REPEATED ADMINISTRATION OF AN INHIBITOR 421 



where (I^Oq and (I„;)o are the initial concentrations of inhibitor and its 

 metabolic product in the body. The curves derived from these equations fit 

 quite accurately the experimental data and the various rate constants were 

 calculated for sulfisoxazole. Although there are many factors that may 

 modify these simple relationships, such an approach is valuable in provid- 

 ing a base from which more complex behavior may be derived. 



REPEATED ADMINISTRATION OF AN INHIBITOR 



Occasionally it is important to know the inhibitor concentration in the 

 animal body when the inhibitor is administered repetitively. Accumulation 

 of the inhibitor will occur to varying extents when the intervals between 

 administrations is shorter than the time required for complete disappearance 

 of the inhibitor from the body. Repeated dosage is one way in which the 

 inhibitor concentration in a tissue may be built up to high levels, without 

 the acute effects sometimes occurring when the total dose of the inhibitor is 

 given all at once. Such considerations are particularly important when an 

 inhibitor is being used to suppress a particular type of cell, as in the growth 

 inhibition of neoplastic cells. There are two basic questions: (1) what will 

 be the final concentration achieved upon repeated administration? and (2) 

 how long will it take to achieve this level or any particular concentration? 



The simplest situation is when the inhibitor is introduced suddenly 

 and disappears at a rate proportional to its concentration, the concentra- 

 tion at any time after the administration being given by (I) = (I)^ e~*' as 

 shown in Fig. 8-7. If a second administration of inhibitor is made while 

 the concentration is falling, the maximal concentration reached will be the 

 sum of that already present and the added inhibitor; for example, if the 

 second dose is given at time 10 in the case chosen, the concentration will 

 immediately rise to 13.7 mM, and if a third dose is given at time 20, the 

 level reached will be 15.05 mil/. Each additional dose will produce a pro- 

 gressively smaller increment to this maximal concentration until, for prac- 

 tical purposes, a constant level is reached. This is illustrated in Fig. 8-8, 

 where in the case chosen the maximal concentration of inhibitor is essen- 

 tially reached after the fifth dose. If the administration is stopped at 

 this point, the time taken for the concentration to fall to some designated 

 low level will be greater than after a single dose. 



It may easily be shown that the concentration level reached following 

 the nth dose will be (I)„ = (1)^ [1 + g-*'" + e -2*'« + ... + e-<"-i)^' "]. 

 This geometrical series may be written in its equivalent form: 



1 0-nkJt 



(I)n = (I). -. r-u- (8-30) 



