Phurma~, 7her, Vol. 17. pp. 143 to 163. 1982 0163-7258 82 020143-21510.50'0 Printed in Great Britain. All rights reserved (opyright ~ 1982 Pergamon Press Ltd Specialist Subject Editors: M. ROWLAND and G. T. TUCKER DOSAGE REGIMEN DESIGN C. LINDSAY DFVANE* and WILLIAM J. JUSKOt *Divi.sion tf Clinical Pharmaeokinetics, College of Pharmacy, Unirersity of Florida, Gainesville, FL 3261tl, U.S.A. ~'Department q/ Ptlarmtu'eutic.~. School of Pharmacy. State Uni~'ersity of New York. BUI]ulo. N Y 14260, U.S.A. 1. INTRODUCTION Dosage regimen design is the selection of drug dosage, route, and frequency of admin- istration in an informed manner to achieve therapeutic objectives. Deliberate planning of drug therapy is necessary because the administration of drugs usually involves risk of untoward effects. Specific drugs have inherently different risks associated with their use and a dosage regimen should be selected which will maximize safety. At the same time, the variability among patients in pharmacodynamic response demands individualized dosing to assure maximum efficacy. Some factors which influence the selection of a dosage regimen include the dosage form of the drug, its pharmacokinetic characteristics, the patient's pathophysiology, and the patient's therapeutic needs. The suggested dosage regimens supplied with a drug product formulation are gradually improving in the use of pharmacokinetic principles and in providing allowances for individual patient needs. This article will review the general pharmacokinetic principles involved, the established methods, and some recent proposals for the design of drug dosage regimens. 1.1. PHARMACOLOGIC EFFECTS Drugs are administered for their reversible or irreversible pharmacologic effects. Examples of the former type include the reduction of seizure activity from administration of anticonvulsants and the anesthesia produced by halothane. Irreversible effects occur following attenuated viral vaccine innoculation, ablative therapy in hyperthyroidism with 3~i, and treatment of infectious diseases with antibiotics. With the early selection of an accurate dose and suitable method of administration, a pharmacologic response may indicate achievement of one or more therapeutic objectives. At other times, pharmacolo- gic effects serve as feedback control in refinement of the dosage regimen. This process works best when the pharmacologic effects are direct and easily and accurately measure- able, such as the reduction in heart rate caused by beta-adrenergic blockers or the increase in bleeding time from heparin administration. If the desired pharmacologic effects occur indirectly, then a longer time may elapse between a dosage change and appearance of the full intensity of the effect. An example is the delay in full anticoagulant effect which follows an adjustment in warfarin dosage. When pharmacologic effects are not easily quantified, evaluation of efficacy may be especially difficult. During maintenance therapy of manic-depressive illness with lithium salts, a loss in efficacy may not be apparent for months following a reduction in dosage until recrudescence of symptoms occur. Similar examples occur with antiepileptic therapy. ÷Correspondence to: Dr. William J. Jusko, Division of Clinical Pharmacy Sciences. 319 Cooke Hall, Buffalo, NY 14260, U.S.A. J~r, I? 2-A 143
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`144 C.I.INI)SAY DEVANI. and Will IAM J JISK() The safety component of appropriate drug therapy may be difficult to assess from pharmacologic effects alone. Prophylaxis of endocarditis may require administration of an aminoglycoside antibiotic for six weeks or longcr. Evidencc of etficacy may bc present as sterile blood cultures, but the dosage regimen may allow insidious drug accumulation to occur which could lead to nephrotoxicity (Schentag et al., 1977). In thc evaluation of atrial fibrillation during digoxin therapy, cither a loss of drug efficacy or a toxic drug effect might be present. Here, a serum drug concentration measurcment might be diagnostic. The most effective and realistic method for assuring safe and efficacious drug therapy is an integrated approach using both pharmacologic effects and serum drug concentrations to serve as feedback control in refinement of the dosage regimcn. 1.2. SERUM DRU(_; CONCENTRATIONS When either a minimum or threshold concentration has an established relationship with a pharmacologic effect or when an upper concentration boundary is associated with decreased efficacy or with toxicity, serum drug concentrations become relevant markers of appropriate therapy. A practical example of this concept is the threshold concen- tration that exists for antimicrobial therapy where in ritro testing of a patient's infecting organism with serial dilutions of an antibiotic can be used to determine the effective minimum inhibitory concentration (MIC) (Tallarida and Jacob, 1979). An alternative to individual MIC determinations is large scale testing using different strains of the same pathogen to determine MIC's for several antibiotics. Data derived from these types of studies are useful to design a dosage regimen whercin the MIC is exceeded during each dosage interval. A minimum effective concentration (MEC) can be