Fourier analysis of cardiac action potentials

J. ELECTROCARDIOLOGY 14 (2), 1981, 139-142

Fourier Analysis of Cardiac Action Potentials BY AKE OBERG, PH.D.* AND ROLF G. SAMUELSSON, M . D . t

SUMMARY Fourier analysis of the repolarization phases of cardiac action potentials showed clear differences in the frequency characteristics of atrial and ventricular recordings. The frequency spectrum of the atrial repolarization phase was in the range of 0-45Hz, with a predominant power spectral density between 0-15Hz. The frequency spectrum of the ventricular repolarization phase was in the range of 0-20Hz, with a predominant power spectral density between 0-10Hz. Physiological changes that accentuate the differences in shape between atrial and ventricular APs also accentuate the differences in frequency spectrum of their repolarization phases. Fourier analysis therefore could be a complement to the current methods used to describe and quantify differences in the shape of cardiac action potentials. The transmembrane action potential recorded f r o m m y o c a r d i a l fibers differs f r o m those r e c o r d e d f r o m m o s t o t h e r e x c i t a b l e cells, in s h o w i n g a slow, d e l a y e d r e p o l a r i z a t i o n . I n c h a r a c t e r i z i n g t h e cardiac a c t i o n p o t e n t i a l , t h e d e p o l a r i z a t i o n p h a s e ( p h a s e 0) c a n be a c c u r a t e l y described by t h e r a t e of r i s e (volts/sec) a n d a m p l i t u d e (mV) as c a n p h a s e 4 b y t h e r a t e of s p o n t a n e o u s d e p o l a r i z a t i o n a n d a m p l i t u d e of t h e t h r e s h o l d p o t e n t i a l , w h e r e a s t h e r e p o l a r i z a t i o n p h a s e ( p h a s e 1-3) h a s a t i m e course t h a t is m o r e difficult to describe b y q u a n t i t a t i v e m e a n s . T h e s h a p e of t h e r e p o l a r i z a t i o n phase varies considerably among the different fiber t y p e s t h a t c o n s t i t u t e t h e h e a r t a n d f r o m one species to a n o t h e r . T h e r e is, for e x a m p l e , little or no p l a t e a u p h a s e ( p h a s e 2) in action p o t e n t i a l s r e c o r d e d f r o m m o s t of t h e m a m m a l i a n a t r i a l fibers, w h e r e a s action p o t e n t i a l s f r o m m a m m a l i a n v e n t r i c u l a r fibers m o s t often show a w e l l - m a r k e d 9p l a t e a u phase. T h e c u r r e n t m e t h o d s for c h a r a c t e r i z i n g t h e rep o l a r i z a t i o n p h a s e of m y o c a r d i a l action p o t e n t i a l s i n v o l v e m e a s u r i n g t h e d u r a t i o n of t h e action pot e n t i a l a t c e r t a i n levels of r e p o l a r i z a t i o n 1,2 a n d d e f i n i n g t h e t a n g e n t s to t h e slopes of p h a s e 2 a n d

3. 3,4 H o w e v e r , t h e s e m e t h o d s m u s t be r e g a r d e d as s e m i q u a n t i t a t i v e , e s p e c i a l l y w i t h r e g a r d to s m a l l a l t e r a t i o n s of t h e r e p o l a r i z a t i o n p h a s e f r o m action potentials with no well-defined plateau phase. T h e p u r p o s e of t h i s p a p e r is t h e r e f o r e to describe a n e w m e t h o d for c h a r a c t e r i z i n g t h e rep o l a r i z a t i o n p h a s e of m y o c a r d i a l action p o t e n t i a l s by determining the frequency content using Fourier analysis.

