J. ELECTROCARDIOLOGY, 10 (2) 1977, 149-155
A New Method for Quantifying Ventricular Regularization During Atrial Fibrillation BY JAMES H. WARE, PH.D., PAUL L. TECKLENBERG, M.D., MARTIN MILLER, B.A., MORTON S. RAFF, M.A., LEONARD GRAUER, M.D. AND ROBERT E. GOLDSTEIN, M.D.
accounting for this is poorly understood at present. When a patient with AF is treated with excessive amounts of digitalis, regular atrioventricular junctional rhythms (AVJR) m a y be superimposed upon the usual random sequence. 1,2 Detection of minor degrees of "regularization"* of the ventricular r h y t h m during atrial fibrillation m a y provide an important early sign of incipient digitalis toxicity before the drug excess causes gross regularization of R-R intervals. These considerations have s t i m u l a t e d a continuing search for means of identifying and quantitating ventricular regularization during AF. Using a variety of methods, some investigators have detected evidence of regular R-R intervals in patients with AF and no overt evidence of digitalis toxicity. 3-s Other investigators have failed to find any evidence of ventricular regularization under similar circumstances.9 lo T h e w o r k of U r b a c h a n d a s s o c i a t e s s suggested an approach that may prove particularly sensitive in detecting nonrandom activity. These investigators regarded the sequence of R-R intervals as a random process, interrupted for brief periods by a competing mechanism of r h y t h m generation that produces regular R-R intervals. T h e y identified sequences of regular R-R intervals of various types, classified them according to R-R i n t e r v a l l e n g t h a n d c o m p a r e d t h e i r number to a frequency that would result from an entirely random process. By m a k i n g a large number of such comparisons for each patient record, U r b a c h and his colleagues were able to identify instances of nonrandom activity in 18 of 31 patients in atrial fibrillation, while only three records were recognized as nonrandom by visual electrocardiographic interpretation. While the several methods of Urbach et al could identify isolated episodes of nonrandomness, they were less suitable for summarizing the extent of nonrandom activity in
SUMMARY Atrial fibrillation (AF) characteristically results in random variation of the intervals between successive ventricular depolarizations. However, when a patient with AF is treated with excessive amounts of digitalis, regular junctional rhythms may occur. The detection of "regularization" of the ventricular rhythm in patients with AF may signal early digitalis toxicity. In this paper, we describe a new method for quantifying the ext e n t of ventricular regularization by the statistical analysis of the intervals between successive ventricular depolarizations (R-R intervals). This method yields a single index (Z score) which reflects the degree to which a sequence of R-R intervals deviates from a random distribution. S i m u l a t i o n s t u d i e s demonstrate that our method is sensitive to "regularization" of as little as two to four percent of R-R intervals, even when equal intervals occur in small groups that might easily escape detection by visual electrocardiographic interpretation. A n a l y s i s of records from six nondigitalized subjects in AF shows that the sequence of R-R intervals is usually random, or very nearly so. Records obtained from the same patients when digitalized often demonstrate more regularized activity, reflected by an index (Z score) which is higher than expected from chance deviation if a random process is assumed. Preliminary data also suggest that exercise is associated with substantial regularization of ventricular depolarization. Atrial fibrillation is characterized by a seemingly random variation of the length of intervals between successive ventricular depolarizations (R-R intervals). The mechanism From the Biometrics Research Branch, Cardiology Branch, and Clinic of Surgery, of the National Heart and Lung Institute and the Computer Systems Laboratory, Division of Computer Research and Technology, of the National Institutes of Health, Bethesda, Maryland. Reprint requests to: James H. Ware, Ph.D., National Heart and Lung Institute, Biometrics Research Branch, Division of Heart and Vascular Diseases, 7910 Woodmont Ave., Room C837, Bethesda, MD 20014.
*The terms "regularization" and "regularized" refer to the occurrence of runs or sequences of consecutive "equal" R-R intervals interposed within a series of apparently randomly varying R-R intervals. Adjacent R-R intervals are considered "equal" if they differ by less than a small prespecified value, r.
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a l a r g e sequence of R-R intervals. We t h e r e fore devised a statistical a p p r o a c h t h a t permits q u a n t i t a t i o n of i n t e r m i t t e n t n o n r a n d o m a c t i v i t y b y a single n u m e r i c a l v a l u e (Z score). We t e s t e d t h i s m e t h o d b y a s i m u l a t i o n t e c h n i q u e to assess its s e n s i t i v i t y , a n d we applied t h e m e t h o d to d a t a obtained from pat i e n t s w i t h A F to develop a n idea of its potential clinical value.