established for many drug classes. The usual procedure is to construct dose-response curves in relation to plasma concen- tration and to identify the concentration below which 20% of the study population fails to exhibit the measured pharmacologic response as the MEC. The upper limit to the 'therapeutic range' is established as either the concentration below which 80-85°,0 of the study population responds, or response is limited by intervening toxicity. This concept is illustrated in Fig. 1. The therapeutic concentration range may be dctermined by prospec- tive clinical trial, as was done for theophylline (Mitenko and Ogilvie, 1973: Weinberger and Bronsky, 1974) or by retrospective data examination, as was done with the antimanic effect of lithium (for review, see Amdisen, 1978). The ratio of the upper to lower concen- tration boundary has been termed the 'therapeutic index" (TI) and is a useful concept in dosage regimen design. An additional term, 'therapeutic window', has been applied to drugs with a therapeutic range above which toxicity docs not necessarily intervene but I00 Z _w 80 {3. ~o 60 ZD wZ rra" 40 w(.o uj ~ > ~ zo o / I eropeutlc I l( Ronge ), / i ~/¢ i i ~/ i i 20 40 60 80 I00 CONCENTRATION FIG. 1. The cumulative per cent reslxmse, or dosc response curse. For man) drugs the character- istic shape of the cumulative curve is seen when the abscissa is expressed as log concentration rather than concentration. A "therapeutic range" may be established wherein 20 80"0 of the patient population shows the desired pharmacologic response v, ithout intervening toxicity.
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`Dosage regimen design 145 the desired pharmacologic response appears less likely to occur. An example is the 150 ng/ml steady-state concentration of nortriptyline above which spontaneous remission of depression may be inhibited (Kragh-Sorensen et al., 1976). A serum concentration within a reported therapeutic range provides evidence that the drug dosage regimen employed should be appropriate for patients with characteristics similar to the study population in which the range was determined. Therapeutic ranges have been reported for numerous drugs, but these data usually reflect the results of a limited selection of patients and may not apply to a specific individual. In utilizing data of this nature, one should critically examine the characteristics of the patients studied and the details of the dosage regimen used to establish the particular range. This latter fact can be important because sampling time differences among studies can lead to different conclusions. A common caveat is that serum drug measurements must be inter- preted in the context of the patient's therapeutic needs and clinical response to the drug. 2. THEORETICAL PRINCIPLES Mathematical models to describe the sojourn of drug and metabolites in the body are becoming increasingly sophisticated. An impediment to progress in clinical pharmaco- kinetics is obtaining biological samples to confirm these models. Nevertheless, a math- ematical basis for serum concentration predictions has practical utility. The advantage of theoretical insight is that it enables us to evaluate experimental data critically, to deter- mine the relative meaning of unexpected results, and in general, to reduce the amount of uncertainty that lies in applying empiric observations to the pragmatic task of dosage regimen design. 2.1. LINEAR DRUG DISPOSITION When the rate of drug elimination from the body at any time is proportional to the amount of drug in the body at that time, a first-order or linear process is operative. Invoking the assumption of linearity also means that a drug undergoes each kinetic process in the body, e.g. distribution across membranes or binding to tissue proteins, without appreciably disturbing that process. Linearity for any drug occurs only over a finite concentration range, and any dose producing concentrations within the linear range will follow the same fate in the body as another. Many clinically useful drugs produce their desired pharmacologic response without exceeding a concentration range associated with linearity. 2.1.1. Single Doses The blood (serum or plasma) concentration-time profile following single doses of many therapeutically useful drugs resembles that shown in Fig. 2. Drug concentration, C, at any time, t, can be described by a polyexponential equation generally consisting of four terms or less C = ~ C,-e -~'''1 (1) i=1 where C, is the hybrid coetficient associated with the ith exponent. The £, and C, values represent the slopes (S) and heights (H), respectively, of the concentration-time curve and can be determined by linear regression analysis using manual (Riggs, 1963; Gibaldi and Perrier 1975) or computer fitting techniques (Daniel and Wood, 1980) without recourse to any particular pharmacokinetic model (see also Metzler, 1981). Along with the area under the curve (A, AUC) and the area of the first moment curve (M, AUMC), they constitute the SHAM properties of an observed kinetic process (Caprani et al., 1975). These properties can be used to either calculate rate constants associated with a variety of models or to calculate model-independent parameters (Wagner, 1976).
