“I suppose it is tempting, if the only tool you have is a hammer, to treat everything as if it were a nail.” – Abraham Maslow Modeling is an indispensable tool in drug development. It can save countless hours and dollars, as well as help make decisions at critical points in the process. Modeling is a broad methodological category with many techniques. All too often though, modelers become enamored with specific methods and try to shoehorn one particular method into every problem. Each modeling method is best-suited for answering specific questions. This post will explain the differences between two of the most widely-used pharmacokinetic modeling methods, physiologically-based pharmacokinetic (PBPK) modeling and population pharmacokinetic (popPK) modeling and provide some examples of when to use each tool.
Physiologically-Based Pharmacokinetic (PBPK) Modeling
PBPK modeling is a compartment and flow-based type of pharmacokinetic modeling and relatively easy to conceptualize. In PBPK models, each compartment represents a physiologically discrete entity, such as an organ or tissue, and the blood flow into and out of those entities. For example, a simple PBPK model might contain one compartment representing the blood linked to two other compartments in parallel, one that represents the liver, and one that represents the lungs. The distribution of drug into and out of that organ will be related to the blood flow into and out of that organ, the concentration in the blood, and a partition coefficient. In theory, if a PBPK model contained a compartment for each organ in the body, it could facilitate the simultaneous description of drug concentration changes over time in each organ. The compartments are not limited to entire organs, and often PBPK models contain nested compartments that represent different cell types within an organ, and even different organelles within a cell. These levels of hierarchical complexity permit modeling of molecularly-driven events, such as specific metabolic pathways. Mathematically, the blood flows and partition coefficients that link the compartments together are initially estimated from animal and in vitro data, though clinical data can be used when known. The parameters and compartments are then optimized to fit the model to existing data. Because PBPK models are constructed with such granular detail, they can help answer very specific questions. For example, the molecular signature of a disease can be incorporated into a PBPK model by altering key parameters to help predict how drug concentration will change in a specific patient population. This type of prediction can help inform dosing recommendations or influence the design of clinical trials when evaluating a drug for a new indication. Similarly, drug-drug interactions (DDI) can be predicted and simulated, given that metabolic and transport information is known for both drugs. PBPK models are typically limited by the available level of mechanistic knowledge. For instance, in the case of a DDI, it would be impossible to predict the impact of concomitant drug administration if the enzymes involved in their metabolism are not known. Quantitative systems pharmacology (QSP) is an extension of PBPK modeling. In addition to describing the change in drug concentration as a function of time in specific compartments, QSP models the pharmacodynamic effect of the drug on tissues and organs. A limitation of PBPK models is that they are commonly so complex (having many, many parameters, organ volumes, organ specific blood flows, and partition coefficients) that the parameters cannot be estimated using traditional statistical methods. Sometimes the parameters can be fixed to data collected in vitro or pre-clinically, but this requires the availability of such data (which is not typically available during drug development). Also, it is never clear if the parameter estimates from in vitro data or nonclinical species are the same as human parameters. When human plasma concentration-time data are available, the variables can be manually adjusted to improve the model’s fit.
Population Pharmacokinetic (popPK) Modeling
PopPK modeling (covered in this previous post) is also a compartment-based type of pharmacokinetic modeling. Unlike PBPK, however, the compartments do not necessarily have distinct physiological meaning. Rather, popPK modeling takes all available pharmacokinetic information, and builds a model that fits the data. Thus, these models are “top down,” starting with data observed, while PBPK models are “bottom up,” starting with what is understood at the organ, or tissue level. The fundamental difference between physiologically-based models and most Population PK models is that popPK models are largely empiric. For example, a popPK model development typically starts with a very simple model, often one compartment, linear elimination, and linear absorption. Additional “features,” such as peripheral compartments, absorption lag time etc. are then added to the model, one at a time, and tested for statistical significance. Note that these compartments are called “central” and “peripheral,” not, “plasma” and “adipose.” Occasionally, these compartments might correspond to actual anatomic compartments or processes. For example, large proteins are usually restricted to the plasma volume, and aminoglycoside clearance correlates very well with glomerular filtration rate. But, in general, these “compartments” are just an empiric description of the behavior of the drugs. That said, the biological plausibility of the models, and each additional “feature” is carefully considered when constructing these models, especially when considering clearance models. For example, we might test whether the clearance of a drug known to be cleared renally is related to creatinine clearance or age but would be unlikely to consider whether clearance is related to formulation, or fed/fasted state, since the latter two are not biologically plausible. Allucent uses popPK models to identify the sources of variability in a drug’s kinetic profile. This is a necessary step in any drug’s successful clinical implementation. These sources of variability can include both intrinsic factors (such as age, weight, and gender) and extrinsic factors (such as food and other drugs). PopPK can frequently describe the relationship between drug clearances and organ function. This relationship is derived from empirical observations – that is, from data, not a theoretical understanding of drug clearance. But, again, these relationships must be consistent with our understanding of the mechanisms if they are to be extrapolated with confidence. PopPK models also estimate the individual variability in PK parameters like clearance and volume of distribution and residual (or unexplained) variability. This is in contrast to PBPK models that usually describe the typical subject without variability. PopPK models have enormous utility in answering questions about drug kinetics related to multifactorial variables. Importantly, they are useful for formal testing of hypotheses, such as a relationship between clearance and creatinine clearance. Like PBPK models, they are often useful for prediction, even outside of the range of the available data. The extrapolation outside the range of available data requires that the model make biological sense. This means that if you have a model that includes an effect of creatinine clearance on drug clearance, and you have data in a range of creatinine clearance from 60-120 ml/min, that a model can likely predict, with confidence, the clearance in patients with a creatinine clearance of 30 ml/min.
PBPK vs. PopPK Models
Both popPK models and PBPK models can be used to predict exposure in pediatric patients. Empiric popPK models can predict exposure in pediatrics down to age 2 years for most drugs. If the enzymes responsible for metabolism are one of the common enzymes, there are maturation models that can be added to predict exposure in even younger pediatric subjects. The outcome is understanding the range of potential exposures in pediatrics (conservative information). PBPK models can predict exposure in pediatric patients regardless of age, however, a very thorough understanding of the metabolism is needed as well as in vitro and pre-clinical data to have a better chance of successfully predicting the average exposure in pediatric patients. Regulatory agencies are getting more interested in PBPK models, especially for complex drug interactions with multiple substrates or inhibitors when traditionally, they have not advocated for popPK. In contrast, both modeling approaches are well-suited to predict exposure in pediatrics. Therefore, companies can make a decision about which approach they want to take for predicting exposures in pediatrics, depending on how much knowledge is known about how the drug is metabolized, available in vitro and pre-clinical data to help with parameter estimates in PBPK, and whether they are interested in the average pediatric subject (which they will get from PBPK) or the variability in pediatric exposures (which they will get from popPK).
PBPK and popPK modeling are complementary techniques in the pharmacokineticist’s toolbox. They both possess powerful descriptive and predictive potential and can help make decisions throughout the drug development process. Importantly, PBPK and popPK methods are not mutually exclusive. While popPK models are traditionally described as “empiric,” we commonly include theoretical features into these models – including those not supported by any specific data, but rather by theoretical understanding of drug properties. Deciding which tool (or a hybrid of the two) to use requires a careful assessment of the specific questions to be answered and the type of data available. At Allucent, our scientists have the training and experience necessary to determine which modeling technique is most appropriate. Contact us for guidance on your drug development needs.