MATERIALS AND METHODS The presence or absence of regularization in the ventricular rhythm during atrial fibrillation is assessed by examining adjacent pairs of R-R intervals. If two adjacent intervals are part of a wholly random sequence, the length of the first is totally unrelated to the length of the second. If regularization occurs, however, the length of the second interval is equal to the length of the first (or, in practical terms, the two interval lengths differ by less than a small number, r). Adjacent intervals of equal length occasionally will occur by chance alone, even in a purely random series of R-R intervals. The likelihood of this event ("expected frequency") and the associated standard deviation can readily be calculated from the distribution of R-R interval lengths in the entire sequence under study. Using the expected frequency of regularization under purely random conditions and the actual number of adjacent "equal" R-R intervals Cobserved frequency"), one can construct an index (Z score) of regularization as follows: Z -- observed frequency - expected frequency standard deviation Since the probability distribution of Z, when computed from a record of random R-R intervals, can be derived, this index can help decide when the occurrence of equal interval lengths during AF becomes too frequent to attribute to chance alone. Our analytic methods were applied to a sampling of 2,000 successive R-R intervals recorded from each patient studied. (The same sample size was used in simulations.) This sampling is subsequently termed a patient record. Previous experience 7 has shown that the sample size used here is suitable for statistical analysis of AF. Mathematical Model Details of the derivation and the properties of Z are available from the authors in an unpublished Appendix. These calculations demonstrate that, when applied to long sequences of randomly and independently occurring R-R intervals, Z will be distributed as a Gaussian random variable with mean of 0 and standard deviation of 1. In this random situation, Z will have a 90% probability of falling between + 1.64 and - 1.64. ~Regularization" of R-R intervals, i.e., the occurrence of runs of R-R intervals of the same length, will shift Z toward larger positive values provided that r (the upper limit of difference between intervals accepted as equal) is larger than the fluctuations of interval length within the runs of regular R-R intervals. Hence, Z is a suitable statistic for investigating whether a particular sequence of R-R intervals represents a random arrangement. Moreover, Z will increase progressively with increasing
frequency of regularized runs, permitting a quantitative assessment of nonrandom activity. In this way, a series of patient records can be compared numerically with regard to the extent of regularization. Although Z may be influenced significantly by the particular value assigned to ~, an optimal value for r cannot be chosen on a theoretical basis. Ideally, r should be slightly larger than the largest fluctuation in regularized interval lengths. Although regularized portions of atrial fibrillation (presumably short runs of AVJR) are generally thought to have nearly equal interval lengths, the limits of variability of this rhythm have not been firmly established. Based upon their experiences with a sample of regular AVJR, Urbach and coworkers s suggested that r should be approximately 32.5 msec. Whether the regularized portions of AF obey this rule remains uncertain. Gross underestimation of r would be undesirable, in that many genuinely regularized intervals would be missed. Conversely, overestimation of r would increase the likelihood that regularization is mimicked by chance occurrences. In either case, the sensitivity of Z as an index of regularization would be diminished. To explore this issue, Z for each patient record was calculated repeatedly, using several different values of r. Using a one-tailed test, when Z exceeds +1.64 the probability is less than 0.05 that the degree of regularization in the associated patient record occurred as a chance fluctuation in a random process. We have arbitrarily picked this 0.05 probability level to discriminate random from regularized patient records for the purpose of demonstration. It should be recognized that this arbitrary choice can be modified and does not represent an intrinsic feature of the methods presented. We have considered a negative value of Z (relative deficiency of adjacent equal intervals) an unusual chance occurrence. Simulation To investigate the sensitivity of Z, four random R-R interval records were produced and then artifically '~regularized" by substituting intervals of a constant length for certain of the randomly varying intervals. Two of the random records were made by generating sequences of 2,000 independent, normally distributed random numbers with mean of 652 msec and a standard deviation of 100 msec. In addition, a patient record identified by our analysis as random (i.e., Z very nearly equal to 0) was included in the simulation study, and a patient record identified as partially regularized was also included after the order of the R-R intervals had been scrambled to achieve random arrangement. Regularization was simulated in these four records by introducing runs or sequences of equal R-R intervals. The frequency, run length and common interval length of the equal intervals were systematically varied to assess the importance of each attribute. The resulting sequences were analyzed by computer to yield values for Z. For each simulation, calculations of Z were made with r, the maximum nonrandom difference between adjacent intervals, set at 20 and at 36 msec. Analysis of Patient Records Seventeen patients with atrial fibrillation due to
J. ELECTROCARDIOLOGY, VOL. 10, NO. 2, 1977
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stable, moderately symptomatic rheumatic heart disease were selected arbitrarily from an outpatient population. All were treated with digoxin as part of their usual clinical management. None had evidence of thyroid overactivity and none was taking propranolol. Informed consent was obtained prior to study. Electrocardiograms (ECGs) were obtained by tape recording a continuous single lead ECG containing approximately 2000 R-R intervals. The patients remained at supine rest while recordings were made, except for the exercise studies. Unless specifically noted, no cardioactive drugs were given for at least two hours prior to recording. The recorded lead was chosen to optimize the shape of the QRS complex for automated processing. The presence of AF (characterized by chaotic atrial activity and grossly evident ventricular irregularity) was confirmed before and after each tape recording. No patient was included who manifested frequent premature ventricular contractions or other obvious nonfibrillatory arrhythmias at the time of recording, except as noted in Results. The analog record was amplified and digitized by a Geo-Space SS100 computer. It was then analyzed by a pattern recognition program written by one of the authors (M.M.), which searched for QRS complexes and computed R-R interval lengths, n Premature ventricular contractions were identified by the program, and R-R intervals on either side of these complexes were excluded from subsequent analysis. A resulting list of 2,000 R-R interval lengths was submitted to computerized statistical analysis to calculate Z.
RESULTS Simulation Data Both the artificially constructed and t he n a t u r a l l y r a n d o m p a t i e n t records y i e l d e d values of Z th at behaved in a similar manner. Hence, no distinction will be made among the results from t he four records of different origin. The sensitivity of Z for t he detection of nonrandom activity w~s studied by varying t hr ee characteristics of the simulated records: 1) t h e percent of the intervals which were regularized; 2) the common R-R interval length, L, of regularized portions; and 3) the length of regularized runs. For each of t he four simulated records, Z was calculated at r = 20 msec and r = 36 msec for each value of L: the values of L ranging from the mode (M) of the r a n d o m distribution to M-250 msec. Hence, eight values of Z were calculated at each part i c u l a r p e r c e n t a g e of r e g u l a r i z e d activity, length of regularized beats, and r u n length studied. As anticipated, when no regularized activity was introduced, each of the records consistently yielded values of Z smaller t h a n + 1.64 (Fig. 1). In theory, 95% of Z values from random records should fall below this limit. As the percentage of nonr andom activity was increased, the average value of Z obtained from J. ELECTROCARDIOLOGY, VOL. 10, NO. 2, 1977
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t he four simulated records increased in an a p p r o x i m a t e l y l i n e a r f a s h i o n ( F i g . 1). Eleven of t he 16 values of Z exceeded 1.64 when 2% of the intervals were regularized, and 15 of t he 16 values of Z exceeded 1.64 at 3% regularization. Because the simulated r e g u l a r activity was given a constant R-R i nt erval length, analysis using r = 20 msec gave consistently larger values of Z. Smaller values oft , however, m a y n o t m a k e Z m o r e s e n s i t i v e in s i t u a t i o n s where the length of regularized interval fluct uat es by more t h a n r. S m a l l e r Z val ues occurred w h e n L, t h e length of t he r e g u l a r runs, was set equal to the mode of t he random activity, i.e., the interval occurring most frequent l y in t he random record. Z increased, on the average, as L was set at values f a r t h e r from t he mode (Fig. 2). However, the simulation studies indicated t h a t this effect was very small, so t h a t t he ability of t he method to detect regularization was not greatly influenced by the length of t h e regularized intervals. The effect of varying the length of runs (i.e., the n u m b e r of consecutive r e g u l a r intervals) while percent regul ari zat i on was held const ant (at 5%) is shown in Fig. 3. Although all values of Z exceeded 1.64, Z was smallest w hen the run length was 2. A single r u n of t en equal intervals contributes nine adjacent e q u a l R-R i n t e r v a l s , w hi l e five s e p a r a t e "runs" of length 2 contribute only five equal R-R i n t e r v a l pairs. Hence, Z val ues for a given percent r e g u l a r i z a t i o n w ere s m a l l e r when run lengths were shorter. Nevertheless, t h e simulations showed t h a t our m et hod was capable of detecting small percentages of regularization even when regularized intervals occurred only in pairs. Patient Data Records obtained from t en patients in at ri al fibrillation were analyzed for five values of r r a n g i n g from 16 to 40 msec (Fig. 4). A l t hough Z varied slightly in each individual record as r was c h a n g e d , no c o n s i s t e n t p a t t e r n of change was evident. T he significance (or lack of significance) of Z was dependent upon t he choice of r in only one instance, a record in which Z varied between 1.5 and 1.9. Although an optimal choice of r is not clearly evident, t he choice of r in t he r a n g e of 16 to 40 msec did not appear crucial in separat i ng r a n d o m and nonrandom records in most cases. T he ability of Z to identify differing degrees of vent ri cul ar regularization is illustrated in Fig. 5. In patient G.P., borderline evidence of n o n r a n d o m a c t i v i t y was o b s e r v e d in t h e baseline state (patient had received his usual dose of digoxin). This record is also t he borderline record in Fig. 4. N onrandom ness increased after atropine, 2 mg iv, and increased
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Fig. 2. Relationship between Z score and the length (L) of sequences of regular activity relative to M, the R-R interval length occurring most frequently in the underlying record. The shaded area represents a smoothed histogram for R-R intervals whose length has a Gaussian distribution centered at M. For other definitions, see Fig. 1.