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`146 (. LINI)S,',,'~ DI \"~Xl and V¢III.IAM .I. Jt SK() I00 Ct 50 z c2 (2_ 20 Z W z tO 0 LD O0 ~ 5 Xo I I I I I ki I X 2 or k z I I i | A I I I ! I 0 2 4 6 8 tO TIME FE(;. 2. Log linear intravenous drug disposition curve showing the biexponenUal decline in con- centration as a function of time. The slopes (;,o,).~, ;.,. or ;.:) and Heights (('~ and C., ) are part of the SHAM properties of the curve. Following a bolus intravenous dose (D), several model independent parameters can be determined to enhance the ability to individualize dosage regimens. The volume of the central distribution space (V1) (Riegelman et al.. 1968) is calculated from I/1 = D..Ho = D..52Ci (2) where H0 is the sum of the heights or zero time intercepts. The volume of distribution at steady-state (V,0 (Benet and Galleazzi, 1979) can be calculated from V,~ = D(AUMC..AUC2). (31 Equation (31 applies only to single dose administration when drug input is by a non-first- pass route and clearance occurs from the central compartment of a mamillary model. If an intravenous infusion is administered a correction must be made for the infusion time, linr V~ D'AUMC D'tin ~ = (AUC) z 2(AUC)' (4) The total plasma clearance (CL) (Rowland et al., 1973) from D CL - (5) AUC can be calculated for parenteral input. The total clearance is equal to the sum of all organ clearance processes CL = CL. + CL R + CLot.e r (6) where CL. is the hepatic clearance and CL R, the renal clearance. If the bioavailability, F. is known, the apparent oral clearance (CLp,,) following an oral dose, Dp,,, (Wilkinson and Sband. 1975) is CLI,,, = F' Dpo:AUC. (7)
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`Dosage regimen design 147 The above parameters have limited applicability in the selection of single doses since serum drug concentrations can be measured only after drug therapy has been initiated. However, if the volume of distribution is known or a reasonable estimate available (I/J, then the dose required to achieve a target concentration, C(o), can be calculated Dose = V~. C(o). (8) This relationship is useful when drug disposition is lengthy so that a single dose produces a sustained concentration within the presumed therapeutic range to achieve the treat- ment objectives. This situation may occur when clearance depends predominately upon an organ currently in a nonfunctioning state (Eqn 6) and is illustrated by the use of aminoglycoside antibiotics in severe renal failure. Here a single dose may provide tissue concentrations above the MIC for much or all of the required period of therapy. Equation (8) is useful to calculate the dose to attain the serum concentration that would result if drug input and distribution were instantaneous. However, a transient peak concentration higher than expected may occur when calculated intravenous doses are administered due to the time necessary for mixing and distribution. If used for oral doses, Eqn (8) will likely under-estimate the required dose to achieve a target concen- tration, especially if bioavailability is less than complete. 2.1.2. Multiple Bolus Doses The assumption of linearity implies that drug inputs are superimposible, i.e. a direct proportionality exists between drug concentration at any time and the size of the dose. It is upo n this principle of superposition that calculations involving multiple doses are possible. Additional assumptions are an equal dose administration at a constant interval and the condition that no time dependent changes in pharmacokinetics occur. Bolus doses are usually administered as either multiple dose intravenous therapy or oral doses. Equation (1) can be converted to describe C after N number of bolus doses by any route of administration /1 - e-~'~'~\ where t is the time lapse since the last dose, z is the dosage interval, and the parenthetical term represents the multiple dosing function developed by Dost (1953). At steady-state, when an infinite number of doses have been given, Eqn (9) reduces to C~., = _ C~ (10) i=! where C,, is the concentration of drug within a dosing interval at steady state. Assuming that each dose in a multiple dosing regimen is administered in the post- absorptive, post-distributive phase of the preceeding dose, all exponential terms approach zero in Eqn (10) except for the 2, term. Letting r equal the end of the dosage interval, the quotient of Eqns (10) and (1) indicates