Читать книгу Physiologically Based Pharmacokinetic (PBPK) Modeling and Simulations - Sheila Annie Peters - Страница 36

Equation 1.50 suggests three different possibilities:

1 Metabolite disposition is formation rate‐limited (kel,M > kf,M ) – commonly observed

2 Metabolite disposition is elimination rate‐limited (kf,M > kel,M )

3 Neither of the two steps above are rate limiting

The first 2 cases are illustrated in Figure 1.9.

In the first case, when metabolite disposition is limited by its formation, the half‐life of parent is greater than that of its metabolite and the following equation holds:

(1.51)

CL_M is the clearance of the metabolite, CL_f,M is the metabolic clearance of the parent drug related to the formation of metabolite, V_M is the volume of distribution of the metabolite, and V is the volume of distribution of the parent drug. The PK profiles of the parent drug and its metabolite are characterized by parallel terminal slopes (see Figure 1.9). The metabolite is eliminated as soon as it is formed. Consequently, the right‐hand side of Equation 1.50 becomes zero leading to

(1.52)

Rearranging Equation 1.52,

(1.53)

If the parent and metabolite have similar volumes of distribution, according to Equation 1.51, the clearance of the metabolite is greater than that of the parent drug. Thus, the amount of parent drug in the body is always greater than the metabolite. If the volume of distribution of the metabolite is much smaller compared to that of parent drug, then according to Equation 1.51, it is possible that the ratio of the elimination rate constants of the parent and metabolite is ≫1, provided V_M /V is smaller than CL_M /CL_f,M . It is therefore not necessary that CL_M should be greater than CL_f,M . In other words, the amount of parent drug in the body need not be always greater than the metabolite, if the metabolite is polar and has a relatively low volume of distribution compared to the more lipophilic parent drug (see Figure 1.9). An example of this is propranolol where the amount of parent compound is less than that of the metabolite.

In the second case, the metabolite disposition is limited by its elimination and the half‐life of the metabolite is greater than that of its parent drug. This may lead to accumulation of the metabolite in the body and requires careful safety monitoring.

Lastly, in the event of comparable half‐lives of drug and metabolite, the terminal slope of the metabolite appears to decline slower than would be expected from its elimination rate constant, sustained by the parent drug.

Figure 1.9. Limiting conditions on metabolite disposition. (a) Formation‐limited metabolite kinetics when the volume of distribution of parent is similar to the volume of distribution of its metabolite. (b) Formation‐limited metabolite kinetics when the volume of distribution of parent is greater than the volume of distribution of its metabolite. (c) Elimination‐limited metabolite kinetics.