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Fig. 1. Relationship between Z score and the percentage of regularity in a sequence of R-R intervals whose lengths vary randomly when not regular. Regular activity was simulated by sequences of 10 adjacent R-R intervals of equal length. The lower dashed line is that value of Z which would be exceeded one time in 20 (p = .05) by an R-R interval record free of regular activity. The upper dashed line would be exceeded one time in 100. r is the m a x i m u m allowable difference (msec) between adjacent R-R intervals considered part of a regular sequence, L is the length of the regular R-R intervals, and the mode is the R-R interval length occuring most frequently in the R-R interval record. Since each point is the average of values from four records, a standard error is obtained at each point but shown here only for the lower line as a representative value.
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to a g r e a t e r e x t e n t d u r i n g t r e a d m i l l exercise. B o t h a t r o p i n e a n d exercise r a i s e d t h e m e a n v e n t r i c u l a r r a t e f r o m 60 to 95 b e a t s / m i n . Subsequently, digoxin was discontinued while t h e p a t i e n t r e m a i n e d a t r e s t in t h e hospital. A t 8 a n d 11 d a y s a f t e r digoxin w a s stopped, m e a n v e n t r i c u l a r r a t e i n c r e a s e d to 80. T h e Z score a t e i g h t d a y s was s i m i l a r to t h e b a s e l i n e value. T h e Z score 11 d a y s aider d i s c o n t i n u i n g digoxin was consistent with a completely r a n d o m v e n t r i c u l a r response. A second e x a m p l e of t h e b e h a v i o r of Z is also g i v e n in Fig. 5. I n t h i s p a t i e n t (W.C.), a t r o p i n e , 2 m g iv, i n c r e a s e d m e a n v e n t r i c u l a r
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Fig. 3. Relationship between Z score and the length of runs in which simulated regular sequences of ventricular depolarization occur. For definitions of symbols used, see Fig. 1. J. E L E C T R O C A R D I O L O G Y ,
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QUANTIFYING REGULARIZATION DURING AF
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Fig. 5. Variation in Z score with changes in medication and activity level in two patients. See Fig. 1 for additional definitions.
T (msec)
Fig. 4. Relationship between Z score and ~, the maximum distance between adjacent R-R intervals considered as part of a regular sequence, when ten patient records were analyzed with different values of r. Some records were obtained during periods of digoxin therapy (DIG). See Fig. 1 for additional definitions.
ra t e from 60 to 100 beats/min, but had relatively little influence on Z. In contrast, exercise th at increased m e a n v e n t r i c u l a r r a t e to 120 resulted in a m a r k e d rise in Z. Discontinuance of digoxin for eight days resulted in a Z score consistent with random intervals. In g e n e r a l , a t r o p i n e produced a v a r i a b l e response in the Z score, but exercise (resulting in an increase in m ean hear t r at e comparable to t h a t following atropine) yielded a rise in Z score in four of five subjects tested. Our results suggest that ordinary t h e rap eu tic doses of digoxin in patients with no overt manifestation of digitalis toxicity m a y be associated with slight increases in Z score. Eleven of 13 patients receiving digoxin m a n i f e s t e d n e i t h e r clinical nor electrocardiographic evidence suggestive of digitalis toxicity. Computer analysis showed t h a t none of these 11 had more t h a n four equal R-R interval lengths in a row (r = 36 msec). The two r e m a i n i n g patients had brief episodes of regular ventricular activity noted clinically; one of J. ELECTROCARDIOLOGY, VOL. 10, NO. 2, 1977
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Fig. 6. Comparison of Z score obtained from patient records obtained during and without digoxin therapy. Lines connect records obtained from the same patient.
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these two had an elevated serum digoxin level (3.5 nanograms per ml) at the beginning of study. Of the 11 patients, four had Z scores consistent with purely random distribution of R-R intervals. Four of the 11 patients, however, had borderline Z scores (Z between 1.64 and 2.33), and three had frankly elevated Z scores (Z greater t h a n 2.33) without any clinically detectable evidence of ventricular regularization. The Z scores of these 11 patients were considerably below those of the two patients with clinically detectable periods of ventricular regularization. When digoxin was stopped for a period of three to eleven days in six patients, the Z score was found to decrease in every case (Fig. 6). Of those five patients without clinical evidence of ventricular regularization, four had scores consistent with a completely random d i s t r i b u t i o n of R-R i n t e r v a l s w h e n ree x a m i n e d after digoxin was discontinued. Discontinuation of digoxin in one patient, who had regularized intervals detected clinically, resulted in a decrease in serum digoxin level from 3.5 to 0.8 nanograms per ml and a fall in Z score from 13.9 to 3.7. At the same time, the m a x i m u m number of regularized R-R i n t e r v a l s o c c u r r i n g s e q u e n t i a l l y decreased from 27 while on digoxin to eight while offdigoxin. In one of the nonregularized patients, intravenous administration of 0.5 mg digoxin following prolonged withdrawal of all digoxin therapy resulted in an increase in Z score from 2.86 to 5.63 associated with a transient rise in serum digoxin level from 0.5 to 6.2 nanograms per ml. This administration of digoxin did not result in any clinically overt manifestations of digitalis toxicity.
