Almost everyone familiar with pharmaceuticals has heard a conversation like this before:

Scientist 1: “What are the pharmacokinetics of Drug X?”

Scientist 2: “Drug X follows a 1-compartment model in rats, but in monkeys it tends to have a distribution phase and seems to follow 2-compartment kinetics.”

Scientist 1: Thinks to himself/herself …’What does a compartment have to do with this! A compartment is something you find in a train!’

Compartments are an important concept in pharmacokinetics (and pharmacodynamics), but they are rarely explained to other scientists. Hopefully this post will demystify the idea of compartments and show you that the concept of compartments is simple.

To understand compartments, think about your heart for a minute. A human heart has 4 distinct chambers, each with a specific function. Blood, which has been depleted of oxygen returns through the veins to the right atrium. It is then transferred to the right ventricle. The right ventricle pumps the blood into the lungs and then the blood moves into the left atrium. Finally the blood moves into the left ventricle which pushes the blood through the arteries of the body to distribute the oxygenated blood to all of the organs and tissues of the body. Each chamber of the heart has a specific function, and there is a specific flow of blood involved. The following schematic depicts the 4 chambers of the heart along with the direction of blood flow.

As you can see, the blood has unidirectional flow from one chamber to the next. In other words, the blood does not move from the right ventricle back into the right atrium (at least it doesn’t happen with a normal, healthy heart!). If this makes sense to you, then you now understand the idea of compartments. In a very real way, the chambers of the heart are separate “compartments” that the blood passes through.

In pharmacokinetics we don’t use tangible “compartments” like the chambers of the heart. Instead we use theoretical, or imaginary “compartments”. If you were to draw a picture of all the organs and tissues of the body, each as a separate compartment, it would look something like this (image from dougneubauer.com):

Even this model is a bit simplistic for the body, are all muscles the same? What is the “Rest” of the body? Clearly, if we tried to identify every single different tissue in the body, we would have infinite “compartments” in our model. Pharmacokineticists like to simplify things significantly. Thus, instead of defining tangible compartments, we design theoretical compartments with *unique* names like 1, 2, 3, central, peripheral, etc. (I hope you noticed the sarcasm!). Then we draw arrows between these compartments to show how the drug travels from one compartment to the other. Here are 2 examples:

#### 1-Compartment Model

- Drug enters the central compartment (or compartment 1) from somewhere outside of the body.
- Drug then leaves the central compartment. This is analogous to the drug leaving the body.
- Drug recirculation does not occur (output line does not reconnect with input line).
- The 1-compartment model considers the entire body, and all of the organs and tissues to be one giant bucket.

#### 2-Compartment Model

- Drug enters the central compartment (or compartment 1) from somewhere outside of the body.
- Drug then leaves the central compartment by one of two paths:
- the peripheral compartment (also called compartment 2) or
- drug leaves the body

- Drug that is in the peripheral compartment can return to the central compartment.
- Drug recirculation occurs between the central and peripheral compartment, but once drug leaves the body, it does not re-enter the body.
- The 2-compartment model considers the entire body, and all of the organs and tissues to be two buckets, but all drug must leave the body through a single bucket.

In many ways the compartmental models are very similar to the heart chamber model. These models show movement from one “chamber” to another. The 2 key differences are that the pharmacokinetic models are not closed systems (drug is not recirculated from output to input); and pharmacokinetic models permit bi-directional movement (the heart chamber model only allows unidirectional movement).

Hopefully you now understand what is meant by compartmental models in pharmacokinetics. In essence, the number (1, 2, 3) refers to the number of circles drawn on the paper. Many may be asking * why* we use compartment models in pharmacokinetics. The brief answer is that the mathematical functions associated with compartment models seem to describe the observed data very well. It is for practical reasons, not physiologic reasons that we use compartmental models. I will leave the detailed explanation for another blog post.

The methods used to characterize the pharmacokinetics (PK) and pharmacodynamics (PD) of a compound can be inherently complex and sophisticated. PK/PD analysis is a science that requires a mathematical and statistical background, combined with an understanding of biology, pharmacology, and physiology. PK/PD analysis guides critical decisions in drug development, such as optimizing the dose, frequency and duration of exposure, so getting these decisions right is paramount. Selecting the tools for making such decisions is equally important. Fortunately, PK/PD analysis software has evolved greatly in recent years, allowing users to focus on analysis, as opposed to algorithms and programming languages. Read our white paper to learn about the key considerations when selecting software for PK/PD analysis.

Hi Dr Nathan,

Thank you for the great explanation on these compartmental model.

May I know what is the difference between non-compartmental and 1-compartmental model?

I am also confused with certain equation such as (I couldn’t find such a thread in this blog)

1. Vd= dose/Co

2. Vd= dose/ Kel*Total AUC

I am not sure which is right to be used for I.P route analysis

Would you please comment on this?

Thanks,

Sophie

Sophie,

Thank you for your comments and questions. I will try to answer them in the order you presented.

1. What is the difference between non-compartmental and 1-compartmental models?

A1. Non-compartmental analysis does not assume any compartmental model. It simply calculates PK parameters from observed data. 1-compartment models are mathematical models that assume that drug distribution follows the characteristics of 1-compartment.

