- Email: [email protected]
An analysis of the circadian rhythmicity of atrial and ventricular rates in complete heart block
J. ELECTROCARDIOLOGY, 8 (1) 69-72, 1975
An Analysis of the Circadian Rhythmicity of Atrial and Ventricular Rates in Complete Heart Block* BY JOHN E. CHRIST, M.D., PH.D. AND HEBBEL E. HOFF, M.D., PH.D.**
SUMMARY
Some 2400 years ago Hippocrates recognized r e g u l a r i t y as a sign of h e a l t h and i r r e g u l a r body functions or habits as disturbances of the normal state. The measurement of biological periodicity was initiated around 300 BC by Herophilus of Alexandria when he advocated the practice of counting the pulse with the help of a water clock. However, the concept of the absolute regularity of body function became less valid as consecutive serial measurements were extended to include several 24 hour periods. Quantitative measurements demonstrated t h a t biological processes were not only a function of the immediate metabolic state of the organism, but also varied with the time of day. Attempts to express time functions in a mathematical way failed when the relationship y = f (t), where y is the observed phenomenon and fis a function of t, was used. In m a n y cases a time plot of the biologic data showed a recurring pattern, so t h a t the expression y = f (T + t) where t is the time of day and T the period of the r h y t h m u n d e r study, more accurately predicted the observed data. is Since not all functions fall exactly in a 24 hour r h y t h m , but only approximately so, the term circadian has generally supplanted the term diurnal with its more precise definition. 2~ While the rhythmicity of the heart has been the subject of study in h e a l t h and disease since ancient times, it was not until well into this century, with the development of interest in consecutive serial measurements extending over 24 hour periods of time, t h a t extensive circadian studies were carried out. In 1932, Boas and Goldschmidt demonstrated in a series of 51 healthy young males and 52 healthy young females t h a t the average heart rate was greater during waking hours t h a n during sleeping hours. 2 Although the heart r a t e s in this s t u d y d e m o n s t r a t e d m a r k e d variations during the day, day rates were
A 19 year old female human subject with complete heart block was put at complete bed rest for 63 hours during which a Lead II EKG was monitored at half hour intervals. Atrial and ventricular rates demonstrated cyclic activity with peaks during the day and troughs during the night. A correlation coefficient of +0.85 and a slope of +1.0 from a linear regression between atrial and ventricular rates demonstrated a close parallel. Calculation of the crosscovariances confirmed the observed cyclic activity with a period of 24 hours and a phase angle of zero degrees between the two chambers. The data may be explained by one or all of the following mechanisms: (1) both chambers are subject to the same internal milieu, (2) autonomic nervous system discharge and associated reflexes may integrate relative changes in rate, (3) direct mechanical or e l e c t r o t o n i c f o r c e s may result in alteration of rates in direct proportion to the magnitude of the dominant chamber, (4) each chamber has its own inherited cyclic program which operates independent of external factors. The question remains for dir e c t e x p e r i m e n t a l data to d e m o n s t r a t e whether the observed phenomenon is an intrinsic biologic rhythm within the heart or in its control system.
* S u p p o r t e d by U.S. Public H e a l t h G r a n t H L-05125-17 **Department of Physiology, Baylor College of Medicine, Houston, Texas 77025. Reprint requests to: Hebbel E. Hoff, M.D., Baylor College of Medicine, Texas Medical Center, Houston, Texas 77025. 69
70
C I R C A D I A N R H Y T H M IN H E A R T B L O C K
higher t h a n night rates, decreasing during sleep with the lowest rate found shortly before or upon awakening in the morning. This data, in current terminology, showed a circadian pattern of the normal heart rate. Following the study of Boas and Goldschmidt, the circadian r h y t h m of heart rate has been w e l l e s t a b l i s h e d in t h e n o r m a l h u m a n subject .1,2,4,9,13,14,18,19 In complete heart block where the atria and ventricles are no longer physiologically connected by the intrinsic conduction system, the atria and ventricles beat at their own rates. Boas and Goldschmidt studied the ventricular rates of a few patients with complete heart block and found t h a t the proportionate difference in day (waking) and n i g h t (sleeping) rates was of the same magnitude as in the normal subjects. The atrial rates were not examined. This report demonstrates the interrelationships of the circadian r h y t h m s of both atria and ventricles in a h u m a n subject with complete heart block.
