Analysis of cardiac chronotropic responses to some autonomic blocking agents in conscious trained dogs

European Journal of Pharmacology, 39 (1976) 193--202

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© Elsevier/North-Holland Biomedical Press, Amsterdam -- Printed in The Netherlands

ANALYSIS OF CARDIAC CHRONOTROPIC RESPONSES TO SOME AUTONOMIC BLOCKING AGENTS IN CONSCIOUS TRAINED DOGS ICILIO CAVERO *, HANS RIGGENBACH, MICHAEL WALL and MARCEL GEROLD **

Department of Experimental Medicine, F. Hoffmann--La Roche & Co., Ltd., Basle, Switzerland Received 6 January 1976, revised MS received 14 April 1976, accepted 20 May 1976

I. CAVERO, H. RIGGENBACH, M. WALL and M. GEROLD, Analysis of cardiac chronotropic responses to some autonomic blocking agents in conscious trained dogs, European J. Pharmacol. 39 (1976) 193--202. The changes of heart rate in response to i.v. administration of methylatropine (0.5 mg/kg) and/or propranolol (2 m g / k g ) o r practolol (2.5 mg/kg)were studied in conscious trained dogs. Cholinergic blockade alone or combined blockade of sympathetic and parasympathetic effector systems resulted in cardiac acceleration. Conversely, ~adrenoceptor antagonism with either propranolol or practolol reduced heart rate. The data were analysed by means of a new method, whereby the heart rate (HRN) of the dog is considered to be the product of the intrinsic heart rate (HR0) and 3 further factors: HR N = HR0 • S • V • W (multiplicative model). 2 of these factors represent the tonic sympathetic (S) and parasympathetic (V) influences, whereas the third (W) represents the sympathetic-parasympathetic interaction. This type of analysis reveals that W was approximately 1, i.e., the sympathetic-parasympathetic interaction did not play any significant role in determining the heart rate of conscious resting dogs (HRN ffi HR0 • S • V • W = HR0 • S • V). The change of heart rate due to the action of parasympathetic system (--53% of the intrinsic heart rate) was more important than the change caused by the action of the sympathetic system (26% of the intrinsic heart rate). Sympathetic--parasympathetic interaction Heart rate analysis

Intrinsic heart rate

1. Introduction The changes of heart rate resulting from stimulation of the cardiac sympathetic and/or parasympathetic nerves have been the object of numerous publications. In 1934, Rosenblueth and Simeone presented the first satisfactory mathematical description of the autonomic control of cardiac rate. Their results showed that the absolute reduction in heart rate following electrical stimulation of the vagus was greater in the presence of sympathetic activity than in its absence. However, the relative slowing elicited by a given vagal stimulation was the same whether or not a simultaneous accelerator tonic discharge was present. Therefore, the hypothesis was ad* Present address: Groupe Recherche Cardiovasculaire, Synth~labo, L.E.R.S., 58, rue de la Glaci~re, 75621 Paris, France. ** For reprints, please write to Dr. M. Gerold.

Autonomic control

vanced that neural control of the heart rate was exerted on a completely antagonistic basis as though each division of the autonomic system were acting independently. Saaman (1935) did not agree with these conclusions and gave experimental evidence indicating that the responses to electrical stimulation of the vagus were not always a constant fraction of the basal heart rates. He reported that electrical stimulation of the vagus produced a negative chronotropic effect which masked the effect of cardioaccelerator stimulation, even when expressed in relative terms. Saaman's data suggested that the 2 divisions of the autonomic nervous system interact in controlling cardiac heart rate. This conclusion has been generally confirmed by recent investigations and attempts have been made to quantify the extent of the interaction by using various mathe~natical approaches (Warner and

