A Simulation Study of the Ventricular Myocardial 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 ventricular myocardial fibers. The complete model is constituted in part from the representation used by Beeler and Reuter [1] and from a simplified version of a model used by us to simulate the Purkinje fiber action potential [3]. The experimental results from the frog ventricular myocardial preparation were reconstructed successfully in the present study. It was also shown that the Purkinje fiber and ventricular myocardial action potentials could be simulated by means of qualitatively similar models. The major differences are a simpler representation of the potassium current and a more prominent role of the calcium current in the representation used for the ventricular myocardial fiber.     

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.     

Prediction of myelinated nerve fiber stimulation thresholds: limitations of linear models

Computer models of neurons are used to simulate neural behavior, and are important tools for designing neural prostheses. Computation time remains an issue when simulating large numbers of neurons or applying models to real time applications. Warman et al. developed a method to predict excitation thresholds for axons using linear models and a predetermined critical voltage. We calculated threshold prediction error as a function of the location of an extracellular electrode using two different axon models to examine further threshold prediction using linear models. Threshold prediction error was low (<3% error) under the conditions examined by Warman et al., but under more general conditions, threshold prediction error was as high as 23.6%. Linear models were limited as effective tools for single fiber threshold prediction because accuracy was dependent on the nonlinear and linear models used, and any parameter that affected the extracellular potential distribution. Threshold prediction could be improved by appropriately choosing the membrane conductance of the linear model, but determination of an optimal conductance was computationally expensive. Finally, although single fiber threshold prediction error was partially masked when considering the input-output (I/O) properties of populations of axons, relatively large errors still occurred in population I/O curves generated with linear models.     

Action Potential Collision in Heart Tissue-Computer Simulations and Tissue Expenrments

The electrical effects of action potential collision were studied using a computer simulation of one-dimensional action potential propagation and tissue experiments from isolated cardiac Purkinje strands and papillary muscles. The effects of collision, when compared to normal one-way propagation, included quantitative changes in all of the measured indexes of action potential upstroke and repolarization. These changes can be attributed to spatiotemporal changes in the net membrane current. Parameter sensitivity and analytic techniques identified five factors which determine the collision-induced decrease in action potential area: conduction velocity, action potential height, cable radius, specific intracellular resistivity, and the specific membrane resistance during action potential repolarization. The simulations demonstrated that collision effects were independent of inhomogeneity in action potential duration, the spatial extent of the collision effects was greater than the passive space constant, and certain simulated abnormal conditions (e. g., discontinuous propagation, ischemic tissue) increased the magnitude of the collision effects. The tissue experiments supported the simulations regarding the changes in action potential configuration directly at and on each side of the collision site. Elevated [K+]0 increased the changes in action potential duration in both tissue preparations. In papillary muscles, collision effects in the transverse direction were confined to a narrower region than collision effects in the longitudinal direction with no difference in the peak magnitude of the changes. Action potential collision is a common occurrence in the heart.     

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     

An Efficient Simulation Model of the Erbium-Doped Fiber for the Study of Multiwavelength Optical Networks

The first part of this paper reviews the spectrally resolved erbium-doped fiber model by Saleh, Jopson et al. (1990, IEEE Photon Technol. Lett.2, 714; 1991, Fiber Laser Sources and Amplifiers III, Vol. 1851, pp. 114–119, SPIE). This model is adequate for fast simulation of erbium-doped fiber amplifiers pumped at 980 or 1480 nm which are not self-saturated by amplified spontaneous emission noise. The second part of this paper reviews the wavelength-domain representation of optical signals and network components at the optical transport layer of multiwavelength optical networks. This representation stems from the spectrally resolved model of erbium-doped fiber amplifiers. Optical signals are represented by their carrier wavelength and average power exclusively and not by their temporal waveform, as is customary in simulation of analog and digital communication systems. In addition, network components are fully characterized by their loss or gain as a function of wavelength. The wavelength-domain representation is adequate for efficient steady-state and transient power-budget computations; i.e., it can be used to evaluate the optical signal, amplified spontaneous emission noise, and linear optical crosstalk average powers at all points in a multiwavelength optical network. To illustrate the capabilities of the spectrally resolved erbium-doped fiber model by Saleh, Jopson et al. and the wavelength-domain representation, transient power fluctuations caused by the dynamic interaction of saturated erbium-doped fiber amplifiers and servo-controlled attenuators in a bidirectional ring composed of four wavelength add–drop multiplexers are studied. The mechanisms responsible for this oscillatory behavior are identified and remedies are proposed.     