;4:
, mARCH2g ~
~"
UAeCN~0 ~
~Ancasl
_
ATRIA
~
TVENTRICLES
.L
IL~ ,
,,L
T I M [ (in k i l l . klur I l t l r ~ l l s )
Fig. 1. Plot of atrial and ventricu]ar rates over 63
hours. Highest rates occur during the day and lowest during the night. While there is a positive correlation with zero phase relationship on a beat-by-beat basis, it should be noted that in general ventricular rates tend to continue downward from 12:00 midnight to 6:00 a.m. while atrial rates tend to rise during this period. (Upper curve represents atria, lower, ventricles.)
CASE REPORT The subject of this study was a 19 year old student nurse with complete heart block who has been the subject of previous reports of the beat to beat interaction between atria and ventricles. 5'~ On March 20, 1969, she was admitted to the Clinical Research Center of Ben Taub General Hospital in Houston, Texas in good health and kept at bed rest with bathroom privileges only. Beginning at 5:30 p.m. t h a t day, a Lead II EKG was monitored at h a l f hour intervals until 9:00 a.m: March 31, 1969. Average atrial and ventricular rates were plotted for every h a l f hour, the rates were correlated, and the crosscovariances were computed. All data were then plotted.
RESULTS During the 63 hour monitoring period, the atrial rate varied from 58 to 80 beats per minute with a m e a n of 67 beats per minute (std. Dev. -+ 4.5). The ventricular rate varied from 33 to 47 beats per minute with a m e a n of 40 beats per m i n u t e (std. dev. -+ 3.4). Atrial rates were t h u s always greater t h a n ventricular rates. The plot of atrial and ventricular rates (Fig. 1) d e m o n s t r a t e s a close parallel; t h a t is, whenever the atrial rate is high, the corresponding v e n t r i c u l a r rate is also high. The highest rates, both atrial and ventricular, are in t h e m o r n i n g s h o r t l y after a w a k e n i n g ; whereas the lowest rates are seen early in the m o r n i n g shortly before awakening. Atrial and ventricular rates therefore rise within one hour from their lowest levels to their
highest levels upon awakening and take 24 hours to return to their initial levels. Atrial rates were plotted against corresponding ventricular rates (Fig. 2) and a linear regression and a correlation coefficient were calculated. The slope of the line determined the linear regression was + 1.0 and the correlation coefficient was + 0.83. Therefore there appears to be a proportional change in atrial and ventricular rates. The calculation of crosscovariances allows the e x a m i n a t i o n of s i m u l t a n e o u s periodic events, in order t h a t their periodicity may be determined, and, if periodic, what the relationship exists between these two events. 8,7,s,1~ However, the exact relationship between these events is also directly related to the total number of data points t h a t are collected, t h u s crosscovariance implies the degree of probability of a relationship. Both atrial and ventricular rates were found to have a cyclic periodicity of 24 hours, with each rate synchronized with each other, i.e., a zero phase angle.
