PK/PD module

See also: VoseODE






ModelRisk’s PK/PD (Pharmacokinetic /Pharmacodynamic ) tool allows the user to define a PK/PD model and return simulation results in Excel. It uses the fourth order Runga-Kutta method (also known as RK4) for generating projections, a more sophisticated  method based on the same principles as the Euler method, because of RK4’s much greater accuracy and computational efficiency. Input parameters to the model can be linked to ModelRisk’s probability distribution functions within Excel allowing the user to see the uncertainty in the resultant model outputs.

PK/PD menu

Three PK/PD – related buttons are available in a special sub-menu on the ModelRisk Ribbon:

  1. Library, which opens a library of PK/PD models, offering the options to select/use a particular model
  2. Create model, which opens the interface that allows creating custom PK/PD models
  3. Convert NONMEM, which allows importing a NONMEM output file into Excel/ModelRisk.


The Library is organized into 3 categories: PK, PD and PK/PD models. For each category there are 2 sub-categories: Standard and User-defined models.

The Standard models come with the ModelRisk installation file, and the User-defined models are created by users and stored on the user’s PC. All library models are saved into a "ModelRisk Library" folder under user’s "My Documents". For each Standard model in the Library, there is a Name, a Description, and a schematic picture of the model.  For each user-defined model, the interface allows the user to define a Name and a Description. However, the schematic picture of the model can be set to a user-defined model manually, by copying the picture of the model to the same folder in the ModelRisk Library as the model file, and making sure that the picture file name matches the model file name. For example, if the model file name is "1-CMT", then the name of the picture file should be "1-CMT CL.png". The picture format should always be PNG and the picture dimensions set to 230x152 pixel.

To use a Library model, select the model and click the "Select" button, which will load the model and proceed to the next interface window, the Dosing Regime window.

To delete a User-defined Library model, select the model and click the Delete button.

If a user wishes want to send user-defined models to another user, s/he would need to go to "My Documents\ModelRisk Library\PKPD", find the user-defined model files (e.g. "1-CMT"), and send them to the other user, who would needs to place them in the ModelRisk Library on his or her computer.

Create model

The Create model interface enables users to create user-defined PK/PD models and save them in the Library.

The user has the option to add an existing Library model (or several) into the window and modify it, or simply start from scratch. Each user-defined model needs a Name and a Description, and then a 4-step process:

  1. Differential equations. This is where the differential equations need to be entered. Each equation needs to take the following form:
    Each differential equation needs to have a "/dt" part, i.e. differentiation is always over t (time). "x"  and par may be any letter or set of letters and numbers, but cannot start with a number.
  2. Initial condition. This sets the initial condition for the differentiated variables, i.e. the values that the variables will have at time zero.
  3. Model outputs. Model Outputs are entered in the form of expressions, e.g.
  4. Model parameters. This last section prompts for the default parameter values. It is important to note that all time-dependent parameters have units = Hours (or 1/Hours). E.g. if K01 is a rate parameter and is equal to 2, then the model will interpret it as "2 per hour".

When all steps are complete, one can either save the model to the Library (by clicking the "Save" button), or click "Next" to proceed to the next interface without saving the model.

Dosing regime

The Dosing regime window controls  doses into model compartments:

The window above has a picture of the model on the top left, a table for inserting the dosing logic at the bottom, and a chart visualizing the selected dosing regimen on the top right.

Doses can be added by clicking the "…" button and selecting the required configuration for each entry. Switching a dosing entry from "Single" to "Multiple" unlocks the "Dose Interval" and "Dosing Duration" controls, which allows specifying the interval and duration of the dosing. Changing the "Dose Input Rate" from "Instant" to "Zero-order" unlocks the "Input duration" control, which allows specifying the duration of the dosing injection.  Doses may be introduced into any model compartment.

PK/PD model

This is the main PK/PD module window that provides a visual representation of the PK/PD model.

The left side of the window has four input tables:

  1. Differential equations. This is a read-only table that shows the differential equations used in the model and provides the option to view them on the chart.
  2. Initial condition. This section allows setting the initial condition for the differentiated variables.
  3. Model parameters. This section is used for initializing the model parameters. Note that the time-dependent model parameters are in the units of "hours".
  4. Model outputs. This section lists the model outputs and allows setting of a threshold for each model output. If a threshold is set, the model will return the "time above threshold" to Excel. The "time above threshold" is calculated as the total time starting from 0 to the largest value in the "Output Time Points" list where the selected output exceeds the threshold.

The upper part of the window has input controls for the Output Time Points, i.e. the time points at which the output values are required. The reference lines showing the Output Time Points on the chart can be switched on and off via the control below the chart.

If any of the model parameters are linked to volatile cells in Excel (e.g. probability distributions), clicking the F9 key refreshes the interface and the chart with the new values.

One or two variables can be displayed at the same time and against a different x-axis variable selected at the top right of the screen.

Placing the model into Excel is done by clicking the "To Excel" button, which prompts the user to select the upper-left corner of the area where the model needs to be pasted. Since the model inputs and outputs occupy a large spreadsheet area, it is better to paste the model into a blank worksheet.  This output also includes the variables "Cmax" and "Tmax" that return the maximum value and time of maximum value for each compartment and Model output from 0 to the largest value in the "Output Time Points" list. 

Using View Function to return to a window

Some model inputs can be edited directly in the Excel sheet (e.g., change model output times), or you can re-open the window for a ModelRisk function that is in a spreadsheet cell by using View Function. Select the spreadsheet cell and then select View Function from the ModelRisk menu/toolbar/ribbon.

NONMEM converter

The NONMEM converter is able to input native NONMEM output files and paste the extracted model parameter estimates and covariance matrix (if available) to Excel, preserving the correlation structure between the parameters.  Appropriate multivariate normal distribution arrays (VoseMultinormal) are implemented, to allow sampling from random-effect parameters and from the covariance matrix to address parameter uncertainty.

Clicking the "Convert NONMEM"  icon from the PK/PD menu under "More Tools" will pop-up a file browse dialog prompting to select the NONMEM output file. Once the file is selected, the converter produces an Excel worksheet with extracted model parameters that can be used as inputs in ModelRisk’s PK/PD module.

The output structure includes the NONMEM "PROBLEM NO." and any character description of the Problem (if provided).  If the covariance matrix is included in the file, three tables are produced. If the covariance matrix is not included, only the first table is produced.

Output tables:

  1. Final Parameter estimates (THETAs, OMEGAs, SIGMAs), with multivariate normal distributions to sample from OMEGA and SIGMA matrices.
  2. Parameter estimates including parameter uncertainty ("Unc"). Structure is similar to above, but the parameter estimates also are randomly sampled from a multivariate normal distribution.
  3. The covariance matrix, used to provide parameter estimates ("Unc") that include parameter uncertainty.  

The values of "Sample", "EstimateUnc", "MeanUnc", and "SampleUnc" can be refreshed by clicking F9, or randomly sampled a number of times according the value set in the "Samples" window.



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