Single PBPK model tutorial

PBPK models are valuable tools in predicting the absorption, distribution, metabolism, and excretion (ADME) of drugs in humans and animals. They provide a mechanistic framework to simulate drug behavior in the body, considering physiological and biochemical processes. PBPK models are widely used in drug development, regulatory submissions, and clinical trial design to optimize dosing regimens, assess drug-drug interactions, and predict pharmacokinetics in special populations.

This section provides a comprehensive tutorial on utilizing Teoreler for pharmacokinetic simulations. It covers various aspects, including understanding the interface, data collection, model building, verification, and refinement. Each subsection offers step-by-step guidance to help users navigate the platform effectively and make the most of its features.

By the end of this tutorial, users will have a good understanding of how to leverage Teoreler for their pharmacokinetic modelling needs, enabling them to conduct simulations with confidence and accuracy.

Teoreler provides a structured workflow for conducting PBPK simulations, guiding users through the essential steps to achieve accurate and reliable results. The workflow encompasses the following key stages:

1. Data Collection: Gather relevant physiological, biochemical, and drug-specific data required for model development.
2. Model Building: Construct the PBPK model using Teoreler's user-friendly interface, incorporating the collected data and defining compartments, parameters, and equations.
3. Model Verification: Validate the model by comparing simulated results with observed data to ensure its accuracy and reliability.
4. Model Refinement: Fine-tune the model based on verification results, adjusting parameters and equations as necessary to improve predictive performance.

Data necessary for building a PBPK model can be broadly categorized into physiological data, in vitro data, and drug-specific data. Teoreler provides a user-friendly interface to input and manage these data types effectively.

1. Drug parameters: Molecular properties such as molecular weight, lipophilicity (logP), solubility, permeability, and pKa values are essential for accurate PBPK modelling.
2. In vitro data : Apparent permeability (P_app), intrinsic clearance (CL_int), fraction unbound in plasma (fu), and blood-to-plasma ratio (B/P) are crucial for predicting drug absorption, metabolism, and distribution.
3. Dosing regimen : Route of administration, dose, dosing interval, number of administrations, total simulation time.
4. In-built parameters : Species-specific anatomical and physiological parameters such as age, weight, height, organ volumes, blood flow rates, and enzyme expression levels are pre-loaded in Teoreler for human, rat, and mouse models.

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).

Subsequent to data collection, the next pivotal step in the PBPK modelling workflow is model construction. This phase involves the systematic assembly of the PBPK model using Teoreler's intuitive interface, seamlessly integrating the previously gathered data in the provided input boxes.

The drug name can be changed in the 'Drug Profile' tab. The entered name shall be displayed on the simulated plot.

In the 'Characteristics' tab, since the clinical study was conducted in 1976, the appropriate study year can be selected. The simulation is conducted in 100 virtual individuals (50% males and 50% females) between the ages of 25 and 53.

Next, the route of administration followed by drug-specific parameters collected from the literature are entered into the respective fields in absorption, distribution, metabolism and elimination tabs, where applicable. In the distribution tab, we shall leave the volume of distribution method as 'Rodgers & Rowland - Schmitt' for now and come back to this later. A summary of the model parameters used in the simulation are shown in the table above.

A single 20 mg dose was administered in this study. The observed data had concentrations reported until 24 h, therefore a total simulation time of 24 h was chosen for this example.

Optionally, observed data can be uploaded from the 'Observed Data' tab in a .csv or .xlsx format with five columns - time, concentration, time units, concentration units and reference. A template file of the observed data can be downloaded on clicking the download template link.

Click on 'Run simulation' button after uploading the observed data (if any). This will allow Teoreler to simulate the pharmacokinetics of Teoreler in various organs and tissues and overlay the simulated and observed data on a plot. A toggle has been provided to switch between plot and table view of the results. Also various other options are provided to customize the plot as per user preference.

The initial simulation based on the input parameters is shown in the figure above. 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 user can download the simulated results in a .csv format by clicking on the 'Download Simulation Data' button in the 'Simulation Results' tab.

Verification is a crucial step in the PBPK modelling workflow, ensuring the accuracy and reliability of the constructed model. This phase involves comparing the simulated results generated by Teoreler with observed data from clinical studies or experiments. By validating the model against real-world data, users can assess its predictive performance and identify any discrepancies that may require refinement.

The average fold error (AFE) is a commonly used metric to assess the predictive performance of PBPK models. It quantifies the average deviation between simulated and observed pharmacokinetic parameters, providing insights into the model's accuracy. The AFE is calculated using the following formula:

Where n is the number of observations, Predicted is the simulated pharmacokinetic parameter, and Observed is the corresponding observed value from experimental data.

In PBPK modelling, an AFE value of 1 indicates perfect agreement between predicted and observed values, while values greater than 1 indicate overprediction and values less than 1 indicate underprediction.

Also, an additional validation with < 2-fold difference between the simulated and observed PK parameters - C_max (maximum concentration), C_min (minimum concentration), AUC_0-t (area under the curve), T_max (time to reach maximum concentration) and T_half (elimination half-life) values improves the confidence in the model.

The initial simulation shows a value of AFE = 0.83 as seen in the figure above which is between the 0.5 and 2-fold difference. This indicates that the model is able to reasonably predict the pharmacokinetics of sotalol in adults. However, further refinement can be done to improve the model's predictive performance.

Model refinement is the final step in the PBPK modelling workflow, aimed at enhancing the model's predictive performance based on verification results. This phase involves fine-tuning the model by adjusting parameters, equations, or assumptions to better align simulated results with observed data.

In this example, the initial simulation showed a reasonable agreement with observed data, but further refinement can be undertaken to improve accuracy. Potential areas for refinement include:

1. Re-evaluating drug-specific parameters such as absorption rate constants, clearance rates, or tissue partition coefficients to ensure they accurately reflect the drug's pharmacokinetics.
2. Incorporating additional physiological factors or modifying existing assumptions to better capture the complexities of drug behavior in the body.

By systematically refining the model based on verification outcomes, users can enhance its predictive capabilities, ultimately leading to more reliable and accurate PBPK simulations.

First, the volume of distribution method was changed as this can play a vital 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 changing the method from 'Rodgers & Rowland - Schmitt' to 'Poulin and Theil' in the 'Distribution' tab improved the fit of the simulated data to the observed data to an AFE value of 1.14. However, lets stick to 'Rodgers & Rowland - Schmitt' method for this example.

Increasing or decreasing the scalar values for absorption, distribution and clearance from 1.0 would alter the respective parameter by the specified factor. For example, decreasing the V_d scalar to 0.6 would decrease the tissue-to-plasma ratios of all the organs and tissues by a factor of 0.6 and would also decrease the volume of distribution meaning that the drug is distributed less into the tissues and more stays in the blood thereby getting cleared quicker. This adjustment would bring the AFE to 1.04.

In this example, although changing the volume of distribution method to Poulin and Theil improved the fit, the predicted Ctrough was lower than the observed value. Also at the initial time points, the simulated data was higher than the observed data. Even though scalar adjustments can be made to the volume of distribution, this may not be sufficient to fully capture the observed behaviour.

The final refined model shows a good agreement with observed data with an AFE value of 1.04 which is close to 1.0 indicating a good predictive performance of the model. This validated model can now be used for further simulations and predictions of alternative dosing regimens of sotalol in adults.

1. Khalil F, Läer S. Physiologically Based Pharmacokinetic Models in the Prediction of Oral Drug Exposure Over the Entire Pediatric Age Range—Sotalol as a Model Drug. The AAPS Journal. 2014;16(2):226-39. https://doi.org/10.1208/s12248-013-9555-6.