MATERIALS A N D METHODS In order to analyze the frequency spectrum of the repolarization phase of a typical atrial and a typical ventricular t r a n s m e m b r a n e action potential, and to evaluate the effects of alterations in the shape induced by physiological or pathophysiological influences curves of repolarization phases from action potential recordings presented in the literature were reproduced (Figs. 1A and 2A). The effect of vagal stimulation on the repolarization phase of atrial action potentials consists of a marked shortened time course with an overall steepening of the repolarization curve, whereas separate effects upon phase 2 and phase 3 can hardly be distinguished. The effect of reduced temperature on the repolarization phase of ventricular action potentials consists of a marked prolonged time course, essentially due to a prolongation of the plateau phase. For the analysis, the amplitude (in mV) between the baseline and the repolarization curve was measured at regular time intervals. In order to avoid so-called aliasing distortion of the spectrum, the sampling time interval was chosen as 0.0015 sec (640 Hz) for the atrial AP and 0.008 sec (125 Hz) for the ventricular AP. This choice of sampling intervals also gives a sufficient frequency resolution in the spectral representation (3.3 Hz). The data then were programmed into a computer (IBM 370-155) for power spectral analysis, using a s t a n d a r d computer p r o g r a m for Fourier analysis (BMD-02T P r o g r a m Reference). This type of data

*Professor of the Department of Biomedical Engineering, University of Linkoping, Linkoping, Sweden. tAssociate Professor, Department of Internal Medicine, University Hospital, Uppsala, Sweden. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked '~advertisemenf' in accordance with 18 U.S.C. w 1734 solely to indicate this fact. Reprint requests to: R. G. Samuelsson, M.D., Department of Internal Medicine, University Hospital S-75014, Uppsala, Sweden. 139

140

C)BERG AND SAMUELSSON Vagat

nerve

analysis. The total power was calculated by numerical integration of the power spectral density curve.

stimulation

on atrial AP

RESULTS

I

100 rnV

200msec

Fig. IA. The repolarization phase of a transmembrane action potential recorded from a single fiber of an in situ dog atrium prior to and during vagal stimulation (A-F). (The curves are reproduced from Hoffman and Suckling, Am J Physiol 173:312, 1953.) analysis can be easily performed on a mini or laboratory computer. In this case the computer manufacturer often supplies software for power spectral density

The frequency spectrum of t he atrial repolarization curve was in the r a n g e of 0-45 Hz, with a predom i nant power spectral density below 20 Hz (Fig. 1B). The effect of increased vagal influence was a decrease in the lower frequency range, and an increase in the hi gher frequency range of the power spectral density, inducing a shift of the point of balance of the curve to the right. The n u m e r i c a l i n t e g r a t i o n of t h e frequency curves showed a decreased total power with increased vagal influence on the repolarization phase. The frequency spectrum of the ventricular repolarization curve was in the range of 0-15 Hz, with a predom i nant power spectral density below 10 Hz (Fig. 2B). Decreased t e m p e r a t u r e resulted in an increased power spectral density in the range of 0-3 Hz and a decreased power spectral density above 3 Hz, inducing a shift of the point of balance of the curve towards the left. The numerical i n t e g r a t i o n of t he s p e c t r a l d e n s i t y curves showed a decreased total power with decreasing t e m p e r a t u r e and p r o l o n g a t i o n of t h e p l a t e a u phase.

POWER SPECTRAL ANALYSIS A t r i a t AP ReL. units

I

200

~'o

A

~. lo0

10

~: ~u

0

5

Increasing vagat i n f t u e n c e ~

lo r o

A ; x-- x--x

t, o EL 0~o

0.5

Qo

0.1 10

o--o--o

"\

~o

,

,

20

30 Frequency

E A--.--A

.

40

50

Hz

Fig. lB. Power spectral analysis of the repolarization curves (A-F) from Fig. 1A.

J. ELECTROCARDIOLOGY, VOL. 14, NO. 2, 1981

FOURIER ANALYSIS OF ACTION POTENTIALS

technology. The method of signal analysis used describes the general frequency composition in the data in terms of the spectral density of its m e a n square value. An interesting property of the power spectral density function is its relation to the autocorrelation function. The two types of functions are related as a Fourier transform pair. If the a u t o c o r r e l a t i o n function is known, the power spectral density function can easily be calculated by u s i n g the F o u r i e r t r a n s f o r m . The statistical errors of the spectrum are among the other factors d e p e n d e n t on a n a l y s i s time and resolution bandwidth. When using the spectral density function to analyze very reproducible signals like the cardiac action potential which can be considered deterministic in its nature, the errors obtained usually are very small. F r e q u e n c y spectral a n a l y s i s has previously been used to determine the frequency characteristics of various types of recordings obtained in cardiology, for example, pulse waves, 6 ballistocar-

T e m p e r a t u r e influence on ventricutar AP

100 rnV

1

A.

i

141

i

500msec

Fig. 2A. The repolarization phase of a transmembrane action potential recorded from a single fiber of cat papillary muscle during decreased temperature from 29, (A) to 19, C (D). (The curves are reproduced from Hoffman and Cranefield, Electrophysiology of the Heart, 1960.)

DISCUSSION Power spectral density representation of signals is a standard method used in m a n y fields of

POWER

SPECTRAL A N A L Y S I S Ventricu!.ar MAP

Ret. units 100 200 !

A

B

50 ~ 100

b

10 Decreasing t e m p e r a t u r e

e-

5 L

O

a_

1

A: •

0.5

C:m--m D:

o - - o

~ Q 0.1 L

Fig. 2B. Power spectral analysis of the repolarization curves (A-D) from Fig. 2A. J. ELECTROCARDIOLOGY, VOL. 14, NO. 2, 1981

0

*'----~L O

5

10

15

Frequency

20

Hz

142

s

AND SAMUELSSON

diograms, echocardiograms, s and phonocardiograms, 9 but we know of no other report in the l i t e r a t u r e where Four i er analysis has been used to characterize the cardiac action potentials. As is shown in this paper, the frequency spectrum of t h e repolarization phases of atrial and vent r i c u l ar action potentials differ markedly. Physiological changes t h a t accentuate these differences, such as increased vagal influence of the atrial AP and decreased t e m p e r a t u r e on the vent r i c ul a r AP, also accentuate the differences in the frequency spect r u m of the repolarization phases. Each curve in the spectral densitogram differed from t h e o t h e r curves and t h u s c o n s t i t u t e s a specific meas u r e of the shape of the repolarization curve t h a t it represents. Fourier analysis theref o r e c o u l d be a c o m p l e m e n t to t h e c u r r e n t methods used to describe and quantify differences in the shape of the repolarization curve. The effects of physiological, p a t h o p h y s i o l o g i c a l a nd pharmacological mechanisms could more accur a t e l y be quantified: e.g. the basic mechanisms u n d e r l y i n g the incidence of cardiac a r r h y t h m i a s are closely associated with changes in the electrophysiological activity of the different types of myocardial cells. In elucidating the mechanisms of action of a n t i - a r r h y t h m i c drugs, the effect on the action potential of the cardiac cells needs to be assessed. 1~This method therefore m i ght provide a n e w basis for an objective e v a l u a t i o n of t he m e c h a n i s m s g o v e r n i n g t h e e f f e c t s of a n t i a r r h y t h m i c drugs.

REFERENCES 1. SZEKERES,L AND VAUGHAN WILLIAMS, E M: Antifibrillatory action. J Physiol 160:470, 1962 2. GIBSON,J K, SOMANI, P AND BASSETT, A L: Electrophysiological effects of encainide (MJ 9067) on canine Purkinje fibers. Euro J Pharmacol 52:161, 1978 3. SINGH,B N AND VAUGHANWILLIAMS,E M: The effect of Amiodarone, a new antiarrhythmic drug, on cardiac muscle. Br J Pharmacol 39:657, 1970 4. OLSSON, S B: Monophasic action potentials from right atrial muscle recorded during heart catheterization. Acta Med Scand 190:369, 1971 5. DIXON, W Y, (Ed.): BMD Biomedical computer programs, University of California Press, Berkeley, 1974 6. OLIVA, I, IPSER, J AND KOTIKOVAK, A: Bewertung der Forum der Pulswelle mit Hilfe der Harmonischert Fourier-Analyze bei Aorten Insuffizienz. Z Kardiol 64:461, 1975 7. FRANKE,E K: A look at the Fourier spectrum of the ballistocardiogram. Bibl Cardiol 32:109, 1973 8. CHU, W K AND RAESIDE, D E: Fourier analysis of the echocardiogram. Phys Med Biol 23:100, 1978 9. LONGHINE, C, PORTALUPPI, F, ARSLAN, E, PEPRIELLI, F, RAVENNA, I AND TOSELLI,T: Aspetti tecnici e metodoligici dell'introduzione in fonocardiografia dell'analisi di Fourier. G Ital Cardiol 9:329, 1979 10. VAUGHNWILLIAMS,E M: The development of new antidysrhythmic drugs. Schw Med Woch 103:262, 1973

J. ELECTROCARDIOLOGY, VOL. 14, NO. 2, 1981