Lesson Eight:

Mathematical Implementation of
Pharmacokinetic and Pharmacodynamic Models


This lesson will provide an overview of how the pharmacodynamic (PD) effect is described mathematically and how it is included in a PK/PD model to relate drug concentrations to effect. The most common PD models used to describe an immediate or delayed effect of drug concentration will be discussed. Additionally, this lecture will provide a brief introduction of the concepts of allometry, physiologically-based PK (PBPK) modelling and population PK/PD modelling. 

Learning objectives:

  • Understand the Emax model

  • Describe direct PK/PD models

  • Describe turnover (indirect) PK/PD models

  • Understand the basic principles of allometry  

  • Get a basic understanding of PBPK.

  • Understand the basic principles of population PK/PD modelling 



1.1 Please study the video presentations below:
Please note:

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Please make sure that you WATCH the above video files. Additionally, you can download the PDF versions of the above video Files below:


Tasks 1, 2, 3, and 4 below will take you through the main principles of how the pharmacodynamic effect is described mathematically. 


Task 1: Understanding the Emax function

Task 2: Implementation of the direct effect model in Berkeley Madonna

Task 3: Delayed response though an effect compartment

Task 4: Indirect effect model with inhibition of input

Detailed instructions on these tasks are in the PDF file accessible here

The necessary files can be downloaded below


You can view a pre-recorded tutorial of this lesson here. [ Video ] [ Audio ]

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