1 Introduction
This chapter is not intended as an exhaustive, historical and critical review of the theories and models developed for the explanation of fibrillation. The following reviews (de Boer 1923), (Kisch 1950), (Foy 1974), (Kastor 1974), (Schley 1975), (Zipes 1975) and (Lown 1980) have been used to sketch the different types of theories to explain or describe ventricular fibrillation, but even from these extensive reviews one does not always get a clear picture of the definition used for fibrillation, whether the authors discussed by the reviewers assume a myocardial syncytium or not, etc. The picture gets even more complicated by authors which use models of atrial fibrillation like that of Moe et al (Moe 1964) as a basis for the explanation of ventricular fibrillation, regardless of the anatomical and electrophysiological differences between atrium and ventricle. E.g. (Foy 1974) and (Zipes 1975) and (Lown 1980), although the term chaotic rhythm should be avoided, since it is difficult to define chaos (WHO 1978).
The pioneers of the study of ventricular fibrillation mentioned rapid oscillations (Rothberger 1914), (MacWilliam 1887) and (MacWilliam 1919) up to 10 Hz in rabbits (Hoffa 1850), without coordination between adjacent fibers (MacWilliam 1887), (Einbrodt 1859), confirmed by me (Herbschleb 1980b). A low excitability precludes ventricular fibrillation, although normal excitation is still possible (MacWilliam 1887), (de Boer 1921); (Chapter XI) and (Chapter XIII).
The fibrillation frequency decreases in the absence of coronary perfusion (MacWilliam 1887), (Kisch 1921), (Herbschleb 1980b). Different frequencies may be present at the same time at different sites on the heart, although transient synchrony is possible (Kisch 1921), (Herbschleb 1980a).
A critical mass of myocardial tissue must be exceeded for sustained ventricular fibrillation, i.e. if a fibrillating dog heart is divided into pieces smaller than one quarter of the total mass, fibrillation stops (Garrey 1914). The observation of Covino and d’ Amato (Covino 1962) that in hypothermia the ventricles of rats and rabbits did not fibrillate, those of cats seldom and those of dogs easily supports the idea of a critical mass. This critical mass is much larger than the critical mass that must be excited by an electrode in order to excite the whole heart (Lindemans 1975) and (Lindemans 1978). The order of magnitude of the latter mass is 0.5 mm in diameter, enough for short time local fibrillation (Krinsky 1973), (Herbschleb 1982). See Chapter XIII of this book for further comment.
A vulnerable phase is present during the heart cycle in which a single stimulus can elicit ventricular fibrillation (de Boer 1920a), (Wiggers 1940). (Chapter XII).
Any theory about ventricular fibrillation should explain or at least not contradict these observations. Assuming that all authors describe more or less the same phenomenon in the same terms, the theories can be grouped in the following way.
2 Unifocal tachycardia
Rothberger and Winterberg proposed in (Rothberger 1914) the theory that flutter and fibrillation were the same phenomenon, caused by one very rapidly firing focus somewhere in the right or left ventricle. A few cardiologists adhered to this theory for a short while, but the ideas never became popular as they are in contradiction with recordings of different frequencies from one fibrillating heart.
3 Multifocal tachycardia
Engelmann proposed in 1895 (de Boer 1923) the theory that during ventricular fibrillation a lot of independent, rapidly firing foci were to be found in the ventricle, separated by zones of diminished conduction. One of the well-known supporters of this thesis was Kisch (Kisch 1921). The basic objections to this theory (at least in its original form) have already been made by de Boer in 1923. If there are a lot of independent foci, no reason can be found why a critical mass is necessary for ventricular fibrillation. Another objection is that de Boer already observed that the fastest fibrillating area would after some time accelerate the other areas, which can hardly be reconciled with foci separated by zones of diminished conduction.
A recent variant is the hypothesis that ventricular fibrillation is caused by depolarizing afterpotentials or triggered automaticity (Lown 1980). These afterpotentials certainly occur in an ischemic myocard, but most likely not in a healthy heart after electrocution. Moreover, a few cells with depolarizing afterpotentials would start ventricular fibrillation, which is in contradiction with the already mentioned critical mass.
Krinsky (Krinsky 1973) proposed “reverberators” as the principal mechanism for ventricular fibrillation. This concept arose from his work on models of two-dimensionally coupled cells, that could be in three states, viz. excited, refractory or quiescent. If two areas were created with different durations of the refractory states in such a way that the total duration of the excited state plus refractory state in area 1 exceeds the total duration of twice the excited state plus the refractory state in area 2, then a rapid succesion of two stimuli could create the situation of two wavefronts in area 2 and one in area 1. If moreover the border between area 1 and 2 is not perpendicular to the travelling wavefronts, then the second wavefront in area 2 may cause a second front in area 1, that after some time may cause a third front in area 2, etc. This mutual reexcitation is called a reverberator and can be considered a more precise definition of the “focal reexcitation” mentioned by Han (Han 1971). A sudden spatial increase in duration of the refractory state is crucial to this theory, as has been postulated by other authors too, (Schamroth 1980) who considers “the asymmetry of refractoriness” as particularly dangerous. Zipes only considers a circus movement of a wavefront as reentry, but his statement: “if the degree of electrical asynchrony is sufficiently great, then simply increasing the ventricular rate beyond the ability of all myocardial elements to follow in a uniform fashion will begin fibrillation.” (Zipes 1975), fits Krinsky’s idea of a reverberator better than the start of Winfree’s rotor (see next paragraph).
Reverberators can occupy a much smaller area than the microcircuits mentioned in the next paragraph. They have in a heterogeneous medium a limited life-time, but the wavefronts travelling from reverberators will cause new ones at other places, so a certain critical mass should be exceeded in order to create enough space to let the birth rate of reverberators be equal to or greater than the death rate. The entrainment of frequencies cannot be explained in this way, nor the the very high fibrillation frequencies.
4 Circus reentry
Good reviews concerning circus reentry and atrial fibrillation will be found in (Rytand 1966) and in (Allessie 1977). Especially the theories of circus reentry depend heavily upon the ideas about atrial fibrillation, as most researchers consider atrial fibrillation more or less similar to ventricular fibrillation. The latter however is much more difficult to investigate because of the greater complexity of the anatomy and electrophysiology of the ventricular wall.
Different types of circus movement have been proposed:
4.1 macro circuit, fixed path
Mayer proposed in 1906 and 1908 (de Boer 1923) the theory that during ventricular fibrillation an excitation front followed a fixed, circular path through the basis of the ventricles, shooting off many subfronts through the rest of the ventricles. The irregular behaviour of these branches would then account for the irregularity of the ECG. This theory was supported amongst others by Garrey (Garrey 1914), Lewis (Lewis 1920) and in recent times implicitly by Ideker (Ideker 1980). The circulating front has never been proven to confirm any facts observed in the hearts of mammals, despite the great popularity of this theory amongst cardiologists. The already mentioned recordings of different fibrillation frequencies even contradict this theory.
4.2 macro circuit, continuously changing path
In 1923 de Boer stated that during ventricular fibrillation a fractionated wavefront travelled through the ventricle, exciting those fibers that are not refractory and leaving alone the others. In its next passage the front would excite other fibers and thus follow a different path. In his view this would account for the suddenly much higher frequency in ventricular fibrillation compared to flutter. Although the other theories mentioned do not explain this increase in frequency, the theory of de Boer never had any explicit supporters. (de Boer 1923) Wiggers (Wiggers 1930) and (Wiggers 1940) proposed a similar theory to explain the travelling contraction waves seen in his movies, Power (Power 1979) does not mention de Boer but states: “Considerably higher frequencies are indeed observed in the e.c.g. during ventricular fibrillation, but it seems likely that they reflect the chaotic, zigzag pattern of wave travel in that arrhythmia rather than the maximum firing rate of individual cells.” Such ever changing paths have also been proposed by Janse et al (Janse 1980) for their microcircuits. This theory fails to explain different fibrillation frequencies at different sites on the heart.
4.3 micro circuits
Recently models have been constructed that show the possibility of circular paths or “rotors” with a diameter of a few millimeters, (Foy 1974), (van Capelle 1980) and (Winfree 1981), (Winfree 1982a), (Winfree 1982b) and (Winfree 1983), without supposing some kind of obstacle or inhomogeneity in the medium. Motte (Motte 1979) considers these micro circuits essential for ventricular fibrillation and Janse (Janse 1980) published data to support this idea, although the alleged circus movements were seldom completed!
One objection against this theory is the same as against the multifocal theory: why is a critical mass much larger than the area occupied by a micro circuit necessary for perpetual fibrillation? Another objection is based upon the diameter of the quiescent zone enclosed by the circulating wavefront. Foy (Foy 1974) does not state the diameter of this zone in his model, but the pictures by van Capelle and Durrer show a diameter of 3 – 8 mm (3 or 4 elements, each representing 1 to 2 space constants of 1 mm) corresponding to a minimal path of 9 to 24 mm. (van Capelle 1980) These figures contrast with the size of independently fibrillating areas (0.5 mm in Krinsky 1973; <2 mm in our work of 1980), but their magnitude corresponds with a minimal path length of 30 – 50 mm for a travelling wavefront in the myocardium in dog and man (Krinsky 1973) (Herbschleb 1980a). All “rotors” mentioned are two-dimensional, an allowable simplification for atrial fibrillation (in 1977 Allessie showed a quiescent zone of 6 mm diameter), but these will not be stable if the medium is thicker than this central zone (Winfree 1980) (page 310), (Allessie 1977). A left ventricular thickness of more than 10 mm precludes the stability of rotors with a central disk of 3 – 8 mm (van Capelle 1980) or 5 mm (Janse 1980). The graphs of circus movements published by de Bakker et al (de Bakker 1979) do not contain a central quiescent zone, so either they cannot be considered as rotors or this zone is very small (<4 mm), which again precludes stability.
