A model of electrical conduction in cardiac tissue including fibroblasts.

Fibroblasts are abundant in cardiac tissue. Experimental studies suggested that fibroblasts are electrically coupled to myocytes and this coupling can impact cardiac electrophysiology. In this work, we present a novel approach for mathematical modeling of electrical conduction in cardiac tissue composed of myocytes, fibroblasts, and the extracellular space. The model is an extension of established cardiac bidomain models, which include a description of intra-myocyte and extracellular conductivities, currents and potentials in addition to transmembrane voltages of myocytes. Our extension added a description of fibroblasts, which are electrically coupled with each other and with myocytes. We applied the extended model in exemplary computational simulations of plane waves and conduction in a thin tissue slice assuming an isotropic conductivity of the intra-fibroblast domain. In simulations of plane waves, increased myocyte-fibroblast coupling and fibroblast-myocyte ratio reduced peak voltage and maximal upstroke velocity of myocytes as well as amplitudes and maximal downstroke velocity of extracellular potentials. Simulations with the thin tissue slice showed that inter-fibroblast coupling affected rather transversal than longitudinal conduction velocity. Our results suggest that fibroblast coupling becomes relevant for small intra-myocyte and/or large intra-fibroblast conductivity. In summary, the study demonstrated the feasibility of the extended bidomain model and supports the hypothesis that fibroblasts contribute to cardiac electrophysiology in various manners.

Electrophysiological modeling of fibroblasts and their interaction with myocytes.

Experimental studies have shown that cardiac fibroblasts are electrically inexcitable, but can contribute to electrophysiology of myocardium in various manners. The aim of this computational study was to give insights in the electrophysiological role of fibroblasts and their interaction with myocytes. We developed a mathematical model of fibroblasts based on data from whole-cell patch clamp and polymerase chain reaction (PCR) studies. The fibroblast model was applied together with models of ventricular myocytes to assess effects of heterogeneous intercellular electrical coupling. We investigated the modulation of action potentials of a single myocyte varying the number of coupled fibroblasts and intercellular resistance. Coupling to fibroblasts had only a minor impact on the myocyte's resting and peak transmembrane voltage, but led to significant changes of action potential duration and upstroke velocity. We examined the impact of fibroblasts on conduction in one-dimensional strands of myocytes. Coupled fibroblasts reduced conduction and upstroke velocity. We studied electrical bridging between ventricular myocytes via fibroblast insets for various coupling resistors. The simulations showed significant conduction delays up to 20.3 ms. In summary, the simulations support strongly the hypothesis that coupling of fibroblasts to myocytes modulates electrophysiology of cardiac cells and tissues.

Mechanisms in T-wave alternans caused by intraventricular block.

It is recognized that 2:1 intraventricular (IV) block can result in T-wave alternans but is usually assumed that it would also affect QRS waveform. Block in a local region is not, however, varied activation sequence of the same muscle mass because the blocked region is not activated and is not part of the mass that is activated in cycles without block. Also, the block region may have electrocardiogram (ECG) effects when its state differs from other regions. In view of those considerations, the ECG effects of IV block were evaluated by using a computer model of excitation and recovery. ECGs were calculated from differences between the excited state and various degrees of recovery. Results provided evidence that boundaries associated with regions of block rather than regions having varied activation sequence were the major factors in T-wave alternans caused by IV block. Effects of the boundaries included cancellation of the effects of IV block on QRS complexes. Findings suggest that IV block cannot be excluded as a mechanism of T-wave alternans in the absence of QRS alternans.

Simulated torsade de pointes--the role of conduction defects and mechanism of QRS rotation.

A possible mechanism of torsade de pointes consisting of moving sites of reentry in the presence of disparate recovery of excitability has been previously proposed. This study evaluates the role of conduction defects in that mechanism. A computer model that simulated propagation, cycle length dependent recovery of excitability, and slow propagation during incomplete recovery and in conduction defects was used. Localized conduction defects consisting of slow propagation were shown to allow reentry at changing locations in the presence of uniform recovery properties. Later activation within defects resulted in later recovery, which permitted independent antegrade propagation adjacent to the defects. Retrograde propagation in the defects then resulted in reentry. The location of serial reentry changed because retrograde propagation and antegrade recovery had opposing directions and met distal to the origin of antegrade excitation. This mechanism was similar to that produced by disparate recovery and the combination of conduction defects and disparate recovery permitted the mechanism to occur with less marked disparity than otherwise required. The study also showed bidirectional serial reentry around a localized conduction defect or region of disparate recovery, which resulted in rotation of QRS peaks around the isoelectric line. The study provided evidence that either conduction defects or disparate recovery of excitability may be a substrate for torsade de pointes. It also indicated that combination of these factors might permit torsade de pointes when neither alone does so. This provides a possible explanation for the special propensity of quinidine and other drugs that slow conduction as well as prolong recovery to result in torsade de pointes. Findings also suggested a more explicit mechanism for rotation of QRS peaks about the electrocardiogram baseline than was previously available.

