An In-Depth Guide to Pharmacokinetic Modeling

With recent technological advancements and innovations in drug delivery systems and complex molecules, pharmacokinetic modeling (PK modeling) has become an invaluable component of drug discovery and development. Used to help make sense of the highly complex in vivo behavior of drug delivery, PK modeling can help impact both their clinical translation and development.

Let’s take a closer look at PK modeling and the types of PK models most typically used in drug development.

What is pharmacokinetic modeling?

As a branch of pharmacology, pharmacokinetics involves looking at how drugs move into, through, and out of the body. This includes everything from absorption, to distribution, to metabolism, and excretion (ADME).

Pharmacokinetic modeling and simulation is a mechanistic description for both translation and prediction of a drug’s behavior in the human body. Mathematical PK models are used to characterize a drug’s movement once inside the body, quantitatively describing the processes of absorption and disposition. PK equations work by looking at the time courses of drug concentrations in the body, focusing specifically on the fluid volume of the body and the elimination of drugs measured in unit time.

PK models, in conjunction with pharmacodynamic aspects, help quantify the biological system's response to drug administration by looking at the drug itself, the delivery system, and the physiological and/pathological system.

Once the drug concentrations in the body have been determined and quantified at various times and/or formulations, the rate of drug elimination and dose-concentration relationship are considered established. While there are a range of PK models that can be used to achieve this end, in general, the primary objective of all approaches is to determine what happens to the drug once inside the body.

Why do we need pharmacokinetic models?

Because the in vivo behavior of many drug delivery systems are still largely unknown to researchers, translation efforts may be hampered or slowed. Pharmacokinetic models are essential to advancing model-based drug development, as the PK behavior of a drug helps determine the safety and efficacy of novel treatments and predict the correct dosing regimen in humans – optimizing many aspects of drug delivery systems. For example, PK modeling has shown its ability to help in the successful development of new delivery systems like extended-release formulations, liposomal drugs, modified proteins, and antibody-drug conjugates. As a result, in recent years there’s been sustained interest in screening approaches that can help more accurately predict PK behavior in humans. The insights gathered regarding a drug’s PK also provide critical guidance for regulatory authorities like the FDA.

What is the most common pharmacokinetic model?

The two most common pharmacokinetic models are compartmental modeling and non-compartmental modeling.

Compartmental modeling‍

In compartment modeling, human and animal bodies are understood to be a series of interconnected compartments. These compartments can either represent anatomical regions (as in physiology-based PK models) or a grouping of tissues that share similar blood flow and allow for uniform drug distribution. In compartmental modeling the pharmacokineticist makes a series of assumptions to describe the ultimate PK of the drug. This means some variability in the output can be expected.

• One-compartment model – In the one-compartment model, or single-compartment model, it is assumed that all blood, organs (i.e. liver, kidney, heart) and tissues are in a single, uniform, central compartment. In this simple model, the drug enters the central compartment from outside of the body and subsequently exits via the same compartment, with no drug recirculation occuring. This model generally assumes proportional changes between the plasma levels of drugs and the drug concentrations found in tissues.
  
  
• Two-compartment model – In the two-compartment model, drugs are distributed into two, separate compartments: the central compartment and the peripheral compartment. The central compartment contains blood and highly permeated or perfused tissues, while the peripheral compartment contains less-perfused tissues.
  
  
• Three-compartmental model – In the three compartment model, drugs are distributed into three, separate compartments: a central compartment, a highly perfused compartment, and a scarcely perfused compartment. In the central compartment you find the plasma, in the highly perfused compartment the organs and tissues that are most perfused by blood, and in the scarcely perfused compartment, those organs and tissues least perfused by blood.

• Physiology-based PK models - In physiology-based PK models, drugs are distributed in separate compartments based on the biology of the organism and generally corresponding to individually important tissues (i.e. lungs, liver, heart, etc.)

In multi-compartment models, the plasma concentration of the drug will be shown to decay in multiple exponential phases – usually referred to as the distribution (α) and elimination (β) phases. Here, the first dramatic decline of a drug concentration in the central compartment is referred to as the distribution phase of the curve (α). The drug will reach a steady state between the central compartment and the peripheral compartment, before eventually being expelled from the body. This part of the process is known as the elimination phase (β).

Non-compartmental modeling‍

Non-compartment models presume that a drug's blood-plasma concentration is a true reflection of the concentration in other tissues and that the elimination of the drug is directly proportional to the drug's concentration in the organism. Non-compartmental methods rely on equations to estimate PK parameters, which means these methods can be less complex, faster, and more cost-efficient than compartmental models.

Which pharmacokinetic model is best for drug development?

Deciding to use a non-compartmental PK model versus a compartmental PK model depends mostly on the purpose of the analysis, as both models are regularly used successfully as part of the drug development process. For example, compartmental methods are often used to characterize PK across multiple studies, or to look for PK variability that occurs as a result of factors like age, sex, or a specific impairment. Dosages are adjusted according to those findings.

Non-compartmental models, however, are often used to characterize PK within a single study, especially to help inform time-critical dose escalation decisions. This is a common approach used when establishing the initial exposure characteristics of a drug during non-clinical PK, in toxicology studies, and is also routinely used by regulatory agencies during development and approval processes.