Introduction Biopharmaceutics history 2

Renal Clearance section of this chapter.
Noncompartmental Methods
Clearance is commonly used to describe first-order drug elimination from compartment models such as the one-compartment model, C(t) = Cp = Cp0e-kt in which the distribution volume and elimination rate constant are well defined. Clearance estimated directly from the area under the plasma drug concentration time curve using the noncompartmental method is often called a “model-independent” approach as it does not need any assumption to be set in terms of the number of compartments describing the kinetics or concentration-time profile of the drug under study.

It is not exactly true that this method is a “model-independent” one, though, as this method still assumes that the terminal phase decreases in a log-linear fashion that is model dependent, and many of its parameters can be calculated only when one assumes PK linearity. Referring to this method as “noncompart-mental” is therefore more appropriate.

The noncompartmental approach is based on statistical moment theory and is presented in more details in Chapter 25. The main advantages of this approach are that (1) clearance can be easily calculated without making any assumptions relating to rate constants (eg, distribution vs. elimination rate constants), (2) volume of distribution is presented in a clinically useful context as it is related to systemic exposure and the dose administered, and (3) its estimation is robust in the context of rich sampling data as very little modeling is involved, if any (eg, no modeling at steady-state data, and only very limited modeling by way of linear regression of the terminal phase after single dose administration).
Clearance can be determined directly from the time-concentration curve by formula
where D is the dose administered, F is the bioavail-ability factor associated with the administration route used of the drug product, and C(t) is an unknown function that describes the changing plasma drug concentrations.
Using the noncompartmental approach, the general equation therefore uses the area under the drug concentration curve, [AUC]∞0, for the calculation of clearance.

where AUC0-inf = [AUC]∞0 = ∫0∞Cp dt and is the total systemic exposure obtained after a single dose (D) until infinity.
Because [AUC]∞0 is calculated from the drug concentration-time curve from zero to infinity using the trapezoidal rule, no model is assumed until the terminal phase after the last detectable concentration is obtained (Ct). To extrapolate the data to infinity to obtain the residual [AUC]∞t or (Cpt /k), first-order elimination is usually assumed.
Equation 7.2 is used to calculate clearance after administration of a single dose, and where concentrations would be obtained in a rich sampling fashion until a last detectable concentration time point, Ct.
The AUC from time zero to t (AUC0-t) is often described as the “observed” AUC and calculated using the linear or mixed log-linear trapezoidal rule, while the AUC that needs to be extrapolated from time t to infinity (AUCt-inf) is often described as the “extrapolated” AUC. It is good pharmacokinetic practice for the clearance to be calculated robustly to never extrapolate the AUC0-t by more than 20%. In addition, it is also good pharmacokinetic practice for the AUC0-t to be calculated using a rich sampling strategy, meaning a minimum of 12 concentration time points across the concentration-time curve from zero to Ct. At steady state, when the concentration-time profiles between administered doses become constant, the amount of drug administered over the dosing interval is exactly equal to the amount eliminated over that dosing interval (t). The formula for clearance therefore becomes:

If the drug exhibits linear pharmacokinetics in terms of time, then the clearance calculated after single dose administration (Cl) using Equation 7.2 and the clearance calculated from steady-state data (Cl(ss)) using Equation 7.22 will be the same.
From Equation 7.22, it can be derived that follow ing a constant intravenous infusion (see Chapter 6), the steady-state concentration (Css) will then be equal to “rate in,” the administration dosing rate (R0), divided by “rate out” or the clearance:

where R0 is the constant dosing rate (eg, in mg/h), Css is the steady-state concentration (eg, in mg/L), and Cl is the total body clearance (eg, in L/h).