the degree of drug accumulation between the first dose and steady-state, the accumulation ratio, r Cmin(ss ) l r ..... ~ (11) Groin(l) 1 - e -;~ where Cm~n~t~ and Cm~n(,~ are the minimum plasma drug concentrations following the first dose and at steady-state, respectively. Equation (11) reveals that 2z and T are the most important factors controlling the accumulation of drugs and they can be assessed with the first dose. The accumulation ratio, r, is a nonlinear function of 2z and ~ but can be used, as explained below, in dosage selection. Design of multiple dosing regimens is facilitated by knowledge of )~z as it allows a calculation of the time for C to decline to any proportion of an initial concentration or
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`148 ('. .INDSAY DEVANI! and WILt.IAM J. Jt:sKo the time to accrue to any proportion of steady-state. During the terminal phase of drug disposition (following single or multiple doses), a C measurement is related to an initial measurement C(o) by the relationship C= C(o)'c '"' 12) where t is the elapsed time between the two measurements. Taking the natural logarithm of Eqn (12) In C = In C(o) - ).,.t (13) and solving for t In C/C(o) t = ¢14) --}'z The time for any proportional change in C to occur can be calculated by substituting in the quotient C/C(o). By convention, the time for C to decrease by one-half of the initial concentration, the half-life (ti), is In(½) 0.693 - = ..... . 115) t ~ -- ).z ).z Half-life derives its greatest utility in dosage regimen design by allowing a calculation of the time during a multiple dosing regimen to achieve a given proportion of steady-state. Taking the reciprocal of Eqn (11) yields the fractional attainment of steady-state after the first dose C,,i,~l~ _ 1 - e -~': (16) Cmin(ss) and after N doses Cn, l,o,'l - 1 - e - ; :1 ~ ''~ (I 7) Cmin(ss) Arbitrarily solving for the number of dosage intervals to reach 95% of steady-state (r' N95) 0.95 = 1 - e -;z"'~''~ (18) and Solving for rN95 In 0.05 = - 2~(r. N95 ). 3.0 z'N9~ = )-2 (19) and re-arranging Eqn (15) to substitute for )-2 3.0 t~ _ 4.32 t t . (20) r-N95 = 0.693 As the number of dosage intervals can be equated with absolute time, Eqn (20) indicates that between 4 and 5 half-lives are required to reach 95 .... .,, of the ultimate steady-state for any constant multiple dosing regimen. 2.1.3. Dosage and Interval The goal in selecting doses and intervals is to provide a guided accumulation of plasma concentration to a desired steady-state value. The equation which describes C~,
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`Dosage regimen design 149 upon multiple dosing is F.D = . (21) C, CL. z This equation is a mathematical generalization because steady-state concentrations are only momentarily attained for multiple dosing situations, at the time of peak and trough concentration--at other times, concentration is either rising or falling. The more appro- priate expression of what a measured C, represents is obtained by substitution of the dose:area quotient for clearance (Eqn 7) into Eqn (21) F. AUC Car - (22) T where C~v is the time averaged plasma concentration at steady-state. Dose and interval selection will control the magnitude of the peak and trough concentrations produced during multiple dosing, while half-life controls the time to reach steady-state. The therapeutic index (TI) is an integral part of this selection process. The selection of an initial or loading dose (L.D.) can be made by using Eqn (8) and selecting the desired steady-state concentration to be attained. L.D. = V.C~.~. (23) A maintenance dose (M.D.) may then be designed to replace the amount of drug elimin- ated A,, over a conveniently selected dosage interval Ael = 1 -- e -~,~ (24) e.g. substituting for ,;., (Eqn 15) and selecting the interval as equal to half-life Aej = 1 - e-l°693t0(t0 = 0.5. (25) This calculation indicates that half of the previous dose will be eliminated over the dosage interval, and forms the basis of commonly selecting a maintenance dose one-half the size of a loading dose. If the M.D. is administered every half-life, this should maintain a desired steady-state commencing with the first dose. This is an acceptable dosage regimen for drugs whose half-lives are intermediate (4-12 hr) and TI is high so that three to four doses can be administered daily. For drugs whose half-life is too short to correspond to a practical