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:

### 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.

[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}

### Exploration with Mlxplore

We explore the difference between a linear and a saturating absorption using the following Mlxplore script:

<MODEL> [LONGITUDINAL] input={Vm,Km,ka,V,Cl} PK: ; depot for saturating absorption depot(target=Ad) ; model for linear absorption Cc_lin = pkmodel(ka,V,Cl) EQUATION: ; model for saturating absorption 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_sat = Ac/V <PARAMETER> Vm = 10 Km = 10 V = 15 Cl = 1 ka = 0.25 <DESIGN> [ADMINISTRATION] adm = {time=0, amount=100} <OUTPUT> list={Cc_sat, Cc_lin} grid=0.1:0.1:50 <RESULTS> [GRAPHICS] p1 = {y={Cc_sat,Cc_lin}, ylabel='Concentration', xlabel='time'}

Below the linear absorption is shown in blue and the saturating in orange: