One-compartment open model for repeated intravenous administration

5 One-compartment open model for repeated intravenous administration 

It is readily observed that the expression within brackets for the peak concentration C forms a geometric progression in which the first term equals one and with a common ratio of e . (The common ratio is the factor which results from dividing a term of the progression by its preceding one.) For the sum of the finite progression in eq. (39.41) we obtain after n cycles  

In the case of a sufficiently large number of cycles n we thus find that the peak and trough values approach their respective steady-state values and C  

Usually, one has obtained an estimate for the elimination constant and the distribution volume Vp from a single intravenous injection. These pharmacokinetic parameters, together with the interval between administrations 0 and the single-dose D, then allow us to compute the steady-state peak and trough values. The criterion for an optimal dose regimen depends on the minimum therapeutic concentration (which must be exceeded by and on the maximum safe 

In the limit, when the interval 0 between administrations becomes extremely small in comparison with the elimination half-life 0.693/kp, the steady-state solutions are reduced to those already derived for a continuous intravenous infusion (eq. (39.35))  

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