The Automata Model of Arrhythmias and the CVRTI - Part II
J.A. Abildskov, MD
Rate had different effects on QT interval prolongation due to the relative or absolute refractory period. In both cases the QT interval was reduced by increased rate. For a particular QT duration however, the reduction was less marked in the case of prolongation due to the relative refractory period since duration of that period was not affected by rate.
Effects of localized lesions on vulnerability to fibrillation were due to properties of both the lesion and surrounding matrices. Matrix properties determined time of the earliest possible propagated excitation and the frequency of responses to train stimuli. Nonuniform propagation in the matrix resulted in nonuniform delivery of excitation to lesions located within such propagation. Properties of lesions determined the time at which they became excitable and nonuniform recovery in lesions as well as nonuniform delivery of excitation to lesions, were factors in the pattern of lesion excitation at the interface of lesions and matrices. Local properties were a combination of properties of both with different effects than either alone. Various combinations of these multiple factors determined effects of particular lesions on vulnerability to and persistence of fibrillation. In one example, lesions with briefer recovery than that in the surrounding matrix provided a site for reentry which in turn resulted in reentry of the matrix. Those events occurred when the lesion was excited during the initial passage of excitation and reexcited by further matrix excitation adjacent to the lesion. Excitation of the lesion was then the source of premature excitation of the matrix and initiation of fibrillation in vulnerable conditions. Nonuniform delivery of excitation to lesions and nonuniform propagation within lesions due to that delivery and/or disparate recovery in the lesions were factors in the time sequence of events leading to fibrillation.
Lesions with longer recovery than that in the matrix were also capable of initiating fibrillation. Responses in recovered matrices could be premature in such lesions and able to initiate reentry within lesions having nonuniform recovery. Such reentry then initiated fibrillation in matrices with susceptible properties. Some lesions with low mean or high range of K values relative to those in the matrix resulted in fibrillation dependent on events in the lesions. Destruction of such lesions terminated fibrillation. In still other conditions fibrillation depended on the combination of properties at the matrix-lesion interface and destruction of either terminated fibrillation.
The effect of randomly scattered lesions on fibrillation threshold to train stimuli was the result of both lesion and matrix properties. Lesions with K values lower than those in the matrix reduced the mean and increased the range of values compared to the matrix alone. Both of these factors acted to reduce the fibrillation threshold. In one example, fibrillation threshold of a matrix with K values of 3- 5 (mean 4, range 2) was 66. Addition of 100 randomly distributed units with a K value of 2 resulted in overall K values of 2-5 (mean 3.5, range 3) and fibrillation threshold of 53.
Lesion K values higher than those in the matrix increased both the mean and range of K values. These had opposing effects on fibrillation threshold. The effect of range however acts per premature response while increased mean reduced the number of responses to train stimuli so fibrillation threshold was increased. In the matrix with K values 3-5 for example, the addition of 100 units with a K value of 8 increased fibrillation threshold to 93.
Scattered lesions also affected the initiation of fibrillation by single stimuli. Lesions with K values lower than those in the matrix increased duration of the period in which single stimuli initiated fibrillation. In some matrices in which slow propagation of premature responses near the stimulus site allowed distal recovery, and propagation without fibrillation addition of units with briefer recovery, sometimes allowed propagation with less delay near the stimulus site and initiation of fibrillation by earlier responses. Fibrillation was also initiated by later stimuli because of greater availability of units with brief recovery as reentry sites. Some scattered lesions with K values higher than those in the matrix resulted in fibrillation in response to later stimuli than in the matrix alone. Later recovery of the lesion units resulted in nonuniform propagation from such stimuli.
Scattered lesions consisting of “dead” unresponsive units increased fibrillation threshold in some matrices by means of blocking reentry paths. Effects were less marked in matrices with low K value range since local arrangements of those values were more nearly uniform. Scattered lesions were less likely to interrupt reentry circuits in those conditions.