dosage interval, a larger dose size may need to be administered to maintain a desired Car. For a drug with a low TI the necessary dose might produce episodes of toxicity because of high peak concentrations. There is no problem for drugs like penicillins which have short half-lives and can be given in doses which produce peak concentrations greatly exceeding the MEC because they have such high TI s. An alternative for a drug with a short half-life and a low TI would be intravenous infusion. For long half-life drugs, once daily dosing is usually feasible when TI is high, but careful monitoring may be required to avoid toxicity when TI is low. For most therapeutically useful drugs, half-lives are in an intermediate range and thus several doses a day can be given to avoid high peaks and low troughs. The decision of whether a L.D. can be given must be determined by weighing the need of immediately attaining the MEC against TI considerations. 2.1.4. Intravenous Infusion Rather than administering multiple bolus doses, a continuous (zero order) infusion may be administered. This practice has the advantage that plasma concentration at steady-state remains constant without the fluctuations that occur with multiple oral doses or injections which should produce toxicity at the summit concentration and be ineffective at the nadir.
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`150 C.t.lyDsa'f Dt!V..xxl- and Wit.l lasl J. JtsK{~ At steady-state a proportionality exists between infusion rate lRo) and clearance C,~ = R0('L. 126) Equation 26 can be rearranged to solve for clearance, and R0 can be selected to achieve any targeted concentration Ro = (-'~" CL. (27) Plasma concentration at any time during the infusion to steady-state can also be calcu- lated Ro ~ =,) C = ~ (1 - e {28) if,;,, is known. This equation assumes monoexponential disposition but equations similar to this and the ones below apply to drugs with multiexponential disposition curves. If the infusion continues to steady-state, ).= may be determined by concentration measurements during drug accumulation. Substituting Eqn (27) into (28) gives C = C~(I - e -'=') 129) when re-arranged for e "= ' gives C ~;r; -- C~ ,~ = . t = e ~301 C~,,, A semilogarithmic plot of(C~ - (')."C~, versus time should be linear with a slope equal to -2z which can be converted to half-life with Eqn (15). Thus, without any prior knowl- edge of a drug's disposition in a particular patient, pharmacokinetic data may bc gath- ered to predict the dosage necessary to achieve a new steady-state and the time to attain it. The use of Eqn (30) requires absolute attainment of steady-state to be error free and the more usual method of determining ).: is to stop the infusion and assess wash-out data (Loo and Riegleman, 1970). This is the preferred method, especially for drugs which display multiexponential curves as it is less sensitive to distributional effects. Another commonly encountered clinical situation is stopping the infusion before steady-state is reached. Plasma concentration at any time during the infusion and after- ward can be determined R0 C= ~(1 - e-"="°')e ;=' 131) where t represents the time since the infusion was stopped. When pharmacologic effects are dependent upon attainment of some minimum plasma concentration, and half-life is long, a constant infusion may not be the most appropriate method of drug administration because of the time required to/:each steady-state. Several techniques have been devised to obviate this problem (Fig. 3). Generally, they consist of either bolus dose administration followed by an infusion, or a two-step infusion initiated by a rapid infusion before reduction to the maintenance rate. One approach is to select a bolus dose to rapidly achieve the desired steady-state Bolus Dose = C~. V (32) followed by a maintenance infusion based on Eqn (27). A difficulty with this technique is that C falls immediately, then slowly accrues to steady-state. An alternative which was employed in the design of theophylline dosage regimens (Mitenko and Ogilvie, 1972) was to prevent the fall from going below the MEC by using a larger bolus dose. This approach would not be satisfactory if the bolus produces a C associated with toxicity. The ideal concentration versus time profile can theoretically be achieved by using a bolus followed by an exponentially decreasing infusion rate (Kruger-Thiemer, 1968: Vaughan and Tucker, 1976).
