Absorption Modeling of In Vivo Drug Behavior

The rate of change in the amount of drug in solution in an ACAT compartment depends on up to 10 interacting processes:

Release of drug in the compartment for controlled release dosage forms

Flow (transit) of dissolved drug into the compartment from the previous compartment,

Dissolution of solid drug particles

Precipitation of drug in solution

Degradation of drug in solution in the lumen

Absorption of drug into the enterocytes via the transcellular pathway

Exsorption of drug from the enterocytes back into the lumen

Absorption of drug into the portal vein via the paracellular pathway

Exsorption of drug from the portal vein back into the lumen via the paracellular pathway

Flow of drug out of the compartment

Every process that is occurring in every compartment either has an associated model that describes the process with a differential equation or is modeled by interpolating from relevant measured data. (In Figure 1-1, each arrow represents a process that can be modeled, and therefore a differential equation.) Most of the equations involve linear kinetics, which, in the context of the ACAT model, means that the rate of the process is directly proportional to the instantaneous amount of drug. Nonlinear (Michaelis-Menten) kinetics are used to describe saturable carrier-mediated transport, gut metabolism, and liver metabolism.

A transfer rate constant, k_t, that is based on the mean transit time for the compartment, determines the transit rate of drug in any compartment. A rate constant, k_D, which can be computed from standard formulation inputs and the instantaneous conditions (solubility, pH, fluid volume, and bile salt concentration) in the compartment, sets the time scale of the dissolution process. An absorption rate coefficient, k_a(i), that depends on the effective permeability of the drug (paracellular and/or transcellular) and the physiological Absorption Scale Factor (ASF) for the specific compartment sets the time scale that is associated with the absorption process in any compartment. The absorption rate coefficient is multiplied by the lumen volume of fluid for the compartment and the difference in concentration between the lumen and the enterocytes (for transcellular absorption) or between the lumen and the portal vein (for paracellular absorption) for the compartment. A rate constant, k_degrad, that is determined by interpolation from an input table of degradation rate (or half-life) vs. pH and the pH in the compartment sets the time scale for chemical/metabolic degradation in the lumen.

The fraction of dose that is absorbed is calculated as the sum of all drug amounts entering the enterocyte compartments and the portion of drug entering the portal vein via the paracellular pathway as a function of time, divided either by the dose, or, if multiple dosing is used, by the sum of all doses.

Gut metabolism within the enterocytes can result in loss of drug before it crosses the basolateral membrane into the blood, but this drug is still considered to be absorbed.