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Cox, 1962; Warner and Russel, 1969; Levy and Zieske, 1969; Levy, 1971). Very recently, Hondeghem et al. (1975) demonstrated that the mathematical approach of Rosenblueth (1932) could describe the neural control of heart rate provided the frequencies of vagal stimulation were neither t o o high nor t o o low. It is important to note that all the studies reported were performed in anaesthetized animals and involved electrical stimulation of the autonomic nerves to the heart. Evidently, the synchronous discharges elicited by electrical stimulation differ considerably from the asynchronous discharges of sympathetic and parasympathetic nerves occurring in the conscious animal. Furthermore, the anaesthetic agents are not without effect on the intrinsic pacemaker rate, as recently reconfirmed for pentobarbitone, by Lokwandala et al. (1973), nor is the interaction of the sympathetic and parasympathetic nerves likely to be unaffected by general anaesthesia. In order to study the role of the sympathetic and parasympathetic tone and of its drug-induced modifications in the control of the cardiac rate, autonomic blocking agents have been increasingly used. A method analysing heart rate responses in experiments using autonomic antagonists was described by Walsh (1969) and Lin and Horvath (1972). These authors use a simple 'additive' model describing the effect of the 2 nervous divisions by algebraically additive changes of heart rates. However, their approach lacks the basic terms for quantifying a possible sympathetic-parasympathetic interaction: such terms are unavoidable in additive models (Levy, 1971). In our report, we therefore decided to chose a different approach to analyse the autonomic nervous control of heart rate in the conscious dog. Our analysis is based essentially on the relative changes of heart rate obtained by administering classic autonomic blocking agents to conscious trained dogs. We developed a new m e t h o d which allows the quantification of (1) sympathetic, (2) parasympathetic contribution to and (3) sympat h e t i c - p a r a s y m p a t h e t i c interaction on heart

I. C A V E R O ET AL.

rate. The main aim of this method is to permit quantification of the determinants of heart rate modifications by pharmacologically active compounds (Gerold et al., 1976).

2. Materials and methods

2. 1. Preparation o f the animals The experiment~ were carried out in female mongrel dogs with a body weight between 8 and 15 kg. The animals were anaesthetized with sodium pentobarbitone (35 mg/kg i.v.). Under aseptic conditions, the right carotid artery was separated from the vagus and exteriorized in a flap of skin. The animals were allowed 5 weeks for recovery and subsequently were trained to stand quietly during the experimental procedure. Heart rate was measured by palpation of the carotid loop for a 30-sec period. No person unfamiliar to the animals was allowed to enter the laboratory during the experimental period. The heart rate measurements were previously shown n o t to differ from those obtained by counting QRS peaks over 30 sec periods on an electrocardiographic recording. During these experiments blood pressure was measured by a modification of the Van Leersum carotid-looptechnique.

2. 2. Experimental design Experiment A: 1 group of 12 animals received all the treatments reported below (2.3.), each after a 1-week interval. Experiment B: 3 groups of 5 dogs each received only 1 of the treatments reported below (2.3.). Heart rate masurements were c o m m e n c e d 25 min prior to the administration of the treatment and repeated every 5 min, until 30 min after dosing. The median values for each animal (taken over the 5 readings) both prior to and after drug were utilized for statistical analysis.

H E A R T R A T E IN C O N S C I O U S D O G S A F T E R A U T O N O M I C B L O C K A D E

2. 3. Drugs The following blocking agents were slowly administered into the brachial vein: ( 1 ) m e t h ylatropine bromide (0.5 mg/kg i.v.) for the blockade of cholinergic muscarinic receptors; (2) propranolol (2 mg/kg i.v.) or practolol (2.5 mg/kg i.v.) for the b l o c k a d e of cardiac fl-adrenoceptors; (3) simultaneous administration of (1) + (2) for the blockade of both types of autonomic receptors. Preliminary experiments in dogs previously implanted under general anaesthesia with carotid cannulae for chronic measurements of blood pressure, as well as in anaesthetised (chloralose--urethane) dogs, were undertaken to determine suitable blocking doses.