Effects of heart rate on vulnerability to fibrillation in a computer model.

Effects of heart rate on refractory period (RP) duration and disparity have opposing actions on vulnerability to fibrillation. Both bradycardia and tachycardia have been reported to increase vulnerability to fibrillation, and the role of their effects on RP duration and disparity in producing that effect is uncertain. That role has been investigated with a computer model of propagated excitation having nonuniform, cycle length-dependent refractoriness and slow propagation during incomplete recovery of excitability. Vulnerability was assessed as fibrillation threshold (FT), defined as the duration of train stimulation required to initiate simulated fibrillation. When measured as a function of train onset time during a cycle, FT initially decreased to a minimum and then increased to the original level. Slower rates shifted that curve upward and to the right, so that the FT was higher during early portions of the cycle but lower in later portions. Longer mean duration of RPs increased FT during all portions of the cycle, increased the difference of FT at various rates during early portions of the cycle, and decreased differences later in the cycle. Greater RP range reduced the FT and decreased the difference of FT with varied rate in early portions of the cycle, while increasing the difference in later portions. Accelerating rate had additional effects on FT-related to nonuniform propagation of responses prior to train stimulation. The findings defined mechanisms based on established effects of rate on RP, by which either tachycardia or bradycardia could increase vulnerability to fibrillation, and demonstrated the effects of RP range and duration on the mechanisms.

Mechanisms in adrenergic dependent onset of torsades de pointes.

Pause dependent onset of torsades de pointes is characteristic in acquired long QT syndromes, and the probable mechanism is reentry facilitated by increased disparity of refractoriness following a long cycle. Adrenergic dependent onset is usual in familial long QT syndromes, and the mechanism is uncertain. In this study with a computer simulation of torsades de pointes, possible mechanisms of adrenergic dependent onset have been identified. Decreased refractory periods facilitated the initiation of torsades de pointes by permitting earlier premature excitation and allowing reentry in the presence of the shorter refractory period that had been further shortened by the earlier excitation. In addition, accelerating rate resulted in responses occurring in the presence of refractory periods set by the prior response so each response was premature with respect to the preceding one. The difference between cycle lengths and refractory period decreased with increasing rate leading to the functional block required for initiation of simulated torsades de pointes. Findings define possible mechanisms by which the adrenergic effects of reduced refractory period duration and increased rate may lead to the initiation of torsades de pointes.

Effects of premature responses on vulnerability to fibrillation in a computer model.

The purpose of this study was to determine the effects of premature responses on vulnerability to fibrillation using a computer model based on the wavelet hypothesis. The model simulated propagation, nonuniform recovery of excitability, and slow propagation during incomplete recovery. Vulnerability was assessed as the fibrillation threshold, which was defined as the duration of train stimulation required to initiate self-sustained reentrant excitation with multiple excitation fronts. The fibrillation threshold was determined at various premature cycle lengths in the presence of refractory periods of varied range and duration, at various rates, and after compensatory pauses and varied patterns of consecutive premature responses. The fibrillation threshold was found to be reduced by premature responses, and with increasing premature cycle length, there was an initial decrease followed by an increase of fibrillation threshold. The fibrillation threshold was directly related to the duration and indirectly related to the range of the refractory period. The time phase of curves relating premature cycle length and fibrillation threshold was such that premature responses at some cycle lengths were associated with a lower fibrillation threshold in the presence of longer refractory periods, with slower rates, and with an immediately preceding compensatory pause. The mechanism may be important in the proarrhythmia effects of drugs that prolong repolarization and in the bradycardia-tachycardia syndrome. Consecutive premature responses at a constant rate increased the fibrillation threshold in comparison with the initial response, while consecutive responses at an accelerating rate decreased the fibrillation threshold.

Induced termination of fibrillation.