2. Confusion about equations to calculate volume of distribution and which to use for IP route.

Vd = Dose/C0 should only be used for IV doses

Vd = Dose/Kel*Total AUC can be used for any route of administration. This is a combination of 2 equations: CL/V = Kel and CL = Dose/AUC. By rearranging those 2 equations you can get Vd = Dose/Kel*Total AUC.

I hope that helps you!

Nathan

Dear Dr Nathan,

Thank you for the explaining them! I have finally understand which equation to be used in my analysis. Thank you so much.

I also have another one question which is probably relevant to this:

-Given the paucity of time points in my experiment, fitting kel using the final time points could lead to significant error.

-15, 30, 45, 60 & 120 min are my sampling time where Tmax falls at 45 min (bell-shaped graph).

-The concentration of compound after 120 min of sampling is too low to be accurately measured by HPLC.

-To get a better value of Kel, I would need to extrapolate this graph.

-Hence, I have EXTRAPOLATED it up to 360 min by numerically fiting the exponential curve using time points after Tmax (45, 60 & 120 min).

-With extrapolated graph, I then plotted semilog graph of concentration vs time (45 min to 360 min) and get the k value with linear regression equation.

-so my Kel= (k value)(-2.303)

Given, Vd= Dose/Kel*Total AUC as suggested for IP route;

Questions: Total AUC should be from 15 min to 360 min OR from 15 min to 120 min?

Many thanks,

Sophie

Sophie,

If I understand correctly, your Cmax is at 45 minutes. They you have a measurable sample at 60 minutes and a sample at 120 minutes that is below the limit of quantitation. You said you “extrapolated” to 360 minutes … that requires you to use an elimination rate constant. So I presume that the estimated kel after extrapolation is identical to the elimination rate constant that you used for the extrapolation. In your case, you probably don’t have enough data to estimate that terminal slope. You should re-run the study taking more samples between 45 mins and 120 mins and/or validating a new analytical method with a lower limit of quantitation.

Dear Dr Nathan,

Thanks for explaining it, I can see the logic behind it. Thanks again for your opinion.

Regards,

Tan Suk Fei (Sophie)

Hellow, Dr Nathan,

Thank you for your good explanation about pharmacokinetics informations.

I have been confused about necessity of noncompartmental analysis.

I think that compartmental analysis is more accurate and reliable than noncompartmental analysis due to reflecting compartments in body.

Also, compartmental analysis colud calculate PK parameters like AUC and Cmax …etc and complicated calculating equation was processed by many program like WinNonlin.

By the way, Why we use noncompartmental analysis for calculating PK parameters?

Could you please reply on this?

Thank you for your teaching in advance.

Best wishes.

Pita.

Hi Pita,

That is a very good questions. There may be many reasons why noncompartmental analysis (NCA) is used instead of compartmental analysis; however, I think the primary reason is time. Noncompartmental analysis can be completed in a matter of minutes while compartmental analysis requires more time. There is another large distinction between the two types of analysis. NCA is purely observational, meaning it has no predictive properties for what might happen in the future. Compartmental analysis is observational and predictive. Thus, if you only need observational reporting, then NCA is often adequate. But if you need predictive capabilities, you have to use compartmental analysis.

Nathan

Dear Dr Nathan

Could you please, elaborate a bit what you mean by “NCA is only observational and not able to predict what will happen in the future” by using some pharmacokinetic parameters?

Laych,

NCA is a set of mathematical calculations for a given set of data. There is no underlying “model” that can be used to predict what might happen in the future. For example, if you would like to predict the impact of concomitant administration of another drug compound, you cannot use NCA to predict what might happen. You would need a compartmental model to perform that type of prediction.

Nathan

Thank you so much… I first read about compartmental model in graduation 3rd year (2013) but this is the first time that I could understand it 🙂 Thanks a ton 🙂 explaining them using heart has been very helpful to me 🙂 Thank you Dr. Nathan 🙂 Thanks a lot 🙂

Your welcome!

Hi Dr. Nathan, can you please explain the different types of compartmental models? Thank you very much

Hi Hera,

What do you mean by “different types of compartmental models”? I’d be happy to help, but I don’t understand the question.

Nathan

Hi Dr.Nathan ,,vary nice explanation,,i have an small doubt ,,,what is the time taken by Multiple dose to reach at steady state concentration,

Mohanty,

The time required to reach steady-state is a function of the specific compartment model you are using. For a 1 compartment model with linear elimination, the time to reach steady-state is approximately 5 half-lives.

Nathan

Hi Dr. Nathan

I have a query about compartment modeling, I am getting K12=1.0 /hr and K21=0.245 /hr for a drug suspension in sodium CMC and K12=0.521 /hr and K21=0.421 /hr drug-lipid nanoparticles.

where the drug is highly protein bound and nanoparticles are long circulatory (they show more Mean residence time as compared to the drug suspension).

What does it indicate?

Is K12=0.521 /hr and K21=0.421 /hr indicate that nanoparticles are long circulatory?

Thanks

Dear Dr. Nathan,

Thanks for this lecture it really helps. I have one question. Why, with the same drug, does some fit two compartment and some fit three compartment? I have a drug, amodiaquine for malaria, but in the literature I see some used two compartment and others use three compartment. Why this happening?

Thanks.