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.     

Computer simulations of activation in an anatomically based modelof the human ventricular conduction system

Simulations of the electrical activity during excitation were performed in an anatomically based model of the human ventricular conduction system. Each of the 33,000 elements of this model represented a unit bundle of Purkinje or atrioventricular nodal tissue. The Ebihara-Johnson model for sodium defined the active membrane characteristics. Using a combination of new and existing modeling techniques, simulations of excitation were completed in approximately 5 min CPU time on an IBM 3090 at the Cornell National Supercomputer Facility. Activation times at sites in the model were compared to experimental measurements for the excitation of the ventricular myocardium on the endocardial surface. These "literature-based" times were estimated from a number of reported human heart mapping studies. Initially, the times fit poorly. The major factor for the discrepancy was the conduction velocities of the elements, which were a result of the physical and electrical parameters derived from a review of histologic and electrical properties studies. In addition, there was a latency between activation of the system in the left ventricle of the model and that in the right ventricle when compared to the experimental work. When the times were scaled to adjust for the conduction velocity and ventricular latency effects, the match between the simulation and literature-based times was much improved. Quantitative comparison between normalized times resulted in correlation coefficients CCF = 0.76 for the right ventricle and CCF = 0.64 for the left ventricle.     

A method for quantitative display of three-dimensional regional myocardial function

The DSR (dynamic spatial reconstructor), a multiple X-ray source scanner that generates stop action three-dimensional (3-D) images of a cylindrical volume, was used for quantitative imaging of left ventricular 3-D wall geometry and function in experimentally induced canine left ventricular myocardial infarction. Impaired regional myocardial function was induced by myocardial ischemia or infarction in four mongrel dogs by closed-chest occlusion of the proximal left anterior descending (LAD) coronary artery. At intervals of 6-14 weeks post occlusion, the dogs were scanned with the DSR during biatrial contrast injection. The 3-D shape, extent, and function of hypokinetic myocardium was measured from the DSR images utilizing measurement of the rate of local systolic wall thickening to detect regions of normal, ischemic, or scarred myocardium. The results were compared to scar size and anatomic distribution measured at postmortem examination. The anatomic extent and relationship of hypocontractile to normally contracting muscle was visualized by computer generated, pseudo 3-D shaded surface displays of the left ventricular chamber and by topographic projections of regional wall thickening rates onto a map of the left ventricular endocardial surface. The location of myocardial infarction and the surrounding zone of impaired function is clearly defined by this 3-D CT scanning procedure. The display method presented here provides both localization and quantification of the volume of ischemic and infarcted myocardium.     

Propagation of depolarization and repolarization processes in themyocardium-an anisotropic model

A three-dimensional finite-elements model of the left and right ventricles has been developed to study the process of myocardial electrical activation. The experimentally measured velocity is known to depend on membrane processes, the cellular shape, fiber orientation, and the interaction with neighboring cells. The simulated process is, therefore, governed by the geometry and by the directional conduction velocity at each point in the myocardial volume. The geometry of the ventricles is described by ellipsoidal shape, and divided to layers and sections, each filled with "cells" of preassigned properties. It allows for taking into account the local orientation of the myocardial fibers and their distributed velocities and refractory periods. The values are Gaussly distributed around the mean, and the mean and variance differ at each section. A conduction network of Purkinje "cells" is included on the endocardial surface. The anisotropic properties are demonstrated during simulation of an abnormal cardiac cycle, when propagating is initiated at an ectopic ventricular site. Ischemia is simulated by low conduction velocities in the ischemic zone and wide dispersion of values in nearby locations; automaticity is described by restimulating "cells" in the injured area; the dangerous effects of a premature beat leading to reentry are simulated by reduction of propagation velocity in "cells" that are reactivated while they repolarize. The different activation patterns are calculated throughout the myocardium and on its surface. The generated surface activation maps are not sensitive to minute changes in location of the foci of activation within the normal conduction system. The maps show sensitivity to pathological velocities, ischemic areas, and the existence of ectopic foci.(ABSTRACT TRUNCATED AT 250 WORDS)     