A previous communication in the Creative Musings section of this Journal summarized additions to the wavelet hypothesis related to the initiation of cardiac fibrillation. That hypothesis is also relevant to the termination of fibrillation, and further additions related to that event are presented in this report. Findings in both reports were obtained with a computer model based on the wavelet hypothesis, and results concerning initiation and termination of fibrillation were closely related. Refractory period (RP) conditions that terminated fibrillation were the inverse of those that increased vulnerability to the initiation of fibrillation. Increased RP range or decreased RP duration increased vulnerability to the initiation of fibrillation and decreased RP range or increased RP duration were capable of terminating fibrillation. Slow propagation increased vulnerability to initiation of fibrillation and acted to sustain fibrillation when instituted during fibrillation. The combination of increased duration and decreased range of RPs was more effective in terminating fibrillation than either alone. The magnitude of increased RP duration or decreased RP range required to terminate fibrillation and the effects of slow propagation on the maintenance of fibrillation depended on RP duration and range present during fibrillation. The findings extend the wavelet hypothesis of the nature of fibrillation to the prediction of conditions required to terminate fibrillation.

Clinical applications of body surface potential mapping.

Accumulated evidence suggests that the electrocardiographic information provided by the standard 12-lead electrocardiogram can be improved by use of multilead electrocardiograms. The clinical utility of body surface potential mapping is related to the selective regional information provided by the increased number of leads. That clinical utility includes such things as improved localization of accessory pathways in preexcitation syndromes, improved localization of pacing sites within the ventricles, localization of late potentials, and improved recognition of acute myocardial ischemia. Recording equipment and interpretation schemes are available to make possible more widespread application of potential mapping.

Mechanisms in the interruption of reentrant tachycardia by pacing.

The mechanisms by which pacing interrupts reentrant tachycardia associated with a structural obstacle were investigated using a computer model of propagated excitation. The model simulated cycle length-dependent refractoriness and slow propagation during incomplete recovery of excitability. Previously established features of the mechanism consisting of collision of reentrant with paced antidromic propagation and block of orthodromic propagation were demonstrated in the model, and factors affecting the mechanism were defined. Arrival time of paced orthodromic excitation at a potential block site and the duration of refractoriness at that site were major factors. Arrival time was determined by pacing stimulus time and propagation velocity. Slow propagation of a particular response acted to prevent the required block during that response, but enhanced the likelihood of a block of a subsequent response by affects on the onset time and duration of refractoriness at the block site at fast rates. In some conditions, responses to later stimuli resulted in block and interruption of tachycardia, while earlier stimuli with slower propagation during the same cycle failed to. Tachycardia rate affected its interruption by pacing by means of the shorter refractory period of the potential block site at fast rates, so that a paced response with a particular arrival time might fail to block. A greater number of successive paced responses were then required to terminate rapid tachycardia.

Entrainment of reentrant tachycardia in a computer model.

Capture of the cardiac rate by pacing followed by an immediate return to the original rate after pacing has been proposed as characteristic of reentrant rhythms. In this study, such entrainment has been demonstrated using computer-model simulations of propagated excitation and of reentry associated with structural and functional obstacles. With structural obstacles, the mechanism of entrainment was bidirectional propagation of paced excitation in reentry circuits, with collision of the reentrant and paced excitation in one direction and continued propagation of paced excitation in the other direction. The time of pacing onset, rate, and location all affected the QRS waveform during entrainment. With a particular time of onset and rate of pacing, the duration of time during which the QRS waveform underwent dynamic change was directly related to the distance between the pacing site and reentrant circuit. The location of reentry associated with functional obstacles moved so that the relationship between pacing-induced and reentrant excitation varied. In some cycles, pacing did not alter reentrant circuits, that is, entrainment did not occur, while other cycles were entrained, but by a different mechanism than that with structural obstacles. Leading circle reentry circuits, consisting of propagation away from and returning to reentry sites, did not have an excitable gap and paced excitation did not enter those circuits. Paced excitation did, however, enter the propagation paths between leading circle reentry circuits and modified the circuits by affecting the recovery of excitability.

Additions to the wavelet hypothesis of cardiac fibrillation.

