The Automata Model of Arrhythmias and the CVRTI - Part I
J.A. Abildskov, MD
The computer model first used to illustrate Moe's wavelet hypothesis of fibrillation has been used in continuing studies that are part of CVRTI history. Published studies concern the effect of various factors on vulnerability to fibrillation, spiral wave concepts of reentry, torsade de pointes, T wave alternans, entrainment and termination of arrhythmias by pacing, QRST area and arrhythmias and local excitation. Additional findings concerning conduction defects, the relative refractory period, and vulnerability to single stimuli have also been obtained. Am Heart J 1964; 67:200.
The mechanism of refractory period (RP) effects on vulnerability to fibrillation initiated by train stimulation was investigated. Mean RP duration affected the number of responses per unit time and increasing mean reduced vulnerability. RP range affected the degree of nonuniformity of propagation per response and increasing range increased vulnerability. Jpn J Electrocardiol 1990; 10:3-20, J Cardiovasc Electrophysiol 1994; 5:553-559.
Single premature responses increased vulnerability to subsequent train stimulation and certain cycle lengths had greater effects in particular conditions. Nonuniform propagation and vulnerability were greatest after early responses and the earliest responses possible were later during slow rates or with longer RPs. The findings provided a possible explanation for the proarrhythmia effect of drugs that prolong repolarization. J Electrocardiol 1996; 29:213-221.
Mechanisms by which either tachycardia or bradycardia could increase vulnerability were defined. With progressively later onset of train stimulation the duration of the train required to initiate fibrillation first decreased then increased. With increased rate those events occurred earlier due to briefer RPs and vulnerability was greatest during early portions of the cardiac cycle. With slower rates and increased RPs the events were later and vulnerability was greatest during later portions of longer cycle. J Electrocardiol 1997; 30:307-313.
A possible mechanism of the vulnerable period was identified as slow propagation of early premature responses near their site of origin. This permitted sufficient recovery elsewhere that excitation propagated without reentry. Later onset resulted in more rapid local propagation so other regions were excited while recovery was nonuniform. J Cardiovasc Electrophysiol 1990; 1:303-308.
Nonuniform conduction defects (CD) distributed in the matrix increased vulnerability to initiation of fibrillation by train stimulation. The magnitude of the effect depended on the associated recovery characteristics and was most marked when vulnerability was low. Effects of the CDs occurred with each response and were greater when more responses were required. J Cardiovasc Electrophysiol 1992; 3:48-55.
Spiral wave concepts of reentry were investigated. Findings indicated that spiral configuration was a result rather than a mechanism of reentrant excitation. It occurred with both structural and functional reentry and depended on propagation outside as well as within reentrant resultant circuits. Propagation in the reentrant path initiated the wave but it was propagation outside the path that resulted in the spiral contour. The contour was demonstrated with reentry due to disparate recovery times as well as nonuniform refractory periods, which was further evidence that it does not represent a distinct mechanism of arrhythmia. PACE 1994; 17:944-952.
Torsade de Pointes
A possible mechanism consisting of moving sites of reentry was defined. Premature excitation in a region with relatively brief recovery propagated independently in that region before entering a path with later recovery. Reentry of the brief recovery path occurred at changing locations since recovery in one limb and propagation in the other limb of reentry circuits had opposite directions and met distal to the origin of excitation in the initial limb. The mechanism was demonstrated with conduction defects as well as disparate recovery. Findings elucidated the basis of QRS peak rotation, limited duration of episodes and of both pause and adrenergic onset of episodes. They also provided a possible explanation for the propensity of drugs that both slow conduction and prolong recovery to result in torsade de pointes. J Cardiovasc Electrophysiol 1991; 2:224-237; J Cardiovasc Electrophysiol 1993; 4:547-460.
T wave alternans
Evidence was obtained that 2:1 intraventricular block could result in T wave alternans with only slight variation of QRS waveform. ECG effects of failure to activate a refractory region were partially eliminated by activation of the surrounding area with the refractory region contributing to the "activation" boundary. J Electrocardiol 2000; 33:311-319.