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     

Use of the ventricular propagated excitation model in the magnetocardiographic inverse problem for reconstruction of electrophysiological properties

A novel magnetocardiographic inverse method for reconstructing the action potential amplitude (APA) and the activation time (AT) on the ventricular myocardium is proposed. This method is based on the propagated excitation model, in which the excitation is propagated through the ventricle with nonuniform height of action potential. Assumption of stepwise waveform on the transmembrane potential was introduced in the model. Spatial gradient of transmembrane potential, which is defined by APA and AT distributed in the ventricular wall, is used for the computation of a current source distribution. Based on this source model, the distributions of APA and AT are inversely reconstructed from the QRS interval of magnetocardiogram (MCG) utilizing a maximum a posteriori approach. The proposed reconstruction method was tested through computer simulations. Stability of the methods with respect to measurement noise was demonstrated. When reference APA was provided as a uniform distribution, root-mean-square errors of estimated APA were below 10 mV for MCG signal-to-noise ratios greater than, or equal to, 20 dB. Low-amplitude regions located at several sites in reference APA distributions were correctly reproduced in reconstructed APA distributions. The goal of our study is to develop a method for detecting myocardial ischemia through the depression of reconstructed APA distributions.     

Noninvasive reconstruction of three-dimensional ventricular activation sequence from the inverse solution of distributed equivalent current density

We propose a new electrocardiographic (ECG) inverse approach for imaging the three-dimensional (3-D) ventricular activation sequence based on the modeling and estimation of the equivalent current density throughout the entire volume of the ventricular myocardium. The spatio-temporal coherence of the ventricular excitation process has been utilized to derive the activation time from the estimated time course of the equivalent current density. In the present study, we explored four different linear inverse algorithms (the minimum norm and weighted minimum norm estimates in combination with two regularization schemes: the instant-by-instant regularization and the isotropy method) to estimate the current density at each time instant during the ventricular depolarization. The activation time at any given location within the ventricular myocardium was determined as the time point with the occurrence of the maximum local current density estimate. Computer simulations were performed to evaluate this approach using single- and dual-site pacing protocols in a physiologically realistic cellular automaton heart model. The performance and stability of the proposed approach was evaluated with respect to the various levels of measurement noise (0, 5, 10, 20, 40, and 60 microV), the various numbers of ECG electrodes and the modeling errors on the torso geometry and heart position. The simulation results demonstrate that: 1) the single-site paced 3-D activation sequence can be well reconstructed from 200-channel body surface potential maps with additive Gaussian white noise of 20 microV (correlation coefficient = 0.90, relative error = 0.19, and localization error = 5.49 mm); 2) a higher imaging accuracy can be obtained when the activation is initiated from the left/right ventricle (LV/RV) compared to from the septum; 3) the isotropy method gives rise to a better performance than the conventional instant-by-instant regularization; 4) a decreased imaging accuracy results from a larger noise level, a fewer number of electrodes, or the volume conductor modeling errors; however, a reasonable imaging accuracy can still be obtained with a 60 microV noise level, 64 electrodes, or mild errors on both the torso geometry and heart position, respectively; 5) the dual-site paced 3-D activation sequence can be imaged when the two sites are paced either simultaneously or with a time delay of 20 ms; 6) two pacing sites can be resolved and localized in the imaged 3-D activation sequence when they are located at the contralateral sides of ventricles or at the ventricular lateral wall and the apex, respectively.     

Analysis of Left Ventricular Mechanics During Filling, Isovolumic Contraction, and Ejection

The left ventricle (LV) was modeled by two confocal ellipsoids truncated in a plane corresponding to the base of the LV. The ellipsoids were approximated by a series of cylindrical shells. During passive filling, the pressure within the ventricular chamber was determined from chamber volume and a stress-strain relationship for myocardium in the relaxed state. The rapid filling phase of diastole was not analyzed. During isovolumic contraction, the cylindrical shells assumed the properties of myocardium in active contraction. Contraction was sequential, beginning at the ventricular apex, and progressing toward the ventricular base. Geometric changes occurred in the LV model as a function of wall stress, material properties, and timing of myocardial activation. During ejection, viscous and inertial forces were determined as were model output pressure and flow waveforms.     

