Creating Populations

The properties of a population of individuals can be defined in the building block Population using the physiological database of PK-Sim®.

• In case of the various animal species, no age-dependent distribution information for the anatomical and physiological parameters is included in the database so far. The algorithm generates random values in the [Minimum Weight, Maximum Weight] interval defined by the user. The generation of a population is done by linear scaling of an average animal of the given species. This means that all organs always contribute to the same extent to the total body weight without taking into account differences related to, e.g., growth, or to different races of the respective animal species.

• For humans, the population parameters database that comes with PK-Sim® includes information on the dependence of anatomical and physiological parameters relevant for PK-Sim® such as organ weights, blood flow rates, or tissue composition on age, gender, body weight, and body mass index, which have been collected in a comprehensive literature search. The algorithm generating a population then involves the following steps which are repeated until the target number of individuals is reached [97]:

A list of individuals is created with the proportion of males and females as defined by the user. For each individual, the algorithm tries to create a parameter set that fulfills the defined criteria (for more detailed description of the algorithm, see Create Individual Algorithm):

1. An Age value is drawn from a uniform random number distribution in the [Minimum Age, Maximum Age] interval.

2. For the Age assigned above, a Height value is randomly generated according to the height distribution defined in the database for the given Age.

3. The generation of the Height value might fail (i.e., the generated Height is not within the [Minimum Height, Maximum Height] interval for Age drawn in 1.). In that case, the algorithm tries to perform steps 1. and 2. again. After a maximum of 100 attempts, it is assumed that no data is available in the database matching the user inputs, and an exception is thrown.

4. With Age and Height defined, the algorithm tries to create a random individual based on these values. The resulting body Weight should be in the [Minimum Weight, Maximum Weight] interval. The organ volumes are randomly generated according to their organ volume distributions. If the resulting body weight, i.e., the sum of all organ volumes times their density, is in the specified [Minimum Weight, Maximum Weight] interval, the individual is kept. If not, another individual is generated. This step is repeated up to 100 times. If then still no individual with a body weight within the [Minimum Weight, Maximum Weight] interval is found, an exception is thrown.

5. The volume fractions of protein, water, and lipids of different organs are scaled according to the value defined in the database for the given age.

6. Finally, all parameters other than organ volumes for which distributions are available in the database (e.g., blood flow rates, hematocrit, etc.) are being randomly generated according to their distributions.

7. Finally, the algorithm checks that the BMI value corresponding to the generated Height - Weight combination is within the [Minimum BMI, Maximum BMI] interval, which is either defined by the user, or queried from the database for the generated combination of age and weight. If so, the individual is added to the population. If not, the individual is discarded.

The following figures show, as an example, the age dependency of the body weight, body height, and body mass index distributions for a certain population (white males). The data were taken from the NHANES study [82].

Definition of new Populations in PK- Sim®‌

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

• Click on Population in the Create Group of the Modeling & Simulation Tab, or

• Right mouse click on Populations in the Building Block Explorer and select "Add Population...", or

• Use the shortcut Ctrl+Alt+P

A dialog box will open where the properties of the population can be selected and/or defined. The Create Population dialog is subdivided into four tabs: Demographics, Expression, User Defined Variability, and Distribution.

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

Demographics‌ tab

In the first drop-down menu (Based on individual) you can specify an Individual that you previously defined in this project, specify the number of individuals in your population, and the percentage of females therein (only for humans). Further below, the Population Parameters Ranges can be set, i.e., the anthropometry of the individuals can be constrained, at the lower and/or upper ends of the ranges for the different properties.

If no individual has been defined, you can:

• Create a population based on an individual saved as a template:

  • Click on Load in the Demographics tab next to the Based on individual drop-down menu.

  • Select the individual from User Templates or the Predefined Templates

  • Click OK

  • If the name of the Individual loaded from template is already used in the project, a new name has to be defined.

• Create a new individual which serves as a basis individual for the population:

  • Click on Create

  • Define the properties of the Individual. For details see PK-Sim® - Creating Individuals.

If a human population is selected, the following parameters can be defined in the Population Parameters Ranges section:

• Age: The age range in units of year(s), month(s), week(s), or day(s).

The population database contains physiological information starting from preterm newborns to newborns (age "0") to 80 year old (100 years old for the European (ICRP, 2002) population) individuals. When a pediatric or an elderly population is simulated, only the age dependence of anatomical properties (size of the organs, blood flow rates, body composition, etc.) is considered. However, important pharmacokinetic differences in children and elderly can be caused by age-related differences in, for example, hepatic metabolic activity. These effects are automatically accounted for if the ontogeny of the elimination process has been defined in the Expression tab for the underlying Individual. To manually account for variations in elimination, use the User Defined Variability tab.

• Height: The range of body heights of the individuals in units of cm or m.

• Weight: The range of body weight of the individuals in units of kg or g.

