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.     

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.     

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.     

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.     

Modeling of the Electrical Conductivity of DNA

The authors have developed a PSpice model of the electrical behavior of DNA molecules for use in nanoelectronic circuit design. To describe the relationship between the current through DNA and the applied voltage we used published results of the direct measurements of electrical conduction through DNA molecules. The experimental dc current-voltage (-) curves show a nonlinear conduction mechanism as well as the existence of a temperature dependent semiconductive voltage gap. A weighted least-squares polynomial fit to the experimental data at one temperature, with fitted temperature dependent polynomial coefficient of the linear term, was used as a mathematical model of electrical behavior of DNA. An equivalent electrical circuit was created in PSpice in which DNA was modeled as a voltage-controlled current source described by the mathematical model that includes temperature dependence . PSpice simulations with this model generated - curves at other temperatures that were in excellent agreement with the corresponding experimental data (average deviation 5%). This is important because having models of DNA molecules in the form of equivalent electronic circuits would be useful in the design of nanoelectronic circuits and devices.     

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.     

Effect of variation in membrane excitability on propagation velocity of simulated action potentials for cardiac muscle and smooth muscle in the electric field model for cell-to-cell transmission of excitation

We have previously published several studies on the propagation of simulated action potentials (APs) of cardiac muscle and smooth muscle using the PSpice program. Those studies were done on single chains of five to ten cells in length to examine longitudinal propagation between the cells, either not connected by gap-junction (g.j) channels or connected by various numbers of channels. In addition, transverse propagation was examined between parallel chains (two to five chains) not connected by g.j. channels. In all those studies, the myocardial cells and smooth muscle cells (SMCs) were unintentionally somewhat hyperexcitable by virtue of the values inserted into the GTABLEs of the PSpice program. Because transmission of excitation from cell to cell occurred very well in the absence of g.j. channels, by virtue of the electric field (EF) generated in the narrow junctional clefts (negative cleft potential V/sub JC/), the present study was carried out, in which the cells were made hypo-excitable by altering the GTABLE values. Three levels of excitability of the cardiac cells and SMC were examined: 1) high; 2) intermediate; and 3) low. It was found that propagation of excitation, both longitudinally and transversely, can occur by the EF mechanism alone, even when the excitability of the cells was low. Therefore, the EF mechanism alone can account for propagation of excitation in cardiac muscles and smooth muscles that do not possess gap junctions. In those cases in which gap junctions do exist and are functioning, the EF mechanism would act in parallel and thereby increase the safety factor for conduction.     

Propagation loss in single-mode GaAs-AlGaAs microring resonators:measurement and model

We report propagation loss measurements in single-mode GaAs-AlGaAs racetrack microresonators with bending radii from 2.7 μm to 9.7 μm. The experimental data were found to be in good agreement with a physical-loss model which accounts for the bending loss, the scattering loss due to surface roughness on the waveguide sidewalls, and the transition loss at the straight-to-bend waveguide junctions. The model also enables us to identify the dominant loss mechanisms in semiconductor microcavities. We found that for racetracks with large bending radii (greater than 4 μm, in our case) the loss due to surface-roughness scattering in the curved waveguides dominates, whereas for small-radius rings, the modal mismatch at the straight-to-bend waveguide junctions causes the biggest loss. This result suggests that circular-shaped rings are preferable in the realization of ultrasmall low-loss microcavities. We also show that the round-trip propagation loss in small-radius racetrack microresonators can be minimized by introducing a lateral offset at the straight-to-bend waveguide junctions     

Modeling the sensitivity of CMOS circuits to radiation induced single event transients

An accurate and computer efficient analytical model for the evaluation of integrated circuit sensitivity to radiation induced single event transients is presented. The key idea of the work is to exploit a model that allows the rapid determination of the sensitivity of any MOS circuit to single event transients (SETs), without the need to run circuit level simulations. To accomplish this task, both single event transient generation and its propagation through circuit logic stages are characterized and modeled. The model predicts whether or not a particle hit generates a transient pulse which may propagate to the next logic gate or memory element. The electrical masking (attenuation) of the transient pulse as it propagates through each stage of logic until it reaches a memory element is also modeled. Model derivation is in strong relation with circuit electrical behavior, being consistent with technology scaling. The model is suitable for integration into CAD-Tools, intending to make automated evaluation of circuit sensitivity to SEU possible.     