DISCUSSION Many investigators have sought to identify the presence of nonrandom ventricular depolarization during atrial fibrillation. The method presented here permits the calculation of a single numerical index quantitating the presence of nonrandom activity in a given sequence of R-R intervals. Since this method is based upon differences between successive pairs of R-R intervals, complex AVJR (e.g., Mobitz I or Mobitz II exit block) are not separately identified. Although the relation between the Z score and the percentage of regular activity in a record is not exact, our simulation studies suggest, in the context of AF, t h a t the Z score is capable of identifying regularization in a reliable m a n n e r when as few as 4% (sometimes even 2%) of R-R intervals are part of regularized runs or sequences. This degree of sensitivity to regularization probably exceeds the discriminatory capacity of the most diligent visual scanning, particularly when the groupings of regularized in-
tervals are small (e.g., four or less). Any evaluation of regularization of R-R intervals during AF must rely on an arbitrary limit of variability (z) to define intervals t h a t are considered nonrandom. However, evaluation of patient records showed t h a t the assessment of nonrandom activity is not greatly influenced by the choice of T within broad limits (16 to 40 msec). In future use of the methods described here, it would seem prudent to continue to calculate Z scores for each patient record using several different values of T. Although the method is most sensitive when the R-R interval associated with the nonrandom activity differs from the modal R-R interval of the random record, it remains highly sensitive even when the nonrandom activity has the same mean R-R interval as the random ventricular activity. Our method is only slightly less sensitive when the nonrandom intervals occur in pairs (the least favorable case) as opposed to longer runs of regularization. Thus, regularity occurring in small runs, a situation frequently encountered in our patient data, m a y escape recognition by usual methods but m a y be easily detected by the methods described here. Insufficient patient data are presented in this paper to assess the general clinical significance of this technique. However, our preliminary data suggest t h a t most patients with AF receiving digoxin show some minor degree of regularization. Moreover, the frequency with which regularization is observed appears to decrease when digoxin is withheld. F u r t h e r studies are r e q u i r e d to establish whether minor degrees of regularization represent a "digitalis effect" or w h e t h e r they simply reflect a biologic process which is not t r u l y random. More importantly, the Z score (or change in Z score) must be correlated with currently recognized clinical and laboratory evidence of digitalis excess. Our findings suggest t h a t it m a y be possible to distinguish patients with digitalis toxicity or p r e t o x i c i t y on the basis of the Z score. However, the only patients with digitalis toxicity in this study were found to have clinically evident regularization as well as very high Z scores. Thus the clinical utility of the Z scores in assessing digitalis toxicity not detected by routine electrocardiography remains to be determined. Our data also suggest t h a t exercise is associated with an increase in regularization and, therefore, a corresponding elevation in Z score. It is unlikely t h a t this represents only the effect of an increase in mean ventricular rate, since changes were not consistently observed following h e a r t rate increase with atropine, and the statistical properties of Z do not depend on m e a n heart rate. Although O. ELECTROCARDIOLOGY, VOL. 10, NO. 2, 1977
QUANTIFYING REGULARIZATION DURING AF
t h e s e findings are pr e l i m i nar y, t h e y illust r a t e th e ability of the Z score to q u a n t i t a t e t h e presence and extent of nonr a ndom activity during atrial fibrillation. In conclusion, the technique described in this paper permits identification and quantification of nonrandom activity dur i ng atrial fibrillation by a single statistic. This statistic m a y be obtained readily from the electrocardiographic record of a patient monitored for approximately 15 min, if digital dat a processing facilities are available. Calculation of the statistic m a y prove useful in searching for early signs of digitalis-induced regularization during AF. Similar calculations m a y also be helpful in assessing the influence of atonomic changes and physiologic interventions on t he action of the atrioventricular junction in governing th e ventricular response during atrial fibrillation.
4. 5. 6. 7.
8.
9. 10.
REFERENCES 1. KASTOR, J A AND YURCHAK,P M: Recognition of digitalis intoxication in the presence of atrial fibrillation. Ann Int Med 67:1045, 1967 2. THEILEN,E O, WARKENTIN,D L ANDJANUARY, L E: Use of digitalis in arrhythmias. Progr Cardiovasc Dis 7:26, 1964 3. ARNOLDI,W: Die ermittlung yon dominierende rhythmen sowie der schwere der
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rhythmusstorung bei kranken mit arrhythmia perpetua. Klin Wschr 6:1946, 1927 SODERSTROM,N: What is the reason for the ventricular arrhythmia in cases of atrial fibrillation? Am Heart J 40:212, 1950 HORAN, L G AND KISTLER,J C: Study of ventricular response in atrial fibrillation. Circ Res 9:305, 1961 BRAUNSTEIN,J R ANDFRANKE,E K: Autocorrelation of ventricular response in atrial fibrillation. Circ Res 9:300, 1961 GOLDSTEIN,R E ANDBARNETT,G O: A statistical study of the ventricular irregularity of atrial fibrillation. Comput Biomed Res 1:146, 1967 URBACH,J R, GRAUMAN,J J AND STRAUS,S H: Quantitative methods for the recognition of atrioventricular junctional rhythms in atrial fibrillation. Circulation 39:803, 1969 JORDAN, H: Die seitliche schwankungen der h e r z s c h l a g i n t e r v a l l e bei a b s o l u t e r arrhytymie. Arch Kreislaufforsch 21:40, 1954 BOOTSMA,B K, HOELEN,A J, STRACKEE,J AND MEIJLER, F L: Analysis of R-R-intervals in patients with atrial fibrillation at rest and during exercise. Circulation 41:783, 1970 KEMPNER, K M, MILLER, M H ANDHOLSINGER, W P: A computer approach to arrhythmia monitoring. Proceedings of the 8th International Conference on Medical and Biological Engineering, Paper 33.3, July 1969 SNEDECOR,G W AND COCHRAN, W G: Statistical Methods, 6th ed. The University of Iowa Press, Ames, Iowa, 1967 MOOD, A M: The distribution theory of runs. Ann Math Statist 11:367, 1940
A New Method for Quantifying Ventricular Regularization During Atrial Fibrillation BY JAMES H. WARE, PH.D., PAUL L. TECKLENBERG, M.D., MARTIN MILLER, B.A., MORTON S. RAFF, M.A., LEONARD GRAUER, M.D. AND ROBERT E. GOLDSTEIN, M.D.
