Saturation of the absorption rate

In some cases, for instance in case of transporter-mediated uptake, the absorption from the depot compartment into the central compartment can saturate. To model this phenomenon, one can replace the first-order rate of absorption by a Michaelis-Menten term.

Examples of drugs displaying a saturating absorption include Phenylbutazone, Naproxen, Chlorothiazide, beta-lactam antibiotics and are reviewed in:

Wood, J. H., & Thakker, K. M. (1982). Michaelis-menten absorption kinetics in drugs: Examples and implications. European Journal of Clinical Pharmacology, 23(2), 183–188.

Mlxtran model

To describe a saturable absorption, the depot compartment must be explicitly described and the model must be written as an ODE system. Below we present a one-compartment model with linear elimination and saturable absorption.
The depot macro permits to add the doses defined in the data set to the amount in the depot compartment. The Michaelis-Menten term is written using the amount of the depot compartment instead of the concentration as the volume needed to calculate the concentration is unidentifiable.

CODE

[LONGITUDINAL]
input={Vm, Km, V, Cl}

PK:
depot(target=Ad)

EQUATION:
t_0 = 0
Ad_0 = 0
Ac_0 = 0

ddt_Ad = -Vm*Ad/(Ad+Km)
ddt_Ac = Vm*Ad/(Ad+Km) - Cl/V*Ac

Cc = Ac/V

OUTPUT:
output = {Cc}