isa nd Julian
Frieden
lasma ieveB :s rna~~ta~~e~ bezween G~3sevalues Even when selection of an antiarrhythmic drug is correctly based on an understanding of the e~ectro~~ys~o~ogic basis for the abnormality to be treated and the actions of the drug in relation to the existing abnormality, the success or failure of treatment depends strongly on other considerations. Paramount among these is an ~~dersta~d~~~ of the therapeutic range of plasma levels for the drug selected and the rules governing its absorption, distribution, metabolism, and excretion. No therapeutic effect is evident for most drugs nntil a §u~~iel~t concentration is attained in the blood or plasma. Although one would like to know what the drug concentration is at its site or s of action, this information is not available. must assume, therefore, that the plasma level reflects it in a predictable way. Also, if the concentration of drug is excessive, toxic effects appear. For a given drug one thus can define ranges of concentrations or plasma levels within which one can expect the drug to exert its desired and Its toxic actions in most patients. The limits to these ranges are not absolute because there is variability between patients and, in a given patient, with time. Nevertheless, in terms of prior e erience it is permissible to define a minimum e ctive concentration ( EC) and a toxic concentration (TCI (Fig. 41, and to assume that if the From the Department oZPha~macology, of Physicians and Surgeons, New York, Received
for publication
Aug.
Columbia N. Y.
University,
College
5, 1974.
Reprint requests: Dr. Michaei R. Rosen, Department of Pharmacology, Colmnbia University, College of Physicians and Surgeons, 630 IV. 168th St., New Pork, N. Y. 10032.
quate control Also, since the se~~s~t~~~~~ of the ar~~~tbrnia to the drug may change from t time, appropriate adjustments in the p level ma necessary. If one iders first only the ~~~~~~~.~~~c~ of a desired plasma level, under steady-state conditions there are two sig~~~ca~~ variables: the rate of administration and the rate of e~~rninat~o~. The rate of adm~~istrat~o~ (either by ~~~r~ve~o~s infusion or repeated inje tion) and the rate of tabolism, excretion, ts of the total body rib&ion of the dr mine the plasma level. ~The~e~~r the rate of administration ior i elimination ‘,sr out level will increase. put the reverse will be t rates are equal the total level will remain constant. It thus would appear that these two rates, 3) the distr within the body, and (3) one to select a dose and interval, or infusion rate, a~~r~~ria~e hia any desired pla.sma level. In many cases this~is true but other factors may play an ~rnp~~~a~~trole. tion and e~~rn~~at~~~ of moat antian+
Hoffman,
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Toxic TC
4 BLOOD LEVEL
cI
Effects
+
Therapeutic Effects
+
No Therapeutic Effects
MEC
2
0
TIME
4
(hours
1
Fig. 4. Schematic representation of the relationships between plasma levels and the minimum effective concentration (ME0 and toxic concentrations (TC) for a drug. A single dose of drug is given by mouth at zero time and the interrupted curves 1, 2, and 3 show the effect on the rate of change and magnitude of blood level of a progressive decrease in the rate of elimination. c-
2
”
_
_----
,,--/
BLOOD LEVEL (fig/ml)
4
2
/I
’
__-
----
I
-_
$/’ / I l-?..-12345 TIME
(hours)
Fig. 5. Schematic representation of the time-course of the change in blood level of a drug administered by a constant rate intravenous infusion. Note that if the rate of elimination is decreased kurve 2), not only is the steady-state blood level increased but also the time required to attain a steady level is increased.