accounting for this is poorly understood at present. When a patient with AF is treated with excessive amounts of digitalis, regular atrioventricular junctional rhythms (AVJR) m a y be superimposed upon the usual random sequence. 1,2 Detection of minor degrees of "regularization"* of the ventricular r h y t h m during atrial fibrillation m a y provide an important early sign of incipient digitalis toxicity before the drug excess causes gross regularization of R-R intervals. These considerations have s t i m u l a t e d a continuing search for means of identifying and quantitating ventricular regularization during AF. Using a variety of methods, some investigators have detected evidence of regular R-R intervals in patients with AF and no overt evidence of digitalis toxicity. 3-s Other investigators have failed to find any evidence of ventricular regularization under similar circumstances.9 lo T h e w o r k of U r b a c h a n d a s s o c i a t e s s suggested an approach that may prove particularly sensitive in detecting nonrandom activity. These investigators regarded the sequence of R-R intervals as a random process, interrupted for brief periods by a competing mechanism of r h y t h m generation that produces regular R-R intervals. T h e y identified sequences of regular R-R intervals of various types, classified them according to R-R i n t e r v a l l e n g t h a n d c o m p a r e d t h e i r number to a frequency that would result from an entirely random process. By m a k i n g a large number of such comparisons for each patient record, U r b a c h and his colleagues were able to identify instances of nonrandom activity in 18 of 31 patients in atrial fibrillation, while only three records were recognized as nonrandom by visual electrocardiographic interpretation. While the several methods of Urbach et al could identify isolated episodes of nonrandomness, they were less suitable for summarizing the extent of nonrandom activity in
SUMMARY Atrial fibrillation (AF) characteristically results in random variation of the intervals between successive ventricular depolarizations. However, when a patient with AF is treated with excessive amounts of digitalis, regular junctional rhythms may occur. The detection of "regularization" of the ventricular rhythm in patients with AF may signal early digitalis toxicity. In this paper, we describe a new method for quantifying the ext e n t of ventricular regularization by the statistical analysis of the intervals between successive ventricular depolarizations (R-R intervals). This method yields a single index (Z score) which reflects the degree to which a sequence of R-R intervals deviates from a random distribution. S i m u l a t i o n s t u d i e s demonstrate that our method is sensitive to "regularization" of as little as two to four percent of R-R intervals, even when equal intervals occur in small groups that might easily escape detection by visual electrocardiographic interpretation. A n a l y s i s of records from six nondigitalized subjects in AF shows that the sequence of R-R intervals is usually random, or very nearly so. Records obtained from the same patients when digitalized often demonstrate more regularized activity, reflected by an index (Z score) which is higher than expected from chance deviation if a random process is assumed. Preliminary data also suggest that exercise is associated with substantial regularization of ventricular depolarization. Atrial fibrillation is characterized by a seemingly random variation of the length of intervals between successive ventricular depolarizations (R-R intervals). The mechanism From the Biometrics Research Branch, Cardiology Branch, and Clinic of Surgery, of the National Heart and Lung Institute and the Computer Systems Laboratory, Division of Computer Research and Technology, of the National Institutes of Health, Bethesda, Maryland. Reprint requests to: James H. Ware, Ph.D., National Heart and Lung Institute, Biometrics Research Branch, Division of Heart and Vascular Diseases, 7910 Woodmont Ave., Room C837, Bethesda, MD 20014.
*The terms "regularization" and "regularized" refer to the occurrence of runs or sequences of consecutive "equal" R-R intervals interposed within a series of apparently randomly varying R-R intervals. Adjacent R-R intervals are considered "equal" if they differ by less than a small prespecified value, r.
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a l a r g e sequence of R-R intervals. We t h e r e fore devised a statistical a p p r o a c h t h a t permits q u a n t i t a t i o n of i n t e r m i t t e n t n o n r a n d o m a c t i v i t y b y a single n u m e r i c a l v a l u e (Z score). We t e s t e d t h i s m e t h o d b y a s i m u l a t i o n t e c h n i q u e to assess its s e n s i t i v i t y , a n d we applied t h e m e t h o d to d a t a obtained from pat i e n t s w i t h A F to develop a n idea of its potential clinical value.