Electrical stimulation of cardiac tissue: a bidomain model withactive membrane properties

Numerical calculations simulated the response of cardiac muscle to stimulation by electrical current. The bidomain model with unequal anisotropy ratios represented the tissue, and parallel leak and active sodium channels represented the membrane conductance. The speed of the wavefront was faster in the direction parallel to the myocardial fibers than in the direction perpendicular to them. However, for cathodal stimulation well above threshold, the wavefront originated farther from the cathode in the direction perpendicular to the myocardial fibers than in the direction parallel to them, consistent with observations of a dog-bone-shaped virtual cathode made by Wikswo et al., (Circ. Res., vol.68, p.513-30, 1991). The model showed that the virtual cathode size and shape were dependent upon both membrane and tissue conductivities. Increasing the peak Na conductance or reducing the transverse intracellular conductivity accentuated the dog-bone shape, while the opposite change caused the virtual cathode to become more elliptical, with the major axis of the ellipse transverse to the fiber direction. A cathodal stimulus created regions of hyperpolarization that slowed conduction of the wavefront propagating parallel to the fibers. An anodal stimulus evoked a wavefront with a complex shape; activation originated from two depolarized regions 1 to 2 mm from the stimulus site along the fiber direction. The threshold current strength (0.5 ms duration pulse) for a cathodal stimulus was 0.048 mA, and for an anodal stimulus was 0.67 mA. When the model was modified to simulate the effect of electropermeabilization, which may be present, when the transmembrane potential reaches very large values near the stimulating electrode, the authors' qualitative conclusions remained unchanged     

Selective activation of small motor axons by quasitrapezoidalcurrent pulses

We have found a method to activate electrically smaller nerve fibers without activating larger fibers in the same nerve trunk. The method takes advantage of the fact that action potentials are blocked with less membrane hyperpolarization in larger fibers than in smaller fibers. In our nerve stimulation system, quasitrapezoidal-shaped current pulses were delivered through a tripolar cuff electrode to effect differential block by membrane hyperpolarization. The quasitrapezoidal-shaped pulses with a square leading edge, a 350 microsecond(s) plateau, and an exponential trailing phase ensured the block of propagating action potentials and prevented the occurrence of anodal break excitation. The tripolar cuff electrode design restricted current flow inside the cuff and thus eliminated the undesired nerve stimulation due to a "virtual cathode." Experiments were performed on 13 cats. The cuff electrode was placed on the medial gastrocnemius nerve. Both compound and single fiber action potentials were recorded from L7 ventral root filaments. The results demonstrated that larger alpha motor axons could be blocked at lower current levels than smaller alpha motor axons, and that all alpha fibers could be blocked at lower current levels than gamma fibers. A statistical analysis indicated that the blocking threshold was correlated with the axonal conduction velocity or fiber diameter. This method could be used in physiological experiments and neural prostheses to achieve a small-to-large recruitment order in motor or sensory systems.     

Changes occurring on the cell surface during KSHV reactivation

Following an infection, Kaposi's sarcoma-associated herpes virus (KSHV) exists predominantly in its latent state, with only 1-2% of infected cells undergoing lytic reactivation. We have previously demonstrated along with others a relationship between lytic reactivation and cell cycle progression (Bryan et al., 2006. J. Gen. Virol. 87: 519; McAllister et al., 2005. J. Virol. 79: 2626). Infected cells in the S phase are much more likely to undergo lytic reactivation when compared to those in G(0)/G(1) phase. Through the use of scanning electron microscopy (SEM), we analyzed changes occurring on the surface of cells undergoing KSHV reactivation. KSHV reactivation was observed predominantly in cells with smoother surface topology; a hallmark of cells derived from S phase. Interestingly, during the late stages of the reactivation process, we observed KSHV particles to egress cells through budding. Taken together, based on scanning electron microscopy and transmission electron microscopy evidences, we demonstrate for the first time the existence of a direct link between cell surface topology, cell cycle progression and KSHV reactivation.     

A model study of extracellular stimulation of cardiac cells

Point source extracellular stimulation of a myocyte model was used to study the efficacy of excitation of cardiac cells, taking into account the shape of the pulse stimulus and its time of application in the cardiac cycle. The myocyte was modeled as a small cylinder of membrane (diameter 10 μm, length 100 μm) capped at both ends and placed in an unbounded volume conductor. A Beeler-Reuter model modified for the Na⁺ dynamics served to simulate the membrane ionic current. The stimulus source was located on the cylinder axis, close to the myocyte (50 μm) in order to generate a nonlinear extracellular field (φ_e). The low membrane impedance associated with the high frequency component of the make and break of the rectangular current pulse leads to a current flow across the membrane and an abrupt change in intracellular potential (φ_i). Because the intracellular space is very small, φ_e is nearly uniform over the length of the myocyte and the membrane potential (V=φ_i -φ_e) is governed by the applied field φ_e . There is then a longitudinal gradient of membrane polarization which is the inverse of the gradient of extracellular potential. With an anodal (positive) pulse, for instance, the proximal portion of the myocyte is hyperpolarized and the distal portion is depolarized. Based on this principle acid considering the voltage-dependent activation/inactivation dynamics of the membrane, it is shown that a cathodal (negative) pulse is the most efficacious stimulus at diastolic potentials, an anodal current is preferable during the plateau phase of the action potential, and a biphasic pulse is optimal during the relative refractory phase. Thus a biphasic pulse would constitute the best choice for maximum efficacy at all phases of the action potential     

