One of the most misunderstood pharmacokinetic (PK) parameters is volume of distribution. First of all it has numerous abbreviations (V, V_{d}, V_{z}, V_{ss}, V1, V_{c}, V2, etc.), and to make matters worse, many people incorrectly define the parameter. But, once you understand the meaning behind volume of distribution, you will have a solid grasp on the fundamentals of pharmacokinetics.

Let’s start with the basic definition of volume of distribution. The volume of distribution is a proportionality factor that relates the amount of drug in the body to the concentration of drug measured in a biological fluid. That’s it … a proportionality factor … nothing more. You can stump your professor, mentor, or other pharmacokinetic scientists with this little definition.

The power behind understanding volume of distribution comes from the explanation. Think about taking a 500 mg tablet that contains acetaminophen (Tylenol^{®} or paracetamol for those European readers). You have just placed 500 mg of drug in your body, or mathematically:

Amount = 500 mg

Now imagine having a blood sample drawn from your vein about 1 hour later. From that blood sample, we measure the concentration of drug in the plasma (blood = plasma + red blood cells), and it is ~~16~~ 8 μg/mL, or mathematically:

Concentration = 8 μg/mL = 0.008 mg/mL = 8 mg/L

Now, let’s ask a simple question: how much drug is in the body? We know what the concentration of drug is in the plasma, but we cannot convert that to a total amount without knowing the volume of the human container. In the case of acetaminophen, the volume of distribution is about 51 L. Now, you can multiply the concentration times the volume of distribution to arrive at the amount of drug in the body at 1 hour post dose:

Amount (1 hour post dose) = 8 mg/L * 51 L = 408 mg

Now we can compare the amount remaining in the body (408 mg) with the amount of drug administered (500 mg). As you can see volume of distribution is just a proportionality factor that helps convert between amounts and concentrations.

Volume of distribution is called a “primary pharmacokinetic parameter”, which means that this parameter depends on the *physiologic properties of the body* and the *physiochemical properties of the drug*. Volume of distribution is not derived from other PK parameters, instead it is used to estimate the “secondary” PK parameters.

This concept is similar to the primary and secondary colors. Primary colors are RED, YELLOW, and BLUE. These colors are the source for all other colors. Secondary colors are 50/50 mixtures of 2 primary colors, and they are ORANGE (RED + YELLOW), GREEN (YELLOW + BLUE), and PURPLE (BLUE + RED) [Image by Leopard Print]. Much in the same way, combining 2 primary PK parameters will give you a secondary PK parameter. I will give examples of this in a future post, but for now, remember that volume of distribution is primary PK parameter.

But what about all of those different terms? Well, each of the different volume of distribution parameters refer to either volumes associated with different theoretical compartments or different methods of calculating the volume of distribution. There is no consensus on which one is “right”, because each method has its advantages and shortcomings. Future posts will describe the details of each of these versions of the parameter.

At the beginning of this post, I indicated that understanding the definition of volume of distribution would provide significant insight into pharmacokinetics. Now that you understand the the volume of distribution is a proportionality factor, and not a physiologic value, I can explain why this is important. First, there are a few details on the human body that are necessary for this discussion; the human body is primarily (~70%) water, therefore we can think of the body as containers with water:

Body fluid/structure | Actual volume (L) |
---|---|

Blood | |

Plasma | |

Whole Body | 42 |

Drugs that have a volume of distribution ~~7~~ 4 L or less are thought to be confined to the plasma, or liquid part of the blood. If the volume is between ~~7~~ 4 and ~~15~~ 7 L, the drug is thought to be distributed throughout the blood (plasma and red blood cells). If the volume of distribution is larger than 42, the drug is thought to be distributed to all tissues in the body, especially the fatty tissue. Some drugs have volume of distribution values greater than 10,000 L! This means that most of the drug is in the tissue, and very little is in the plasma circulating. The larger the volume of distribution, the more likely that the drug is found in the tissues of the body. The smaller the volume of distribution, the more likely that the drug is confined to the circulatory system.

I hope that helps you understand volume of distribution. It is a critical PK parameter upon which other concepts will be built. Don’t forget, volume of distribution is just a proportionality factor to relate the amount of drug to the measured concentration.

Thank you for your explanation!

I have a question please:

How can we calculate the Volume of Distribution for a new drug?

Best regards.

Volume of distribution can be calculated by running a pharmacokinetic study, collecting blood/plasma samples, measuring drug levels in each sample, and performing either non-compartmental analysis or fitting the concentration-time data to a PK model.

sir

please justify how you have taken volume of distribution of paracetamol is 51L.

Which is neither coming from practical formula of Vd=X/C nor given in literature please justify

Nitish,

Thank you for your question.

Here is a link to one reference that has paracetamol volume of distribution at 65 L (http://sepia.unil.ch/pharmacology/index.php?id=87).

Here is another reference that lists the volume of distribution at 0.9 L/kg (http://link.springer.com/article/10.2165/00003088-198207020-00001).