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`Dosage regimen design 151 ~0 (~ ,5 TOXICITY ~ , Css 2 MEC I t I t Io I e 3 ~ 5 6 TIME, ~al f-byes FIG. 3. Theoretical time course of drug concentration from different intravenous dosage regi- mens. (F) maintenance infusion to steady-state ((_',~); (B) bolus dose to achieve C,~ followed by maintenance infusion; (C) bolus to maintain C above C,, combined with maintenance infusion: (A) bolus followed by exponentially decreasing infusion rate: (E) two-step infusion to maintain C above C,,; (D) two-step infusion to allow C to fall to a selected C~. The clinical situation may not always permit bolus dose administration. Wagner (1974) has developed equations for administering drugs which allow steady-state to be rapidly achieved with a loading infusion (Rot) and sustained with a slower infusion (Ro2), where and Ro2 = C~" CL (33) Ro2 Rot - 1 - e -':''"''°'' (34) where t~,,ot~ is the duration of Rot. The deviation from the ideal concentration profile with this technique is an early overshoot of C over C~. Although the peak C produced is not of the magnitude of that with bolus administration, a longer time elapse occurs before reaching C~,. This method has been successfully employed with procainamide (Lima et al., 1978). Equations for another two-step infusion method have recently been developed by Tsuei et al. (1980) which differ from the Wagner method by allowing C during R02 to decrease below C~, to a predetermined minimum before slowly increasing to C,.,. A lower maximum C during Rot can be achieved in this manner. Factors to consider in designing a multiple dosing regimen also apply to constant infusions (Table 1). 2.2. NONLINEAR DRUGS Drug transfer processes have a limit to their capacity. As a result, an increase in dose beyond some point may result in a noticeable change in a drug's concentration-time profile which is not superimposible on that after smaller doses. For example, a change may occur in the upcurve of drug concentrations with a lowered peak concentration, corrected for dose, if a limited capacity absorption process is exceeded. A change in the time of the peak drug concentration is also likely to occur. The descending phase of a concentration-time curve may be altered by nonlinear plasma protein binding or a dose which exceeds a capacity limited elimination pathway such as a biotransformation step or renal tubular secretion. The implications of these processes have been described (Levy, 1968). Some clinically used drugs which exhibit nonlinearity in the range of doses employed in humans are listed (Table 2) and others are likely to be identified with future pharmacokinetic studies. The perturbation of a minor kinetic process can go unnoticed with the usual array of pharmacokinetic data, yet have a profound clinical effect. Gibaldi et al. (1978) have recently shown that nonlinear tissue drug binding can occur concomitant with a change
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`152 C. I.INI)SAY DEVANF and W~t~tAM J. JtJsKo TABLE 1. Factors to ('onsider in De.~#tn ~71 Dru~l Do.~aye Re.qimen.s" Route of Administration 1. drug absorption characteristics 2. presence of presystemic elimination 3. accumulation of drug at absorption site, e.g. intramuscular depots 4. need for immediate onset of action 5. ease of administration 6. half-life: infusion may be necessary for drugs with short t~ or sustained release formulation 7. patient acceptance of route and dosage form Dose 1. therapeutic index: if high, consider benefits of loading dose 2. volume of distribution: to estimate peak plasma concentration 3. documented nonlinearity of pharmacokinetics 4. cost of medication 5. half-life: tapering of dose may not be necessary for some drugs with long t~'s 6. availability of treatment for overdose 7. existence of a therapeutic or toxic concentration range Dosage lnterral 1. half-life: dosage interval can generally be extended in relation to half-life 2. therapeutic index: the higher the TI, the longer an interval can be spaced with higher doses 3. body clearance: to evaluate accumulation 4. side effects which may require special administration times, e.g. bedtime to avoid sedation Complications 1. analytical methodology and reliability in monitoring ('~ 2. active metabolites 3. changing pathophysiology 4. drug interactions 5. auto or exogenous enzyme induction 6. development of pharmacodynamic tolerance 7. side effects not dose or concentration related 8. need for baseline concentration data with recent history of drug use in intrinsic clearance and no change in drug half-life. This finding suggests that an alteration in