An electronic device for triggering a stimulator during membraneresponsiveness determinations in cardiac tissues

A device is described that monitors the repolarization phase of a cardiac action potential and compares the membrane potential to a voltage selected by the investigator. When the voltages are the same, the device triggers a stimulator that injects the stimulus at the desired membrane potential. The device can stimulate tissue at any membrane potential during the repolarization phase of the action potential between 0 and -100 mV without regard to action potential duration. When it is precisely calibrated, its accuracy is within ±1.0 mV     

Bidirectional Nerve Refractory Characteristics in Simulations of Direct and Remote Stimulation

The effects of remote stimulation on the refractory characteristics of myelinated nerve fibers were investigated using computer simulations of nerve action potentials, in response to spatially separated conditioning and test stimuli. The behavior of the test action potential was strongly influenced by its direction of propagation relative to that of the conditioning action potential. Under certain conditions, the variation of relative refractory period with conduction velocity (CV) changed from inverse, for propagation in opposing directions, to direct, for propagation in the same direction. A similar directionally dependent result occurred in the study of relative refractory period as a function of stimulus intensity. At certain interstimulus intervals, the test stimulus elicited action potentials which would conduct in the direction opposite to the conditioning action potential, but would not conduct in the wake of that conditioning action potential. These results are explained in terms of the spatial spread of stimulus current resulting from distant placement of the stimulating electrode in a volume conductor. Clinical repercussions of these results for correction of refractory period in collision neurography are discussed.     

Contributions of Purkinje-myocardial coupling to suppression and facilitation of early afterdepolarization-induced triggered activity

Electrical loading by ventricular myocardium modulates conduction system repolarization near Purkinje-ventricular junctions (PVJs). We investigated how that loading suppresses and facilitates early afterdepolarizations (EADs) under conditions where there is a high degree of functional coupling between tissue types, which is consistent with the anatomic arrangement at the peripheral conduction system-myocardial interface. Experiments were completed in eight rabbit right ventricular (RV) free wall preparations. Free-running Purkinje strands were locally superfused, and action potentials were recorded from strands. RV free walls were bathed in normal solution. Surface electrograms were recorded near strand insertions into downstream free wall myocardium. Detailed histology was performed to assemble a computer model with interspersed Purkinje and ventricular myocytes weakly coupled throughout the region. Delays from Purkinje upstrokes to downstream peripheral conduction system and myocardial activation were comparable between experiments and simulations, supporting model node-to-node electrical coupling, i.e., the functional coupling. Purkinje action potential duration (APD) prolongation with localized isoproterenol in experiments and calcium current enhancement in simulations failed to establish EADs. With myocardial APD prolongation by delayed rectifier potassium current inhibition or L-type calcium current enhancement accompanying Purkinje APD prolongation in simulations, however, EAD-induced triggered activity developed. Collectively, our findings suggest competing contributions of the myocardial sink when there is a high degree of functional coupling between tissue types, with the transition from suppression to facilitation of EAD-induced triggered activity depending critically upon myocardial APD prolongation.     

Relating the Sodium Current and Conductance to the Shape of Transmembrane and Extracellular Potentials by Simulation: Effects of Propagation Boundaries

The purpose of this paper is to describe how the transmembrane and extracellular potential waveforms, and their derivatives, are related to each other and to the sodium current and conductance in propagating cardiac action potentials. The results show that the shape of the transmembrane potential and the kinetics of the sodium current and conductance are highly determined by boundary effects at sites where impulse conduction begins and where it ends at a collision or an anatomical end. These propagation nonuniformities produced a relationship between Vmax and the internal membrane variables gNa and INa that is just the opposite of the classical relation between Vmax and the magnitude of the sodium current. For example, in these cases, both peak INa and the area under the gNa curve decreased when Vmax increased. In addition, Vmax, was shown to coincide in time with the maximum rate of increase of gNa and INa. The maximum negative slope of the extracellular waveform coincided in time with Vmax of the transmembrane potential for all shapes of the waveforms. Therefore, either the maximum negative slope of the extracellular waveform or Vmax of the action potential provides a time marker for the same underlying depolarizing event, i.e., the maximum rate of increase of the depolarizing current and its conductance.     