MATERIALS AND METHODS The presence or absence of regularization in the ventricular rhythm during atrial fibrillation is assessed by examining adjacent pairs of R-R intervals. If two adjacent intervals are part of a wholly random sequence, the length of the first is totally unrelated to the length of the second. If regularization occurs, however, the length of the second interval is equal to the length of the first (or, in practical terms, the two interval lengths differ by less than a small number, r). Adjacent intervals of equal length occasionally will occur by chance alone, even in a purely random series of R-R intervals. The likelihood of this event ("expected frequency") and the associated standard deviation can readily be calculated from the distribution of R-R interval lengths in the entire sequence under study. Using the expected frequency of regularization under purely random conditions and the actual number of adjacent "equal" R-R intervals Cobserved frequency"), one can construct an index (Z score) of regularization as follows: Z -- observed frequency - expected frequency standard deviation Since the probability distribution of Z, when computed from a record of random R-R intervals, can be derived, this index can help decide when the occurrence of equal interval lengths during AF becomes too frequent to attribute to chance alone. Our analytic methods were applied to a sampling of 2,000 successive R-R intervals recorded from each patient studied. (The same sample size was used in simulations.) This sampling is subsequently termed a patient record. Previous experience 7 has shown that the sample size used here is suitable for statistical analysis of AF. Mathematical Model Details of the derivation and the properties of Z are available from the authors in an unpublished Appendix. These calculations demonstrate that, when applied to long sequences of randomly and independently occurring R-R intervals, Z will be distributed as a Gaussian random variable with mean of 0 and standard deviation of 1. In this random situation, Z will have a 90% probability of falling between + 1.64 and - 1.64. ~Regularization" of R-R intervals, i.e., the occurrence of runs of R-R intervals of the same length, will shift Z toward larger positive values provided that r (the upper limit of difference between intervals accepted as equal) is larger than the fluctuations of interval length within the runs of regular R-R intervals. Hence, Z is a suitable statistic for investigating whether a particular sequence of R-R intervals represents a random arrangement. Moreover, Z will increase progressively with increasing
frequency of regularized runs, permitting a quantitative assessment of nonrandom activity. In this way, a series of patient records can be compared numerically with regard to the extent of regularization. Although Z may be influenced significantly by the particular value assigned to ~, an optimal value for r cannot be chosen on a theoretical basis. Ideally, r should be slightly larger than the largest fluctuation in regularized interval lengths. Although regularized portions of atrial fibrillation (presumably short runs of AVJR) are generally thought to have nearly equal interval lengths, the limits of variability of this rhythm have not been firmly established. Based upon their experiences with a sample of regular AVJR, Urbach and coworkers s suggested that r should be approximately 32.5 msec. Whether the regularized portions of AF obey this rule remains uncertain. Gross underestimation of r would be undesirable, in that many genuinely regularized intervals would be missed. Conversely, overestimation of r would increase the likelihood that regularization is mimicked by chance occurrences. In either case, the sensitivity of Z as an index of regularization would be diminished. To explore this issue, Z for each patient record was calculated repeatedly, using several different values of r. Using a one-tailed test, when Z exceeds +1.64 the probability is less than 0.05 that the degree of regularization in the associated patient record occurred as a chance fluctuation in a random process. We have arbitrarily picked this 0.05 probability level to discriminate random from regularized patient records for the purpose of demonstration. It should be recognized that this arbitrary choice can be modified and does not represent an intrinsic feature of the methods presented. We have considered a negative value of Z (relative deficiency of adjacent equal intervals) an unusual chance occurrence. Simulation To investigate the sensitivity of Z, four random R-R interval records were produced and then artifically '~regularized" by substituting intervals of a constant length for certain of the randomly varying intervals. Two of the random records were made by generating sequences of 2,000 independent, normally distributed random numbers with mean of 652 msec and a standard deviation of 100 msec. In addition, a patient record identified by our analysis as random (i.e., Z very nearly equal to 0) was included in the simulation study, and a patient record identified as partially regularized was also included after the order of the R-R intervals had been scrambled to achieve random arrangement. Regularization was simulated in these four records by introducing runs or sequences of equal R-R intervals. The frequency, run length and common interval length of the equal intervals were systematically varied to assess the importance of each attribute. The resulting sequences were analyzed by computer to yield values for Z. For each simulation, calculations of Z were made with r, the maximum nonrandom difference between adjacent intervals, set at 20 and at 36 msec. Analysis of Patient Records Seventeen patients with atrial fibrillation due to
J. ELECTROCARDIOLOGY, VOL. 10, NO. 2, 1977
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stable, moderately symptomatic rheumatic heart disease were selected arbitrarily from an outpatient population. All were treated with digoxin as part of their usual clinical management. None had evidence of thyroid overactivity and none was taking propranolol. Informed consent was obtained prior to study. Electrocardiograms (ECGs) were obtained by tape recording a continuous single lead ECG containing approximately 2000 R-R intervals. The patients remained at supine rest while recordings were made, except for the exercise studies. Unless specifically noted, no cardioactive drugs were given for at least two hours prior to recording. The recorded lead was chosen to optimize the shape of the QRS complex for automated processing. The presence of AF (characterized by chaotic atrial activity and grossly evident ventricular irregularity) was confirmed before and after each tape recording. No patient was included who manifested frequent premature ventricular contractions or other obvious nonfibrillatory arrhythmias at the time of recording, except as noted in Results. The analog record was amplified and digitized by a Geo-Space SS100 computer. It was then analyzed by a pattern recognition program written by one of the authors (M.M.), which searched for QRS complexes and computed R-R interval lengths, n Premature ventricular contractions were identified by the program, and R-R intervals on either side of these complexes were excluded from subsequent analysis. A resulting list of 2,000 R-R interval lengths was submitted to computerized statistical analysis to calculate Z.
RESULTS Simulation Data Both the artificially constructed and t he n a t u r a l l y r a n d o m p a t i e n t records y i e l d e d values of Z th at behaved in a similar manner. Hence, no distinction will be made among the results from t he four records of different origin. The sensitivity of Z for t he detection of nonrandom activity w~s studied by varying t hr ee characteristics of the simulated records: 1) t h e percent of the intervals which were regularized; 2) the common R-R interval length, L, of regularized portions; and 3) the length of regularized runs. For each of t he four simulated records, Z was calculated at r = 20 msec and r = 36 msec for each value of L: the values of L ranging from the mode (M) of the r a n d o m distribution to M-250 msec. Hence, eight values of Z were calculated at each part i c u l a r p e r c e n t a g e of r e g u l a r i z e d activity, length of regularized beats, and r u n length studied. As anticipated, when no regularized activity was introduced, each of the records consistently yielded values of Z smaller t h a n + 1.64 (Fig. 1). In theory, 95% of Z values from random records should fall below this limit. As the percentage of nonr andom activity was increased, the average value of Z obtained from J. ELECTROCARDIOLOGY, VOL. 10, NO. 2, 1977
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t he four simulated records increased in an a p p r o x i m a t e l y l i n e a r f a s h i o n ( F i g . 1). Eleven of t he 16 values of Z exceeded 1.64 when 2% of the intervals were regularized, and 15 of t he 16 values of Z exceeded 1.64 at 3% regularization. Because the simulated r e g u l a r activity was given a constant R-R i nt erval length, analysis using r = 20 msec gave consistently larger values of Z. Smaller values oft , however, m a y n o t m a k e Z m o r e s e n s i t i v e in s i t u a t i o n s where the length of regularized interval fluct uat es by more t h a n r. S m a l l e r Z val ues occurred w h e n L, t h e length of t he r e g u l a r runs, was set equal to the mode of t he random activity, i.e., the interval occurring most frequent l y in t he random record. Z increased, on the average, as L was set at values f a r t h e r from t he mode (Fig. 2). However, the simulation studies indicated t h a t this effect was very small, so t h a t t he ability of t he method to detect regularization was not greatly influenced by the length of t h e regularized intervals. The effect of varying the length of runs (i.e., the n u m b e r of consecutive r e g u l a r intervals) while percent regul ari zat i on was held const ant (at 5%) is shown in Fig. 3. Although all values of Z exceeded 1.64, Z was smallest w hen the run length was 2. A single r u n of t en equal intervals contributes nine adjacent e q u a l R-R i n t e r v a l s , w hi l e five s e p a r a t e "runs" of length 2 contribute only five equal R-R i n t e r v a l pairs. Hence, Z val ues for a given percent r e g u l a r i z a t i o n w ere s m a l l e r when run lengths were shorter. Nevertheless, t h e simulations showed t h a t our m et hod was capable of detecting small percentages of regularization even when regularized intervals occurred only in pairs. Patient Data Records obtained from t en patients in at ri al fibrillation were analyzed for five values of r r a n g i n g from 16 to 40 msec (Fig. 4). A l t hough Z varied slightly in each individual record as r was c h a n g e d , no c o n s i s t e n t p a t t e r n of change was evident. T he significance (or lack of significance) of Z was dependent upon t he choice of r in only one instance, a record in which Z varied between 1.5 and 1.9. Although an optimal choice of r is not clearly evident, t he choice of r in t he r a n g e of 16 to 40 msec did not appear crucial in separat i ng r a n d o m and nonrandom records in most cases. T he ability of Z to identify differing degrees of vent ri cul ar regularization is illustrated in Fig. 5. In patient G.P., borderline evidence of n o n r a n d o m a c t i v i t y was o b s e r v e d in t h e baseline state (patient had received his usual dose of digoxin). This record is also t he borderline record in Fig. 4. N onrandom ness increased after atropine, 2 mg iv, and increased
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Fig. 2. Relationship between Z score and the length (L) of sequences of regular activity relative to M, the R-R interval length occurring most frequently in the underlying record. The shaded area represents a smoothed histogram for R-R intervals whose length has a Gaussian distribution centered at M. For other definitions, see Fig. 1.