pharmacologic effects could result from changes in free concentration of drug available to exert effects at receptor sites without an observable change in the slope of serum concentration decline. A limitation in predictive pharmacokinetics is that the SHAM analysis yields parameters which are dose and time average values. They may represent the drug in a general sense, but may not apply to drug disposition at other doses, as a function of time, or as a function of plasma or blood concentrations. The Michaelis-Menten function is generally useful to characterize active biotransfor- marion or transport of drugs where limited enzyme capacity exists. The change in plasma concentration is represented as dC _ - Vma," C (35) dt Km + C" V TABt.E 2. Druas Which Exhibit a Nonlinear Pharmacokinetic Process in Humans Aspirin (Salicylic acid) Oxaprozin Cortisol Phenytoin Chlorpromazine Phenylbutazone Disopyramide Prednisolone Ethanol Prednisone Imipramine Propranolol Lidocaine Quinidine Mezlocillin Riboflavin Naproxin Theophylline Nortriptyline Valproic Acid
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`Dosage regimen design 153 30 ° 0 0 ! etx • • £x 200 400 600 B00 PHENYTOIN DOSAGE, mcj./doy Fie;. 4. Steady-state serum concentrations of phenytoin (DPH) at various daily doses in 5 patients (Jusko, 1976). A drug eliminated by first-order kinetics would show linear proportionality between dose/day and C,,. where Vm~x is the maximum rate of metabolism and K,. is the Michaelis--Menten con- stant. The importance of this equation to dosage regimen design is that C, changes disproportionately for a change in dose when a drug's elimination process is exceeded (Fig. 4). As many drugs are eliminated by more than one metabolic pathway, Eqn (35) may be more accurately represented with inclusion of a parallel first order process, e.g. renal clearance dC - CLR Vmax" C ~dt = v .c Kin+ C.V" (36) For drugs with a parallel zero and first order elimination, a steep increase in C, may also occur with an increase in dosing rate, but will eventually plateau (Tsuchiya and Levy, 1972). Quantitation of I/max and K,~ is possible by iterative computer methods (Wagner, 1973) when single doses of drug are administered or when the concentration-time curve can be observed over a broad range of concentrations. Ludden et al. (1976, 1977) and Mullen (1978) have devised a useful approach to employment of the Michaelis-Menten relationship to two or more interim Cmi.(s~) values for improved estimation of maintenance doses of phenytoin. This method can be easily employed using hand-held programmable calculators (Golby, 1978). Theoretically, dose calculations for nonlinear drugs can be made before Cm~,(~.~) is reached (Wagner, 1978). By obtaining Cm~n(N) data for several values of N after constant dosing has been initiated, a linear or parabolic extrapolation will predict Cm~n(~s) from a plot of Cm~,(N- 1) and Cm~,(N) differences versus Cm~n(N). The time to reach 95~o of steady-state can be calculated, or using an approach outlined by Lam and Chiou (1979), the time to reach any fraction of steady-state concentration. This knowledge could be especially helpful for phenytoin as computer simulations (Ludden et al., 1978) indicate that Cm~,(,) may not be reached in patients with usual values of Vm~x and K,, for at least a month of constant dosing. Caution is warranted in adjusting dosage regimens of any nonlinear drug because a seemingly small dosage increment can easily cause serum concentrations to rise to poten- tially toxic levels. 3. METHODS OF OPTIMIZING ADMINISTRATION Pharmacokinetic methods to design dosage regimens which rapidly and safely produce effective serum drug concentrations are potentially most reliable when a complete pharmacokinetic profile for the drug in question is available for the specific individual. Single dose data which can be computer fitted to Eqn (I) for derivation of model independent parameters is desirable but rarely obtainable. Initial dosage estimates and later adjustments are often derived from manufacturer's published recommendations,
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`154 C. ,INDSAY DEVANt. and Wu.t,lasl J. JLSKO previous experience, or one of the published predictive methods which span a broad range of sophistication. 3.1. SERUM CONCENTRATION FEFDBACK The simplest approach to adjustment of a dosage regimen is to obtain a serum concen- tration measurement at steady-state. For intravenous infusions, Ro can be changed to proportionally increase or decrease C~ according to Eqn 126) and dose or dosage interval can be manipulated according to Eqn (21) for multiple bolus doses. The