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Multiple Dose Regimens:
Multiple Dose Regimens:
The pharmacokinetic aspects of treatment schedules that involve more than one dose of a drug are discussed below. The relationships described involve assumptions of instantaneous intravenous administration and distribution of a drug that is eliminated by first-order kinetics from a single-compartment system, and is given in equal doses at equal time intervals. The relationships become less accurate in describing real situations to the extent that the real systems depart from the ideal model, i.e. to the extent that ka is not much greater than kel, and to the extent that Vda is not much smaller than Vdb.
When equal doses are administered at equal intervals, the peak plasma concentration after the nth dose, Cmax,n is given by the relationship:
Cmax,n = C0 (1 - f n)/( l- f)
The "trough" concentrations (Cmin) for the two conditions are:
Cmin,n = Cmax,n - C0, and
Css,min = Css,max - C0, respectively.
Knowing the half-life of a drug and the Css,max and Css,min desired to produce optimum therapy, the dose interval, t (tau), necessary to achieve and maintain these maximum and minimum concentrations can be determined from the relationship:
t= 1.443 (t1/2) ln(Css,max/Css, min).
(Remember that ln X = 2.303 log X, that t1/2 = 0.693/kel, and that 1/0.693 = 1.443.)
The doses to be administered at intervals, t, to produce the desired Css,max and Css,min are inferred from experimental data relating the size of single doses to the peak plasma concentrations (Cmax) each produces, or are estimated from the relationship F · D/Vd = C, when the Vdand F of the drug are known. (The relationship among Css,max, Css,min and expected therapeutic outcome, including occurrence of side effects, are inferred from dose-effect relationships established in clinical pharmacologic experiments.)
With repeated doses, at equal intervals, peak plasma concentrations (Cmax) approach but, in theory, never reach Css,max. In practice, it is useful to know how long it takes for Cmaxto reach some specified level with respect to Css,max, i.e., how long it takes for Cmax/Css,max to reach, say, 0.95. Knowing the expected value of Css,max and the fractional achievement desired, e.g. 0.95, it is easy to compute the desired Cmax. Then, knowing the dose interval, t, and the half-life of the drug, the time required to reach the desired Cmax is given by the relationship:
nt = 1.443 ( t1/2) ln [(Css,max - Cmax)/Css,max]
where the time required (nt) is expressed as the product of the number of doses and the duration of the dose interval (t). The number of doses required to achieve the desired ratio of Cmax to Css,max may be determined by dividing the right hand member of the equation by the length of the dose interval.
When t is long, relative to t1/2, many doses may have to be given, and much time may have to pass if a reasonable fraction of Css,max is to be achieved by administering identical doses at equal interval. Under such circumstances, prompt achievement of therapeutically effective blood levels may require beginning the treatment regimen with a "loading dose" (q.v.).
Cf. Cmax, Css, Infusion Kinetics, First-Order Kinetics, Compartment
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