The value I used was taken from some historical materials that I had and is used for illustrative purposes only. You can change the value to any number you like, but the principle is still the same. Volume of distribution is not a real number that is related to a physical space or volume. It is simply a proportionality constant between the amount of drug in the body and the concentration of drug measured in a body fluid.

Nathan

Thank you for your explanations. Could you please explain us about volume of distribution in tissue as data generated by WINNONLIN in ug/(ng/g)?

Vinod,

I don’t quite understand the question. Perhaps you could expand on your example a bit more.

Dear Dr. Teuscher,

Many thanks for the very interesting article.

Can I say that the volume of distribution indicates the capacity of a drug to “leave” the circulatory system?

Kind regards,

Luiz

Hi Luiz,

I don’t think that the definition you suggested is accurate. The volume of distribution is a proportionality factor between the amount of drug in the body and the concentration that you measure in the biological fluid. Imagine an experiment where you have a water bottle with water. You don’t know how much water is in the bottle, but you want to find out. So you add 100 mg of a chemical. Then you shake up the bottle and take a sample of the water. You measure the concentration of the chemical in the water (suppose it is 1 mg/mL). You now know how much chemical you added (100 mg) and the concentration (1 mg/mL). Using that information you can determine the volume of water (100 mg / 1 mg/mL = 100 mL). This is exactly what you are doing with PK … you give a dose (using in mass units like mg) and then you measure the concentration of drug in the serum or blood. Using that information, you calculate the relationship between the concentration and the amount. We call it a “volume”, but unlike water in a water bottle, humans are made up of complex tissues and fluids, so the “volume” is just a proportionality factor.

Best regards,

Nathan

Is the volume of distribution measured with or without proteins like albumin?

For the drug acitretin I found the values

protein (albumin) binding 99.9%

volume of distribution 9l/kg, that is 630 l for a man of 70 kg

without albumin I would get a value of more than 4000 l (1000 times the free drug in the blood) – much more than the 630 l;

with albumin I have the situation:

less than 1% of the drug is in the 4l (7l) blood, 99% in the remaining 620+ l

nearly all of the 1% in the blood is bound to albumin (it is not saturated because the amount of albumin molecules within the blood is 50 times the number of drug molecules); 0.001% is free in the plasma;

another 1% of the drug should be bound to albumin within the body; about 0.01% should be free in the body liquid;

The drug has nearly no lipid binding (http://www.actasdermo.org/en/guidelines-for-use-acitretin-in/articulo/S1578219013001479/);

The question remains: Where is the drug, or which values are measured in a wrong way?

Andrean,

Volume of distribution is a proportionality factor between the concentration measured in serum/blood/plasma and the amount of drug in the body. It is not a “real” volume. I do not believe that protein binding is a significant factor in any volume of distribution calculations. Protein binding associations are relatively transient, meaning that if the drug finds a better friend, it will leave the plasma protein and bind to a cellular surface protein or tissue protein. There is very little energy required for a drug to bind/unbind from a plasma protein. Thus, the real effect of those protein is negligible or insignificant in nearly all cases.

Based on the numbers you gave (Vd = 9 L/kg or 630 L for a 70 kg person) the drug acitretin is well distributed throughout the tissues in the body. This means that a very small portion is located in the plasma. The total drug in the body is largely unaffected by changes in the plasma, because 99% of the drug is in the tissues of the body.

Hope that helps!

Nathan

why we measure the conc. at plasma not the site of action ?

Thank you for the reply.

Yes, that’s the theory. Large Vd-value means small part in the plasma. Large lipid binding -> large Vd-value;

But the thing is that the Vd-value does not fit to the properties of the drug. The equilibrium between free and bound drug in the plasma is strongly on the side of the albumin; the same should be the case in the other tissues, therefore the distribution should follow the distribution of albumin, and I would await something like 9 L or maybe 0.2 L/kg; lipid binding is small according literature – there is a similar (former) drug etritenate with a 50 times higher lipid binding and a distribution of only about 1.5 L/kg therefore this is not an explanation for the large value for acitretin.

Maybe for extreme examples like here with the 99.9% albumin binding the real plasma concentration could not be measured in the right way therefore the plasma concentration is underestimated therefore the Vd value is overestimated -> therefore other values like therapeutic windows could be wrong as well.

Maybe the values should be reestimated with the newer and better equipment.

Best regards Andrean

Thanks alot for your article.

One thing is yet not clear for me. For hydrophilic drugs such as gentamycin, if the amount of extracellular water increases (for example in infants compared to adults), the Vd increases.So we have to increase the dose in infants to obtain the same plasma concentrations as in adults (https://www.ncbi.nlm.nih.gov/pubmed/25855821). But in case of an obease person (higher fat, higher Vd) we have to reduce the dose for a lipophilic drug.

why?

Thanks alot

Niloufar,

The Vd is not a “real” thing … it is just a proportionality factor. There is no direct relationship between Vd and a physiologic value. Instead Vd is a compilation of physiology and drug properties. There can be some generalizations, but most are not consistent for all drugs and patients.

Nathan

Dear Dr. Teuscher,

Thank you for the great explanation. You explain in a very simple language. Now I would never forget Vd.