2. 4. Description o f the mathematical model In order to quantify the sympathetic and parasympathetic influences which participate in the regulation of the heart rate of the dog, the following mathematical model was applied: (2.4.a)

HRA = HR0 • S

(2.4.b)

HRp = HR0 • V

(2.4.c)

HRN = HR0 • S • V • W

HR0 = H R A p = heart rate following the blockade of the sympathetic and parasympathetic influences (propranolol or practolol + methylatropine). It is also called intrinsic heart rate. HRA = heart rate observed after parasympathetic blockade with methylatropine (A). HRp = heart rate obtained after cardiac fl-adrenoceptor blockade with propranolol or practolol (P). HR N = resting heart rate (in absence of any autonomic blocking agent). Equation (2.4.a) shows that S = HRA/HRo

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is the ratio between the heart rate resulting from sympathetic activity after parasympathetic blockade and the intrinsic heart rate obtained after both sympathetic and parasympathetic blockade. Thus, S quantifies the sympathetic contribution to the heart rate of the dog. Similarly, V quantifies the parasympathetic contribution to the heart rate. The factor W expresses the extent of the neural contribution to the heart rate resulting from a possible sympathetic--parasympathetic interaction. Briefly, the model states that the resting heart rate is the product of the intrinsic heart rate * and of 3 factors quantifying the neural autonomic contributions. We therefore call it the 'multiplicative model'. In order to explain the meaning of the 'interaction factor', W, we introduce 2 further parameters, S* and V*, related to t h e basic parameters S, V, W by S* = S • W = HRN/HRp V* = V • W = HRN/HRA Since S* is the ratio between the normal rate and the heart rate after blockade of sympathetic influences, S* quantifies the sympathetic contribution to heart rate in the presence of vagal tone. Analogously, V* quantifies the parasympathetic contribution in the presence of sympathetic tone. By means of these parameters, the interaction factor W is expressed by W = S*/S, or equivalently, by W = V*/V. Therefore, values of W different from 1 indicate the presence of interaction, which means that the response of heart rate to the activity of 1 nervous division depends on the presence or absence of the other division.

t In the model, intrinsic heart rate is defined as the heart rate after b l o c k a d e o f autonomic cardiac receptors with methylatropine plus p r o p r a n o l o l or practolol. T h e i n f l u e n c e o f circulating catecholamines is also antagonized thereby (Jose, 1 9 6 6 ; Jose and Stitt, 1967 ). This definition does not necessarily exclude that other

humoral factors may influence the activity of the sinus atrial node (pacemaker) after autonomic b l o c k a d e .

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Note that our multiplicative approach is equivalent to describing the autonomic influences by relative percent changes in heart rate. The quantification of sympathetic and parasympathetic tone by means of percent changes in heart rate is easier to understand and will be used to discuss the results of this investigation. These percentages (%) ¢ can be obtained immediately when S, V and W are known: (2.4.d) %S = (S -- 1) • 100: % sympathetic tone in presence of vagal activity; i.e. after vagal blockade (2.4.e) %S* = (S • W -- 1) • 100: % sympatetic tone in presence of vagal activity (2.4.f) %V = ( V - - 1) • 100: %parasympathetic tone in absence of sympathetic activity; i.e. after sympathetic blockade (2.4.g) %V* = (V • W -- 1) • 100: % parasympathetic tone in presence of sympathetic activity The statistical model from which estimates of the parameters are derived is described in the Appendix. 2. 5. Practical calculations

The medians of the 5 pre-drug measurements of heart rate (HRN) and the medians of the 5 post-drug measurements (HRA, HRp, HRAp ) are calculated for each animal. Now, we compute YA = In (HRN/HRA), Yp = In (HRN/HRp), YAe = In (HRN/HRAp). The sympathetic influences (S, S*), parasympathetic influences (V,V*), and sympathetic-parasympathetic interaction (W) are estimated as follows: S = exp(~/Ap -- ~/A), S* = exp(Yp) ¢ %S = (HRA-- HR0)- 100/HRo; %S * = (HRN -- HRp)100/HRp; %V = (HRp -- HR0) • 100/HR0; %V* = (HRN HRA) • 100/HRA. -

-

V = exp(YAp -- Yp), V* = exp(~/A), W = S*/S = V*/V = exp (~/A + YP -- YAe)~/A, ~/e, gAP denote the means of each set of YA, YP and YAP. The actual values of these means are reported in table 3. The computation of upper and lower confidence limits is explained in the Appendix.