Toward a multiscale model of the uterine electrical activity

A comprehensive multiscale model of the uterine muscle electrical activity would permit understanding the important link between the genesis and evolution of the action potential at the cell level and the process leading to labor. Understanding this link can open the way to more effective tools for the prediction of labor and prevention of preterm delivery. A first step toward the realization of such a model is presented here. By using as starting point a previously published model of the generation of the uterine muscle action potential at the cell level, a significant reduction of the model complexity is here achieved in order to simulate 2-D propagation of the cellular activity at the uterine tissue level, for tissue strips of arbitrary dimension. From the obtained dynamic behavior of the electrical activity simulated at the tissue level, the use of a previously validated volume conductor model at the organ level permits us to simulate the electrohysterogram as recorded on the abdominal surface by an electrode array. Qualitative evaluation of the model at the cell level and at the organ level confirms the potential of the proposed multiscale approach for further refinement and extension aiming at clinical application.     

The effect of morphological interdigitation on field couplingbetween smooth muscle cells

The electrical control activity (ECA) in the distal stomach, small intestine, and colon has been modeled by populations of coupled nonlinear oscillators. Coupling has traditionally been explained through gap junctions, but gap junctions alone are inadequate, as they are not always present or cannot account for the observed behavior. Coupling through extracellular electric fields has been proposed as another coupling path which may work instead of, or in conjunction with, gap junctions. A morphological structure, the interdigitation, is studied for its effect on fields produced by a spherical cell. Using boundary element methods, the potential produced by a cell and the transmembrane potential induced in an adjacent cell are considered. Computer simulation results indicate that the presence of an interdigitation between two neighboring cells produces a 60% increase in extracellular potential and a 50% increase in induced transmembrane voltage. The interdigitation length is the most important factor, with radius playing a very small part in determining peak values of potential and voltage. These interdigitation fields may be of appreciable magnitude with regard to coupling. Also, the upstroke phase of the ECA can play a major role in intercellular communication     

Model for Transient Fault Susceptibility of Combinational Circuits

Transient faults (TFs) are increasingly affecting microelectronic devices as their size decreases. During the design phase, the robustness of circuits for high reliability applications with respect to this kind of faults is generally validated through simulations. However, traditional electrical level simulators are too slow for the task of simulating the effects of TFs on large circuits. In this paper, we present a new model to estimate accurately the possible propagation of transient fault-due glitches through a CMOS combinational circuit. We will show how the proposed model can be applied in order to estimate the TF susceptibility of a circuit by simply considering the propagation delay of the datapath. Therefore, the proposed model is suitable to be used into a new simulation tool able to provide good accuracy, while significantly speeding up simulations, with respect to electrical level simulation. In particular, our model allows approximately 90% accuracy with respect to HSPICE simulations.     

Low-loss single-mode GaAs/AlGaAs miniature optical waveguides withstraight and bending structures

Low-loss single-mode GaAs/AlGaAs miniature optical waveguides fabricated for use in monolithically integrated optical circuits are discussed. The propagation characteristics of these waveguides with straight and S-bending structures have been investigated at wavelengths of 1.30 and 1.55 μm. The lowest propagation losses are estimated to be 0.58 dB/cm and 0.69 dB/cm at wavelengths of 1.30 and 1.55 μm, respectively. The total loss of an S-bending waveguide with a curvature radius of 2 mm and with a lateral displacement of 200 μm was 0.61 dB and 0.46 dB at wavelengths of 1.30 and 1.55 μm. The fabricated single-mode strip-loaded waveguides proved to be suitable for application of the semiconductor waveguide into monolithically integrated optical circuits     

Optically controlled contradirectional coupler

A multiple-quantum-well optically controlled contradirectional coupler has been realized following the design criteria discussed here and elucidated by the simulations. Our room-temperature experiments show a power-dependent contradirectional coupling condition, allowing optically controlled switching between two output channels with control energies on the order of 1 pJ, and at a wavelength around 1.55 μm. The device is treated theoretically by a coupled mode analysis in order to compute the linear and nonlinear transmission spectra at the two output ports. The effects induced by the propagation of intense control beams are modeled using a nonlinear two-dimensional beam propagation method     

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.     

