Formulations

In the building block Formulation the properties of the dosage form that is administered can be defined. Most of the predefined formulations are related to formulations typically administered via the oral route, whereas others, such as the Zero Order and the First Order release functions, can technically be administered into any other compartment. Please note that not all combinations of formulations and administration routes are possible. For an intravenous administration (bolus and infusion), formulation is not required as a drug administered intravenously is assumed to be dissolved in a medium.

Definition of new Formulations in PK- Sim®‌

To create a new formulation, do one of the following:

• Click on Formulation in the Create Group of the Modeling Tab, or

• Right mouse click on Formulations in the Building Block Explorer and select Add Formulation..., or

• Use the short cut Ctrl+Alt+F.

A dialog will open where the properties of the formulation can be defined.

The formulation is initialized by giving it a Name in the respective input field. The name is used to identify the formulation when its parameters are saved in the project and/or as a template. The name is also used for identification of the formulation in the simulation.

For the different types of empirical or user-defined release functions, the dissolution curve will be depicted in the adjacent graph as fraction of dose dissolved vs. time.

For Particle Dissolution, the dissolution function represents the result of the mechanistic dissolution model of the Noyes- Whitney type in combination with the physiological conditions, rather than an input function. Thus, the dissolution properties do not only change as a function of the physico-chemical properties of the drug and the formulation characteristic, but also with the physiological conditions of the individual or animal. The resulting fraction dissolved as a function of time within the intestinal segments represents a simulation output that can be displayed in the Results Window of the simulation (see Shared Tools - Chart Component).

From the drop-down menu you can choose from the following predefined formulations:

• Dissolved

• Weibull

• Lint80

• Particle Dissolution

• Table

• Zero Order

• First Order

In the following sections, the different formulation types are described in more detail.

Dissolved‌

Using this type of formulation the drug is assumed to be administered in solution. Therefore, the whole amount of drug becomes available for absorption directly after the administration.

Weibull‌

The Weibull function can be used to empirically (i.e., not mechanistically) describe the dissolution behavior of various dosage forms. The Weibull function can fit almost any kind of dissolution curve and is often used to describe experimental data when the mechanism of the release is not known [7] [30].

When applied to drug dissolution and release from pharmaceutical dosage forms, the Weibull function expresses the accumulated fraction of the drug $m$ in solution at a time $t$ according to the following equation [40]:

$m=1-\exp(\frac{-(t-T_{lag})^b}{a})$

where $a$ is the scale parameter, defining the time scale of the process, $T_{lag}$ the lag time before the onset of the dissolution or the release process, and $b$ the shape parameter characterizing the curve as either exponential ($b = 1$), sigmoid ($b > 1$), or parabolic ($b < 1$).

The following parameters have to be defined when choosing the Weibull function:

• Dissolution shape $b$ characterizing the curve as either exponential ($b = 1$), sigmoid ($b > 1$), or parabolic ($b < 1$).

• Dissolution time (50% dissolved) defining the time (excluding the lag time) at which 50% of the administered dose is dissolved and, thus, corresponding to the scale parameter $a$ of the Weibull function.

• Lag time $T_{lag}$ characterizing the time after which dissolution begins.

• Use as suspension: if selected, the formulation will disintegrate in the stomach and the disintegrated particles will migrate along the gastrointestinal tract compartments. Particle dissolution formulation is always treated as a suspension per construction. If, on the other side, this option is not selected, the tablet will be treated as nondisintegrating tablet with discrete transition in the different intestinal compartments.

Please note that the Weibull function can only be combined with the Administration type Oral.

Lint80‌

The Lint80 is an empirical function assuming linear release until 80% of the administered dose is dissolved. This type of formulation can only be combined with the Administration type Oral.

The following parameters have to be defined when choosing the Lint80 function:

• Dissolution time (80% dissolved), defining the time (excluding the lag time) when 80% of the administered dose is dissolved.

• Lag time characterizing the time after which dissolution starts.

• Use as suspension: if selected, the formulation will disintegrate in the stomach and the disintegrated particles will migrate along the gastrointestinal tract compartments. Particle dissolution formulation is always treated as a suspension per construction. If, on the other side, this option is not selected, the tablet will be treated as nondisintegrating tablet with discrete transition in the different intestinal compartments.