Thank you.

Ripal.

Certainly, It helped. This is the great explanation. You provided the better explanation for Vd that just polished my concept of volume of distribution.

Thanks for the great article.

I can’t understand why some sources express Vd in L instead of L/kg

Do different studies use different calculation methods to arrive at different units or are some drugs better described in units of L versus L/kg?

Vd is just the proportionality factor between the amount of drug in the body and the concentration measured. Thus, if the dose is in mass units (mg, ng, etc.), then Vd will be in volume units. However, if the dose is in mass per body weight units (mg/kg, ng/kg, etc.), then Vd will be in volume/body weight (L/kg).

So it all depends on how the dose was used in the equations to calculate Vd.

Can volume of distribution be significantly lower that total blood volume for example 100-200 mL. If it’s possible when does it happen?

Yes. Again, Vd is not a physiologic value, so it can be anything greater than 0. Very small values of Vd suggest that the drug is not widely distributed througout the tissues of the body. It might be confined to a very small area in the body due to its high specificity for the target.

Hi Dr Teuscher,

Could you please elaborate why the apparent volume of distribution can be smaller than the plasma volume? I understand that Vd is just a parameter that relates Dose and Cp and not a real physiological volume. However, I am struggling to understand how a dose administered by IV bolus can result in a measured Cp than is a *higher* concentration than Dose/Plasma Volume.

Thanks,

Rob.

For a drug to be highly efficient should it have high volume of distribution or low volume of distribution?

I don’t think there is a correlation between efficacy and volume of distribution. There are highly efficacious drugs with both high and low volumes of distribution.

Nice explanation.

I have a question, how does volume of distribution affect half life? Please explain.

Volume of distribution and half life are independent of one another.

A layman will never fail to understand this. Thank you so much, Dr. Nathan.

Thank you professor for this magnificent explanation …

But I have a question: why if the volume of distribution is great it is said that the drug has a great concentration in the tissues, and if it is small it is said that this drug concentrates in the blood?

Ghassen,

In the post above, these generalizations seem to be consistent with observations and physiology. That is why we commonly use these correlations between volume of distribution and concentrations in tissue and blood.

Hi sir, from your article above, it is stated that “Drugs that have a volume of distribution 7.4 L or less are thought to be confined to the plasma, or liquid part of the blood. If the volume is between 7.4 and 15.7 L, the drug is thought to be distributed throughout the blood (plasma and red blood cells). If the volume of distribution is larger than 42, the drug is thought to be distributed to all tissues in the body.” I understand that, but how if I have a volume of distribution of 35 L?

Hope to hear from you soon.

Thank you in advance.

Tang, Thank you for the question. Volume of distribution is only a proportionality factor. Correlations between specific numbers and tissue distributions are only approximate. For a drug with a volume of distribution of 35 L, I would interpret that it is distributed to some, but not all tissues in the body.

Hi,

Is it theoretically possibly to calculate volume of distribution if the compound is administered only in oral administration in single and multiple dosing regimens and not as an i.v. bolus dose?

Many thanks for the answer.

If you do not have IV data, then you can only calculate Vd/F.

Hi,

Your article is extremely helpful. I have encountered a question related to both volume of distribution and clearance. It goes like this: a drug has a volume of distribution of 10L, the Clearance is 7L/h. How long does it take to remove 75% of the drug. How could I calculate the answer?

Many thanks.

After 1 half-life, 50% of the drug is eliminated. After 2 half-lives, 75% of the drug is eliminated. Therefore, if you have the half-life of the drug, you can calculate how long it takes for 75% of the drug to be eliminated. t1/2 = ln(2) / Kel. Kel = CL/V = 7/10 1/h = 0.7 1/h. t1/2 = 1 hr. So 75% of the drug will be cleared in 2 hours.

Hi,

I am so glad I found your post – very helpful!

I have come across this question:

Assuming that a drug is cleared by first order kinetics and is completely distributed, estimate the amount left in the patient following an acute overdose under the following conditions: dose ingested was 50 g 15 hours ago of a drug with a t1/2 of 5.2 hr, patient weight is 140 lbs, the VD is 4.2 L and the current blood concentration is 67 µg/mL.

I am not sure how to calculate the answer since the question says “….is completely distributed” but also with a provided VD of 4.2L….

Any feedback would be very helpful.

Thanks in advance.

Ling,

The phrase “is completely distributed” is confusing. The amount in the body is simply the concentration times the volume of distribution.

Hello Dr. Teuscher, Regarding NCA of a drug administered by a single IV infusion, which volume of distribution (Vz or Vss) is the most appropriate to report and why? There has been some discussion surrounding this. When reviewing literature it wasn’t exactly clear, however there may be instances where one is more appropriate than the other (over or underestimated). Phoenix will report both Vz and Vss for single IV infusion and multiple dose. Many thanks in advance.

LA,

I don’t have a preference for either Vz or Vss as being more accurate. Both are estimates. The best estimate for V would come from a compartmental model of the data (assuming you had a rich profile).

Thank you, this is helpful.