drugs follow what are called first-order kinetics. For such drugs, a constant fraction of the dose is absorbed per unit time and a constant fraction of the amount of drug in the body is eliminated in each unit of time. These processes are described in terms of rate constants or, more frequently, by the half-time (t,,) for absorption or elimination. The t, measures the time required for 50 per cent of the dose to be absorbed or 50 per cent of the body store to be eliminated. It is important to remember, however, that not only is the rate of elimination one of the two determinants of the steady-state drug level, but also it is the un&ue determinant of the rate at which a given steady-state level is attained. These principles are demonstrated most simply by considering first the case in which the drug is administered by a constant intravenous infusion (input rate controlled). We can assume that all the administered drug remains within the vascular compartment and thus only elimination follows first-order kinetics. 254
This example is shown diagrammatically in Fig. 5. When the drug is administered at a constant rate, if there were no elimination, the plasma level and body store would increase linearly with time. However, because elimination does occur, and because the amount eliminated per unit of time is a function of the concentration, the rate of elimination will increase as the plasma level increases until the rates of elimination and infusion are equal. When this condition obtains, the plasma level remains constant. If the rate constant for elimination were to change, both the steady-state plasma level and time required to attain that level would change (Fig. 5). If the infusion (input) rate were changed the steady-state plasma level would change but the time required to attain the steady-state would be unaltered. In reality, the situation is more complex since most drugs are distributed between intravascular and extravascular compartments and thus, during the time required for the plasma levels to attain a steady value, both distribution and “true” elimination influence the rate at which plasma level changes as well as its final steadystate value. This is discussed in the following paragraph. Nevertheless, it is clear that any change in the rate constant for elimination will have a predictable effect on the plasma level, regardless of the route or method of administration. For example, since some antiarrhythmic drugs are eliminated by glomerular filtration, a decrease in glomerular filtration rate will (1) slow the rate of change of blood level and (2) increase the mean blood level. Also, since these agents may exist in tubular urine either in the charged or uncharged form, changes in urinary pH will have appreciable effects on the rate of drug reabsorption from the tubules and thus on the t, for excretion and plasma level. Some additional consideration of the distribution of drug within the body is essential. The simplest example is the case in which the drug is administered fairly rapidly by intravenous injection. When this is done, the initial value of the plasma level depends on the amount injected and the blood volume. The time-course of the change in plasma level initially is determined by the rate at which the drug moves out of the vascular compartment. When distribution is complete, i.e., all body compartments are in equilibrium, once again the rate of change of plasma level depends on the t,h for elimination. February,
1975, Vol. 89, No. 2
An e~a~~~~e of this :s shown diagrammatically in Fig, 6. immediately after injection, the plasma “revel is very high (i , often well above the threshold for toxic e . Typically, the plasma level first falls rapidly, due to redistribution, and then more slowly, due to .elimination. It is importo remember that only free (unbound) drug ses across the capillaries. For this reason, if the drug is bound in la quantity to plasma protein, the plasma level total drug) will remain much higber than if protein binding is minimal. If the is bou in large quantity at extravas sites ( ich may be on or within cells) the plasma level will be proportionately lower. Thus much of the drug may remain within the vascuIar compartment or most of it may leave the vascular compartment promptly. To estimate this tendency, and thus the plasma level which can be expected to result from a single intravenous dose, the concept of the apparent stributio~ (AVD) has been employed. the plasma concentration divided by the dose: mg. / ml. = ml. WG The plasma concentration can be obtained dire~tI~ if, after an initial rapid decline, the plasma level changes only very slowly. More frequently, it is estimated by extrapolation, as shown in Fig. 6. There are some practical points to make in relation to the simple system diagrammed in Fig. 6. B in many instances the drug may distribute rapidly to some and less rapidly to other parts of the body. In this case the change in plasma level with time will not be represented by only two exponential processes, one representing distribution and the other elimination, but rather by a distribution of drug among ents. For the ideal system e initial rate of decline in plasma level represents also the rate at which drug concentration increases at its sites of action in the heart. In reality, this probably is an oversimplification and for many drugs the concentration at sites of action in the heart may increase much more slowly than the initial rapid fall in blood level. This may be a problem of some magnitude when parts of the heart are poorly perfused. The extent to which the drug in the vascular ~om~a~trne~t is bound is important not only in relation to the interpretation of plasma levels but
Fig. 5, Schematnc representation of the time-course of change in blood levei of drug administered by a single ~~~rave~o~ injection and eliminated by a first-order process. Note that levels are plotted on a logarithmic scale. The ~~t~~~u~t~~ curve and dots show the actual blood ieveis at. di%rent times. The solid line US show-s the exponential &&ne o? bid ievels due to eiimination and the dashed !ins 64 shows the rapid decline due to redistribution. ~~~a~o~a~~o~ of curve B to zero time gives the value of blood levei used to estimate the apparent volume of distribution.