Particle Dissolution‌

Particle Dissolution calculates the dissolution kinetics of spherical particles with a predefined particle size distribution based on the Noyes-Whitney approach. The details of the mechanistic dissolution model have been described by Willmann et al [102]. In PK-Sim®, the particle dissolution can only be combined with the Administration type Oral. To simulate the particle size dependent dissolution, the following formulation-dependent parameters have to be defined:

• Thickness (unstirred water layer) - thickness of the diffusion layer.

• Type of particle size distribution - monodisperse or polydisperse.

• Particle radius (mean).

For the polydisperse type of particule size distribution, the following additional parameters can be defined:

• Particle size distribution: either normal or log normal.

• Particle radius (min): the lower limit for the particle radius.

• Particle radius (max): the upper limit for the particle radius.

• Number of bins.

For normal distribution:

• Particle radius (mean)

• Particle radius (SD): Standard deviation of the particle radius.

For log normal distribution:

• Particle radius (geomean).

• Coefficient of variation.

In addition, in order to use the Particle Dissolution formulation, the drug-related parameters have to be defined in the Advanced Parameters tab of the Compound Building Block. These include:

• Aqueous diffusion coefficient.

• Density of the drug material, and the threshold for immediate dissolution. Further, you will have to indicate how the precipitated amount should be treated (either as soluble or insoluble).

Table‌

Table defines the amount of drug applied per unit time as a continuous function. You can either manually specify time and fraction of the applied dose values or import dissolution data from Excel®.

In order to manually enter the values:

• Click on Add Point to add a new row to the table

• Enter appropriate values for Time and Fraction (dose) dissolved

In order to import experimental dissolution data from Excel®:

1. Click Import Formulation

2. Select and open the Excel® file

3. Import and transfer the appropriate Excel® sheet

• Use as suspension: if selected, the formulation will disintegrate in the stomach and the disintegrated particles will migrate along the gastrointestinal tract compartments. Particle dissolution formulation is always treated as a suspension per construction. If, on the other side, this option is not selected, the tablet will be treated as nondisintegrating tablet with discrete transition in the different intestinal compartments.

Zero Order‌

Zero Order defines the application at a constant rate. The total dose (defined in the administration protocol) will be administered at a constant rate until within the specified time [Start of administration, Start of administration + (End time)].

First Order‌

First Order defines the application as a first order input. The required input is the half-life of application value (t1/2). The formulation release is then described by the following equation:

$\frac{dA}{dt}=-k\cdot A$

where $A$ is the amount of drug at time $t$ and $k$ the first order rate constant calculated from the half-life of application value according to:

$k=\frac{\ln(2)}{t_{1/2}}$

Setting or Changing Formulation Properties‌

To set or change the properties of an existing formulation:

1. Right mouse click on the respective formulation in the Building Blocsk Explorer

2. Select Edit...

or simply double click on the formulation in the Building Blocks Explorer

The window with the properties of the formulation will open. The properties can be set or changed appropriately. The changes are saved by closing the window by clicking on .

Cloning Formulations‌

To clone a formulation in the project:

1. Right mouse click on the respective formulation in the Building Blocks Explorer

2. Select Clone...

3. Set an alternative name for the formulation clone and enter a description, if desired.

4. Confirm and close the window by clicking OK .

Formulations as Templates‌

For each project, a number of formulations can be defined. They can be saved as a template and then be shared among several projects and users.

To save an existing formulation as template:

1. Right mouse click on the respective formulation in the Building Block Explorer

2. Select Save as Template...

In case a formulation with the same name already exists, a warning appears and you have the following opportunities:

• Override: This action will override the existing template.

• Save as: You can save the formulation under a different name. In this case, you will be asked to Rename the new template.

• Cancel: This action will abort the saving process.

To load an existing formulation from the template database:

1. Right mouse click on Formulations in the Building Blocks Explorer

2. Select Load From Template...

3. Select the desired formulation from the user templates

In case a formulation with the same name already exists in the project, a warning appears and you will have to Rename the formulation that is to be loaded from template.

1. Click OK

The selected formulation will appear in the Building Blocks Explorer view.

In addition, formulations can be directly loaded from the template database within a simulation (see Simulations).

Deleting Formulations‌

To delete a formulation from the project:

1. Right mouse click on the respective formulation in the Building Blocks Explorer

2. Select Delete...

3. Confirm to by clicking Yes