Structural complexity effects on transverse propagation in atwo-dimensional model of myocardium

A thin sheet of cardiac tissue was modeled as a set of resistively coupled excitable cables with membrane dynamics described by the modified Beeler Reuter model. Transverse connections have a resistance Rn and are regularly distributed with a spacing delta on any given cable, to provide alternating input and output junctions. Flat wave longitudinal propagation corresponds to propagation along a single continuous cable since all units of the network are functionally isolated due to the absence of transverse current flow. Events on a given cable during flat transverse propagation include electrotonic spread of potential from input to output junctions, action potential initiation at input junctions, and collision at output junctions. The propagating two-dimensional transverse wavefront is an undulating transmembrane potential surface with highs at the input junctions and lows at the output junctions. The action potential upstroke is also modulated in a periodic manner with minimum and maximum Vmax at the input and output junctions respectively. Thus, the network is capable of a diversity of dynamic behavior spatially distributed in relation to the specific pattern of transverse connections chosen. Overall, the behavior of the network model is in good agreement with available structural and electrophysiological data on myocardium. In addition, this network topology allows to handle more easily parameters governing propagation and to avoid very large matrices which are costly in computational effort and overall computer time.     

Electrical coupling and impulse propagation in anatomically modeledventricular tissue

Computer simulations were used to study the role of resistive couplings on flat-wave action potential propagation through a thin sheet of ventricular tissue. Unlike simulations using continuous or periodic structures, this unique electrical model includes random size cells with random spaced longitudinal and lateral connections to simulate the physiologic structure of the tissue. The resolution of the electrical model is ten microns, thus providing a simulated view at the subcellular level. Flat-wave longitudinal propagation was evaluated with an electrical circuit of over 140,000 circuit elements, modeling a 0.25 mm by 5.0 mm sheet of tissue. An electrical circuit of over 84,000 circuit elements, modeling a 0.5 mm by 1.5 mm sheet was used to study flat-wave transverse propagation. Under normal cellular coupling conditions, at the macrostructure level, electrical conduction through the simulated sheets appeared continuous and directional differences in conduction velocity, action potential amplitude and V˙_max were observed. However, at the subcellular level (10 μm) unequal action potential delays were measured at the longitudinal and lateral gap junctions and irregular wave-shapes were observed in the propagating signal. Furthermore, when the modeled tissue was homogeneously uncoupled at the gap junctions conduction velocities decreased as the action potential delay between modeled cells increased. The variability in the measured action potential was most significant in areas with fewer lateral gap junctions, i.e., lateral gap junctions between fibers were separated by a distance of 100 μm or more     

The effect of externally applied electrical fields on myocardialtissue

The explanation of the response to electrical stimulus by macroscopic regions of cardiac tissue in terms of the behavior of membrane ion channels requires mathematical models that span the range of spatial scales from the single cardiac cell to the entire heart. This is accomplished by the bidomain model, which successfully characterizes the electrical properties of the heart and the effect of externally applied electric fields on myocardial tissue, Recently the bidomain model has been used to make several specific, testable predictions: (1) a 4-fold symmetric magnetic field pattern is associated with an expanding wave front, (2) a region of positive interstitial potential precedes an expanding wave front in the direction parallel to the myocardial fibers, (3) the rate of rise of an action potential depends on the direction of propagation in superfused tissue, (4) the wave front in superfused strands of tissue is curved (5) a “dog bone” shaped region of depolarization exists under a unipolar cathode, (6) depolarized regions along the fiber direction adjacent to a unipolar anode are responsible for anodal stimulation, (7) interactions between adjacent depolarized and hyperpolarized tissue cause anode-break and cathode-break stimulation, (8) reentry can be induced by successive stimulation using a single unipolar cathode, and (9) a mechanism for far field stimulation depends on fiber curvature. These predictions have been verified qualitatively in every case where they have been tested experimentally. In some cases, such as the mechanisms for reentry induction and far field stimulation, the necessary experiments have not yet been performed     

Simulation of QRST integral maps with a membrane-based computer heart model employing parallel processing

The simulation of the propagation of electrical activity in a membrane-based realistic-geometry computer model of the ventricles of the human heart, using the governing monodomain reaction-diffusion equation, is described. Each model point is represented by the phase 1 Luo-Rudy membrane model, modified to represent human action potentials. A separate longer duration action potential was used for the M cells found in the ventricular midwall. Cardiac fiber rotation across the ventricular wall was implemented via an analytic equation, resulting in a spatially varying anisotropic conductivity tensor and, consequently, anisotropic propagation. Since the model comprises approximately 12.5 million points, parallel processing on a multiprocessor computer was used to cut down on simulation time. The simulation of normal activation as well as that of ectopic beats is described. The hypothesis that in situ electrotonic coupling in the myocardium can diminish the gradients of action-potential duration across the ventricular wall was also verified in the model simulations. Finally, the sensitivity of QRST integral maps to local alterations in action-potential duration was investigated.     

