### Purpose

The elimination macros permits to define different elimination processes (linear or Michaelis-Menten) for compartments. Several eliminations can be defined for the same compartment.

### Arguments

Some arguments are common to the two elimination types, while some are specific to a linear or to a Michaelis-Menten type of elimination.

The arguments that are common to linear and Michaelis-Menten are:

- cmt: Label of the compartment emptied by the elimination process. Its default value is 1.
- V: Volume involved in the elimination process. When not specified, its default value is the volume of the compartment defined by cmt.

Additional arguments are needed to define a linear or Michaelis-Menten elimination type.

### Arguments specific to a linear elimination

The use of one of the following additional arguments defines a linear elimination:

- k: Rate of the elimination.
- Cl: Clearance of the elimination.

Only one of k or Cl must be defined.

Note, that if no volume has been defined for the compartment and no volume has been defined for the elimination process, then the default volume V=1 is assumed.

*Example*:

PK: elimination(cmt=1,k)

### Arguments specific to a Michaelis-Menten elimination

The use of both of the following additional arguments defines a Michaelis-Menten elimination:

- Vm: Maximum elimination rate. The unit of Vm is amount/time.
- Km: Michaelis-Menten constant. The unit of Km is a concentration.

Both arguments must be defined.

*Example*:

PK: elimination(cmt=1, Vm, Km)

**Example with Mlxplore : Comparison of the two eliminations**

In the following example, the difference between the two elimination processes is demonstrated. The model is implemented in the file elimination.mlxplore.mlxtran, available in the Mlxplore demos and shown below:

<MODEL> [LONGITUDINAL] input = {k, Vm, Km} PK: compartment(cmt=1, amount=Alin, concentration=Cc_lin) elimination(cmt=1, k) iv(cmt=1, adm=1) compartment(cmt=2, amount=AMM, concentration=Cc_MM) elimination(cmt=2, Vm, Km) iv(cmt=2, adm=2) <DESIGN> [ADMINISTRATION] adm_lin = {time=5, amount=1, adm=1, rate=.5} adm_MM = {time=5, amount=1, adm=2, rate=.5} <PARAMETER> k = .5 Vm = 2 Km = .5 <OUTPUT> grid = 0:.05:20 list = {Cc_lin,Cc_MM} <RESULTS> [GRAPHICS] p = {y={Cc_lin,Cc_MM}, ylabel='Concentrations', xlabel='Time'}

The two concentrations are presented in the following figure, with the linear elimination in purple and the Michaelis-Menten elimination in light blue.

One can clearly see the nonlinearities in the Michaelis-Menten elimination process.

**Example: PK model with dual elimination pathways**

The following model implemented with PK macros includes two compartments, an oral absorption and a dual elimination pathway with parallel linear and Michaelis-Menten eliminations. An equivalent model, implemented with ODEs, is defined in the TMDD model library: it corresponds to the Michaelis-Menten approximation of a TMDD model.

[LONGITUDINAL] input = {ka, V, Vm, Km, Cl, Q, V2} PK: kel = Cl/V k12 = Q/V k21 = Q/V2 compartment(cmt=1, concentration=Cc, volume=V) absorption(cmt=1, ka) peripheral(k12, k21) elimination(cmt=1, k=kel) elimination(cmt=1, Vm, Km) OUTPUT: output={Cc}

### Rules and Best Practices:

- We encourage the user to use all the fields in the macro to guarantee no confusion between parameters
*Format restriction (non compliance will raise an exception)*- The value after cmt= is necessarily an integer.
- The value after V=, k=, Cl=, Km=, Vm= can be either a double or be replaced by an input parameter. Calculations are not supported.