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.     

Comparative simulation of excitation and body surfaceelectrocardiogram with isotropic and anisotropic computer heart models

Comparative simulations between isotropic and anisotropic computer heart models were conducted to study the effects of myocardial anisotropy on the excitation process of the heart and on body surface electrocardiogram. The isotropic heart model includes atria, ventricles, and a special conduction system, and is electrophysiologically specified by parameters relative to action potential, conduction velocity, automaticity, and pacing. The anisotropic heart model was created by incorporating rotating fiber directions into the ventricles of the isotropic heart model. The orientation of the myocardial fibers in the ventricles of the model was gradually rotated counterclockwise from the epicardial layer to the endocardial layer for a total rotation of 90°. The anisotropy of conduction velocity and intracellular electric conductivity was included in the simulation. Comparative simulations of the normal heart, LBBB, and RBBB showed no significant differences between the two models in the excitation processes of the whole heart or in the body surface electrocardiograms. However, it was easier to induce ventricular fibrillation in the anisotropic model than in the isotropic model. The comparative simulation is useful for investigating the effects of myocardial anisotropy at the whole heart level and for evaluating limitations of the isotropic heart model     

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.     

Stimulation of isolated ventricular myocytes within an open architecture microarray

This paper is concerned with the physiological responses of single heart cells within microfluidic chambers, in response to stimulation by integrated microelectrodes. To enable these investigations, which included the measurement of action potential duration, intracellular Ca2+ and cell shortening, a series of microfluidic chambers (50 microm wide, 180 microm long, 400 microm high, 500 microm pitch) and connecting channels (200 microm wide, 5000 microm long, 50 microm high, 500 microm pitch) were replica-moulded into the silicone elastomer, polydimethylsiloxane (PDMS). The structures were formed against a master of posts and lines, photolithograhically patterned into the high aspect ratio photoresist SU-8. The chambers within the slab of PDMS were aligned against pairs of stimulating gold microelectrodes (50 microm long, 20 microm wide, 0.1-10 microm thick, 180 microm apart) patterned on a microscope coverslip base, thus defining cavities of approximately 4 nL volume. The assembly was filled with physiological saline and single isolated rabbit ventricular myocytes were introduced by micropipetting, thus creating limited volumes of saline above individual myocytes that could be varied between 4 nL and > or = 4 microL. The application of transient current pulses to the cells via the electrodes caused transient contractions with constant amplitude (recorded as changes in sarcomere length), confirming that excitation contraction coupling (EC coupling) remained functional in these limited volumes. Continuous monitoring of the intracellular Ca2+ (using calcium sensitive dyes) showed, that in the absence of bath perfusion, the amplitude of the transients remained constant for approximately 3 min in the 4-nL volume and approximately 20 min for the 4 microL volume. Beyond this time, the cells became unexcitable until the bath was renewed. The action potential duration (APD) was recorded at stimulation frequencies of 1 Hz and 0.5 Hz using potential sensitive dyes and was prolonged at the higher pacing rate. These studies show the prolonged electrical stimulation of isolated adult cardiac myocytes in microchambers with unimpaired EC coupling as verified on optical records of the action potential, Ca2+ transients and cell shortening. The open architecture provided free (pipetting) access for drug dispensation without cross talk between neighboring microwells, and multiplexed optical detection can be realized to study EC coupling on arrays of cells under both control and experimental conditions.     

A model of ultrasound backscatter for the assessment of myocardialtissue structure and architecture

A statistical parametric model of returning echoes from myocardium is theorized in order to investigate the relationship between normal myocardium structure and spectral signatures with the use of ultrasonic tissue characterization. It is hypothesized, that in a clinical setting the normal myofiber architecture in the left ventricular wall is structured as a matrix of cylindrical scatterers whose orientation and spatial distribution vary according to two different statistical distribution laws: (1) a Gaussian law to approximate parametric angular myofiber variability at each site within the myocardial wall; (2) a gamma distribution law to describe parametric regularity in scatterer interdistance. In the model, the effect of the angle of insonification with respect to the alignment of myofibers on ultrasound backscatter was considered. The slope of the power spectral density (PSD) evaluated within the echocardiographic transducer bandwidth has been used as a ultrasonic tissue characterization parameter. The model has been tested by computer simulation and in vitro measurements on myocardial pig tissue specimens. The concordance between experimental and simulated results confirms that the model accounts for the process underlying the echo formation from normal myocardium. Moreover, it provides a simple method of simulation which can be easily implemented and used for the assessment of pathologic alterations     

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.     