3. Results In preliminary experiments, the dose of methylatropine (0.5 mg/kg i.v.) utilized in the present experiments prevented the depressor response to acetylcholine (2 #g/kg i.v.) in the conscious dogs. In anaesthetized dogs, this dose of methylatropine blocked the bradycardia elicited by electrical vagal stimulation at supramaximal voltage. Practolol (2.5 mg/kg i.v.) or propranolol (2 mg/kg i.v.) completely blocked the increase in heart rate observed after isoprenaline (1 pg/kg i.v.) in conscious dogs pretreated with hexamethonium and methylatropine. In anaesthetized dogs, the 2 ~-adrenoreceptor blocking agents antagonized the tachycardia induced by electrical stimulation of the postganglionic trunk of the right stella~e ganglion. Figs. 1 and 2 show the time-related changes in heart rate produced by the administration of autonomic blocking agents to the conscious trained dogs. In 1 experiment (fig. 1), each of 12 dogs received all treatments (methylatropine and/or propranolol or practolol) within a period of 2 weeks. In a second experiment (fig. 2), each treatment was administered to different groups of 5 dogs each. Administration of propranolol or practolol caused a moderate negative chronotropic effect (figs. 1 and 2). By contrast, administration of methylatropine induced a pronounced tachycardia which was rapid in onset and long in duration. No relevant behavioural effects were observed, contrary to what is observed when atropine sulphate is utilized. Blockade of autonomic influences on the heart by giving practolol or propranolol plus methylatropine

HEART RATE IN CONSCIOUS DOGS AFTER AUTONOMIC BLOCKADE 200-

180-

I~'~'~,~,~T

160E 0

140120-

~100~- 8060-=

I AA+P P i "~------1 O--15-10-,5 (~ ,5 1() 15 20 25min 24h time of observation

Fig. 1. Time-related cardiac chronotropic effect prior to and after administration ( t ) o f methylatropine (0.5 mg/kg i.v. • • ) ; propranolol (2 mg/kg i.v. m-.m) and methylatropine plus propranolol (~ V.) in a group of 12 conscious trained dogs. Data are given as means ± S.E.M.

also resulted in cardiac acceleration. The heart rate under the latter experimental conditions is termed 'intrinsic heart rate' since it is independent of sympathetic and parasympathetic neural tone. Concomitant measurement of 20018o-

,L'-L--I---I~I

E 140CO O

60"~

[A A+P fP O--15-10-; () 5 10 15 2~ 2 5 ~ 4 h time of observation

Fig. 2. Time-related cardiac chronotropic effect prior to and after administration ( t ) of methylatropine (0.5 mg/kg i.v. • • ) ; praetolol (2.5 mg/kg i.v. -m) and methylatropine plus practolol (~ ~) in 3 different independent groups of 5 c o n s c i o u s t r a i n e d dogs. Data are g i v e n as m e a n s -+ S.E.M.

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carotid systolic blood pressure during these experiments did n o t reveal any significant changes. However, it c a n n o t be excluded that minor and transitory readjustments of cardiac o u t p u t or peripheral vascular resistance occurred in response to changes in heart rate. Table 1 shows the means of the median heart rates before and after t h e administration of the various antagonists. There was no substantial differences between the results obtained in the group of 12 animals and those in the smaller independent groups. This suggests that both the degree of neural tone and the intrinsic pacemaker rates are within a well-defined range in the conscious trained dog. The value obtained for intrinsic heart rate with methylatropine plus propranolol (or practolol) was confirmed by blocking the autonomic ganglia with hexamethonium (5 mg/kg i.v.) and methylatropine (HR0 = 143.2 + 3 beats/ min) although, in these dogs, the arterial blood pressure was lowered. Methylatropine was also given since this dose of hexamethonium was found not to block completely the vagal nerve activity in conscious dogs (unpublished observations). The heart rate after hexamethonium alone was 134 + 2 beats/min. Fig. 3 clarifies the relations between the results presented in table 1. The diagram shows that the change in heart rate after propranolol in presence of a normal vagal tone expressed by AS* = HRN -- HRp = 15 beats/min is clearly less than that after atropine, AS = H R A - - HR0 = 37 beats/rain. Analogously, the degree of vagal tone expressed as absolute change in heart rate is different if calculated in presence (AV* = HRN -- HRA = --94 beats/ min) or absence (AV = HRp - - H R 0 = --72 beats/ min) of sympathetic tone. If relative changes are considered, however, the effect of the 2 nervous divisions can be described essentially by a single parameter for each division. Indeed, the relative change of heart rate due to the parasympathetic system is nearly the same, whether the sympathetic system is active or not (--53% and --51%, respectively). The same holds t r u e for the sympathetic system (26% in the absence, 22% in the presence

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I. C A V E R O ET AL.