INTRODUCTION: The wavelet hypothesis of Moe relates the initiation of cardiac fibrillation to nonuniform propagation of premature responses in the presence of nonuniform recovery of excitability. Fibrillation itself is characterized by multiple spatially discrete activation fronts (wavelets) resulting in reentry at changing locations. METHODS AND RESULTS: A computer model originally used to demonstrate the hypothesis has been used in further studies of fibrillation and the findings add new details to the hypothesis. The model simulated propagation, cycle length dependent recovery of excitability, and slow propagation of premature responses. Additions to the hypothesis were definition of the different mechanisms by which refractory period (RP) range and mean duration affect vulnerability, explanation of the onset of the vulnerable period later than earliest propagation, and definition of effects of conduction defects on vulnerability. They also include evidence that RP range and duration affect the degree of nonuniform excitation required for fibrillation. CONCLUSION: Findings indicate that mean RP duration affects vulnerability by means of the number of premature responses possible per unit time while RP range affects nonuniformity of propagation per premature response. They also suggest that effects of conduction defects on vulnerability depend on associated RPs and that the degree of nonuniform excitation required to initiate fibrillation varies with recovery properties. In addition, they provide an explanation for onset of the vulnerable period after propagation is possible.

Spiral waves in a computer model of cardiac excitation.

Spiral excitation fronts have been demonstrated in association with reentry in a computer model of propagated excitation. Fronts were initiated by the reentrant circuits but the spiral configurations themselves occurred outside the circuits. Excitation initiated near the initial portion of reentrant circuits propagated greater distances during a particular time period than excitation initiated from later portions of the circuit. This resulted in spiral configuration of excitation fronts in which the front was located at increasing distance from the latest initiating event. Excitation fronts that did not themselves have spiral configurations in certain matrices were identifiable as parts of spiral configurations that occurred when the same reentrant events were present in other matrices. Spiral waves were initiated by either leading circle reentry associated with functional block to propagation or reentry associated with structural obstacles. They also occurred in the presence of initially uniform refractory periods and resulted in self-sustained reentrant excitation. This however, required particular conditions of excitation such that recovery times constituted a functional block permitting leading circle reentry.

Cycle-length effects on the initiation of simulated torsade de pointes.

The sequence of a short and long cycle length has been observed frequently to precede the onset of torsade de pointes in patients. The purpose of this study was to determine the mechanism of that relation by means of a computer model of propagated excitation. The model included cycle length-dependent refractoriness and slow propagation during incomplete recovery and has been used previously to document that changing QRS waveform and limited duration of torsade de pointes episodes can be explained by moving sites of reentrant excitation. In this study, a short-long cycle-length sequence due to a ventricular premature response and compensatory pause was shown to prolong the period during which simulated torsade de pointes could be initiated. A premature response that failed to initiate the arrhythmia in the absence of that sequence did so after the sequence. Both the premature ventricular response and compensatory pause of the short-long cycle-length sequence contributed to prolongation of the torsade period, but by different mechanisms. The compensatory pause prolonged refractory periods and increased their disparity by a direct effect of cycle length. The ventricular premature response had similar effects, but these were indirect and due to the activation sequence of the response. When such a response was followed by a supraventricular response, the ventricular cycle length included atrioventricular conduction time and was longer than that with a series of responses of either supraventricular or ventricular origin. In addition to elucidating the mechanism of the short-long cycle sequence relation to torsade de pointes, the findings suggest that long cycles of whatever nature or the sequence of ventricular and supraventricular responses of whatever cycle length may facilitate initiation of the arrhythmia.

Mechanisms in simulated torsade de pointes.

A mechanism of torsade de pointes consisting of moving sites of reentrant excitation has been proposed on the basis of findings with a computer model. Substantial additions to that mechanism are now proposed based on further studies with the same model. The model simulated propagation, cycle length-dependent recovery of excitability, and slow propagation during incomplete recovery. Regions of relatively short and long recovery were assigned because of evidence of regional prolongation of recovery in long QT syndromes in which torsade de pointes is frequent. As previously reported, premature excitation in the short recovery region initially propagated independently, then entered the long recovery region and reentered the short recovery region distal to the site of origin. Reentrant excitation initiated a similar series of events, and serial reentry at systematically changing locations resulted in changing patterns of excitation compatible with the changing QRS waveform in torsade de pointes. Episodes terminated when reentrant excitation reached the end of unclosed short recovery paths, collided in closed paths, or encountered refractoriness in the presence of nonuniform short recovery. In this study, it was shown that excitation preceding reentry had important effects on the mechanism. These included reversal of the direction of serial reentry, bidirectional serial reentry, reentry at multiple sites from the same parent conditions, and occurrence of reentry without the requirement of slow propagation. Evidence for a Doppler shift of cycle lengths in regions from which serial reentry was receding or approaching was obtained. Sustained serial reentry was also demonstrated and is a possible mechanism for polymorphic ventricular tachycardia. Findings further define a possible mechanism of torsade de pointes.

