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Wanda Krassowska

Publications and source records attributed to Wanda Krassowska.

14 recordsLinked to original sources
PubMed2006

Spatial heterogeneity of the restitution portrait in rabbit epicardium.

Spatial heterogeneity of repolarization can provide a substrate for reentry to occur in myocardium. This heterogeneity may result from spatial differences in action potential duration (APD) restitution. The restitution portrait (RP) measures many aspects of rate-dependent restitution: the dynamic restitution curve (RC), S1-S2 RC, and short-term memory response. We used the RP to characterize epicardial patterns of spatial heterogeneity of restitution that were repeatable across animals. New Zealand White rabbit ventricles were paced from the epicardial apex, midventricle, or base, and optical action potentials were recorded from the same three regions. A perturbed downsweep pacing protocol was applied that measured the RP over a range of cycle lengths from 1,000 to 140 ms. The time constant of short-term memory measured close to the stimulus was dependent on location. In the midventricle the mean time constant was 19.1 +/- 1.1 s, but it was 39% longer at the apex (P < 0.01) and 23% longer at the base (P = 0.03). The S1-S2 RC slope was dependent on pacing site (P = 0.015), with steeper slope when pacing from the apex than from the base. There were no significant repeatable spatial patterns in steady-state APD at all cycle lengths or in dynamic RC slope. These results indicate that transient patterns of epicardial heterogeneity of APD may occur after a change in pacing rate. Thus it may affect cardiac electrical stability at the onset of a tachycardia or during a series of ectopic beats. Differences in restitution with respect to pacing site suggest that vulnerability may be affected by the location of reentry or ectopic foci.

Action Potentials↗
PubMed2006

Modeling electroporation in a single cell.

Electroporation uses electric pulses to promote delivery of DNA and drugs into cells. This study presents a model of electroporation in a spherical cell exposed to an electric field. The model determines transmembrane potential, number of pores, and distribution of pore radii as functions of time and position on the cell surface. For a 1-ms, 40 kV/m pulse, electroporation consists of three stages: charging of the cell membrane (0-0.51 micros), creation of pores (0.51-1.43 micros), and evolution of pore radii (1.43 micros to 1 ms). This pulse creates approximately 341,000 pores, of which 97.8% are small ( approximately 1 nm radius) and 2.2% are large. The average radius of large pores is 22.8 +/- 18.7 nm, although some pores grow to 419 nm. The highest pore density occurs on the depolarized and hyperpolarized poles but the largest pores are on the border of the electroporated regions of the cell. Despite their much smaller number, large pores comprise 95.3% of the total pore area and contribute 66% to the increased cell conductance. For stronger pulses, pore area and cell conductance increase, but these increases are due to the creation of small pores; the number and size of large pores do not increase.

Cell Membrane↗
PubMed2006

Singular perturbation analysis of the pore creation transient.

Electroporation, in which electric pulses create transient pores in the cell membrane, is an important technique for drug and DNA delivery. Electroporation kinetics is mathematically described by an advection-diffusion boundary value problem. This study uses singular perturbation to derive a reduced description of the pore creation transient in the form of a single integrodifferential equation for the transmembrane voltage Vt. The number of pores and the distribution of their radii are computed from Vt. The analysis contains two nonstandard features: the use of the voltage deviation to peel away the strong exponential dependence of pore creation upon the transmembrane potential, and the autonomous approximation of the pore evolution. Comparing the predictions of the reduced equation with the simulations of the original problem demonstrates that this analysis allows one to predict with good accuracy the number and distribution of pores as a function of the electric pulse strength.

Cell Membrane↗
PubMed2005

Bistability and correlation with arrhythmogenesis in a model of the right atrium.

