last updated 11-12-2023

#### Clearance = Dose / AUC

The relationship between Dose and concentration can be calculated independent of time. This now produces the most important formula of kinetics and is the basis of the linear relationship between dose and the Area Under the Curve (AUC). Remember that this only holds if the clearing organs remove a fixed percentage of the amount of drug offered to the organ, in other words, if the extraction ratio is constant.

(CA - CV· Q / CA = CL

• CA=arterial concentration
• CV= venous concentration
• Q = Blood flow
• CL = Clearance

Both sides can be multiplied by CA:

(CA - CV· Q / CA · CA = CL · CA

(CA - CV· Q  = CL · CA

If the left side of the equation is added up to infinity it equals the dose. Why? Because (CA - CV·corresponds to the amount that is removed. Is this amount is determined for all time points (until 'infinity', when all drug has left the body), then all these amounts added up correspond to the total amount that should have entered the body in the first place, which equals the dose.  In addition, If we do the same approach for the right side, with all the arterial concentrations (CA) added up to infinity, all these plasma concentrations added up for each time point is equal to the area under the plasma concentration vs time curve: the AUC. Thus, the complete right side of the equation is equal to clearance times the AUC:

Dose = CL · AUC      or      CL = Dose / AUC

Note that if the Dose vs AUC is not a straight line, this is an indication for non-linear kinetics, often related to saturation of one of the ADME aspects. For example, if a small increase in dose leads to saturation of the metabolism, this immediately leads to a sharp increase in AUC. A clinical relevant example is phenytoin dosing.

Here are some challenging thoughts. All of them are true:

• If the clearance is diminished by half and the absorption kinetics remain the same, the AUC doubles after all administration.
• If the volume of distribution doubles, then:

• the half-live doubles
• it takes longer to reach tmax
• the maximum concentration (Cmax) is lower.
• the AUC of both curves remain equal.

1

You are called to the renal department, because patient A developed tremor, confusion, agitation and headache. Next to patient A lies patient B, who is doing fine. You are struck by the fact that both had a kidney transplantation on the same day, and both are prescribed the exact same oral dose of sirolimus. As usual, Therapeutic Drug Monitoring of sirolimus was performed in both cases, and you notice that the AUC in patient A is 3 times higher than in patient B.

The diagnosis seems clear, but what is the best possible explanation for these differences between patient A and B?

2

Phenytoin is known for its non-linear dose-concentration relationship in the clinically relevant dosing range. This is quite commonly the case when saturation of a specific ADME-aspect is playing a role. What could be a reasonable explanation for the non-linear relationship at higher doses of phenytoin?