Effects of premature excitation and tachycardia on the spatial distribution of refractoriness and propagation of excitation in a computer model.

In this study, the spatial pattern of refractoriness and its effects on propagation of excitation during premature responses and tachycardia have been investigated using a computer model. The model simulated propagation, cycle length-dependent refractoriness, and slow propagation during the relative refractory period. Findings showed slow propagation near the origin of premature responses resulting in longer cycle lengths distal to the slowing. The nonuniform cycle lengths terminated by a premature response also represented the onset of the subsequent cycle, so the pattern of refractoriness was altered after both the premature and following cycle. This occurred even though cycle length affected only the immediately following refractory period in the model. The effect of nonuniform cycle lengths during a premature response on refractory periods after the subsequent response occurred with all cycle lengths of the later response. When the cycle length of that and further responses was sufficiently shortened to result in slowed propagation, changing spatial patterns of refractoriness and propagation occurred. The findings are evidence that responses with slow propagation during incomplete recovery of excitability can affect conduction velocity and refractoriness during multiple subsequent cycles. These effects are likely to occur in the heart but are modified by features such as sustained effects of cycle length on refractoriness, anisotropy, and electrotonic interactions.

ACC policy statement. Recommended guidelines for training in adult clinical cardiac electrophysiology. Electrophysiology/ Electrocardiography Subcommittee, American College of Cardiology.

Training in clinical cardiac electrophysiology should take place in an Accreditation Council for Graduate Medical Education accredited cardiology program, and the electrophysiology training program itself should be accredited by the Council. Each trainee must be eligible for board certification in Internal Medicine and either eligible for certification in Cardiovascular Diseases or in a program leading to eligibility. Training faculty should be certified in clinical cardiac electrophysiology or demonstrate equivalent credentials. At least two training faculty members are preferred. The faculty must be dedicated to teaching, active in performing or promoting research and must spend a substantial portion of their time in research, teaching and practice of clinical electrophysiology. A curriculum of training should be established. Faculty experts in the related basic sciences should be available and involved in teaching. The institution should have a fully equipped clinical electrophysiology laboratory and complete noninvasive capabilities. A close working relation with a cardiac surgery faculty member skilled in surgical treatment of arrhythmias is required. Training in application of pharmacologic and all current nonpharmacologic therapies, in the outpatient and inpatient setting, is necessary. The clinical exposure must include all facets of arrhythmia diagnosis and treatment and must be quantitatively sufficient to allow the trainee to develop proficiency. The period of training should not be less than one year in addition to the period of cardiology fellowship required by the ABIM for board eligibility. A continuous period of training is preferred.

Distribution of QRST deflection areas in relation to repolarization and arrhythmias.

QRST area maps were calculated from a computer model of propagated excitation with nonuniform cycle length-dependent recovery. Vulnerability was independently assessed as fibrillation threshold (FT). Separate effects of varied range and mean recovery durations on FT and QRST maps were determined. FT was inversely related to the range of recovery durations and that range was related to QRST area map features including magnitude, nonuniformity, and gradients. Mean recovery duration was directly related to FT but did not alter QRST maps unless changes of recovery duration were localized. Locally decreased mean duration resulted in decreased FT and increased magnitude and nonuniformity and gradients in QRST maps. Locally increased mean duration had similar effects on QRST maps, but FT was increased. Results support the validity of QRST map features as markers of vulnerability due to disparity of recovery duration or locally decreased mean recovery duration but not due to widespread changes of mean duration or locally increased duration.

Electrocardiographic wave form and cardiac arrhythmias.

In addition to its established diagnostic uses, the electrocardiogram may be useful for predicting ventricular fibrillation and other arrhythmias. Non-uniform recovery of excitability, which is a factor in vulnerability, is the determinant of QRST deflection area, and regionally selective sampling by body surface electrocardiographic mapping may permit recognition of the locally disparate recovery related to fibrillation. Preliminary experimental and clinical studies support this possibility and suggest that the multipolar content of QRST area distributions on the body surface is a marker of vulnerability.