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Fig. 1. Relationship between Z score and the percentage of regularity in a sequence of R-R intervals whose lengths vary randomly when not regular. Regular activity was simulated by sequences of 10 adjacent R-R intervals of equal length. The lower dashed line is that value of Z which would be exceeded one time in 20 (p = .05) by an R-R interval record free of regular activity. The upper dashed line would be exceeded one time in 100. r is the m a x i m u m allowable difference (msec) between adjacent R-R intervals considered part of a regular sequence, L is the length of the regular R-R intervals, and the mode is the R-R interval length occuring most frequently in the R-R interval record. Since each point is the average of values from four records, a standard error is obtained at each point but shown here only for the lower line as a representative value.
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to a g r e a t e r e x t e n t d u r i n g t r e a d m i l l exercise. B o t h a t r o p i n e a n d exercise r a i s e d t h e m e a n v e n t r i c u l a r r a t e f r o m 60 to 95 b e a t s / m i n . Subsequently, digoxin was discontinued while t h e p a t i e n t r e m a i n e d a t r e s t in t h e hospital. A t 8 a n d 11 d a y s a f t e r digoxin w a s stopped, m e a n v e n t r i c u l a r r a t e i n c r e a s e d to 80. T h e Z score a t e i g h t d a y s was s i m i l a r to t h e b a s e l i n e value. T h e Z score 11 d a y s aider d i s c o n t i n u i n g digoxin was consistent with a completely r a n d o m v e n t r i c u l a r response. A second e x a m p l e of t h e b e h a v i o r of Z is also g i v e n in Fig. 5. I n t h i s p a t i e n t (W.C.), a t r o p i n e , 2 m g iv, i n c r e a s e d m e a n v e n t r i c u l a r
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Fig. 5. Variation in Z score with changes in medication and activity level in two patients. See Fig. 1 for additional definitions.
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Fig. 4. Relationship between Z score and ~, the maximum distance between adjacent R-R intervals considered as part of a regular sequence, when ten patient records were analyzed with different values of r. Some records were obtained during periods of digoxin therapy (DIG). See Fig. 1 for additional definitions.
ra t e from 60 to 100 beats/min, but had relatively little influence on Z. In contrast, exercise th at increased m e a n v e n t r i c u l a r r a t e to 120 resulted in a m a r k e d rise in Z. Discontinuance of digoxin for eight days resulted in a Z score consistent with random intervals. In g e n e r a l , a t r o p i n e produced a v a r i a b l e response in the Z score, but exercise (resulting in an increase in m ean hear t r at e comparable to t h a t following atropine) yielded a rise in Z score in four of five subjects tested. Our results suggest that ordinary t h e rap eu tic doses of digoxin in patients with no overt manifestation of digitalis toxicity m a y be associated with slight increases in Z score. Eleven of 13 patients receiving digoxin m a n i f e s t e d n e i t h e r clinical nor electrocardiographic evidence suggestive of digitalis toxicity. Computer analysis showed t h a t none of these 11 had more t h a n four equal R-R interval lengths in a row (r = 36 msec). The two r e m a i n i n g patients had brief episodes of regular ventricular activity noted clinically; one of J. ELECTROCARDIOLOGY, VOL. 10, NO. 2, 1977
(13.9)%
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Fig. 6. Comparison of Z score obtained from patient records obtained during and without digoxin therapy. Lines connect records obtained from the same patient.
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these two had an elevated serum digoxin level (3.5 nanograms per ml) at the beginning of study. Of the 11 patients, four had Z scores consistent with purely random distribution of R-R intervals. Four of the 11 patients, however, had borderline Z scores (Z between 1.64 and 2.33), and three had frankly elevated Z scores (Z greater t h a n 2.33) without any clinically detectable evidence of ventricular regularization. The Z scores of these 11 patients were considerably below those of the two patients with clinically detectable periods of ventricular regularization. When digoxin was stopped for a period of three to eleven days in six patients, the Z score was found to decrease in every case (Fig. 6). Of those five patients without clinical evidence of ventricular regularization, four had scores consistent with a completely random d i s t r i b u t i o n of R-R i n t e r v a l s w h e n ree x a m i n e d after digoxin was discontinued. Discontinuation of digoxin in one patient, who had regularized intervals detected clinically, resulted in a decrease in serum digoxin level from 3.5 to 0.8 nanograms per ml and a fall in Z score from 13.9 to 3.7. At the same time, the m a x i m u m number of regularized R-R i n t e r v a l s o c c u r r i n g s e q u e n t i a l l y decreased from 27 while on digoxin to eight while offdigoxin. In one of the nonregularized patients, intravenous administration of 0.5 mg digoxin following prolonged withdrawal of all digoxin therapy resulted in an increase in Z score from 2.86 to 5.63 associated with a transient rise in serum digoxin level from 0.5 to 6.2 nanograms per ml. This administration of digoxin did not result in any clinically overt manifestations of digitalis toxicity.
