Introduction Biopharmaceutics history 2

Compartmental Methods
Clearance is a direct measure of elimination from the central compartment, regardless of the number of compartments. The central compartment consists of the plasma and highly perfused tissues in which drug equilibrates rapidly (see Chapter 5). The tissues for drug elimination, namely, kidney and liver, are considered integral parts of the central compartment.
Clearance is always the product of a rate constant and a volume of distribution. There are different clearance formulas depending on the pharmacokinetic model that would describe appropriately the concentration-versus-time profiles of a drug product.
The clearance formulas depend upon whether the drug is administered intravenously or extravascularly and range from simple to more complicated scenarios:
Drug that is well described pharmacokinetically with a one-compartment model After intravenous administration, such a drug will exhibit a concentration-time profile that decreases in a straight line when viewed on a semilog plot and would therefore be well described by a monoexponential decline. This is the simplest model that can be used and often will describe well the pharmacokinetics of drugs that are very polar and that are readily eliminated in the urine. Clinically, aminoglycoside antibiotics are relatively well characterized and predicted by a one-compartment model.
Cl = lz × Vss
where lz is the only rate constant describing the fate of the concentration-time profile and dividing 0.693 by its value, therefore, estimates the terminal halflife. Vss is the total volume of distribution, and in this case, there is only one volume that is describing the pharmacokinetic behavior of the drug.
Calculated parameters:
The terminal half-life of the drug is T1/2 = 0.693/lz
After oral administration the formula for clearance is exactly the same but a Cl/F is calculated. There is also an absorption process in addition to an elimination one. If the absorption process is faster than the elimination, the terminal rate constant, lz, will describe the elimination of the drug. If the drug exhibits a “flip-flop” profile because the absorption of the drug is much slower than the elimination process (eg, often the case with modified release formulations), then the terminal rate constant, lz, will be reflective of the absorption and not the elimination. It is sometimes not possible to know if a drug exhibits a slower absorption than elimination. In these cases, it is always best to refer to lz as the “terminal” rate constant instead of assuming it is the “elimination” rate constant.

Relationship with the noncompartmental approach after IV administration:

Therefore, MRT (mean residence time2) = 1/lz and Vss = Dose/(AUC0-inf × lz).
Relationship with the noncompartmental approach after extravascular administration:

MRT and Vss /F are not computable directly using noncompartmental methods after extravascular administration, but only MTT (mean transit time), which is the sum of MAT (mean absorption time) and MRT.
But we have seen that MRT = 1/lz and Vss/F =Dose/(AUC0-inf × lz). MAT can then be calculated by subtracting MRT from the MTT.
Drug that is well described pharmacokinetically with a two-compartment model
After intravenous administration, such a drug will exhibit a concentration-time profile that decreases in a profile that can be characterized by two different exponentials or two different straight lines when viewed on a semilog plot (see Chapter 5). This model will describe well the pharmacokinetics of drugs that are not so polar and distribute in a second compartment that is not so well perfused by blood or plasma. Clinically, the antibiotic vancomycin is relatively well characterized and predicted by a two-compartment model.
Cl = k10 × Vc (7.24)
where k10 is the rate constant describing the disappearance of the drug from its central volume of distribution (Vc).
The distributional clearance (Cld) describes the clearance occurring between the central (Vc) and the peripheral compartment (Vp), and where the central compartment includes the plasma and the organs that are very well perfused, while the peripheral compartment includes organs that are less well perfused.
The concentration-time curve profile will follow a biexponential decline on a semilog graph and the distributional rate constant (l1) will be describing the rapid decline after IV administration that describes the distribution process, and the second and last exponential (lz) will describe the terminal elimination phase.
The distribution (l1) and terminal elimination (lz) rate constants can be obtained with the following equations:

The distribution and terminal elimination half-lives are therefore:

The total volume of distribution Vss will be the sum of Vc and Vp:
Vss = Vc + Vp (7.25)
Relationship with the noncompartmental approach after IV administration:

Relationship between Rate Constants, Volumes of Distribution, and Clearances
As seen previously in Equation 7.24, Cl = k10 × Vc, which for a drug well described by a one-compartment model can be simplified to Cl = lz × Vss.
It is often stated that clearances and volumes are “independent” parameters, while rate constants are “dependent” parameters. This assumption is made in PK models to facilitate data analysis of the underlying kinetic processes. Stated differently, a change in a patient in its drug clearance may not result in a change in its volume of distribution or vice versa,

while a change in clearance or in the volume of distribution will result in a change in the appropriate rate constant (eg, k10, lz). While mostly true, this statement can be somewhat confusing, as there are clinical instances where a change can lead to both volume of distribution and clearance changes, without a resulting change in the rate constant (eg, k10, lz).

A common example is a significant abrupt change in actual body weight (ABW) as both clearances and volumes of distribution correlate with ABW.
A patient becoming suddenly edematous will not see his or her liver or renal function necessarily affected. In that example, both the patient’s clearance and volume of distribution will be increased, while half-life or half-lives will remain relatively unchanged. In that situation the dosing interval will not need to be changed, as the half-life will stay constant, but the dose to be given will need to be increased due to the greater volume of distribution and clearance.