Tutorial

Introduction

Welcome to this tutorial on validating physiologically based pharmacokinetic (PBPK) models! In this tutorial, we will explore the essential steps involved in validating PBPK models, both using published PBPK models and building one from scratch.
PBPK models are valuable tools in pharmacokinetic (PK) research, offering a mechanistic understanding of how drugs distribute within the body. Validating these models enhances their accuracy and reliability in predicting drug behaviour.
By the end of this tutorial, you should have a solid understanding of the validation process, enabling you to assess PBPK models confidently and potentially develop your own. Let's delve into the intricacies of PBPK model validation and unlock the potential of this powerful PK tool.

Basic PBPK validation workflow

Validating a PBPK model involves several crucial steps to ensure its accuracy and reliability. The figure below shows a flowchart of a basic PBPK model validation. A more detailed description follows.

1. Data Collection : Begin by gathering experimental data relevant to the compound of interest. These data should include parameters categorised as follows:
   • Drug parameters: Compound properties including molecular weight, logP, pKa, polar surface area, number of hydrogen bond and donors, protein binding, blood-to-plasma ratio, etc.
   • In vitro parameters (if any): Apparent permeability (P_app), apparent clearance (CL_app), intrinsic clearance, renal clearance, enzyme induction and/or inhibition parameters etc.
   • Dosing regimen: Route of administration, dose, dosing interval, number of administrations, total simulation time.
   • In-built parameters: These are already available and are integrated into the PBPK models on Teoreler.
     • Species characteristics - Age, weight, height, body mass index (BMI) and body surface area (BSA)
     • Anatomical values - individual organ or tissue weights, volumes, enzyme abundances etc.
     • Physiological parameters - Gastroinstestinal tract (GIT) transit rates, blood flow rates etc.

   As an example, the table below is collated from Khalil F. & Läer S. 2014¹ (although there are reference values provided, in this tutorial, we shall use only the two columns shown below since tables in a similar format are usually published in all peer-reviewed PBPK manuscripts).

   Table: Drug input parameters for an example drug - Sotalol from a published manuscript ¹

   (Software 1 is Simcypᵀᴹ and Software 2 is PK-SIM®)
2. Model building : Once all the necessary data are collated, enter these into the relevant input boxes provided on Teoreler. The video below shows the drug and ADME parameters entered using the Simcypᵀᴹ column for an intravenous route.
   Please note: A default 20% standard deviation to the mean clearance value would be added to accommodate variability.

   Next, the dosing regimen should be entered and make sure the displayed units for time are same as the observed data. A single 20 mg intravenous dose is being simulated for 100 virtual individuals (50% males and 50% females) between the ages of 25 and 53. The observed data has concentrations reported until 24 h, therefore a total simulation time of 25 h was chosen for this example.
   Please note: On selecting Sex as 'Both', an equal distribution of female to male population is automatically simulated.

   

   Moving on to the optional inputs tab, since we are interested in the plasma concentration over time, this should be selected as the lead plot. For this example, we are not interested in a specific target concentration, so we can set this to zero. Also, the observed data was reported in μg/mL (or mg/L), so please make sure the concentration units are the same as they are reflected in the plots. This clinical study was conducted in 1976, so the appropriate year should be selected. The remaining scalar values can be left at 1.0 for now.

   

   Also, upload the relevant clinical data to compare against the simulation from the 'Upload data' tab using the 'Browse' button. Once a file is uploaded, the user can select the appropriate time and concentration units of the uploaded data. Sotalol observed data can be downloaded here
   . Please note: A template file can be downloaded on clicking the icon adjacent to 'Browse' button.

   

   On completing this, click on 'Run simulation' button. This will allow Teoreler to compute the other essential model parameters to output the pharmacokinetics of sotalol in various organs and tissues.

3. Model verification: The initial simulation based on the input parameters is shown below. The mean plasma concentration is shown as solid blue line with the shaded area showing the 90% confidence interval. The orange dots show the uploaded observed data.

   The average fold-error (AFE) describes the closeness of the simulated data against the observed values (see Pharmacokinetic Summary Table below). An AFE value of 1.0 indicates that the simulated curve is identical to the observed data. Conventionally, in research, a model is acceptable if the AFE value is between 0.5 and 2 but improving the AFE closer to 1.0 would improve the reliability of the model predictions. Also, extra validation with < 2-fold difference between the simulated and observed PK parameters - C_max, C_trough, AUC, T_half and T_max values improves the confidence in the model.

   In this example, the AFE was computed to be 0.85 ± 0.11, and the correlation plot shows the simulated vs. observed data points fall within the 2-fold range, which indicates the model performs well. However, visually there is a slight deviation of the PK at the final data point at 24 h.
   Please note: The AFE values may change slightly since the population generated each time is randomly sampled from a normal distribution.

   
4. Model refinement: In the cases where the model performance is sub-optimal, parameters should be adjusted to fit the observed data. From our example, there is deviation at the end at 24 h with simulated concentrations higher than the observed values. Therefore the model can be further refined to improve the closeness of the simulated data or decrease the AFE value. This can be achieved using the scalar factors in the 'Other Inputs' tab.

   Increasing or decreasing the scalar values from 1.0 would alter the respective parameter by the specified factor. For example, increasing the clearance to 1.2 would eliminate the drug quicker and decrease the overall PK as shown. Although the simulated C_trough is now closer to the observed data, the AFE has decreased to 0.8 ± 0.11, since the curve slightly deviated from the other observed data points.

   

   Secondly, the volume of distribution can play a key role in defining the distribution profile. The available volume of distribution methods can give a close approximation to the observed value, however, they may not be accurate. Therefore adjusting this value using a scalar of 0.65 would reduce the tissue-to-plasma ratios of all organs and tissues, thus reducing the volume of distribution. This would further increase the AFE to 0.94 ± 0.16.

   

   Now, the model is refined and its performance is enhanced. This model can be used to predict other routes of administration, or for other physiologies of the same species and can be used to inform alternative dosing regimens as required.

Further information

PBPK models of drugs completely depend on the quality of the input data. If the input data are sub-optimal, the predictions would reflect the same. For example, if we consider the data from PK-Sim® which has a different blood-to-plasma ratio and the clearance specified in L/h/kg, the output would be slightly different. A comparison of the plots from Simcypᵀᴹ and PK-Sim® input parameters is shown below and the mean AFE are 0.89 and 1.02 respectively.