DISCUSSION Explanation of the data cannot as yet be given in terms of any one particular hypothesis but the following may be considered: (1) A t r i a and ventricles, being subject to the same i n t e r n a l m i l i e u , respond equally to changes in t h e i r biochemical and physical environment, and therefore each would be affected equally and their mathematical relationship maintained. (2) The heart is innerJ. ELECTROCARDIOLOGY, VOL. 8, NO. 1, 1975
CHRIST AND HOFF
vated by the autonomic nervous system which m a i n t a i n s control of t he h e a r t rate. Since both atr ia and ventricles are supplied with s y mp ath etic fibers, the sympathetic nervous system m a y be the d e t e r m i n i n g factor. (3) The p a r a s y m p a t h e t i c division m a y play an indirect role th r o u g h the baroreceptor-vagal reflex activated by v e n t r i c u l a r pulse pressure. A priori such a relation ought to cause atrial ra t e to v ar y inversely to v e n t r i c u l a r rate. In addition, such a hypothesis would d e m a n d t h a t v e n t r i c u l a r changes preceded the atrial chambers by some finite interval despite the d e m o n s t r a t i o n of a zero phase angle. Intervals were clearly too widely spaced to give conclusive evidence on this point. (4) Direct mechanical or electrotonic effects m ay cont r i b u t e to circadian syncronicity. V ent r i c ul a r systole t h r o u g h t r a c t i o n on the a t r i a m a y alter the m e m b r a n e properties of the pacem a k e r or a direct electrotonic effect of one c h a m b e r mig h t influence the r at e of pacem a k i n g of the other chamber, e ve nt ua l l y resulting in parallel changes of rate. According to this hypothesis, the driving chamber might be influenced by 1, 2, or 3. (5) Since a t r i a and ventricles have the same embryologic origin, the only difference being t hei r own intrinsic r h y t h m i c i t y and i nner va t i on, it is possible t h a t wh at is seen as an appar e nt interaction of proportionality of rates m a y simply represent the inborn cyclic pr ogr am of cardiac cells which is independent of almost all external factors.
The last hypothesis m a y be considered to be most in accord with the observation of P-wave activity of donor and recipient atria in a circadian study of a h e a r t t r a n s p l a n t patient. 15 In t h a t study donor and recipient pacemaker activity had a periodicity of 24 hours but were out of~hase, recipient rat e leading the donor by 135 minutes. This suggests t h a t donor and recipient pacemakers had different biologic constitutions, and therefore this formed an intrinsic basis for t hei r difference in r h y t h m s and phase angle. Each of the proposed mechanisms may totally or in part contribute to the apparent synchronization and proportionality of cyclic activity of cardiac chambers, but final decision m ust await f u r t h e r evidence. Changing levels of activity due to inherited genetic program s have only recently been recognized a n d should be actively considered in any future investigation.
REFERENCES
a
A A A
a A A ~
A
a A A
a
A/~
A a
m A A
&/
'
30
~
'
A~
A
~ &
A
& A A a
'
I
'
'
'
'
35 V(NTRICULAR
I
'
'
'
'
40 RATE
(beats/
I
'
'
'
'
45
I
50
minute)
Fig. 2. Plot of atrial rates against ventricular rates. The linear regression line is plotted on the data. Slope = 1.0. Correlation coefficient = + 0.83. J. ELECTROCARDIOLOGY, VOL. 8, NO. 1, 1975
71
1. ASCHOFF, J: Circadian rhythms in man. Science 148:1427, 1965 2. BOAS, E AND GOLDSCHMIDT,E T: The Heart Rate. Charles C. Thomas, Springfield, 1932 3. BLACKMAN, R B AND TUKEY, J W: The Measurement of Power Spectra. Dover Publications, Inc., New York, 1958 4. BUNNING, E: Opening address - - biological clocks. In Cold Spring Harbor Symp on Quant Biology 25:1, 1960 5. CHRIST, J E AND HOFF, H E: A statistical analysis of atrial arrhythmia in A-V block. J Electrocardiol 4:331, 1971 6. CHRIST, J E AND HOFF, H E: An analysis of atrioventricuiar synchronization in complete A-V block. J Electrocardiol 6:53, 1973 7. ENRIGHT, J T: The search for rhythmicity in biological time series. J Theoret Biol 8:426, 1965 8. GRANGER, C W J: Spectral Analysis of Economic Time Series. Princeton Univ Press, Princeton, 1964 9. HALBERG, F: Circadian rhythms in experimental medicine. Proc Roy Soc Med 56:253, 1963 10. HARTLEY,H O: Tests of Significance in Harmonic Analysis. Biometrika 36:194, 1949 11. HURWICZ, L: Basic mathematical and statistical considerations in the study of rhythms and near rhythms. Ann NY Acad Sci 98:753, 1962 12. KENDALL, K G: Contribution of the Study of Oscillatory Time-Series. Cambridge Univ Press, Cambridge, 1946