TABLE 1 Heart rates ( H R ) p r i o r t o (N) and f o l l o w i n g i.v. a d m i n i s t r a t i o n o f m e t h y l a t r o p i n e (A) (0.5 mg/kg) a n d / o r j3a d r e n o c e p t o r b l o c k i n g agents (P) ( p r o p r a n o l o l : 2.0 m g / k g ; p r a c t o l o l : 2.5 mg/kg). In e x p e r i m e n t A, all 12 animals received the 3 t r e a t m e n t s w i t h i n a 2-week period. In e x p e r i m e n t B, each t r e a t m e n t was given to d i f f e r e n t groups o f 5 dogs. Data are given as m e a n s + S.D. Variable

Treatment

Experiment A

Experiment B

HR N HR A HR N HRp HR N HRAp

None A None P None A + P

83,0 177,7 86.0 69.3 82.7 141.4

86.4 180.0 84.0 71.8 82.4 141.2

± ± + + ± +

2.5 1.7 2.2 1.1 1 1.6 2.4 1

~_ 2.7 *- 5.6 ~ 3.6 ± 2.2 2 ± 1.6 ± 3.0 2

1 Propranolol. 2 Practolol.

of parasympathetic tone). Therefore, percentage changes of heart rate describe our data better than do absolute changes, since they take the initial heart rate into consideration (Rosenblueth and Simeone, 1934). The parameters used in our model were estimated separately from the data obtained in

each of 2 similar experiments A and B (see 2.2.). Table 2 shows the stimated parameter values together with 90% confidence limits. The values of the basic expressions used for the calculation of these parameters (2.5.) are reported in table 3. Note that the estimated values of the interaction term, W, are nearly

.141 beats/rain /

effect of VAG in absence of SYMP relative change = °laY=-51 °lo of HRo absolute change = ~ ~ ~= -72 l beats/mio V

relatlve ¢honge :°loS= 26 % of HRo I /'

t "RA: ,70 beat,l.in)

relative chanae=°/oS*=2a°/oOf ge=wo~ --z~- . . . . HR~I PJ / ~

heart beats/rain/ rate, . / /HR,,=84

l t / /

/ ! HIR~: 69 beats/,rain/

]bso4ute change = A S ~_- 15 beets/mE'n~

~(

/

/ Fig. 3. A c o m p a r i s o n b e t w e e n relative and a b s o l u t e changes o f h e a r t rate due to s y m p a t h e t i c (SYMP) or vagal ( V A G ) t o n e . Means o f E x p e r i m e n t A as given in table 1 are used for h e a r t rate HR0, HRA, HRp, H R N.

HEART RATE IN CONSCIOUS DOGS A F T E R AUTONOMIC BLOCKADE

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TABLE 2 S and S* (= S • W) are the factors quantifying the sympathetic influences on the basal heart rate of conscious dogs in the absence (S) and in presence (S*) of vagal tone; V and V* (= V • W) quantify the vagai influence in the absence (V) and in the presence (V*) of sympathetic tone. W = S*/S = V*/V is a measure of the interaction between the 2 divisions of the autonomic nervous system. The percent sympathetic contribution in presence (%S*) or absence (%S) of parasympathetic tone are given. Similarly %V* and %V are the percent parasympathetic influence in presence or absence of sympathetic tone. For the meaning of Exp. A and B see table 1. Estimates are given as means together with 90% confidence limits. Parameter

S V W S* = S • W V* = V • W %S %S* %V %V*

Estimates from Experiment A (90% confidence limits) 1.257 0.471 0.985 1.239 0.465 25.7% 23.9% --52.9% --53.5%

Estimates from Experiment B (90% confidence limits)

