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# Basic syntax for equations

Introduction

Equations are implemented in the block EQUATION: of the [LONGITUDINAL] section. In this section parametric functions of the form $f(t;\phi)$ where $\phi$ is a vector of structural parameters can be defined.

Example

We consider in this example a model where a function f depending on a vector of parameters $\phi=(ka, V, k)$ is defined as: $f(t) = \frac{D, k_a}{V(k_{a} - k)}(e^{-kt} - e^{-k_{a}t})$

where D=100 is given.This example corresponds to the analytical solution of a one compartmental model with a constant rate absorption, a linear elimination and a dose at time 0.

DESCRIPTION: Model description with an analytical expression
[LONGITUDINAL]
input = {ka, V, k}

EQUATION:
D = 100
f = D*ka/(V*(ka-k))*(exp(-k*t) - exp(-ka*t))


The simulation is computed with Mlxplore using (ka=1, V=10, k=0.05). The result is shown in the figure below. One can see the variation of f w.r.t. time. Rules and Best Practices

• t is a reserved keyword and represents the time. t must not be defined in the model and the name t can not be used in the model for any other parameter or variable. All Mlxtran reserved keywords are listed here.
• Mlxplore only: make sure all your parameters are defined in the input = { } list so they become available in the user interface for the exploration of your model. By default, parameters are initialized at 0 and this value can be updated on the interface.