Repetitive Intravenous Dosing

The series can be carried further for more doses:

C_P2^T = (C_P1^OR + C_P1^O)R

C_P3^O = (C_P1^OR + C_P1^O)R + C_P1^O

C_P3^T = [(C_P1^OR + C_P1^O)R + C_P1^O]R,...,etc.

The nth dosing interval has plasma concentrations at the beginning and end equalling:

Beginning = C_P1^O + C_P1^OR + C_P1^OR² +...+C_P1^OR^n-1

End = C_P1^OR + C_P1^OR² + C_P1^OR³ +...+C_P1^ORⁿ

R is always smaller than 1 and so Rⁿ becomes smaller as n increases.  High power terms therefore become neglible as n increases.  Additional doses to the system will not change the value of C_Pn^O or C_Pn^T significantly and so is why the plasma concentrations reach a plateau instead of continuing to rise as more doses are given.  Hence, we define C_max and C_min as the plasma concentrations at the beginning and end, respectively, of the nth dosing interval after the plateau has been reached.  When n = infinity,

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B.9b-2