llSil7j free, unbound ood and bo$~ A level of a drug which is in ge part boaxnd to protein may have the same :t as a lower level tensively. This is of a drug which is bound le in relation
nly
rug is excreted by in binding thus will retard excretion of some drugs. Finallyl the ing sites are a variable reservoir for the changes in pH may increase ~i~?.~i~g decrease the level of free tion of another agent m drug from its bi~~~~~ sites on plasma thus intensify its action. monly used ~~t~~r~b~~~~~~ drugs, with the ex~e~tio 0rall.y in repeate course of the pla mmvalue of the plasma lewd under d&ions, will depend on the rate ~o~~t~~~t fo absorption and ~~~~inati~~, the &se, a dosing interval. Clearly, there are many variaHesinvolved and changes in each can occur. It is possible, nevertheless, to fo~~~~te s rules which hold true for typical co I. For any drug, when it is ~~~~~~~~~~~~in oses at regular intervals, if ~~~~~i~~ is more et will rise more (i~,~shorter) the plas y and reach a high delayed, the opposi ven rate of absorptio
Hoffman,
Rosen,
and
Wit
tion will influence both the rate of change of plasma level and the peak level. If elimination is more rapid, the plasma level will peak sooner after administration of a given dose and the highest value attained will be reduced; in addition, with more rapid elimination, the plasma level will fall to a lower value before the next dose. These considerations emphasize the importance of evaluating the t, for absorption and elimination in relation to the dose and dosing interval. Failure to do so may result in selection of a dose and dosing interval that periodically create either a toxic or ineffective plasma level, or both. There are other practical advantages to knowing something about the rate constant of halftimes for absorption and elimination when drugs follow first-order kinetics. For example, regardless of the dose and dosing interval, the time required to attain the mean steady-state plasma level is approximately 3.5 times the th for elimination. This provides a means of estimating the time required to attain a blood level higher than the MEC. A priming dose can be used to bring the plasma level into this range more rapidly, as can a shorter than normal dosing interval for the first few doses. It must be remembered, however, that the ability to make a semiquantitative estimate of the time-course of the bloodlevel is limited by the predictability of absorption. This depends on the pH of the gastric and intestinal contents, the presence of food, and substances that directly or indirectly interfere with absorption and the level of motility. Absorption rate also is influenced by the rate at which the drug dissolves after ingestion; this can be controlled to some extent by pharmaceutical formulations. All in all, while it usually is impossible to predict precisely what the time-course of blood level will be for any particular patient, an appreciation of the rules governing the absorption and elimination of drugs greatly increases the likelihood that any possible therapeutic effects will be attained and overt toxicity avoided.
ment of an apparently reasonable approach to treatment of cardiac arrhythmias. Some of the rules derived from an appreciation of cardiac electrophysiology are generally applicable. Others appear to require further testing. There are many discrepancies between what can be predicted or expected and what happens; these discrepancies result from many factors. It is likely that cardiac disease in humans has effects on the electrical activity of cardiac cells which have not been reproduced in the laboratory. It is likely, also, that disease modifies the response of cardiac cells to drugs in ways that have not yet been discovered. Nevertheless, some progress has been made and further experiment and thought may provide both better understanding and new and better therapeutic agents. REFERENCES 1. 2.
3.
4.
5.
6. 7. 8.
9.
10.
11.
12.
Summary
Studies on the electrophysiologic mechanisms responsible for disturbances of cardiac rate, rhythm, and conduction, and studies on the actions and mechanisms of action of antiarrhythmic and other drugs, permit the develop-
256
13.
14.