DISCUSSION Many investigators have sought to identify the presence of nonrandom ventricular depolarization during atrial fibrillation. The method presented here permits the calculation of a single numerical index quantitating the presence of nonrandom activity in a given sequence of R-R intervals. Since this method is based upon differences between successive pairs of R-R intervals, complex AVJR (e.g., Mobitz I or Mobitz II exit block) are not separately identified. Although the relation between the Z score and the percentage of regular activity in a record is not exact, our simulation studies suggest, in the context of AF, t h a t the Z score is capable of identifying regularization in a reliable m a n n e r when as few as 4% (sometimes even 2%) of R-R intervals are part of regularized runs or sequences. This degree of sensitivity to regularization probably exceeds the discriminatory capacity of the most diligent visual scanning, particularly when the groupings of regularized in-
tervals are small (e.g., four or less). Any evaluation of regularization of R-R intervals during AF must rely on an arbitrary limit of variability (z) to define intervals t h a t are considered nonrandom. However, evaluation of patient records showed t h a t the assessment of nonrandom activity is not greatly influenced by the choice of T within broad limits (16 to 40 msec). In future use of the methods described here, it would seem prudent to continue to calculate Z scores for each patient record using several different values of T. Although the method is most sensitive when the R-R interval associated with the nonrandom activity differs from the modal R-R interval of the random record, it remains highly sensitive even when the nonrandom activity has the same mean R-R interval as the random ventricular activity. Our method is only slightly less sensitive when the nonrandom intervals occur in pairs (the least favorable case) as opposed to longer runs of regularization. Thus, regularity occurring in small runs, a situation frequently encountered in our patient data, m a y escape recognition by usual methods but m a y be easily detected by the methods described here. Insufficient patient data are presented in this paper to assess the general clinical significance of this technique. However, our preliminary data suggest t h a t most patients with AF receiving digoxin show some minor degree of regularization. Moreover, the frequency with which regularization is observed appears to decrease when digoxin is withheld. F u r t h e r studies are r e q u i r e d to establish whether minor degrees of regularization represent a "digitalis effect" or w h e t h e r they simply reflect a biologic process which is not t r u l y random. More importantly, the Z score (or change in Z score) must be correlated with currently recognized clinical and laboratory evidence of digitalis excess. Our findings suggest t h a t it m a y be possible to distinguish patients with digitalis toxicity or p r e t o x i c i t y on the basis of the Z score. However, the only patients with digitalis toxicity in this study were found to have clinically evident regularization as well as very high Z scores. Thus the clinical utility of the Z scores in assessing digitalis toxicity not detected by routine electrocardiography remains to be determined. Our data also suggest t h a t exercise is associated with an increase in regularization and, therefore, a corresponding elevation in Z score. It is unlikely t h a t this represents only the effect of an increase in mean ventricular rate, since changes were not consistently observed following h e a r t rate increase with atropine, and the statistical properties of Z do not depend on m e a n heart rate. Although O. ELECTROCARDIOLOGY, VOL. 10, NO. 2, 1977
QUANTIFYING REGULARIZATION DURING AF
t h e s e findings are pr e l i m i nar y, t h e y illust r a t e th e ability of the Z score to q u a n t i t a t e t h e presence and extent of nonr a ndom activity during atrial fibrillation. In conclusion, the technique described in this paper permits identification and quantification of nonrandom activity dur i ng atrial fibrillation by a single statistic. This statistic m a y be obtained readily from the electrocardiographic record of a patient monitored for approximately 15 min, if digital dat a processing facilities are available. Calculation of the statistic m a y prove useful in searching for early signs of digitalis-induced regularization during AF. Similar calculations m a y also be helpful in assessing the influence of atonomic changes and physiologic interventions on t he action of the atrioventricular junction in governing th e ventricular response during atrial fibrillation.
4. 5. 6. 7.
8.
9. 10.
REFERENCES 1. KASTOR, J A AND YURCHAK,P M: Recognition of digitalis intoxication in the presence of atrial fibrillation. Ann Int Med 67:1045, 1967 2. THEILEN,E O, WARKENTIN,D L ANDJANUARY, L E: Use of digitalis in arrhythmias. Progr Cardiovasc Dis 7:26, 1964 3. ARNOLDI,W: Die ermittlung yon dominierende rhythmen sowie der schwere der
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12. 13.
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rhythmusstorung bei kranken mit arrhythmia perpetua. Klin Wschr 6:1946, 1927 SODERSTROM,N: What is the reason for the ventricular arrhythmia in cases of atrial fibrillation? Am Heart J 40:212, 1950 HORAN, L G AND KISTLER,J C: Study of ventricular response in atrial fibrillation. Circ Res 9:305, 1961 BRAUNSTEIN,J R ANDFRANKE,E K: Autocorrelation of ventricular response in atrial fibrillation. Circ Res 9:300, 1961 GOLDSTEIN,R E ANDBARNETT,G O: A statistical study of the ventricular irregularity of atrial fibrillation. Comput Biomed Res 1:146, 1967 URBACH,J R, GRAUMAN,J J AND STRAUS,S H: Quantitative methods for the recognition of atrioventricular junctional rhythms in atrial fibrillation. Circulation 39:803, 1969 JORDAN, H: Die seitliche schwankungen der h e r z s c h l a g i n t e r v a l l e bei a b s o l u t e r arrhytymie. Arch Kreislaufforsch 21:40, 1954 BOOTSMA,B K, HOELEN,A J, STRACKEE,J AND MEIJLER, F L: Analysis of R-R-intervals in patients with atrial fibrillation at rest and during exercise. Circulation 41:783, 1970 KEMPNER, K M, MILLER, M H ANDHOLSINGER, W P: A computer approach to arrhythmia monitoring. Proceedings of the 8th International Conference on Medical and Biological Engineering, Paper 33.3, July 1969 SNEDECOR,G W AND COCHRAN, W G: Statistical Methods, 6th ed. The University of Iowa Press, Ames, Iowa, 1967 MOOD, A M: The distribution theory of runs. Ann Math Statist 11:367, 1940