(1.217, 1.298) (0.445, 0.499) (0.940, 1.034) (1.191, 1.290) (0.441, 0.490) {21.7%, 29.8%) (19.1%, 29.0%) (--55.5%, --50.1%) (--55.9%, --51.0%)

1.216 0.498 0.965 1.173 0.480 21.6% 17.3% --50.2% --52.0%

(1.086, 1.361) (0.445, 0.557) (0.840, 1.108) (1.083, 1.270) (0.443, 0.520) (8.6%, 36.1%) (8.3%, 27.0%) (--55.5%, --44.3%) (--55.7%, --48.0%)

TABLE 3 The values of YA, YP, YAP, In S, In V, In W and their standard errors are basic to the calculation of the model parameters. Variables

Value of variable ± S.E. Experiment A

Y A = M e a n ofln ( H R N / H R A ) = In V * ~fp = M e a n of In ( H R N / H R p ) = In S* ~'/AP = Mean of In (HRN/HRAp) In S = g A P -- YA InV=Y-_Ap--jp _ In W = YA + Y P - - YAP

-0.7659 0.2147 -0.5373 0.2286 --0.7520 -0.0139

equal to 1.0 and the 90% confidence intervals from both experiment A and experiment B c o n t a i n 1. T h e r e f o r e , t h e h y p o t h e s i s W = 1 may not be rejected. This means that the relative contribution to the basal heart rate due t o 1 n e r v o u s d i v i s i o n is i n d e p e n d e n t o f t h e presence or absence of the other division. This f a c t is a l s o e v i d e n c e d b y t h e s i m i l a r i t y b e t w e e n t h e l e v e l o f s y m p a t h e t i c t o n e in t h e a b sence of vagal activity (%S = 25.7%) and in the presence of a normal vagal activity (%S* = 2 3 . 9 % ) ( t a b l e 2). A n a l o g o u s l y , t h e l e v e l o f v a g a l t o n e i n t h e a b s e n c e o f s y m p a t h e t i c ac-

± ± ± ± ± ±

0.0297 0.0221 0.0214 0.0179 0.0317 0.0265

Experiment B -0.7339 0.1595 -0.5384 0.1955 -0.6979 -0.0360

± 0.0481 ± 0.0485 ± 0.0368 ± 0.0633 ± 0.0633 ± 0.~)755

t i v i t y (%V = - - 5 2 . 9 % ) w a s s i m i l a r t o t h a t in the presence of normal sympathetic activity (%V* = --53.5%).

4. Discussion I n t h e c o n s c i o u s a n i m a l , t h e h e a r t r a t e is determined by a sympathetic and a parasympathetic modulation of the sinus node or predominant pacemaker. The present findings confirm this classical concept. Selective cholinergic blockade or simultaneous blockade of

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the 2 divisions of the autonomic nervous system resulted in marked acceleration of cardiac activity. Conversely, fl-adrenoceptor blockade with either practolol or propranolol reduced the heart rate slightly. Preliminary experiments using anaesthetised and conscious dogs showed that the 2 fl-adrenoceptor antagonists were similarly effective in the doses given. It appears unlikely that changes in blood pressure significantly influenced heart rate after methylatropine and/or propranolol or practolol, since the slow i.v. administration of these blocking agents produced no significant alteration in carotid blood pressure. There are 2 basic questions which should be considered when a u t o n o m i c blockers are used to study the influence of the sympathetic and parasympathetic systems on the cardiovascular system: (1) Do these agents act only as specific blockers? (2) Does the blockade of 1 c o m p o n e n t (vagal or sympathetic) affect the other system? With respect to the first question, conscious resting dogs receiving combinations of methylatropine plus propranolol or practolol or hexamethonium showed similar levels of intrinsic heart rate. Furthermore, methylatropine administration to vagotomized anaesthetized dogs does n o t induce any modification of heart rate (unpublished observation). Therefore, we can assume that in the doses utilized here, these c o m p o u n d s have n o significant unspecific effect on the cardiac pacemaker. Additionally, methylatropine, propranolol and practolol, in concentrations which block the respective receptors, do n o t change the intrinsic rate of spontaneously beating rat or guinea pig atria (unpublished observation). The second question cannot be answered in a satisfactory way. We assume, as have many authors utilizing autonomic blockers, that the peripheral blockade of 1 c o m p o n e n t does n o t influence the other. To date, there is no serious experimental indication that such an assumption may n o t be valid. Despite a wide use of drugs affecting the sympathetic or parasympathetic control of heart rate, to our knowledge no attempt has