Rotors as envisaged by Winfree (Winfree 1981), (Winfree 1982a), (Winfree 1982b), (Winfree 1983) are unlikely to occur for other reasons as well. In short Winfree’s theory states that if a wavefront traverses the heart orderly, a phase gradient is present perpendicular to that wavefront. A weak extra stimulus will change that phase in a degree depending upon that phase, but a very strong stimulus will exert its influence regardless of that phase. As a consequence somewhere in this 3-dimensional phase-resetting space a phase singularity occurs. According to Winfree phases are distributed in an orderly, circular two-dimensional way around this singularity, so a rotor comes into being. However, it is highly unlikely that the impulses reaching the heart during e.g. electrocution can be considered “weak” at one spot and “strong” just 5 or 10 mm further. Even if this would occur, why then should the new phases lie orderly in a plane in the myocardium?
An older rotor-like concept is the reverberator (Krinsky 1973), based upon a two-dimensional medium of discrete elements in a finite number of states. As the reverberator can occupy a much smaller area than a rotor, the result will be more like multiple foci than circus reentry, so this concept has been treated in paragraph 4.
5 Weakly coupled relaxation oscillators
All theories mentioned above are insufficient in the sense that they do not explain how the supposed conditions do arise in the simple case of electrocution of a healthy subject. Stimulating the heart with an alternating current of 50 or 60 Hz will invariably cause ventricular fibrillation, but why should this create one or more foci, zones of diminished conduction, micro circuits etc, specially if the electrical current is not applied directly to the myocardium but enters the body via e.g. the extremities? Another drawback of these theories, except de Boer’s theory, is that they do not explain the sudden increase of frequency in fibrillation compared to the preceding tachycardia or flutter. Some authors have tried to improve the theories by combining some features of the above sketched theories like Cranefield who states: “There can be no doubt that the waves of excitation seen in a fibrillating ventricle or atrium undergo circus movement and that incessant reentry occurs during fibrillation. This does not, however, prove that it is circus movement that perpetuates the arrhythmia, since the activity of multiple foci … might be essential to the perpetuation of fibrillations … … although areas of depressed conduction are necessary to permit fibrillation, the sustained activity characteristic of fibrillation is not caused by circus movement but by the activity of automatic foci.” (Cranefield 1975) (page 309). Since Van der Pol and Van der Mark described the sinus rhythm as resulting from coupled relaxation oscillators, there has been interest in the question whether this model also could describe ventricular fibrillation. (van der Pol 1928) (van der Pol 1929). This does not seem possible (Power 1979) and nowadays it seems likely that the proposed oscillators do not describe the activity of the atria or ventricles, but the oscillators embedded in the sino-atrial node and the atrialventricular node (Guevara 1982). During fibrillation these nodes are not supposed to play any role in sustaining this arrhythmia.
Nevertheless, a model of coupled relaxation oscillators in the myocardial wall has some interesting properties (Grasman 1979). One of the characteristics of such a network of oscillators with different intrinsic repetition rates is the phase shift between two synchronized oscillators, apparently looking like a time delay or conduction time. If the oscillators get synchronized, the fastest will lead in phase explaining de Boer’s observation. When all oscillators get synchronized (and one oscillator is leading), the situation looks like the unifocal tachycardia. On the other hand, if all phase shifts form a continuum around the network, no leading oscillator will be seen but something like a travelling pseudowave in a circular path. The term pseudowave is used as nothing moves nor is conducted, but the small phase shifts between adjacent areas give the impression of conduction. Partial frequency entrainment with more or less fixed or random phase shifts will give the impression of a multifocal tachycardia, random waves or fractionated contractions. The remaining problem in this theory is how to fit the idea of a multitude of relaxation oscillators in the ventricular wall into the body of theories about anatomy and electrophysiology. The reverberators of Krinsky (Krinsky 1973) or rotors of Winfree (Winfree 1983) would (with some extensions) be good candidates for such relaxation oscillators, but for reasons given in the previous paragraphs these concepts are considered inadequate to explain ventricular fibrillation. In 1982 I presented a model for local fibrillation that describes how after rapid stimulation “focal reexcitation due to the flow of current between adjacent myocardial fibers that are repolarized at grossly disparate times” (Han 1971) will arise. (Herbschleb 1982)
Moreover, the model showed that the adjacent fibers would be in antiphase, giving rise to an apparent doubling of frequency. Even a group of 1000 simulated cells would only show stable, persistent activity if the outer shell of cells was stimulated from the environment, which points into the direction of a critical mass for fibrillation, i.e. a much larger mass of active tissue is required to keep a small oscillator active. Whether adjacent myocardial cells can be in antiphase will be discussed in chapter V of this book.
6 Final remark
Allessie (Allessie 1977) stresses that not enough knowledge is available to decide unequivocably which of the various theories is “true” and so one can choose the most elegant or otherwise preferable theory. A reason for this undecidability could be that ventricular fibrillation is not one syndrome, but just a name for a set of superficially similar, yet fundamentally quite different syndromes. Another way is to construct a theory that unites in some way the previous ones, provided ventricular fibrillation can reasonably well be considered one syndrome. An attempt will be made in this study following the lines sketched in the previous paragraph.