Averaging over depth during optical mapping of unipolar stimulation

Numerical simulations have predicted the distribution of transmembrane potential during electrical stimulation of cardiac tissue. When comparing these predictions to measurements obtained using optical mapping techniques, the optical signal should not be compared to the transmembrane potential calculated at the surface of the tissue, but instead to the transmembrane potential averaged over depth. In this paper, the bidomain model is used to calculate the transmembrane potential in a three-dimensional slab of cardiac tissue, stimulated by a unipolar electrode on the tissue surface. For an optical decay constant of 0.3 mm and an electrode radius of 1 mm, the surface transmembrane potential is more than a factor of three larger than the transmembrane potential averaged over depth. Our results suggest that optical mapping underestimates the surface transmembrane potential during electrical stimulation.     

Influence of tissue inhomogeneities on noninvasive muscle fiberconduction velocity measurements-investigated by physical and numericalmodeling

The determination of conduction velocity in the muscle fibers of single motor units from noninvasive recordings of single motor unit action potentials can be improved by the method of spatially filtering multielectrode EMG. The use of this conduction velocity as a diagnostic tool requires a high reliability of the detected values. However, experiments did reveal that the measured conduction velocity values showed remarkably high fluctuations depending on the recording site along the muscle fibers which could not be attributed to the influence of the endplate and tendon region. The present work examines the hypothesis that the observed fluctuations in propagation velocity were caused by electrically inhomogeneous tissue, regions of different electrical conductivity which are located between the excited muscle fibers and the recording electrodes and which cause a deformation of the extracellular electric current field. The investigation was performed by means of a physical model as well as by finite element model calculations. In both models single, simple shaped (cylindrical) inhomogeneity regions with a conductivity of 0.1 to 10 times that of the surrounding medium and diameters ranging between 1.6 and 2.7 mm were placed between excitation sources and recording site. The results indicate that the observed conduction velocity fluctuations of up to some 10% can be well attributed to inhomogeneity effects of the tissue conductivity. Based on these results, one may look for signal processing methods to cut down such fluctuations in conduction velocity measurements.     

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.     

A time-dependent adaptive remeshing for electrical waves of the heart.

In this work, a time-dependent remeshing strategy and a numerical method are presented for the simulation of the action potential propagation of the human heart. The main purpose of these simulations is to accurately predict the depolarization-repolarization front position, which is essential to the understanding of the electrical activity in the myocardium. A bidomain model, which is commonly used for studying electrophysiological waves in the cardiac tissue, will be employed for the numerical simulations. Numerical results are enhanced by the introduction of an anisotropic remeshing strategy. The illustration of the performance and the accuracy of the proposed method are presented using a 2-D analytical solution and a test case with re-entrant waves.     

Microwave properties of silicon junction tunnel diodes grown bymolecular beam epitaxy

The bias dependence of the single-port microwave reflection gain of 15 μm-diameter Si Esaki tunnel diodes, grown by molecular beam epitaxy, was studied as a function of frequency. A simple equivalent circuit accurately modeled the data and yielded the forward-bias junction capacitance, which cannot be obtained by conventional low frequency capacitance-voltage techniques. The diodes were highly-doped step p-i-n junctions and exhibited a peak current density of 16 kA/cm ². The microwave reflection gain and cut-off frequency were 12 dB land 1.6 GHz, respectively, with a speed index (slew rate) of 7.1 V/ns