The magnetic field associated with a plane wave front propagating through cardiac tissue

An action potential propagating through a two-dimensional sheet of cardiac tissue produces a magnetic field. In the direction of propagation, the intracellular and extracellular current densities are equal and opposite, so the net current is zero. However, because of the unequal anisotropy ratios in the intracellular and extracellular spaces, the component of the current density perpendicular to the direction of propagation does not, in general, vanish. This line of current produces the magnetic field. The amplitude of the magnetic field is zero only if the action potential propagates parallel to or perpendicular to the fiber direction, or if the tissue has equal anisotropy ratios.     

The role of the hyperpolarization-activated inward current If in arrhythmogenesis: a computer model study.

Atrial fibrillation is the most common cardiac arrhythmia. Structural cardiac defects such as fibrosis and gap junction remodeling lead to a reduced cellular electrical coupling and are known to promote atrial fibrillation. It has been observed that the expression of the hyperpolarization-activated current If is increased under pathological conditions. Recent experimental data indicate a possible contribution of If to arrhythmogenesis. In this paper, the role of If in action potential propagation in normal and in pathological tissue is investigated by means of computer simulations. The effect of diffuse fibrosis and gap junction remodeling is simulated by reducing cellular coupling nonuniformly. As expected, the conduction velocity decreases when cellular coupling is reduced. In the presence of If the conduction velocity increases both in normal and in pathological tissue. In our simulations, ectopic activity is present in regions with high expression of If and is facilitated by cellular uncoupling. We conclude that an increased If may facilitate propagation of the action potential. Hence, If may prevent conduction slowing and block. Overexpression of If may lead to ectopic activity, especially when cellular coupling is reduced under pathological conditions.     

Sensory Effects of Transient Electrical Stimulation?Evaluation with a Neuroelectric Model

A model of myelinated nerve axon was used to study the initiation and propagation of action potentials for a variety of extracellular electrical stimuli. Frankenhaeuser-Huxley nonlinearities were incorporated at each of several nodes in a longitudinal array, and the extracellular current pulse was modeled as a spatial distribution of voltage disturbance along the membrane. Results from the model were compared to data from human sensory experiments and from animal electrophysiological experiments. Effects of polarity, electrode position, pulse duration, and biphasic oscillation frequency were examined. Biphasic pulses have higher excitation thresholds than monophasic pulses, provided the duration of a single phase is short relative to the time constant of the membrane depolarization process. The shapes of strength/duration curves from sensory experiments conform well to model predictions for monophasic stimuli. Strength/frequency curves derived from the model are similar to those from sensory stimulation with sinusoidal currents. The shapes of strength/frequency curves can be explained by membrane integration effects at high frequencies and membrane leakage effects at low frequencies. The model predicts lower thresholds for cathodal than for anodal stimulation: the predicted degree of polarity selectivity is confirmed by direct stimulation of axons in animal experiments, but is at variance with the selectivity found in human transcutaneous stimulation.     

Simulation of surface EMG signals generated by muscle tissues with inhomogeneity due to fiber pinnation

Surface electromyographic (EMG) signal modeling has important applications in the interpretation of experimental EMG data. Most models of surface EMG generation considered volume conductors homogeneous in the direction of propagation of the action potentials. However, this may not be the case in practice due to local tissue inhomogeneities or to the fact that there may be groups of muscle fibers with different orientations. This study addresses the issue of analytically describing surface EMG signals generated by bi-pinnate muscles, i.e., muscles which have two groups of fibers with two orientations. The approach will also be adapted to the case of a muscle with fibers inclined in the depth direction. Such muscle anatomies are inhomogeneous in the direction of propagation of the action potentials with the consequence that the system can not be described as space invariant in the direction of source propagation. In these conditions, the potentials detected at the skin surface do not travel without shape changes. This determines numerical issues in the implementation of the model which are addressed in this work. The study provides the solution of the nonhomogenous, anisotropic problem, proposes an implementation of the results in complete surface EMG generation models (including finite-length fibers), and shows representative results of the application of the models proposed.     