Late phase of repolarization is autoregenerative and scales linearly with action potential duration in mammals ventricular myocytes: a model study

Scaling of action potential (AP) duration (APD) in mammals of different size is a rather complex phenomenon, dominated by a regulatory type mechanism of ion channels expression. By means of simulations performed on six published mathematical models of cardiac ventricular APs of different mammals, it is shown that AP repolarization is autoregenerative in its later phase (ARRP) and that the duration of such phase scales linearly with APD. For each AP, a 3-D instantaneous time-voltage-current surface is constructed, which has been recently described in a more simplified model. This representation allows us to measure ARRP and to study the contribution to it for different ion currents. It has been found that the existence of an ARRP is not intrinsic to cardiac models formulation; one out of the six models does not show this phase. A linear correlation between ARRP duration and APD in the remaining models is also found. It is shown that ARRP neither simply depend on AP shape nor on APD. Though I(K1) current seems to be the main responsible for determining and modulating this phase, the mechanism by which ARRP scales linearly with APD remains unclear and raises further questions on the scaling strategies of cardiac repolarization in mammals.     

Evidence for voltage-gated potassium channel beta-subunits with oxidoreductase motifs in human and rodent pancreatic beta cells

Voltage-gated K(+) channel alpha subunits (K(V) alpha) have been previously identified in pancreatic islet beta-cells where it has been suggested they have a role in membrane repolarization and insulin secretion. Here we report the cloning of the three mammalian K(V) beta subunits, including splice variants of these subunits, from both human and rat pancreatic islets and from the rat insulinoma cell line INS-1. Two of the splice variants, K(V) beta1a and K(V) beta3, previously reported to be neuronal tissue specific, are expressed in islets and INS-1 cells. In addition, a splice variant of K(V) beta2 that lacks two potential protein kinase C phosphorylation sites at the amino terminus is present. Immunoblot analysis suggests a high level of K(V) beta2 subunit protein in rat pancreatic islets and immunoprecipitation with anti-K(V) beta2 antibody pulls down a protein from INS-1 cells that reacts with anti-aldose reductase antibody. The K(V) beta subunits, which are attached to the cytoplasmic face of the alpha subunits and are members of the aldose reductase superfamily of NADPH oxidoreductases, may have an as yet undetermined role in the regulation of insulin secretion by the intracellular redox potential. Finally, we suggest that a systematic nomenclature for K(V) beta subunits first proposed by McCormack et al. be adopted for this family of potassium channel subunits as it corresponds with the nomenclature used for their cognate K(V) alpha subunits.     

Automated On-Line Determination of Membrane Responsiveness Curves

A system has been designed which provides automated on-line continuous plots of membrane responsiveness curves. The system is composed of amplifiers, positive peak-detecting and sample-and-hold circuitry, control logic, and display oscilloscopes. With an intracellular recording microelectrode impaled in a cardiac Purkinje fiber, the system acquires the membrane potential and maximum upstroke velocity of an action potential elicited from the resting or take-off potential. The resulting X-Y plot of varying membrane take-off potentials versus maximum upstroke velocity gives the "membrane responsiveness" relationship. This relationship reflects the relative availability of the depolarizing sodium system at different membrane potentials.     

Magnetic Measurements of Action Currents in a Single Nerve Axon: A Core-Conductor Model

Measurements have been performed on the medial giant axon of the crayfish in which both microelectrode recordings of the transmembrane action potential and magnetic recordings of the axial, intracellular action current were obtained at a single location along the nerve. This approach is unique because the combination of electric and magnetic techniques allows for independent measurements of transmembrane potential and intracellular current without assumptions regarding membrane capacitance or axonal resistances. The availability of both types of data recorded at a single location on the axon allows the core-conductor model to be solved explicitly for the internal axial resistance of the axon, the membrane capacitance, and the membrane conduction current density without the need to make a series of subthreshold measurements of passive cable properties. The extracellular magnetic measurements can be used both to determine the transmembrane action potential without the need to penetrate the nerve membrane with a microelectrode, and to obtain approximate values for the sodium and potassium peak conductances.     