72
CIRCADIAN RHYTHM IN HEART BLOCK
13. KLEITMAN, N AND RAMSAROOP, A: Periodicity in body temperature and heart rate. Endocrin 43:1, 1948 14. KOCHLER, F, OKANO, F K, ELVEBACK, L R, HALBERG, F AND BITTNER, J J: Periodograms for the study of physiologic daily periodicity in mice and in man. Exp Med Surg 14:5, 1956 15. KRAFT, I A, ALEXANDER, S, FORS~ER, D, LEACHMAN, R D AND LIPSCOMB, H-S: Circadian Rhythms in Human Heart Homograft, Science 169:694, 1970 16. MAYERSBACH,H V, ed: The Cellular Aspects of Biorhythms. Springer-Verlag, Berlin, 1967
17. MERCER, D M A: The Limitations of Detection of Periodicities in Random Noise, NorthHolland Publishing Co, Amsterdam, 1965 18. MILLS, J N: H u m a n c i r c a d i a n r h y t h m s . Physiological Reviews 46:128, 1966 19. WEYSSE, A W AND LUTZ, B R: Diurnal Variations in Arterial Blood Pressure, Am J Physiol 37:330, 1915 20. WURTMAN, R J: Ambiguities in the term circadian. Science 156:104, 1967 21. YULE, G U: On a method of investigating periodicities in disturbed series. Proc Roy Soc A 226:267, 1927
J. ELECTROCARDIOLOGY, VOL. 8, NO. 1, 1975
An Analysis of the Circadian Rhythmicity of Atrial and Ventricular Rates in Complete Heart Block* BY JOHN E. CHRIST, M.D., PH.D. AND HEBBEL E. HOFF, M.D., PH.D.**
SUMMARY
Some 2400 years ago Hippocrates recognized r e g u l a r i t y as a sign of h e a l t h and i r r e g u l a r body functions or habits as disturbances of the normal state. The measurement of biological periodicity was initiated around 300 BC by Herophilus of Alexandria when he advocated the practice of counting the pulse with the help of a water clock. However, the concept of the absolute regularity of body function became less valid as consecutive serial measurements were extended to include several 24 hour periods. Quantitative measurements demonstrated t h a t biological processes were not only a function of the immediate metabolic state of the organism, but also varied with the time of day. Attempts to express time functions in a mathematical way failed when the relationship y = f (t), where y is the observed phenomenon and fis a function of t, was used. In m a n y cases a time plot of the biologic data showed a recurring pattern, so t h a t the expression y = f (T + t) where t is the time of day and T the period of the r h y t h m u n d e r study, more accurately predicted the observed data. is Since not all functions fall exactly in a 24 hour r h y t h m , but only approximately so, the term circadian has generally supplanted the term diurnal with its more precise definition. 2~ While the rhythmicity of the heart has been the subject of study in h e a l t h and disease since ancient times, it was not until well into this century, with the development of interest in consecutive serial measurements extending over 24 hour periods of time, t h a t extensive circadian studies were carried out. In 1932, Boas and Goldschmidt demonstrated in a series of 51 healthy young males and 52 healthy young females t h a t the average heart rate was greater during waking hours t h a n during sleeping hours. 2 Although the heart r a t e s in this s t u d y d e m o n s t r a t e d m a r k e d variations during the day, day rates were
A 19 year old female human subject with complete heart block was put at complete bed rest for 63 hours during which a Lead II EKG was monitored at half hour intervals. Atrial and ventricular rates demonstrated cyclic activity with peaks during the day and troughs during the night. A correlation coefficient of +0.85 and a slope of +1.0 from a linear regression between atrial and ventricular rates demonstrated a close parallel. Calculation of the crosscovariances confirmed the observed cyclic activity with a period of 24 hours and a phase angle of zero degrees between the two chambers. The data may be explained by one or all of the following mechanisms: (1) both chambers are subject to the same internal milieu, (2) autonomic nervous system discharge and associated reflexes may integrate relative changes in rate, (3) direct mechanical or e l e c t r o t o n i c f o r c e s may result in alteration of rates in direct proportion to the magnitude of the dominant chamber, (4) each chamber has its own inherited cyclic program which operates independent of external factors. The question remains for dir e c t e x p e r i m e n t a l data to d e m o n s t r a t e whether the observed phenomenon is an intrinsic biologic rhythm within the heart or in its control system.