Rapid pacing is an important tool for understanding cardiac arrhythmias. A recent experiment involving rapid pacing of sheep atria indicated that the initiation of atrial arrhythmias may be related to the 1:1/2:1 bistability. To elucidate the mechanism of this relation, this study applied the pacing protocol from the sheep study to an idealized model of the right atrium. The model included all major anatomical features, the sino-atrial node, and the regional differences in the action potential duration (APD). A pacing protocol was applied, in which the basic cycle length (BCL) was decreased in steps of 10 ms until the response switched to 2:1, then BCL was increased. The 1:1-to-2:1 transitions occurred at shorter BCLs than the 2:1-to-1:1 transitions yielding a global bistability window of 60ms. As in the sheep study, idiopathic waves were observed at BCLs within or near the bistability window. The model was used to quantify the types, prevalence, and persistence of idiopatic waves, study their initiation and termination, and relate them to the model components. The results demonstrate that idiopatic waveforms move with the shift of the bistability window and that they disappear when bistability is eliminated. Thus, this modeling study supports causal relationship between the 1:1/2:1 bistability and the initiation of arrhythmias.

Action Potentials↗
PubMed2005

Reproducing cardiac restitution properties using the Fenton-Karma membrane model.

Modern models of cardiac membranes are often highly complex and computationally expensive, particularly when used in long simulations of spatially extended models of cardiac tissue. Therefore, there is a need for simpler membrane models that preserve the features of the complex models deemed important. This communication describes an empirical procedure that was used to choose the parameters of the three-variable Fenton-Karma (FK3V) model to reproduce the restitution properties of the Courtemanche-Ramirez-Nattel model of atrial tissue. The resulting parameter values for the FK3V model and the sensitivity table for all its parameters are provided. Thus, this study gives insight into the behavior of the FK3V model and the effect of its parameters on restitution properties.

Animals↗
PubMed2005

Restitution in mapping models with an arbitrary amount of memory.

Restitution, the characteristic shortening of action potential duration (APD) with increased heart rate, has been studied extensively because of its purported link to the onset of fibrillation. Restitution is often represented in the form of mapping models where APD is a function of previous diastolic intervals (DIs) and/or APDs, A(n+1)=F(D(n),A(n),D(n-1),A(n-1),...), where A(n+1) is the APD following a DI given by D(n). The number of variables previous to D(n) determines the degree of memory in the mapping model. Recent experiments have shown that mapping models should contain at least three variables (D(n),A(n),D(n-1)) to reproduce a restitution portrait (RP) that is qualitatively similar to that seen experimentally, where the RP shows three different types of restitution curves (RCs) [dynamic, S1-S2, and constant-basic cycle length (BCL)] simultaneously. However, an interpretation of the different RCs has only been presented in detail for mapping models of one and two variables. Here we present an analysis of the different RCs in the RP for mapping models with an arbitrary amount of memory. We determine the number of variables necessary to represent the different RCs in the RP. We also present a graphical visualization of these RCs. Our analysis reveals that the dynamic and S1-S2 RCs reside on two-dimensional surfaces, and therefore provide limited information for mapping models with more than two variables. However, constant-BCL restitution is a feature of the RP that depends on higher dimensions and can possibly be used to determine a lower bound on the dimensionality of cardiac dynamics.

Action Potentials↗
PubMed2004

Model of creation and evolution of stable electropores for DNA delivery.

Electroporation, in which electric pulses create transient pores in the cell membrane, is becoming an important technique for gene therapy. To enable entry of supercoiled DNA into cells, the pores should have sufficiently large radii (>10 nm), remain open long enough for the DNA chain to enter the cell (milliseconds), and should not cause membrane rupture. This study presents a model that can predict such macropores. The distinctive features of this model are the coupling of individual pores through membrane tension and the electrical force on the pores, which is applicable to pores of any size. The model is used to explore the process of pore creation and evolution and to determine the number and size of pores as a function of the pulse magnitude and duration. Next, our electroporation model is combined with a heuristic model of DNA uptake and used to predict the dependence of DNA uptake on pulsing parameters. Finally, the model is used to examine the mechanism of a two-pulse protocol, which was proposed specifically for gene delivery. The comparison between experimental results and the model suggests that this model is well-suited for the investigation of electroporation-mediated DNA delivery.

