With an intravenous bolus, a continuous level of drug is not maintained in the body. If this is necessary, an infusion has to be administered. As the drug is infused over a longer period of time, the concentration will rise until the absolute amount removed from the body is exactly the same as the amount that is infused. This situation is called steady-state.
Infusion rate (IR) = (CA - CV) · Q
If both terms of the equation are divided by the arterial concentration near the clearance mechanism, the equation is now:
IR / CA = (CA - CV) · Q / CA
Since the right term (CA - CV) · Q / CA is equal to the Clearance, the equation is as follows:
IR / CA = Cl
As this system is in steady-state, the concentration is not changing and this means that the arterial concentration near the clearance organ is equal to the steady state concentration.
IR / Css = Cl or IR = Cl · Css or Css = IR / Cl