基于新的2DEG速场特性的HEMT分析模型(英文)

A novel analytic model for HEMT's is developed. In this model, the empirical formula suggested by Yeager et al. is used to approach the behavior of electron drift velocity vs electron field of 2DEG. And the diffusion component of the current and the effect of the parasitic resistance of the undoped GaAs buffer layer are properly involved in this model. The model is divided into two regions: the linear region and the saturation region, being continuous at the pinch-off voltage. The calculated output current-voltage characteristics are in excellent agreement with experimental data. Using this model, the microwave parameters of HEMT such as channel conductance, transconductance, gate capacitance, and cut-off frequency are derived.     

Analysis of a Model for Excitation of Myelinated Nerve

Excellent models have been presented in the literature which relate membrane potential to transverse membrane current and which describe the propagation of action potentials along the axon, for both myelinated and nonmyelinated fibers. There is not, however, an adequate model for nerve excitation which allows one to compute the threshold of a nerve fiber for pulses of finite duration using electrodes that are not in direct contact with the fiber. This paper considers this problem and presents a model of the electrical properties of myelinated nerve which describes the time course of events following stimulus application up to the initiation of the action potential. The time-varying current and potential at all nodes can be computed from the model, and the strength-duration curve can be determined for arbitrary electrode geometries, although only the case of a monopolar electrode is considered in this paper. It is shown that even when the stimulus is a constant-current pulse, the membrane current at the nodes varies considerably with time. The strength-duration curve calculated from the model is consistent with previously published experimental data, and the model provides a quantitative relationship between threshold and fiber diameter which shows there is less selectivity among fibers of large diameter than those of small diameter.     

A model of the rat phrenic motor neuron

We have developed a model for the rat phrenic motor neuron (PMN) that robustly replicates many experimentally observed behaviors of PMNs in response to pharmacological, ionic, and electrical perturbations using a single set of parameters. Our model suggests that the after-depolarization (ADP) response seen in action potentials is a result of the slow deactivation of the fast sodium channel in the range of the ADP coupled with the activation of the L-type calcium channel (I(CaL)). This current and its interactions with the small and large conductance calcium-activated potassium currents (I(KCaSK) and I(KCaBK), respectively) is also important in the generation of spike frequency adaptation in the repetitive firing mode of activity. Other aspects of the model conform very well to experimental observations in both the action potential and repetitive firing mode of activity, including the role of I(KCaSK) in the medium after-hyperpolarization (AHP) and the role of I(KCaBK) in the fast AHP. We have made a number of predictions using the model, including the characterization of two putative sodium currents (fast and persistent), as well as functional roles for the N- and T-type calcium currents.     

Three-Dimensional Simulation of the Ventricular Depolarization and Repolarization Processes and Body Surface Potentials: Nornal Heart and Bundle Branch Block

A three-dimensional computer model has been constructed to simulate the ventricular depolarization and repolarization processes in a human heart. The electrocardiogram (ECG), the vectorcardiogram(VCG), and the body surface potential map (BSPM) during the QRS-T period are obtained automatically under certain heart conditions such as bundle branch block and myocardial infarctions. The ventricles, together with bundle branches and the Purkinje fibers, are composed of approximately 50 000 cell units which are arranged in a cubic close-packed structure. A different action potential waveform was assigned to each unit. The heart model is mounted in a homogeneous human torso model. Electric dipoles, which are proportional to the spatial gradient of the action potential, are generated in all the cell units. These dipoles give rise to a potential distribution on the torso surface, which is calculated by means of the boundary element method. The resulting ECG's, VCG's, and BSPM's are within the expected range of clinical observations.     

A model analysis of aftereffects of high-intensity DC stimulationon action potential of ventricular muscle

The mechanism for aftereffects of high-intensity dc stimulation on ventricular muscle was studied by using Beeler-Reuter's action potential model. A leak conductance (G_pore maximal value from 40 to 80 μS for 1 cm² of membrane), which mimics reversible dielectric breakdown of the cell membrane by the shock, was incorporated into the model. To simulate resealing process, G_pore was assumed to decrease after the shock exponentially at a time constant (τ_pore) of 5-50 s. The simulation results are qualitatively consistent with the authors' experimental observations in guinea pig papillary muscle (Amer. J. Physiol., vol. 267, p. H248-58, 1994); they include prolonged depolarization, diastolic depolarization or oscillation of membrane potential leading to a single or multiple spontaneous excitation. The phase-independence and shock intensity-dependence can also be reproduced. Analysis of current components has revealed that: (1) a large inward leak current (l_leak) is responsible for the prolonged depolarization (2) time-dependent decay of outward current (I_X1) in combination with I_leak and slow inward current (I_s) results in diastolic depolarization or oscillation of membrane potential; (3) spontaneous excitation depends on an activation of I_s. These findings support the authors' hypothesis that strong shocks (>15 V/cm) will produce abnormal arrhythmogenic responses in ventricular muscle through a transient rupture of sarcolemmal membrane