in direct contact with the outside volume conductor and that the inside of the cells is separated from the outside by the membrane. From this microscopic model, a homogenization process and boundary layer analysis derive effective boundary conditions applicable to macroscopic volume-averaged potentials. These effective boundary conditions call for the extracellular potential and current density to be continuous with the potential and current density in the volume conductor, and for the intracellular current to vanish. Hence, the long-debated appropriate boundary conditions for the bidomain model are established.

Electric Conductivity↗
PubMed1994

Strength-interval curves in canine myocardium at very short cycle lengths.

While ventricular electrophysiological properties have been intensively studied at normal heart rates, little is known about these properties at the very short cycle lengths (approximately 100 msec), which are present in ventricular fibrillation. We examined refractoriness in the right ventricles of six dogs at stimulation intervals of 80 to 300 msec. Starting at 300 msec, the basic (S1) cycle length was decremented by 10 msec each beat to 200, 150, or 125 msec. A 1-msec premature (S2) stimulus of 1, 5, 10, or 20 mA was then introduced. The S1-S2 interval was decremented until capture was lost. The refractory period was considered to be the shortest interval that captured the heart for each S2 strength. Only pacing episodes that did not induce fibrillation were included. Strength-interval curves maintained the same hyperbolic shape but shifted to very short refractory periods as the S1-S1 interval was decreased. At the shortest S1-S1 intervals, premature stimuli were capable of capturing the heart without inducing ventricular fibrillation for S1-S2 intervals as short as 83 +/- 3 msec. Thus, decremental rapid pacing can produce refractory periods shorter than the cycle length during ventricular fibrillation. This finding suggests that there is no need to postulate a discontinuous jump to new electrophysiological properties or relationships at the onset of fibrillation, but that the capability for fibrillation is an integral part of normal electrophysiological parameters when they are pushed to values that do not occur normally. The results of this study should be useful in the further development of active membrane models and cellular automata models of cellular electrical behavior.

Animals↗
PubMed1993

Effective defibrillation in pigs using interleaved and common phase sequential biphasic shocks.

Previous studies have shown that low internal defibrillation thresholds (DFTs) can be attained by using two pairs of electrodes and combining biphasic shocks with sequential timing. The purpose of this two-part study was to test the defibrillation efficacy of two new shock sequences, an interleaved biphasic, and a common phase sequential biphasic, that utilized two pairs of electrodes and were developed from the concept of sequential biphasic shocks. In the first part, defibrillation catheters were placed in the right ventricle and the superior vena cava of six anesthetized pigs. A small patch electrode was placed on the LV apex through a subxiphoid incision and a cutaneous patch was placed on the left thorax. The mean DFT energies for the interleaved biphasic (5.2 +/- 0.4 J) and the common phase sequential biphasic waveforms (5.4 +/- 0.4 J) were substantially less (P < 0.0001) than those for either the sequential monophasic (10.6 +/- 1.0 J) or single biphasic waveforms (9.0 +/- 1.0 J). In the second study, which used nine anesthetized pigs, the importance of phase reversal was demonstrated by the finding that the DFT energy of a common phase sequential biphasic shock (6.2 +/- 0.4 J) was much less than a common phase sequential monophasic shock (17.9 +/- 1.3 J, P < 0.0001); furthermore, the average DFT for four common phase sequential biphasic configurations (5.7 +/- 0.2 J) was much less than for a configuration that was similar except that current flow was not reversed in one phase so that no biphasic effect was present (19.7 +/- 1.2 J). The efficacy of common phase sequential biphasics was comparable to that of sequential biphasics. The effectiveness of sequential biphasics, interleaved biphasics, and common phase sequential biphasics is possibly due to two mechanisms: (A) an increase in the potential gradient during a later phase in regions that were low during the first phase, and (B) the exposure of most of the myocardium to a biphasic shock that reduces the minimum extracellular potential gradient needed to defibrillate.

Animals↗
PubMed1993

Homogenization of syncytial tissues.

This article derives a continuum representation of a multicellular, syncytial tissue directly from its microstructure and basic physical principles. The final equations for the homogenized syncytium contain the bidomain model as a special case. The derivation begins with an idealized, periodic representation of the tissue microstructure. Potentials inside the cells and in the extracellular fluid are governed by the Laplace equation. Electrical properties of the membrane separating those two regions are represented by the boundary conditions on the potentials. An homogenization process based on a two-scale asymptotic expansion converts this microscopic, pointwise description into an averaged, continuum representation by two reaction-diffusion equations. The same process also yields formulas for the effective conductivities of the tissue in terms of its microstructure and specific conductivities of cytoplasm and extracellular fluid. The validity of the homogenized syncytium model is assured deep in the tissue for autonomous processes, such as propagation, and in the presence of external fields that are nearly uniform and limited in strength. The derived model is not formally valid on the surface of tissue, in the proximity of sources, and under strong or rapidly changing electrical fields.

Cell Communication↗
PubMed1992

Propagation versus delayed activation during field stimulation of cardiac muscle.

This modeling study seeks to explain the experimentally detected delay between the application of an electric field and the recorded response of the transmembrane potential. In this experiment, conditions were deliberately set so that the field should excite all cells at once and so that no delay should be caused by a propagating wave front. The explanation of the observed delay may lie in the intrinsic properties of the membrane. To test this hypothesis, the strength latency curves were determined for three cases: (1) for a membrane patch model, in which the membrane is uniformly polarized and its intrinsic properties can be studied; (2) for the cardiac strand directly excited by the electric field; and (3) for the cardiac strand excited by a propagating wave front. The models of the membrane patch and the directly excited strand yield excitation delays that are comparable to those observed experimentally in magnitude and in the overall shape of the strength latency curves. The delays resulting from propagation are, in general, dependent on the position along the strand, although for some positions the strength latency curves for propagation are similar to those obtained from the directly activated strand and from the patch model. Therefore, the delay in excitation does not necessarily imply the presence of propagating wave fronts and can be attributed to intrinsic membrane kinetics.

Animals↗
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↗