Pharmacokinetic modelling Flashcards
Population pharmacokinetics
In phase 3 trials, when you give the drug to a larger population, you may notice that there is some variation in PK. You can try to separate the population into multiple subpopulations to identify why you are observing these changes, i.e. what are the key contributors to variability for your drug.
Population PK (pop-PK) provides an understanding of PK of drugs within a population using PK data obtained from individuals.
Mathematical and statistical methods are used to describe PK data.
Population pharmacokinetics is often employed in clinical trials or where we have large numbers of patients but with poor sampling.
Pop-PK aims to identify sources of variability in plasma and determine the magnitude of influence on PK.
This provides a framework for optimising dosing strategies in subpopulations driving significant variabilities in plasma concentration.
Dividing the population into 2+ sub-populations can give us multiple mean concentration-time profiles which fit each population better, so dosing regimes can be better optimised in each subpopulation.
Pop-PK vs classical PK
In pop-PK, sampling is often less structured and more sparse. We cannot collect plasma samples every hour/half-hour from one patient for ethical reasons, so data from different patients is combined in pop-PK.
In classical PK studies, the population is selected to healthy volunteers, so variation is limited. In pop-PK, a larger population of target patients is used, so there is more variation.
Sampling in classical PK is dense following drug administration, but in pop-PK it is sparse as a few samples are collected from many patients and combined.
With classical PK, as healthy volunteers are used, prediction is limited. Pop-PK enables more extensive analysis and prediction about future events like steady state concentration and efficacy, guiding dose adjustments and allowing the determination of a therapeutic window.
In classical PK, a model is fitted to the data without consideration of multiple patient variability.
In population PK, a model is fitted to the data and variability is then quantified. This is done using the variable ε, a measurement of inter-individual error (as deviation from the predicted curve).
Types of variability
One type of variability is inter-patient variability, also called between subject variability (BSV).
For example, 5 patients receiving 80mg of propranolol orally can result in large differences in plasma concentration-time profiles.
We can also get intra-patient variability, also known as between occasion variability (BOV).
For example, two patients receiving verapamil on two occasions, separated by a washout period. On each occasion the resultant profiles are different, despite the same dose being administered.
Therefore, not only can there be differences between the two patients, but there are also differences in the PK profile of the same patient between two different doses.
Pop-PK - Mixed effect modelling
Mixed effect modelling is a statistical model containing both fixed effects and random effects.
In an ideal trial, 100 patients would receive a 100 mg oral dose once daily. Blood samples would be collected every hour over a 24 hour period. However, in actual trial implementation, there is sparse sampling. Data collected across the population at scattered time points is used to generate a mean.
Cp = Ri/Cl * (1-e^-kt) +/- ε
In an individual PK model, the ε is the difference between observed and predicted values, so if your data does not fit the predicted model, this is quantified. The statistical model can also be used to tell you what variable is causing these differences if there is a pattern.
In a population PK model, we add models that account for the magnitude, and sometimes the sources, of variability in model parameters between individuals.
Observed Value = Predicted + Some Error
PKobs,i = PKpred,i + ε
A statistical model known as non-linear mixed effect (NLME) modelling can be used to estimate the variables in a model.
All data, including demographic and plasma concentration data, from all subjects is included in the model. Demographic data is mapped to the PK profile of a specific patient, then:
- Estimate population PK parameters for the target patient.
- Estimate variation between individual PK parameters and population PK parameters. Pop-PK tells you how different individual points are from your mean.
- Estimate the residual variable that the model cannot explain from demographic information.
- Keep doing this until the estimate no longer changes (minimisation), at which point the model stops with your result.
NLME modelling
In any population pharmacokinetic model, the following elements are often included in the final statistical model developed.
Theta (θ) - population estimate for the PK parameters of interest (ka, V, CL). These are fixed effects.
Eta(η) - describes inter and intra-individual variability. An individual value for clearance could be described as θCL*e^η(CL) → θCL, the clearance in the average data, is expressed as an exponent if the variability (eta). This is a random effect (BSV, BOV) explaining variability.
Epsilon (ε) - the unexplained residual variability, for example misrecording the time of sampling, mistreatment of samples, error induced by analytical methods, model misspecification, etc.
Non-linear mixed effect (NLME) modelling involves 3 key models which should be defined:
- Structural model - determine the best compartmental model that fits the data. This would be the Cp equation in the case of a single IV bolus.
