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# pkmodel

### Introduction

The function pkmodel permits to define common PK models in a very concise way. The purpose of this macro is to simplify the modeling of classical pharmacokinetics. The PK model is inferred from the provided set of named arguments. Most of the arguments are optional, and the pkmodel function enables several parametrizations, to select different models of absorption, elimination, etc. With the pkmodel function, the most common PK models are available. The concentration within the central compartment is the main output of the function. If an effect compartment is defined, its concentration defines the second output. The administration of the doses is always supposed to be of type 1, and the default absorption is the IV bolus one. The label of the central compartment is 1. The pkmodel function can also be used within the block EQUATION: or the block PK:.

### Rules

• Only one central compartment is allowed
• Only one type of administration is allowed
• Only one pkmodel function is allowed in the Mlxtran file
• Arguments must be from the list of defined arguments for pkmodel. Arguments with different names are not recognised.
• pkmodel can not be used together with any macros for the administration. The administration is defined exclusively with the arguments supplied to pkmodel()
• pkmodel output can be used with ODEs or with macros.
• pkmodel can also be defined in the PK: block or the EQUATION: block.

### Examples

EQUATION:
Cc = pkmodel(V, Cl)


This simple set of named arguments for pkmodel defines a PK model with one central compartment of label 1, with the default iv bolus absorption for doses of administration type 1 and a linear elimination with the clearance parametrization in Cl. The volume of the central compartment is V. The concentration in the central compartment is the output Cc of the function. The following example shows a more complex PK model using the function pkmodel.

Example:

EQUATION:
{Cc, Ce} = pkmodel(Tlag, ka, p, V, Vm, Km, k12, k21, k13, k31, ke0)

This more complex set of named arguments for pkmodel defines a PK model of one central compartment, with a first order absorption of rate ka for doses of administration type 1, and a Michaelis-Menten elimination of parameters Vm and Km. The volume of the central compartment is V. The concentration in the central compartment is the first output Cc of the function. An effect compartment is defined with a rate ke0 and its concentration is the second output Ce. Two peripheral compartments of labels 2 and 3 are linked to the central compartment of label 1. The respective couples of exchange rates are (k12, k21) and (k13, k31). The first order absorption has a lag time Tlag and the absorbed amount is scaled with a proportion of p.

The complete set of named arguments and output for pkmodel follows. They belong to the central compartment, the absorption process, the elimination process, the exchanges with the peripheral compartments, or an effect compartment. Some arguments are mutually exclusive, or require other ones to be also defined. Most of them are optional, so the mandatory arguments are stated.

### Arguments for the central compartment

• Cc = pkmodel(…): The first output is the concentration within the central compartment. Another name can be used. Mandatory.
• V: Volume of the central compartment. Mandatory.

### Arguments for the absorption process of a standard PK model

• Tk0: Defines a zero order absorption of duration Tk0. Excludes ka, Ktr and Mtt.
• ka: Defines a first order absorption of rate ka. Excludes Tk0.
• Ktr: Along with ka and Mtt, defines an absorption with transit compartments, with transit rate Ktr. Excludes Tk0.
• Mtt: Along with ka and Ktr, defines an absorption with transit compartments, with mean transit time Mtt. Excludes Tk0.
• Tlag: Lag time before the absorption.
• p: Final proportion of the absorbed amount. Can affect the effective rate of the absorption, not its duration.
• default if no argument supplied for the absorption process: iv bolus

### Arguments for the elimination process of a standard PK model

• k: Defines a linear elimination of rate k. Excludes Cl, Vm and Km.
• Cl: Along with V, defines a linear elimination of clearance Cl. Excludes k, Vm and Km.
• Vm: Along with V and Km, defines a Michaelis-Menten elimination of maximum elimination rate Vm. Excludes k and Cl.
• Km: Along with V and Vm, defines a Michaelis-Menten elimination of Michaelis-Menten constant Km. Excludes k and Cl.

### Arguments for the peripheral compartments of a standard PK model

• k12: Along with k21, defines a peripheral compartment 2 of input rate k12.
• k21: Along with k12, defines a peripheral compartment 2 of output rate k21.
• k13: Along with k31, defines a peripheral compartment 3 of input rate k13.
• k31: Along with k13, defines a peripheral compartment 3 of output rate k31.

### Arguments for the effect compartment of a standard PK model

• {Cc, Ce} = pkmodel(…): The second output is the concentration within the effect compartment. Another name can be used.
• ke0: Defines an effect compartment with transfer rate ke0 from the central compartment.