* S u p p o r t e d by U.S. Public H e a l t h G r a n t H L-05125-17 **Department of Physiology, Baylor College of Medicine, Houston, Texas 77025. Reprint requests to: Hebbel E. Hoff, M.D., Baylor College of Medicine, Texas Medical Center, Houston, Texas 77025. 69
70
C I R C A D I A N R H Y T H M IN H E A R T B L O C K
higher t h a n night rates, decreasing during sleep with the lowest rate found shortly before or upon awakening in the morning. This data, in current terminology, showed a circadian pattern of the normal heart rate. Following the study of Boas and Goldschmidt, the circadian r h y t h m of heart rate has been w e l l e s t a b l i s h e d in t h e n o r m a l h u m a n subject .1,2,4,9,13,14,18,19 In complete heart block where the atria and ventricles are no longer physiologically connected by the intrinsic conduction system, the atria and ventricles beat at their own rates. Boas and Goldschmidt studied the ventricular rates of a few patients with complete heart block and found t h a t the proportionate difference in day (waking) and n i g h t (sleeping) rates was of the same magnitude as in the normal subjects. The atrial rates were not examined. This report demonstrates the interrelationships of the circadian r h y t h m s of both atria and ventricles in a h u m a n subject with complete heart block.
;4:
, mARCH2g ~
~"
UAeCN~0 ~
~Ancasl
_
ATRIA
~
TVENTRICLES
.L
IL~ ,
,,L
T I M [ (in k i l l . klur I l t l r ~ l l s )
Fig. 1. Plot of atrial and ventricu]ar rates over 63
hours. Highest rates occur during the day and lowest during the night. While there is a positive correlation with zero phase relationship on a beat-by-beat basis, it should be noted that in general ventricular rates tend to continue downward from 12:00 midnight to 6:00 a.m. while atrial rates tend to rise during this period. (Upper curve represents atria, lower, ventricles.)
CASE REPORT The subject of this study was a 19 year old student nurse with complete heart block who has been the subject of previous reports of the beat to beat interaction between atria and ventricles. 5'~ On March 20, 1969, she was admitted to the Clinical Research Center of Ben Taub General Hospital in Houston, Texas in good health and kept at bed rest with bathroom privileges only. Beginning at 5:30 p.m. t h a t day, a Lead II EKG was monitored at h a l f hour intervals until 9:00 a.m: March 31, 1969. Average atrial and ventricular rates were plotted for every h a l f hour, the rates were correlated, and the crosscovariances were computed. All data were then plotted.
RESULTS During the 63 hour monitoring period, the atrial rate varied from 58 to 80 beats per minute with a m e a n of 67 beats per minute (std. Dev. -+ 4.5). The ventricular rate varied from 33 to 47 beats per minute with a m e a n of 40 beats per m i n u t e (std. dev. -+ 3.4). Atrial rates were t h u s always greater t h a n ventricular rates. The plot of atrial and ventricular rates (Fig. 1) d e m o n s t r a t e s a close parallel; t h a t is, whenever the atrial rate is high, the corresponding v e n t r i c u l a r rate is also high. The highest rates, both atrial and ventricular, are in t h e m o r n i n g s h o r t l y after a w a k e n i n g ; whereas the lowest rates are seen early in the m o r n i n g shortly before awakening. Atrial and ventricular rates therefore rise within one hour from their lowest levels to their
highest levels upon awakening and take 24 hours to return to their initial levels. Atrial rates were plotted against corresponding ventricular rates (Fig. 2) and a linear regression and a correlation coefficient were calculated. The slope of the line determined the linear regression was + 1.0 and the correlation coefficient was + 0.83. Therefore there appears to be a proportional change in atrial and ventricular rates. The calculation of crosscovariances allows the e x a m i n a t i o n of s i m u l t a n e o u s periodic events, in order t h a t their periodicity may be determined, and, if periodic, what the relationship exists between these two events. 8,7,s,1~ However, the exact relationship between these events is also directly related to the total number of data points t h a t are collected, t h u s crosscovariance implies the degree of probability of a relationship. Both atrial and ventricular rates were found to have a cyclic periodicity of 24 hours, with each rate synchronized with each other, i.e., a zero phase angle.
DISCUSSION Explanation of the data cannot as yet be given in terms of any one particular hypothesis but the following may be considered: (1) A t r i a and ventricles, being subject to the same i n t e r n a l m i l i e u , respond equally to changes in t h e i r biochemical and physical environment, and therefore each would be affected equally and their mathematical relationship maintained. (2) The heart is innerJ. ELECTROCARDIOLOGY, VOL. 8, NO. 1, 1975
CHRIST AND HOFF
vated by the autonomic nervous system which m a i n t a i n s control of t he h e a r t rate. Since both atr ia and ventricles are supplied with s y mp ath etic fibers, the sympathetic nervous system m a y be the d e t e r m i n i n g factor. (3) The p a r a s y m p a t h e t i c division m a y play an indirect role th r o u g h the baroreceptor-vagal reflex activated by v e n t r i c u l a r pulse pressure. A priori such a relation ought to cause atrial ra t e to v ar y inversely to v e n t r i c u l a r rate. In addition, such a hypothesis would d e m a n d t h a t v e n t r i c u l a r changes preceded the atrial chambers by some finite interval despite the d e m o n s t r a t i o n of a zero phase angle. Intervals were clearly too widely spaced to give conclusive evidence on this point. (4) Direct mechanical or electrotonic effects m ay cont r i b u t e to circadian syncronicity. V ent r i c ul a r systole t h r o u g h t r a c t i o n on the a t r i a m a y alter the m e m b r a n e properties of the pacem a k e r or a direct electrotonic effect of one c h a m b e r mig h t influence the r at e of pacem a k i n g of the other chamber, e ve nt ua l l y resulting in parallel changes of rate. According to this hypothesis, the driving chamber might be influenced by 1, 2, or 3. (5) Since a t r i a and ventricles have the same embryologic origin, the only difference being t hei r own intrinsic r h y t h m i c i t y and i nner va t i on, it is possible t h a t wh at is seen as an appar e nt interaction of proportionality of rates m a y simply represent the inborn cyclic pr ogr am of cardiac cells which is independent of almost all external factors.
The last hypothesis m a y be considered to be most in accord with the observation of P-wave activity of donor and recipient atria in a circadian study of a h e a r t t r a n s p l a n t patient. 15 In t h a t study donor and recipient pacemaker activity had a periodicity of 24 hours but were out of~hase, recipient rat e leading the donor by 135 minutes. This suggests t h a t donor and recipient pacemakers had different biologic constitutions, and therefore this formed an intrinsic basis for t hei r difference in r h y t h m s and phase angle. Each of the proposed mechanisms may totally or in part contribute to the apparent synchronization and proportionality of cyclic activity of cardiac chambers, but final decision m ust await f u r t h e r evidence. Changing levels of activity due to inherited genetic program s have only recently been recognized a n d should be actively considered in any future investigation.