The Simulation of Repolarization Events of the Cardiac Purkinje Fiber Action Potential

A mathematical model based on the formalism of the Hodgkin-Huxley equations was implemented on a microcomputer system and used to simulate the membrane action potential of cardiac Purkinje fibers. The complete model is a modification of the representation used by McAllister et al. [1], mainly with respect to the outward current components during the late plateau, the repolarization phase, and the slow repolarization phase of the action potential. A new formulation of the potassium conductance was used, involving two distinct types of ionic channels corresponding, respectively, to the experimentally observed inward-going and outward-going rectification properties of the Purkinje fiber membrane. A unified representation of the Purkinje fiber current components was thus obtained which provides a more satisfactory interpretation of experimental results than was possible with the original model of McAllister et al. [1]. The membrane channel for the potassium pacemaker current is characterized by a set of first-order activation?inactivation variables and a constant fully activated conductance. The other channel carries the potassium current involved in the late plateau and repolarization phase of the action potential.     

The Role of the Hyperpolarization-Activated Inward Current$I_rm f$in Arrhythmogenesis: A Computer Model Study

Atrial fibrillation is the most common cardiac arrhythmia. Structural cardiac defects such as fibrosis and gap junction remodeling lead to a reduced cellular electrical coupling and are known to promote atrial fibrillation. It has been observed that the expression of the hyperpolarization-activated current$I_ f$is increased under pathological conditions. Recent experimental data indicate a possible contribution of$I_ f$to arrhythmogenesis. In this paper, the role of$I_ f$in action potential propagation in normal and in pathological tissue is investigated by means of computer simulations. The effect of diffuse fibrosis and gap junction remodeling is simulated by reducing cellular coupling nonuniformly. As expected, the conduction velocity decreases when cellular coupling is reduced. In the presence of$I_ f$the conduction velocity increases both in normal and in pathological tissue. In our simulations, ectopic activity is present in regions with high expression of$I_ f$and is facilitated by cellular uncoupling. We conclude that an increased$I_ f$may facilitate propagation of the action potential. Hence,$I_ f$may prevent conduction slowing and block. Overexpression of$I_ f$may lead to ectopic activity, especially when cellular coupling is reduced under pathological conditions.     

Magnetic fields from simulated cardiac action currents

A digital simulation has been performed of an idealized, thin, 2D cardiac slice in the x-y plane. The slice is stimulated near the center and the resulting action potential propagates outward, developing a distribution of electrical current with nonzero curl. An anisotropic bidomain model is used for the calculation, with membrane physiology based upon either just fast sodium flues or the more complete Beeler-Reuter myocardial model. The electrical anisotropy, expressed as the ratio of longitudinal to transverse electrical conductivity, is much greater for the inner domain than for the outer one, and this results in current loops that develop ahead of and behind the wavefront and produce a B_z magnetic field of order 10^-9 T 1 mm above the tissue, similar to recent experimental observations on canine cardiac tissue slices. The fields exhibit a quatrefoil symmetry which can be distorted by nonuniformities in the tissue. The field from repolarization currents is larger by almost an order of magnitude than might be predicted from considerations of rate of change of voltage     

Monte Carlo modeling for implantable fluorescent analyte sensors

A Monte Carlo simulation of photon propagation through human skin and interaction with a subcutaneous fluorescent sensing layer is presented. The algorithm will facilitate design of an optical probe for an implantable fluorescent sensor, which holds potential for monitoring many parameters of biomedical interest. Results are analyzed with respect to output light intensity as a function of radial distance from source, angle of exit for escaping photons, and sensor fluorescence (SF) relative to tissue autofluorescence (AF). A sensitivity study was performed to elucidate the effects on the output due to changes in optical properties, thickness of tissue layers, thickness of the sensor layer, and both tissue and sensor quantum yields. The optical properties as well as the thickness of the stratum corneum, epidermis, (tissue layers through which photons must pass to reach the sensor) and the papillary dermis (tissue distal to sensor) are highly influential. The spatial emission profile of the SF is broad compared that of the tissue fluorescence and the ratio of sensor to tissue fluorescence increases with distance from the source. The angular distribution of escaping photons is more concentrated around the normal for SF than for tissue AF. The information gained from these simulations will be helpful in designing appropriate optics for collection of the signal of interest.     

