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 it’s 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.

so, how is the volume of distribution calculated? in an example you mentioned that acetaminophen has a V of 51L. where does this come from and does it vary from individual to individual?

thanks.

Good questions. Volume of distribution is estimated as a parameter from a model fit of the data, or calculated in a noncompartmental analysis. As I noted, volume is a proportionality factor between the concentration measured and the amount of drug in the body. Thus, volume varies across individuals based on their physiologic makeup.

so does changing the dose change the volume of distribution ,for the same individual ?

In most cases, the volume of distribution does not change with dose. However it is possible that distribution is dose-dependent.

You said that some drugs have Vd greater than 10000L……..and they are mostly distributed in the tissues…….

suppose they are almost completely distributed in the tissues but even then how can they occupy 10000L????

Thank you for the question. You are correct that a human being does not have a volume of 10000 L!

The Volume of Distribution is not a physical volume, instead it is a proportionality factor between the amount of drug in the body and the concentration measured in the circulatory system. Drugs that reside primarily in the tissue will have small concentrations in the plasma. Imagine giving a dose of 100 mg (100,000,000 ng) and only measuring 10 ng/mL in the plasma. Also, lets assume 100% bioavailability. Given that Concentration = Amount / Volume, you can calculate the volume of distribution as 100000000 / 10 = 10,000 L.

The key is remembering that the Volume of Distribution is a proportionality factor, not a physical volume.

Hi,

Regarding the example above, does the total amount of drug include free drug molecules and drug molecules that are bound to plasma proteins etc?

Thanks.

These examples are based on the total amount of drug in biological fluid.

Nathan

I have a question about your acetaminophen example in your article. was 51 L given somewhere or found on some other reference? say that we were looking for the volume of distribution of acetaminophen instead of how much of the drug is left in the body.

if concentration = amount/volume, flipping it around to find volume, you would get 500mg/8mg/L = 62.5 L. would 62.5 L be the volume of distribution?

Thank you!!

Thanks for your question. The 51 L was taken from a published evaluation of the pharmacokinetics of acetaminophen.

The calculation of V can be performed using a variety of methods. Follow this link for the equations: http://learnpkpd.com/2011/03/31/the-difference-between-vd-and-vss/

Your equation is not accurate because you haven’t accounted for drug that has been eliminated from the body. At 1 hour post-dose, some of the drug has been eliminated, so it is less than 500 mg. There is no exact way of measuring the amount of drug in the body at a specific time, so you could not calculate Volume of distribution using the equation you listed.

Hope that helps!

drug with high Vd are distributed to tissues only small amount reaches plasma…? then what happens to the drug in tissues ? is it slowly released in plasma after the plasma drug being excreted out ? or drug remains in tissue for so long ?

Your interpretation is correct. Drug molecules are constantly moving between tissues and the plasma. As a drug molecule is eliminated from the plasma, the drug molecules in the tissue move to replace it. Since movement from tissue to plasma slower than clearance from the plasma, this distribution process becomes the rate limiting step. Eventually all of the drug molecules leave the tissue and are cleared from the body.

Thank YOu very much Mr. Nathan… thats very easy explanation i had to present on TDM to Physicians and your this post helped me alot… just have to ask can i ask u question when i feel stuck somewhere in PK of drugs

I’m happy to help! You are welcome to ask questions anytime. You can post on my blog, or use the contact menu at the top of the page.

please Mr Nathen how dose Vd change with disease

Nabeil,

Thank you for the question. Changes in the volume of distribution may occur with different diseases, but I haven’t found a lot of research on the topic. There is one publication from 1976 on the topic that you may want to review (Klotz U., Pathophysiological and disease-induced changes in drug distribution volume: pharmacokinetic implications. Clin Pharmacokinet. 1976;1(3):204-18.). The change in volume of distribution depends on the type of disease and how that disease affects the physiology of the individual.

Dear Nathan,

I have a few questions:

1) I might be missing something but the actual volume of blood in the body should be about 5.5 liter (male). How come that in your table it is 15?