Hoffman, B. F., and Cranefield, P. F.: Physiological basis of cardiac arrhythmias, Am. J. Med. 37:670, 1964. Hoffman, B. F.: Possible mode of action of antiarrhythmic agents. In: The Myocardial Cell, Briller, S. A., and Conn, H. L. Jr., editors. Philadelphia, University of Pennsylvania Press, 1966, pp. 251-267. Fenoglio, J. J., Jr., Pham, T. D., Wit, A. L., Bassett, A. L., and Wagner, B. M.: Canine mitral complex: ultrastructure and electromechanical properties, Circ. Res. 31:417, 1972. Rosen, M. R., Gelband, H., Merker, C., and Hoffman, B. F.: Mechanisms of digitalis toxicity: effects of ouabain on phase four of canine Purkinje fiber transmembrane potentials, Circulation 47:681, 1973. Ferrier, G. R., Saunders, J. H., and Mendez, C.: Cellular mechanism for the generation of ventricular arrhythmias by acetylstrophanthidin, Circ. Res. 32600, 1973. Spotnitz, A., and Rosen, M. R.: Unpublished observation. Lown, B.: Electrical stimulation to estimate the degree of digitalization, Am. J. Cardiol. 22:251, 1968. Hagemeijer, F., and Lown, B.: Effect of heart rate on electrically induced repetitive ventricular responses in the digitalized dog, Circ. Res. 28:333, 1970. Hoffman, B. F., and Singer, D. H.: Appraisal of the effects of catecholamines on cardiac electrical activity, Ann. N. Y. Acad. Sci. 139:914, 1967. Cranefield, P. F., Wit, A. L., and Hoffman, B. F.: The genesis of cardiac arrhythmias, Circulation 47:190, 1973. Rosen, M. R., and Hoffman, B. F.: Brief reviews: mechanisms of action of antiarrhythmic drugs, Circ. Res. 32:1, 1973. Weidman, S.: Effects of calcium ions and local anesthetics on electrical properties of Purkinje fibers, J. Physiol. 129568, 1955. Singer, D. H., Lazzara, R., and Hoffman, B. F.: Interrelationships between automaticity and conduction in cardiac Purkinje fibers, Circ. Res. 21:537, 1967. Saunders, J. H., Ferrier, G. R., and Moe, G. K.: Conduction block associated with transient depolarizations induced by acetyl strophanthidin in isolated canine Purkinje fibers, Circ. Res. 32:610, 1973.
February,
1975, Vol. 89, No. 2
15. 16.
j 7.
18. 19.
Fen-e:, hi. 1.. Sick sin113 syndrome in atriai disease, J. A. M. k ~~~:~45, 1988. Vassalle, M., Vagnini, F. J., Gourin, A., and Stuckey, 9. M.: Suppression and initiation ofidioventricular automaticity during vagal stimuiation, Am. J. Physiol. 2421, 1967. Wassalle. M.: Electrogenic suppression of automaticity 1x1 sheep and dog Purkinje fibers, Circ. Res. 27:361, 1970. Gelband, H.: Unpublished observation. ?lashimoto, K.: and Moe, G. K.: Transient depolarizations induced by acetyl strophanthidin in specialized tissue of dog atrium and ventricle, Circ. Res. 32:618, ! 973.
20.
21. 22.
23.
Rosen, ?k X7 ilvento, Z., Ge,bano, -I., aa %ierker, 2.: .EEect of verapamil on ~iect~~~b~si~~~~~~~ properties of canine cardiac Purkinje fibers, J. Pharmaco!. Exp. Ther. 1 :414, 1974. Singer, D. FL, and Te ick. R. E.: Anerrancy: electropbysiclogic aspects, Bigger, 9. T., Jr., Bassett, Slectrophysiologica! effects of ~~~~~o~~~~byd~~to~n on canine Purkinje fibers, Circ. Res. 22:22b, I.968 Singer, D. Il., and Ten Eick, Ft. E.: ~b~~~~~~co~o~~ of cardiac arrhythmias, in Friedberg, C. KY,> ed.: Current status of d in cardiovascular disease, Mew York, 1969, Grun Stratton, Inc., pp. 98-124.