Other studies contributed to the definition of mechanisms in entrainment and termination of reentrant rhythms by pacing. With structural obstacles entrainment was the result of bidirectional propagation of paced excitation. Paced excitation collided with reentrant excitation in one direction but continued propagation in the other. With functional obstacles, paced excitation did not enter reentrant circuits but modified them by affecting recovery between the circuits. Termination of reentry with structural obstacles required collision of paced with reentrant excitation and block of paced excitation in the other direction. J Cardiovasc Electrophysiol 1996; 7:71-81; J Electrocardiol 1994; 27:277-286.
Relations of QRST area distributions and vulnerability to train stimulation initiation of fibrillation were investigated. The features of magnitude, nonuniformity and gradients in the distributions were directly related to vulnerability and to the range of recovery durations. Mean recovery durations however, did not alter QRST area distributions unless changes of recovery were localized. J Electrocardiol 1991; 24:197-203.
Local excitation and propagation within and near stimulus sites were shown to influence the effectiveness of stimulation. Effects include both inhibition and facilitation by sequential stimuli and are possible factors in the measurement of physiologic conduction and initiation of arrhythmias. J Cardiovasc Electrophysiol 1991; 2:45-57.
Primary Conduction Defects
Slow conduction secondary to incomplete recovery of excitability is an important and well-established factor in reentrant arrhythmias. Defective primary conduction must also be a factor but its role has not been well defined. Observations with the automata model were important in defining the role of secondary defects and the model is also applicable to determining effects of primary defects. Findings include the published evidence that distributed defects increased vulnerability to train stimulation and the magnitude of the effect depended on the refractory periods with which they were associated. Further studies have provided evidence that reflected reentry from CDs is a possible mechanism of premature responses, ectopic tachycardia and the initiation of fibrillation including fibrillation whose persistence depends on a local CD.
Locally delayed activation of sufficient duration that adjacent units recovered excitability resulted in reflected reentry. If reflected excitation propagated without further reentry it resulted in premature responses and their pattern depended on the magnitude of delay in the CD and recovery of excitability outside the defect. With a particular rate and set of recovery characteristics, the pattern of premature responses was determined by the duration of CD delay. Interpolated premature responses occurred when the delay was sufficient to allow reflection and recovery occurred prior to the next basic response. Longer delay and later recovery of the matrix prevented the next basic response and resulted in a bigeminal pattern with a compensatory pause after each premature. Further increases of CD delay resulted in interpolated premature responses after every second basic response and still further delay resulted in premature responses with compensatory pauses in every other basic cycle. With a particular CD delay changes of rate or of matrix characteristics changed the pattern of premature responses. For example, the pattern of bigeminal responses was changed to interpolated premature responses by a slower rate since the premature response no longer blocked the subsequent basic response. The refractory period within CDs which affected whether defects were excited in all basic cycles was also a factor in the pattern of premature responses.
Fibrillation Initiated by Reflection
In vulnerable matrices fibrillation could be initiated by single reflected responses near the time of earliest propagation. One result was fibrillation initiated by less severe CDs but not by more severe defects with greater delay and later reflection.
When CDs consisted of multiple units with nonuniform RPs and/or delays propagation within the defects also affected the initiation of fibrillation. In the case of delays too brief to result in propagation outside the defects, internal reflection resulted in effective delay sufficient to allow such propagation and initiate fibrillation.
A possible mechanism of tachycardia based on reflected reentry alternating between two reentry sites was identified. The onset of that rhythm required initial reflection from only one of the sites due to either temporal or spatial conditions. The necessary temporal condition was different refractory periods of the two sites such that a premature response failed to excite one of the sites. The required spatial condition was geometry of the CD such that one portion was exited only after delayed excitation in another portion. Following initial reflection from one site, reflected excitation from the two sites alternated and acted as a pacemaker for the matrix. Multiple factors were involved in the occurrence and specific manifestations of the mechanism. These included the magnitude of delay at the reflection sites, refractory periods of the sites and the matrix as well as cycle lengths preceding onset of the tachycardia. Effects of the factors were interrelated so the mechanism of reciprocating reflection was possible in a variety of conditions. Tachycardia rate was related to the degree of delay in the CD with less delay resulting in faster rate.