Localized Lesions and ECG Waveform
These effects were determined in matrices simulating the endocardial-epicardial gradient of long to short recovery duration with excitation originating at the endocardium. Effects were due to boundaries between lesions and the surrounding matrix when they were in different states. In the case of lesions with prolonged recovery located in the endocardium, a boundary occurred when the matrix had recovered but the lesion had not. Only the terminal T wave was altered and the difference between control and lesion records reflected the difference of the longest recovery duration in the matrix and that in the lesion. Lesions with short recovery duration located in the endocardium resulted in a boundary prior to onset of the control T wave. The boundary persisted until completion of endocardial recovery and of the T wave. The difference of control and lesion records reflected the difference of the brief recovery duration in the lesion and the longest duration in the matrix.
Epicardial lesions with prolonged recovery altered the T wave during its entire duration. A boundary between recovered matrix and lesion occurred at the onset of the T wave and persisted until recovery in the lesion occurred. The difference of control and lesion records reflected the different durations of the shortest matrix recovery and that in the lesion.
Epicardial lesions with shorter recovery duration than that in the matrix resulted in a boundary prior to the onset of the control T wave. The boundary persisted only until epicardial recovery was complete. Difference of the control and lesion records reflected the different duration of shortest matrix recovery and that of the lesion.
Scattered lesions recovered excitability in the same sequence as that of activation. In the case of lesions with briefer recovery than that in the matrix this resulted in T wave alterations of opposite polarity to that of the QRS complex. Lesions with longer recovery than the matrix resulted in T wave changes of opposite polarity to the QRS.
Effects of rate on refractory period (RP) duration and disparity had opposing actions on fibrillation threshold (FT). Increased rate reduced RP duration which acted to reduce FT by allowing more responses per unit time. RP range was also reduced but acted to increase FT by decreasing nonuniformity of propagation per response. With the cycle length – RP relations of the model FT decreased with increased rate. The magnitude of decrease was greater when RP duration was longer and smaller when RP range was wide.
The decreased mean and range of RPs with increased rate resulted in earlier onset and decreased duration of the period in which fibrillation could be initiated by single stimuli. For particular rate changes the time of that period varied most when RP mean was high and duration of the period was longest when RP range was wide.
Rate and Waveform
Rate affected the times of onset, termination and amplitude of T waves. In matrices with a simulated endocardial-epicardial gradient of long to short recovery duration, increased rate reduced that gradient. With the square root CL-RP relation longer endocardial RPs decreased more than shorter epicardial ones and T wave amplitude was decreased in leads reflecting the gradient. T wave onset and termination were both earlier and onset time changed less than that of termination.
Effects of sudden and gradual changes of rate on the initiation of fibrillation were determined. Each stimulus acted in the presence of refractory periods set by the previous cycle length. A stimulus at a particular cycle length might therefore result in normal, slow or blocked propagation depending on the preceding cycle length. When a response was propagated nonuniformly, cycle lengths within the matrix differed and modified matrix behavior. In those conditions, gradually increasing rate was protective with respect to initiation of fibrillation compared to sudden rate increases. When responses occurred in fully recovered matrices, propagation was not affected by prior cycle length and their resulting refractory periods. When, however, responses occurred in incompletely recovered matrices, propagation was affected by refractory periods set by the previous cycle. Subsequent responses with decreasing cycle lengths then resulted in increasing nonuniformity of propagation, cycle lengths and resulting refractory periods. The magnitude of these effects associated with a particular response depended on the previous cycle and were more marked when that cycle length was longer. In one example, decreasing cycle lengths in increments of 10 time steps resulted in fibrillation following a cycle length of 30 time steps. In the same matrix decreasing cycle lengths in increments of 5 time steps resulted in fibrillation only following a cycle length of 25 time steps.
The normal endocardial-epicardial distribution of long to short ventricular recovery RPs had a protective role in initiation of arrhythmias. Following normal excitation originating at the endocardium, the minimum cycle length of responses at the endocardium was determined by the latest recovery in the matrix. At the epicardium, the minimal cycle length of responses was determined by the brief RPs at that location plus the endocardial-epicardial conduction time. In both cases, nonuniform propagation due to nonuniform recovery was limited to local conditions at the site of origin and further propagation was into recovered portions of the matrix.
An example of the above effects was a matrix with K values of 3-5 at the endocardium and 2-4 at the epicardium. After excitation from the endocardium fibrillation was initiated by stimuli at 32 to 42 time steps at the endocardium and 45-46 time steps at the epicardium.