A dynamic action potential model analysis of shock-inducedaftereffects in ventricular muscle by reversible breakdown of cellmembrane

To elucidate the subcellular mechanism underlying the aftereffects of high-intensity dc shocks, a small pore, which mimics reversible breakdown of the cell membrane (electroporation), was incorporated into the phase-2 Luo-Rudy (L-R) model of ventricular action potentials. The pore size was set to occupy 0.15%-4.25% of the total cell membrane during the 10-ms shock. The pore was assumed to decrease after the shock exponentially with a time constant of 100-1,400 ms to simulate resealing process. In normal myocytes, the pore formation results in a delay of repolarization of the shocked action potential, which is followed by prolonged depolarization and oscillation of membrane potential like early afterdepolarization (EAD). Time- and voltage-dependent changes in the delayed rectifier K+ currents (IKr, IKs) in combination with those of L-type Ca2+ current (ICa,(L)) and ion flux through the pore (I(pore)) are responsible for the potential changes. Spontaneous excitation from the oscillation depends on activation of ICa,(L). In myocytes overloaded with Na+ and Ca2+ secondary to 90% inhibition of Na+-K+ pump, the pore formation results in a delay of repolarization of the shocked action potential, which is followed by slower cyclic depolarization in response to spontaneous release of Ca2+ from the sarcoplasmic reticulum (SR). This delayed afterdepolarization-type oscillation is abolished by complete block of Ca2+ release from the SR. These findings suggest that high-intensity electric field application will cause arrhythmogenic responses through a transient rupture of sarcolemma with different subcellular events in ventricular cells under normal and pathological conditions.     

A model study of propagation of early afterdepolarizations

Early afterdepolarizations (EAD's) are irregularities of the cardiac action potential that interrupt or retard repolarization. EAD's have been linked to the development of specific types of cardiac arrhythmias, however, the mechanism underlying the development of these arrhythmias remains unclear. The authors implemented a two-element kinetic model of the ventricular action potential to investigate a potentially arrhythmogenic form of triggered activity. By approximating EAD's by a sinusoidal driving force, the authors were able to study the effects of interelement coupling resistivity and sinusoidal frequency and amplitude on the triggering of action potentials. They demonstrated EAD's in a ventricular action potential model by altering the potassium and calcium channels to simulate experimental conditions under which EAD's occur. They also found that triggered activity depends critically on the frequency and amplitude of the driving force and also on the degree of cellular uncoupling between the elements. The authors' results suggest that triggered activity (due to EAD's) may be suppressed by drugs that improve coupling in unhealthy tissue, or ones that prevent EAD formation by inhibiting calcium channels     

Impact of physiological ventricular deformation on the morphology of the T-wave: a hybrid, static-dynamic approach

Ventricular wall deformation is widely assumed to have an impact on the morphology of the T-wave that can be measured on the body surface. This study aims at quantifying these effects based on an in silico approach. To this end, we used a hybrid, static-dynamic approach: action potential propagation and repolarization were simulated on an electrophysiologically detailed but static 3-D heart model while the forward calculation accounted for ventricular deformation and the associated movement of the electrical sources (thus, it was dynamic). The displacement vectors that describe the ventricular motion were extracted from cinematographic and tagged MRI data using an elastic registration procedure. To probe to what extent the T-wave changes depend on the synchrony/asynchrony of mechanical relaxation and electrical repolarization, we created three electrophysiological configurations, each with a unique QT time: a setup with physiological QT time, a setup with pathologically short QT time (SQT), and pathologically long QT time (LQT), respectively. For all three electrophysiological configurations, a reduction of the T-wave amplitude was observed when the dynamic model was used for the forward calculations. The largest amplitude changes and the lowest correlation coefficients between the static and dynamic model were observed for the SQT setup, followed by the physiological QT and LQT setups.     

Interaction of specialized cardiac conduction system with antiarrhythmic drugs: a simulation study

The use of antiarrhythmic drugs is common to treat heart rhythm disorders. Computational modeling and simulation are promising tools that could be used to investigate the effects of specific drugs on cardiac electrophysiology. In this paper, we study the multiscale effects of dofetilide, a drug that blocks IKr, from cellular to organ level paying special attention to its effect on heart structures, in particular the specialized cardiac conduction system (CCS). We include a model of the CCS in a patient-specific anatomical ventricular model and study the drug effects in simulations with and without a CCS. Results confirmed the expected effects of dofetilide at cellular level, increasing the action potential duration, and at organ level, prolonging the QT segment. Notable differences are shown between models with and without the CCS on action potential duration distributions. These techniques show the importance of heart heterogeneity and the global effects of the interaction of drugs with cardiac structures.