### Description

In the [LONGITUDINAL] sections the structural model and the observation model (error model) are described.

### Scope

The [LONGITUDINAL] section is mandatory for all Mlxtran models for Monolix, Mlxplore and Simulx.

### Inputs

The input = { } list of the [LONGITUDINAL] section declares the variables that were defined outside of the [LONGITUDINAL] section and enables them. These parameters are obtained from either the calling software itself (e.g. Monolix), or the [INDIVIDUAL] section. For Monolix all parameters in the input = { } list define the parameters that are estimated or used as regressor variables. The following example shows how the inputs are declared for 4 parameters.

[LONGITUDINAL] input = {V1, V2, Cl, reg_var1} reg_var1 = {use = regressor}

### Outputs

The output and table lists in the OUTPUT: block declare variables whose values are exported for the various tasks. The keyword ** output** declares the main variables to output (which can be mapped to the data), whereas table declares the variables to record in tables.

OUTPUT: output = {y1, y2, y3} table = {Ap, Rin}

For Monolix, the * output* list identifies the predictions or the modeled outputs that are fitted against the data set observations. In case of several outputs, the order of the model predictions in the output list must match the alphabetical order of the observation identifiers used in the column-type YTYPE of the data set.

The parameters or variables listed in the table list are outputted in the result folder of Monolix.

Note that it is not allowed to do calculations directly in the output or table statement.

### Usage

Along with the input= and the OUTPUT: block detailed above, [LONGITUDINAL] section can contain three different blocks. The PK: block permits to define PK models using macros, and to link the administration information of the data set with the model. The EQUATION: block is for mathematical equations including ODEs and DDEs. The DEFINITION: block is used to define a random variable and its probability distribution. The OUTPUT: block contains the [LONGITUDINAL] section outputs. In the following, the different possibilities of the [LONGITUDINAL] section are explained in detail:

### Structural model description using PK: and EQUATION:

Administration definition and PK modelling with the PK: block: Macros for flexible PK model definition

Dynamical system modeling with the EQUATION: block.

### Observation model description using DEFINITION:

Observation models for continuous data

Observation models for discrete data

### Rules and differences between software

- There are reserved keywords that cannot be used as names for other parameters.
- Mlxtran is a declarative language, not an imperative language. Therefore equations are mathematical definitions rather than a series of instructions.
- Mlxtran differences between Monolix and Simulx

### Library of models and macros

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. It is complementary to models that are not in the library, and/or if the user want to combined it with other models.

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.

In addition to the macros, Lixoft is providing model library to simplify the use of the software by decreasing the necessity of coding.

### PK/PD model library

These libraries provide all the classical pharmacokinetic and pharmacodynamic models. The pharmacometric models allows to model several types of administrations (IV bolus, infusion, zero and first order absorption), any number of compartment (between 1 and 3), several elimination process (linear and Michaelis-Menten), and to manage lag-time. In addition, the some usual pharmacodynamical models are proposed.

To see the compete description, see here.

### Target-mediated drug disposition (TMDD) model library

An introduction to the TMDD concepts, the description of the library’s content, a detailed explanation of the hierarchy of TMDD model approximations, and guidelines to choose an appropriate model is proposed here along with the model library.

The library contains a large number of TMDD models corresponding to different approximations, different administration routes, different parameterizations, and different outputs. In total 608 model files are available.