I. C A V E R O ET AL.

been made to formulate a mathematical model to analyse these cardiac chronotropic responses in the conscious dog. The most sophisticated models have been built on data obtained by electrical stimulation of cardiac accelerator and decelerator nerves (Rosenblueth and Simeone, 1934; Warner and Russel, 1969; Levy and Zieske, 1969). Application of the models proposed by these workers requires the knowledge of the frequencies of stimulation delivered to the cardiac sympathetic and parasympathetic fibres. These models are therefore, unsuitable for the analysis of heart rate responses after administration of autonomic blockers to the conscious dog. In the present study, heart rate responses to autonomic blocking agents were used to determine the efferent autonomic neural participation to cardiac chronotropism. For this purpose, it seemed important to us to propose a precisely defined mathematical model in which the parameters could be estimated by a clear-cut statistical procedure. In our 'multiplicative model', the resting heart rate ( H R N ) is the product of the intrinsic heart rate (HR0) with 3 factors (S, V, W)describing the neural autonomic contributions. The model permits the assessment of the relative percent contribution of the sympathetic and parasympathetic systems to the heart rate. The results of the present analysis confirmed that the vagal influence (--53%) on the intrinsic heart rate is greater than that of the sympathetic system (+25%) in determining the basal cardiac rate of resting conscious dogs (Glick and Braunwald, 1965). In view of the objections made in several papers (e.g. Levy, 1971) against the classical Rosenblueth--Simeone approach, we might have expected the W factor measuring the sympathetic--parasympathetic interaction to be substantially different from 1, thus indicating the presence of interaction. Contrary to such expectations, the W factor was approximately 1. This means that the relative slowing contributed by vagal tone to the heart rate was the same whether the sympathetic tone was blocked or not. Similarly, the

H E A R T R A T E IN C O N S C I O U S DOGS A F T E R A U T O N O M I C B L O C K A D E

percent cardiac acceleration contributed by the sympathetic tone was n o t influenced by the presence or absence of parasympathetic tone. Thus, whereas this conclusion is consistent with results obtained in the anaesthetised cat by Rosenblueth and Simeone (1934), it was arrived at differently in this investigation, i.e. by using autonomic blocking agents in conscious dogs. Furthermore, unlike the model these authors used, the concept of the multiplicative model is such that the interaction can always be quantified, i.e., it does not require any absence of interaction to be applied. Our conclusions could be interpreted as being in contrast with the current view of autonomic control of heart rate (Levy, 1971). However, in line with our findings, the results of Hondeghem et al. (1975) and in part even those of Saaman (1935; see Introduction) suggest that for a certain range of atrial rates, no interaction was detectable if the data were expressed as percentage changes. In fact, Hondeghem et al. (1975) showed that the decreases in atrial rates as a function of the frequency of vagal stimulation, before and during norepinephrine infusion, are a fixed percentage of the basal rate. This excludes a significant vagosympathetic interaction at least over a wide physiological range of atrial rates. Therefore, we suggest that in our experiments the physiological level of parasympathetic (or sympathetic) tone was not influenced {absence of interaction) by the presence or absence of the sympathetic (or parasympathetic) activity. This could be due to the fact that we investigated the heart rate control in the unrestrained dog at rest. It may well be that a significant interaction could contribute to the heart rate levels resulting from other physiological states (for example: exercise, postural changes, sleep) or from the administration of drugs modifying cardiac chronotropism. The major difference between the multiplicative and the published additive models (Walsh, 1969; Lin and Horvath, 1972) is that the additive model does not permit the assessment of the interaction between sympathetic and parasympathetic systems. It assumes that

201

the influence of 1 system is completely independent of the presence or absence of the other; however, this is an assumption to be verified. Furthermore, the mathematical approach of the simple additive model is considered inadequate to describe the autonomic control of heart rate (Rosenblueth and Simeone, 1934; Levy and Zieske, 1969; Warner and Cox, 1962; Warner and Russel, 1969; Hondeghem et al., 1975). In conclusion, the multiplicative model offers the possibility of an adequate expression and analysis of the autonomic nervous influences on the cardiac pacemaker. Moreover, it can be applied to quantify the modifications induced by certain compounds in the neural control of heart rate (Gerold et al., 1976).