• BMI: The range of body mass index of the individuals in units of kg/m2.

The BMI is a measure for the human fat content. It is given by the individual's height (H) and body weight (BW) according to the equation $BMI = \frac{BW}{H^2}$.

If the population Preterm is selected, an additional age scale has to be taken into account. Preterm neonates are characterized by their gestational age (GA), which ranges between about 24 and 37 weeks, and their postnatal age (PNA, what we usually refer to as "Age"). In the model, preterm neonates catch up growth during their first two years of life so that there are no differences between a > 2 year old individual of the same race and gender born either preterm or term.

Expression tab

In the tab Expression, proteins that should be expressed in the population can be defined. See section PK-Sim® - Expression for details on how to define the expression of proteins in an individual.

User Defined Variability tab

In the User Defined Variability tab, further physiological parameters can be varied, e.g., the gastrointestinal transit pattern, or transport or elimination via active processes. The parameters that are available for additional statistical variation are grouped based on their function and displayed, using the default settings, in a tree structure on the left hand side. Two parameter groups will always be available, namely the Anatomy and the Physiology parameter groups. The appearance of a third parameter group, the Relative expressions, is dependent on the processes defined in the underlying individual.

To select a parameter in the tree view, do the following:

1. Click the plus sign (+) to open the respective tree view node

2. If present, click the next plus sign (+) to open the subsequent level of the tree view

3. Click on the desired parameter

Selected parameters can be added to the box on the right hand side by clicking Add. Accordingly, parameters can be removed from the box by clicking Remove. Parameters added to the box on the right hand side can be varied within the population simulation. For each parameter, a type of distribution and associated properties of the distribution can be chosen. Four types of distributions are available:

• Normal: The parameter is normally (Gaussian-like) distributed. Mean and standard deviation must be given. Select the unit accordingly.

• LogNormal: The parameter is log-normally distributed. Mean and geometric standard deviation must be given. Select the unit for the mean value accordingly. The standard deviation can be given as a (dimensionless) relative standard deviation.

• Uniform: The parameter is evenly distributed between the minimum and maximum value. Select the unit accordingly.

• Constant: The mean value is used for all individuals. Select the unit accordingly.

Distribution tab

In the Distribution tab, the distribution of parameters that are variable in the virtual population are shown. To select a certain parameter, mark it in the parameter tree on the left hand side. Again, you can use the Filter function above the tree view to find parameters more quickly. The distribution of the parameter selected will be depicted in the adjacent graphic. The parameter distribution can either be displayed as absolute counts or as percentage. Choose either Count or Percent from the drop-down menu below the parameter tree. For human populations, the parameter distributions are color coded. In case of a virtual human population that contains male and female individuals, you can select from the first drop-down menu whether all, only male, or only female individuals should be displayed. If All is selected, the gender specific data can either be shown as neighboring bars or stacking bars.

Setting or Editing Population Properties‌

To set or edit the properties of an existing population:

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

2. Select Edit...

or simply double click on the existing population in the Building Block Explorer.

The window with the properties of the population will open. The properties defined in the Additional Parameters tab can be set or changed appropriately. Changes can be verified in the Distribution tab. After having set or changed the properties, the window can be closed by clicking on which will save the changed population properties.

Exporting Populations to CSV‌

Populations generated in PK-Sim® can be exported to a CSV format. The file, which can be opened in Excel®, contains all anatomical and physiological parameter values of each individual of the population. In order to export a population to csv:

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

2. Select Export to CSV...

3. Choose directory and enter file name

4. Click Save. The file is saved and can be subsequently opened with excel

Extracting individuals

You can extract specific individuals from a population and add them as standalone building blocks to the project for follow-up analyses.

Individuals of interest can be identified within a population analysis (e.g. individuals associated with the percentiles displayed in a population Box-Whisker plot)

To extract individuals from a population, right click on the respective population in the Buildings Block Explorer and select Extract Individuals....

Cloning of Populations‌

To clone populations in the project:

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

2. Select Clone...

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

4. Confirm and close the window with OK

Saving Populations as Templates‌

Previously defined populations can be saved as templates and then be shared among several projects and users.

To save an existing population as template:

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

2. Select Save as Template...

   In case a population with the same name already exists, a warning message will pop up and you have the following options:

   • Override: This action will override the existing template

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

   • Cancel: This action will abort the saving process

Loading of existing Populations from Templates‌‌

To load an existing population from the template database:

1. Right mouse click on Populations in the Building Block Explorer

2. Select Load From Template...

3. Select the desired population from the user templates

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

4. Click OK

The selected population will appear in the Building Block Explorer view.

In addition, populations can be directly loaded from the template database within a simulation (see PK-Sim® - Simulations.

Deleting Populations‌

To delete a population from the project:

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

2. Select Delete...

3. Confirm to delete the population by clicking on Yes