Biological Evolution↗
PubMed2004

The restitution portrait: a new method for investigating rate-dependent restitution.

INTRODUCTION: Electrical restitution, relating action potential duration (APD) to diastolic interval (DI), was believed to determine the stability of heart rhythm. However, recent studies demonstrate that stability also depends on long-term APD changes caused by memory. This study presents a new method for investigation of rate- and memory-dependent aspects of restitution and for assessment of mapping models of APD. METHODS AND RESULTS: Bullfrog ventricular myocardium was paced with a "perturbed downsweep protocol." Starting from a basic cycle length (BCL) of 1,000 ms, the tissue was paced until steady state was achieved, followed by single beats of longer and shorter cycle lengths. BCL was decreased by 50 to 100 ms and the process repeated. All APDs were plotted as a function of the preceding DI, which allowed simultaneous observation of dynamic, S1-S2, and two constant-BCL restitution curves in a "restitution portrait." Responses were classified as 1:1 (stimulus:response), transient 2:2, or persistent 2:2 (alternans) and were related to the slopes of the restitution curves. None of these slopes approached unity for the persistent 2:2 response, demonstrating that the traditional restitution condition does not predict alternans. The restitution portrait was used to evaluate three mapping models of APD. The models with no memory and with one-beat memory did not produce restitution portraits similar to the experimental one. A model with two-beat memory produced a qualitatively similar portrait. CONCLUSION: The restitution portrait allows a more comprehensive assessment of cardiac dynamics than methods used to date. Further study of models with memory may result in a clinical criterion for electrical instability.

Action Potentials↗
PubMed2003

Modeling postshock evolution of large electropores.

The Smoluchowski equation (SE), which describes the evolution of pores created by electric shocks, cannot be applied to modeling large and long-lived pores for two reasons: (1) it does not predict pores of radius above 20 nm without also predicting membrane rupture; (2) it does not predict postshock growth of pores. This study proposes a model in which pores are coupled by membrane tension, resulting in a nonlinear generalization of SE. The predictions of the model are explored using examples of homogeneous (all pore radii r are equal) and heterogeneous (0<or=r<or=r(max)) distributions of pores. Pores in a homogeneous population either shrink to zero or assume a stable radius corresponding to the minimum of the bilayer energy. For a heterogeneous population, such a stable radius does not exist. All pores, except r(max), shrink to zero and r(max) grows to infinity. However, the unbounded growth of r(max) is not physical because the number of pores per cell decreases in time and the continuum model loses validity. When the continuum formulation is replaced by the discrete one, the model predicts the coarsening process: all pores, except r(max), shrink to zero and r(max) assumes a stable radius. Thus, the model with tension-coupled pores does not predict membrane rupture and the predicted postshock growth of pores is consistent with experimental evidence.

Journal Article↗
PubMed2003

Electrical energy required to form large conducting pores.

This study computes the contribution of the externally induced transmembrane potential to the energy of large, highly conductive pores. This work was undertaken because the pore energy formulas existing in the literature predict qualitatively different behavior of large pores: the original formula proposed by Abidor et al. in 1979 implies that the electrical force expanding the pore increases linearly with pore radius, while later extensions of this formula imply that this force decreases to zero for large pores. Starting from the Maxwell stress tensors, our study derives the formula for the mechanical work required to deform a dielectric body in an ionic solution with steady-state electric current. This formula is related to a boundary value problem (BVP) governing electric potentials and fields in a proximity of a pore. Computer simulations yield estimates of the electrical energy for pores of two different shapes: cylindrical and toroidal. In both cases, the energy increases linearly for pore radii above approximately 20 nm, implying that the electrical force expanding the pore asymptotes to a constant value for large pores. This result is different from either of the two energy formulas mentioned above. Our study traces the source of this disagreement to approximations made by previous studies, which are suitable only for small pores. Therefore, this study provides a better understanding of the energy of large pores, which is needed for designing pulsing protocols for DNA delivery.