Appendix Statistical consideration and computations Let, as in YA = l n ( H R N / H R A ) , YP = ln(HRN/HRp), YAP = ln(HRN/HRAp). With regard t o equations (2.4.a,b,c) these variables are supposed to satisfy the rela.tions of the following (linear) statistical model: YA

= ln(V) + In(W) + EA,

Yp

= ln(S) + ln(W) + Ep,

YAP = ln(S) + ln(V) + ln(W) + EAp , where S, V, W are fixed constants and EA, Ep, EAp are r a n d o m error variables with zero expectation. It is further assumed that the error variables are normally distributed with a c o m m o n variance. These assumptions are usually applied to simplify the statistical procedure; furthermore, the experimental data do not contradict the assumption of equal variances. Now, define ~, ~*,/3, fl*, and 3' as follows: O/ = YAP -- ~-~A,Ot * = ~-Ip, ]~ = YAp--~-Ip,~* = ?A, 'y=O~*--O~=~*--/~=

YA+yp--~ZAp.

YA, YP, YAP d e n o t e the sample mean of the corresponding variable obtained f r o m the experimental data. It followd from our assumptions that a, a*, ~, fl*, 7 are normally distributed r a n d o m variable with expections ln(S), ln(S*) = ln(S • W), ln(V), ln(V*) = ln(V • W), and ln(W), respectively, and therefore provide unbiased estimates of the logarithms of S, S*, V, V*, W. This leads to the estimates given in 2.5.

202

Computation of confidence limits T h e 90% l o w e r (S-, ( S * ) - , etc.) a n d u p p e r (S ÷, (S*) ÷, etc.) c o n f i d e n c e limits are c o m p u t e d using the following formulas: S ± = e x p ( a + t SE(0~}), (S*) -+ = e x p ( a * + t S E { a * } ) , V ± = exp(fl -+ t S E ~ ) ) , ( V * ) ± = exp(~* + t SE{~*)), W ± = e x p (7 -+ t S E ( ~ } ) . SE d e n p t e s t h e s t a n d a r d e r r o r o f t h e variable e n c l o s e d in p a r e n t h e s e s . T h e t value is read f r o m a two-tail t a b l e c o r r e s p o n d i n g to, t h e 90% p r o b a b i l i t y level a n d to n A ( f o r E x p e r i m e n t A) or n B ( E x p e r i m e n t B) degrees o f f r e e d o m : n A = n - - 1 w i t h n = 12 = n u m e r of a n i m a l s in E x p e r i m e n t A, a n d n B = 3(n -- 1) w i t h n = 5 = n u m ber of a n i m a l s in each t r e a t m e n t g r o u p of E x p e r i m e n t B. T h e c o m p u t a t i o n of s t a n d a r d errors as well, dep e n d s o n t h e e x p e r i m e n t a l design: In e x p e r i m e n t A we have SE{a} = SEM{YAp -- YA}, S E ( a * } = S E M ( Y p } ,

SE~} = SEM(YAp- Yp}, SE{/3*) = SEM(YA}, SE{7} = SEM{Y n + Yp -- YAP( • w h e r e SEM d e n o t e s t h e usual s t a n d a r d e r r o r of the mean. In e x p e r i m e n t B, a d i f f e r e n t p r o c e d u r e is utilized since t h e variables were o b t a i n e d f r o m d i f f e r e n t samples: If C is a c o m m o n s t a n d a r d e r r o r given b y C 2 = 1/3 (SEMZ{YA} + S E M 2 { y p }

+ SEM2{YAp}), then SE{a} = SE{~} = ~/2C, S E { a * } = SE(~*} : C, S E ( 7 } : x/dC. T h e actual values of m e a n s a n d SEM used in these calc u l a t i o n s are r e p o r t e d in t a b l e 3.

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