# Compartmental Modeling in Pharmacokinetics

Pharmacokinetic (PK) modeling is a tool used to help drug developers understand a drug’s effects on the body by analyzing its absorption, distribution, metabolism, and excretion (ADME) properties. These effects are typically summarized using PK parameters such as clearance and volume of distribution which are necessary for understanding the effects of a drug on the body.

PK models can range in complexity from models with a single compartment to models containing hundreds of compartments. Each type of model from the simplest, one-compartment model to more complex models have their own applications and can be used to gain valuable information from clinical or non-clinical data.

Let’s explore a one-compartment model with an analogy. One-compartment modeling views the human body as one large bucket with one outflow port at the bottom. Imagine water being poured into the bucket. This is analogous to drug absorption into the body. Then imagine the water in the bucket dripping out of the bottom through the port. This is analogous to drug clearance from the body.

In our analogy, a one-compartmental model uses mathematical equations to describe the concentration of water (drug) in the bucket (body) at any given time as water is being poured into the bucket (absorption) and begins dripping out (clearance/excretion). A two-compartment model adds an additional bucket to the system. In this analogy, the first and second buckets are connected by a tube or valve so that water (drug) can flow between them (distribution/metabolism).

These buckets (or compartments) are used to better estimate PK parameters by modeling the flow of a drug throughout the body. Examples of possible compartments range from specific tissues and organs, such as the liver, kidneys, lungs, or even the blood’s circulatory system, to more general groupings, such as incorporating all highly-perfused tissues into one compartment.

## What is a Compartmental Model?

Compartmental modeling is a model-based method used for estimating PK parameters. To apply this method, the body is divided up into hypothetical compartments. Often, the containers used in compartmental modeling do not represent actual physiological tissues in the body but are used as a proxy so that PK parameters can be determined. For example, in compartmental modeling, the rates of absorption and/or clearance can be modified between compartments to model the effect of such changes, representing a disease state or induction of metabolism.

Compartmental modeling is a general term that refers to a model with at least one compartment. Typical compartmental models have between one and three compartments, but more compartments can be added to the model depending on the application. For example, in a type of compartmental modeling known as whole-body physiologically based pharmacokinetic (PBPK) modeling, there can be as many as one compartment for each organ of the body.

### Compartmental Model vs. Noncompartmental Analysis

Compartmental models can reveal insights into a drug’s underlying effects that are not always obvious from a noncompartmental analysis (NCA). While a one-compartment model and a non-compartmental analysis both assume that the entirety of the body exists as one container, the difference between the two is that since the one-compartment model is a model-based method, parameters, such as clearance, can be changed to explore the effects of specific disease states, such as renal impairment, or induction of metabolism on the PK characteristics of a drug.

An NCA is a model-independent method, where PK parameters are estimated directly from the observed data requiring no historical knowledge of the PK characteristics of the drug in the body (i.e., absorption rate or rate of elimination, etc.). Partitioning the body into compartments is not necessary for an NCA. The benefit of conducting an NCA is that no drug-specific characteristics are required, making it less complex and more cost-efficient than compartmental modeling while still providing valuable information on a drug’s PK characteristics.

The value of compartmental models over an NCA is that they can be useful for a wider range of applications. For example, in a compartmental model, the dosing regimen can be altered to produce simulated concentration-time profiles that can be used to understand the impact of changing the dose.

In an NCA, PK parameters are estimated directly from the data and since this is a model-independent approach, changes to the protocol (such as an alternate dosing regimen) can only be extrapolated using simple superposition but is limited by what dosing regimens can be used. Not only can compartmental models be used to estimate PK parameters, they can also be used to address inter-subject variability, such as how patient-specific covariates affect drug disposition when performing a population PK (popPK) analysis.

## One-Compartment Model

A one-compartment model assumes that all the tissues in the body are contained in a single compartment called the “central compartment.” The simplicity of this model makes it easy to construct, provides a straightforward interpretation, and is cost-efficient. The drawback of this type of model is that, by its construction, the drug is assumed to be equally distributed throughout the whole body, which is rarely true.

Furthermore, since there is no distribution parameter, clearance is assumed to occur linearly. For drugs that do not distribute throughout the body, the simplification that this type of model provides may make it the most appropriate option. For drugs that are highly distributed throughout the body, a more complex model may be necessary.

## Two-Compartment Model

Two-compartment models account for the distribution parameter that a one-compartment model cannot by dividing the single compartment into two separate containers called the “central” and “peripheral” compartments. The central compartment represents plasma and highly perfused tissues including the kidneys and the liver. The peripheral compartment represents poorly perfused tissues such as muscle.

In this model, the drug is not assumed to be evenly distributed throughout the body but disbursed between these two different compartments. Grouping together tissues with similar blood flow rates allows for parameters such as drug distribution to be more accurately represented. However, in cases where the drug has three distinct elimination phases, a two-compartment model may not be sufficient.

## Three-Compartment Model

Three-compartment models include another peripheral compartment in addition to the two compartments listed above. This additional peripheral compartment is used to separate the highly perfused tissue from the plasma. In the three-compartment model, the central compartment represents only the plasma. The first peripheral compartment represents the highly perfused tissues and the second peripheral compartment represents the scarcely perfused tissues.

This type of model has all of the benefits of the two-compartment model and may be able to better describe a drug which exhibits three stages of elimination. The drawback to this type of model (and all of the aforementioned compartment models) is that distribution to a specific tissue cannot be explored which might be beneficial if drug concentration in the liver, for example, is of particular importance.

## Whole-Body PBPK Model

Whole-body PBPK modeling is a type of compartmental modeling in which each tissue of the body is represented by its own compartment. In contrast to a one, two, or three-compartment model, the compartments in a PBPK model are physiologically-based and grounded in biology. Blood flow rates between specific organs, tissue partitioning coefficients, and organ size can all be included in this model.

Adding this physiology makes a whole-body PBPK model much more versatile. PBPK models have been used in a wide range of applications from first-in-human (FIH) dose prediction to drug-drug interaction (DDI) studies. However, this added complexity increases the time and costs necessary to construct the model. Additionally, the data requirements for creating this type of model are much larger compared to smaller compartmental models.

## Conclusions

Compartmental modeling is a tool that allows drug developers to understand the effects that drugs have on the body. This could include estimating PK parameters, characterizing PK across multiple studies, understanding observed patient variability, and much more. There are different types of compartmental models, such as one-compartment, two-compartment, three-compartment, and whole-body PBPK models. Each type of model has its own advantages and disadvantages.

The overall advantage of using a compartmental model is the diversity in application. A compartmental model can be used during many different stages of drug development and, importantly, adding multiple compartments to a model may help to better explain the observed data.

Nuventra has a team of experienced pharmacometricians who are experts in designing models tailored to fit your program’s needs. Contact us to learn more about Nuventra’s compartment modeling and PBPK services.