Vulnerability to Single Stimuli
In published studies vulnerability was assessed as the duration of train stimuli required to initiate fibrillation. Possible clinical counterparts of such stimulation are triggered activity, late potentials due to asynchronous activation or tachycardia of whatever type. Fibrillation is also known to follow single premature responses in patients and occurred in some matrices in the model. The general requirement was sufficiently slow propagation of the premature response that recovery occurred in adjacent portions of the matrix allowing reentry.
Factors were: 1) K values and cycle lengths that determined refractory periods, 2) maximum refractory period that determined the latest response with slow propagation, 3) minimum refractory period that determined the time at which reentry became possible and, 4) the degree of slowing of propagation. Vulnerability was defined in terms of the duration of the period during which a single stimulus initiated fibrillation or the latest stimulus with that effect. Increased refractory period range increased vulnerability to single stimuli in terms of both the duration of the period and latest stimulus resulting in fibrillation. The shorter minimum refractory period allowed reentry at an earlier time and the longer maximum refractory period resulted in the required slow propagation of later responses. The effects of refractory period range on vulnerability to single stimuli were similar to those on vulnerability to train stimuli.
Increased mean refractory period duration, which decreased vulnerability to train stimuli, also reduced vulnerability in terms of duration of the period of single stimulus initiation of fibrillation. The first effective stimulus was later due to the higher minimum RP and was responsible for reduction of the fibrillation period. The higher maximal RP allowed nonuniform slow propagation of later responses but reentry of these was prevented by the longer minimum RP. The latest response resulting in fibrillation itself was not altered by increased mean RP duration (i.e. increased mean RP was not protective with respect to late premature initiation of fibrillation).
The Relative Refractory Period (RRP) affected vulnerability by means of the degree and duration of slow conduction during that period. Increased duration of the RRP increased vulnerability to both train stimulation and single stimuli. In the case of train stimulation effects were less marked when the RP range was high or mean was low since fewer responses were required to initiate fibrillation and effects of slow propagation due to the RRP occurred with each response. With single stimuli, higher RP range permitted earlier activation and the slower conduction due to the RRP allowed earlier reentry. Higher RP range permitted later stimulation prior to recovery of all units so slower conduction during the RRP resulted in later reentry. Increased mean RP reduced the period during which single stimuli resulted in fibrillation. Earliest activation was later due to the higher minimum RP. The increased maximum RP allowed later stimulation prior to full recovery but its effect on initiation of fibrillation was opposed by the higher minimum RP that acted to prevent reentry.
Effects of the relative refractory period (RRP) were of special interest since prolongation may be a mechanism in long QT syndrome. In the model prolongation resulted in increased vulnerability to fibrillation and prolonged QT with normal time of T onset in calculated ECGs. Prolongation of high together with reduced duration of low RPs also resulted in increased vulnerability and prolonged QT but T wave onset was early. Prolongation of both high and low RPs resulted in QT prolongation and late T wave onset and vulnerability was reduced. Prolongation of only high RPs resulted in QT prolongation and normal T wave onset but with reduced vulnerability. In contrast to prolongation of the RRP however, T waveform changes were mainly confined to terminal portions of the wave.
Figure 1 shows ECGs calculated from a matrix with layered recovery properties simulating their endocardial-epicardial distribution. Solid lines represent control conditions and dashed lines conditions that prolong the QT interval. Panel A illustrates QT prolongation due to prolongation of the relative refractory period and the time of T wave onset is not affected. Panel B shows QT prolongation due to prolongation of absolute refractory periods with delayed T wave onset. Panel C illustrates effects of increased refractory period range with prolonged QT and early T wave onset. Panel D shows effects of prolongation of only the longest RPs.