Methodology for Jointly Assessing Myocardial Infarct Extent and Regional Contraction in 3-D CMRI

Automated extraction of quantitative parameters from cardiac magnetic resonance images is crucial for the management of patients with myocardial infarct. This paper proposes a postprocessing procedure to jointly analyze Cine and delayed-enhanced (DE) acquisitions, in order to provide an automatic quantification of myocardial contraction and enhancement parameters and a study of their relationship. For that purpose, the following processes are performed: 1) DE/Cine temporal synchronization and 3-D scan alignment, 2) 3-D DE/Cine rigid registration in a region about the heart, 3) myocardium segmentation on Cine-MRI and superimposition of the epicardial and endocardial contours on the DE images, 4) quantification of the myocardial infarct extent (MIE), 5) study of the regional contractile function using a new index, the amplitude to time ratio (ATR). The whole procedure was applied to ten patients with clinically proven myocardial infarction. The comparison between the MIE and the visually assessed regional function scores demonstrated that the MIE is highly related to the severity of the wall motion abnormality. In addition, it was shown that the newly developed regional myocardial contraction parameter (ATR) decreases significantly in delayed enhanced regions. This largely automated approach enables the combined study of regional MIE and left ventricular function.     

不完全屏蔽腔体辐射耦合电场增强效应防护方法

针对武器装备机箱内部电磁辐射防护的技术需要,从不完全屏蔽腔体辐射耦合电场增强效应形成机理出发,对孔缝耦合及贯通导体耦合导致的屏蔽腔体内部局部电场增强效应防护方法进行了研究.仿真计算了屏蔽腔体内部加载吸波材料、腔体分区隔断以及贯通导体安装金属导管等防护方法对不完全屏蔽腔体电磁耦合的影响,研究结果表明:在屏蔽腔体内部加载吸波材料能够有效降低由于腔体谐振产生的电场增强效应,相同的吸波材料放置在强场位置防护效率会更高;采用分区隔断的屏蔽腔体能够提高腔体的谐振频率,大幅降低腔体内大部分位置的电磁耦合能力;贯通导体通过金属导管进入屏蔽腔体能够有效降低贯通导体的电磁耦合能力,削弱屏蔽腔体内部的电场增强效应,屏蔽腔体内部及外部的金属导管长度越长,其防护效果越明显.     

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.     

MCG simulations of myocardial infarctions with a realisticheart-torso model

Data from simulations of the anterior myocardial infarction (AMI) and inferior myocardial infarction (IMI) are presented. One infarct located in the anterior section of the left ventricle and a second one in the inferior wall of the left ventricle were modeled. A high-resolution finite element model of a heart and torso was used in this study. Differences in the normal and infarcted fields were computed. The authors data suggest that the infarcted region contribution to the total magnetic field can be accounted for by an equivalent current dipole. It might also be possible to detect an infarct from these difference fields constructed for different cases of myocardial infarction. More simulations are needed to determine the relations between infarct sizes and locations and magnetic fields. These relations might then be used to detect various cases of myocardial infarction     

Heterojunction bipolar transistors with SiGe base grown bymolecular beam epitaxy

High-quality SiGe heterojunction bipolar transistors (HBTs) have been fabricated using material grown by molecular beam epitaxy (MBE). The height of parasitic barriers in the conduction band varied over the wafer, and the influence of these barriers on controller current, early voltage, and cutoff frequency were studied by experiments and simulations. Temperature-dependent measurements were performed to study the influence of the barriers on the effective bandgap narrowing in the base and to obtain an expression for the collector-current enhancement. From temperature-dependent measurements, the authors demonstrate that the collector-current enhancement of the HBTs can be described by a single exponential function with a temperature-independent prefactor