- Covariate model - determines the effect of covariates on PK parameters such as weight on Vd. This gives you the eta value - magnitude of particular variable on clearance, Vd, etc.
- Statistical model - models BSV and BOV and determines why this variation is happening
PBPK modelling
Physiologically-Based Pharmacokinetic (PBPK) modeling was first proposed in 1937 by Torsten and Theorel. It is also called mechanistic modelling.
In PBPK modelling, you have not given your drug to individuals, but you are trying to predict the PK profile from the physiological properties of your drug. You need to understand all elements that affect the PK of a drug and integrate these.
It integrates a range of preclinical and physicochemical data to predict in vivo PK early during drug development. Variables used include logP, pKa, solubility, permeability, protein binding, and in vivo animal data.
It enables prediction of:
- PK in preclinical species and humans
- Drug concentration in all tissues - difficult to actually sample this in clinical trials due to a lack of accessibility to these sites
- Changes in PK as a result of altered physiology states or in special populations, e.g children, by tweaking uour model and seeing how this affects the predicted PK
PBPK is used in industry across many sectors, Modelling is evolving very fast with the rise of AI and it has been used to study DDI, drug disposition in pediatrics, FIH dose predictions, etc.
PBPK modelling differs from empirical modelling, which involves 1, 2 or 3 compartments and required a priori data. Mechanistic models do not require any clinical data for development, and include a detailed description of the mechanisms that influence ADME of a compound in the body.
Empirical models have very little physiological relevance. We can’t extrapolate the data to different drugs or patients. Mechanistic models have physiological relevance and they can be extrapolated to different patients.
Developing PBPK models
To develop a model, we create ‘virtual humans’ by presenting them as physiological compartments which are PK relevant based on what you want to study.
Compartments within a virtual human model include a range of tissues and organs that may be important for the ADME of the drug.
These are considered real compartments, different from compartmental analysis which may not be physiologically relevant. Volume, blood flow and the biochemistry of the compartment have to be defined.
Mathematical expressions are used to determine how drug parameters (e.g. concentration) change with time.
PBPK model development involves a whole body PBPK (WB-PBPK) model, which usually comprises of 14 compartments.
The compartments are linked with arterial and venous circulation, organs critical for circulation, elimination organs and large/lipophilic organs.
Using mathematical principles, changes in drug concentration over time in each tissue compartment can be predicted
All organs are linked together with blood flows, therefore total organ blood flows must equal cardiac output → follows the law of mass balance
Can predict PK profiles in tissues following most administration routes
Tissue types need to be defined as wither well-stirred tissues (limited by perfusion) or permeability limited tissues.
Parametrisation of PBPK models
The data requirement for PBPK models is often larger than for empirical models, but the model built is more realistic and representative of real physiology.
Requires two kinds of data: system data and compound data. These can be obtained from literature or generated in-house
System data includes physiological parameters, like organ perfusion/volume, GFR and body weight/composition, and biochemical data like enzyme and transporter abundance.
Compound data includes physicochemical parameters, like pKa, fu, MW, lipophilicity and tissue partition coefficient (Kp), permeability data (Papp, Peff), and metabolic parameters like intrinsic Cl, Km and Vmax.
You need to include all parameters you know about the physiology of your target population, as well as all drug-related data you have for your compound
Simulating the PBPK model
Data is integrated into your model and used to predict the plasma-concentration profile of your drug.
An example of PBPK application can be seen with the process of optimising Chloroquine (CQ) dosing for repurposing for Zika virus disease in pregnancy.
Zika virus (ZIKV) disease may cause serious developmental problems in the foetus, such as encephalopathy.
CQ has good safety profile for malaria treatment during pregnancy and there is evidence of in vitro activity against ZIKV.
We can optimise CQ dosing in pregnancy to prevent ZIKV transmission to the foetus.
The optimised dosing strategy could provide a framework for larger trials.
A PBPK model is created and validated in healthy non-pregnant subjects.
Optimisation and validation are then performed in pregnant subjects.
The prediction across gestational ages was then developed to optimise dosing. This was done using simulations.
In vitro data was used to parameterize the model.
PK modelling summary
Population PK and PBPK modelling approaches are useful during different stages of drug development.
The modelling approach used depends on the type of data you have available, e.g. in vitro vs in vivo, as well as what questions you want to answer. If you have more in vitro data, PBPK is used. If you have in vivo data, Pop-PK is used.
They guide dosing strategies.
They are useful for optimising dosing strategies in special populations and pathophysiological conditions.