Biological Transport↗
PubMed2003

Field stimulation of cardiac fibers with random spatial structure.

Polarization of individual cells ("sawtooth") has been proposed as a mechanism for field stimulation and defibrillation. To date, the modeling work has concentrated on the myocardium with periodic spatial structure; this paper investigates potentials arising in cardiac fibers with random spatial structure. Ten different random fibers consisting of cells with varying length (l(c) = 100 +/- 50 microm), diameter (d(c) = 20 +/- 10 microm), thickness of extracellular space (t(e) = 1.18 +/- 0.59 microm), and junctional resistance (R(j) = 2 +/- 1 M(omega)) are studied. Simulations demonstrate that randomizing spatial structure introduces to the field-induced potential (V(m)) a randomly varying baseline, which arises due to polarization of groups of cells. This polarization appears primarily in response to randomizing t(e); R(j), l(c), and d(c) have less influence. The maximum V(m) increases from 3.5 mV in a periodic fiber to 20.5+/-4.7 mV in random fibers (1 V/cm field applied for 5 ms). Field stimulation threshold E(th) decreases from 6.9 to 1.59 +/- 0.43 V/cm, which is within the range of experimental measurements. Thresholds for normal and reversed field polarities are statistically equivalent: 1.59 +/- 0.43 versus 1.44 +/- 0.41 V/cm (p value = 0.453). Thus, V(m) arising due to random structure of the myocardium may play an important role in field stimulation and defibrillation.

Computer Simulation↗
PubMed2003

Viability of cancer cells exposed to pulsed electric fields: the role of pulse charge.

The goal of this study was to collect a comprehensive set of data that related lethal effects of electric fields to the duration of the pulse. Electric pulses of different strengths and durations were applied to a suspension of HEp-2 cells (epidermoid carcinoma of the human larynx) using a six-needle electrode array connected through an autoswitcher to a square wave generator. Pulse durations varied from 50 micros to 16 ms and the ranges of electric field were adjusted for each duration to capture cell viabilities between 0% and 100%. After pulsation, cells were incubated for 44 h at 37 degrees C, and their viability was measured spectrophotometrically using an XTT assay. For each pulse duration (d), viability data were used to determine the electric field that killed half of the cells (E50). When plotted on logarithmic axes, E50 vs. d was a straight line, leading to a hyperbolic relationship: E50=const/d. This relationship suggests that the total charge delivered by the pulse is the decisive factor in killing HEp-2 cells.

Carcinoma, Squamous Cell↗
PubMed1998

The induction of reentry in cardiac tissue. The missing link: How electric fields alter transmembrane potential.

This review examines the initiation of reentry in cardiac muscle by strong electric shocks. Specifically, it concentrates on the mechanisms by which electric shocks change the transmembrane potential of the cardiac membrane and create the physiological substrate required by the critical point theory for the initiation of rotors. The mechanisms examined include (1) direct polarization of the tissue by the stimulating current, as described by the one-dimensional cable model and its two- and three-dimensional extensions, (2) the presence of virtual anodes and cathodes, as described by the bidomain model with unequal anisotropy ratios of the intra- and extracellular spaces, (3) polarization of the tissue due to changing orientation of cardiac fibers, and (4) polarization of individual cells or groups of cells by the electric field ("sawtooth potential"). The importance of these mechanisms in the initiation of reentry is examined in two case studies: the induction of rotors using successive stimulation with a unipolar electrode, and the induction of rotors using cross-field stimulation. These cases reveal that the mechanism by which a unipolar stimulation induces arrhythmias can be explained in the framework of the bidomain model with unequal anisotropy ratios. In contrast, none of the examined mechanisms provide an adequate explanation for the induction of rotors by cross-field stimulation. Hence, this study emphasizes the need for further experimental and theoretical work directed toward explaining the mechanism of field stimulation. (c) 1998 American Institute of Physics.

Journal Article↗