REFERENCES
a
A A A
a A A ~
A
a A A
a
A/~
A a
m A A
&/
'
30
~
'
A~
A
~ &
A
& A A a
'
I
'
'
'
'
35 V(NTRICULAR
I
'
'
'
'
40 RATE
(beats/
I
'
'
'
'
45
I
50
minute)
Fig. 2. Plot of atrial rates against ventricular rates. The linear regression line is plotted on the data. Slope = 1.0. Correlation coefficient = + 0.83. J. ELECTROCARDIOLOGY, VOL. 8, NO. 1, 1975
71
1. ASCHOFF, J: Circadian rhythms in man. Science 148:1427, 1965 2. BOAS, E AND GOLDSCHMIDT,E T: The Heart Rate. Charles C. Thomas, Springfield, 1932 3. BLACKMAN, R B AND TUKEY, J W: The Measurement of Power Spectra. Dover Publications, Inc., New York, 1958 4. BUNNING, E: Opening address - - biological clocks. In Cold Spring Harbor Symp on Quant Biology 25:1, 1960 5. CHRIST, J E AND HOFF, H E: A statistical analysis of atrial arrhythmia in A-V block. J Electrocardiol 4:331, 1971 6. CHRIST, J E AND HOFF, H E: An analysis of atrioventricuiar synchronization in complete A-V block. J Electrocardiol 6:53, 1973 7. ENRIGHT, J T: The search for rhythmicity in biological time series. J Theoret Biol 8:426, 1965 8. GRANGER, C W J: Spectral Analysis of Economic Time Series. Princeton Univ Press, Princeton, 1964 9. HALBERG, F: Circadian rhythms in experimental medicine. Proc Roy Soc Med 56:253, 1963 10. HARTLEY,H O: Tests of Significance in Harmonic Analysis. Biometrika 36:194, 1949 11. HURWICZ, L: Basic mathematical and statistical considerations in the study of rhythms and near rhythms. Ann NY Acad Sci 98:753, 1962 12. KENDALL, K G: Contribution of the Study of Oscillatory Time-Series. Cambridge Univ Press, Cambridge, 1946
72
CIRCADIAN RHYTHM IN HEART BLOCK
13. KLEITMAN, N AND RAMSAROOP, A: Periodicity in body temperature and heart rate. Endocrin 43:1, 1948 14. KOCHLER, F, OKANO, F K, ELVEBACK, L R, HALBERG, F AND BITTNER, J J: Periodograms for the study of physiologic daily periodicity in mice and in man. Exp Med Surg 14:5, 1956 15. KRAFT, I A, ALEXANDER, S, FORS~ER, D, LEACHMAN, R D AND LIPSCOMB, H-S: Circadian Rhythms in Human Heart Homograft, Science 169:694, 1970 16. MAYERSBACH,H V, ed: The Cellular Aspects of Biorhythms. Springer-Verlag, Berlin, 1967
17. MERCER, D M A: The Limitations of Detection of Periodicities in Random Noise, NorthHolland Publishing Co, Amsterdam, 1965 18. MILLS, J N: H u m a n c i r c a d i a n r h y t h m s . Physiological Reviews 46:128, 1966 19. WEYSSE, A W AND LUTZ, B R: Diurnal Variations in Arterial Blood Pressure, Am J Physiol 37:330, 1915 20. WURTMAN, R J: Ambiguities in the term circadian. Science 156:104, 1967 21. YULE, G U: On a method of investigating periodicities in disturbed series. Proc Roy Soc A 226:267, 1927
J. ELECTROCARDIOLOGY, VOL. 8, NO. 1, 1975