2) Is it possible that Vd<Volume of plasma (drug conc measured in plasma)

3) Imagine that you work w poorly absorbed drug w absolute BA of c.a. 1%. So you administer it orally and measure a tiny fraction of it in the plasma. Will your PK model show a big Vd value because it thinks that all the drug sits in the tissues but instead 99% is excreted w feces?

Thank you in advance!

Basil, Thank you for your questions. Here are brief responses:

1. Total blood volume includes plasma as well as the cellular components of blood. It has been estimated that total blood volume is about 15 L.

2. It is possible that Vd is less than plasma volume. Remember, that volume of distribution is simply a proportionality factor between measured concentrations and amount of drug in the body. While this situation is rare, it is possible.

3. As I mentioned in answer #2, Vd is a proportionality factor. If you don’t know the absolute bioavailability of a drug, then you cannot calculate Vd, you can only calculate Vd/F. However, if you know the absolute bioavailability, then you are calculating the actual proportionality factor between the amount of drug and concentration of drug in the body. This number is unaffected by the bioavailability, therefore it would be incorrect to say that Vd is large because of low bioavailability. If on the other hand, you don’t know the absolute bioavailability of your compound, then large values of Vd/F could be due to low bioavailability or wide tissue distribution.

I hope that helps.

-Nathan

Till now I do not understand what is the difference between Vd and apparent Vd ?? ,,, and is it right that vd = dose \ concentration of drug in blood

Vd is the volume of distribution which is a proportionality factor between the amount of drug in the body and the concentration measured in blood/plasma/serum. Apparent Vd is Vd/F, or volume of distribution adjusted for bioavailability. Following oral administration, unless you know the absolute bioavailability, you cannot determine the actual volume of distribution. Many drugs are not able to be administered intravenously, making it very difficult to determine the absolute bioavailability. Therefore many reports will list the “apparent Vd” or Vd/F.

thank you,very educative

if volume of distribution if proportionality factor then factor should not change from one person to another. it should stay constant. And you are saying “volume varies across individuals based on their physiologic makeup.”

Please Explain

Ashok,

Thank you for your comment. I believe both statements to be accurate, but I can see the confusion that it might cause. Volume of distribution is a mathematical term that represents the relationship between the amount of drug in the body and the concentration measured in the blood or plasma. Another similar term is “lung capacity” or amount of air that can be held in the lungs. Both of these are mathematical terms; however, they are impacted by changes in physiology. With respect to lung capacity, individual people may have different capacities based on body size, gender, race, and disease status. And individuals may have changing lung capacity if key factors change (e.g., body weight, smoking activities, tumor growth, etc.). Thus lung capacity can change within an individual person, and it is different across different people. The volume of distribution is similar, but the factors are different (e.g., % body fat, body weight, gender, drug permeability, etc.). Thus, individuals may have changing volume of distribution if their factors change, and different individuals will have different volume of distribution values.

Hopefully that helps you differentiate between a proportionality factor, and a mathematical constant (unchanging value).

Best regards,

Nathan

Thanks Nathan

Dear nathan, As you mentioned, Vd= Dose amount/ concentration in blood. But the concentration in blood is lower and lower with the time pasted. How to understand this?

Qiangang,

The equation used, is based on the initial drug concentration in blood at time=0, or the theoretical maximum. Because Vd is a ratio, the true equation is Vd = amount of drug in the body/concentration of drug in the blood. Unfortunately it is very difficult to know the amount of drug in the body after dose administration because of the elimination processes which remove drug from the body.

Nathan

Hi,

I understood the VD of APAP to be ~ 1L/Kg, or 0.95 L/kg. In the example the VD is 51, so the patient is around 118 lbs give or take. If you took a 70kg person, with a larger VD, and given the same example, a measured concentration of 8 mg/L, the calculated amount is in excess of the administered dose. What am I missing? Thanks

Thanks for the question. As you indicate, a larger person would have a larger Vd (~67 L for a 70 kg person). With a larger Vd, the concentration measured in the plasma will be lower since the concentration is equal to the amount divided by the volume (C = A/V). Thus, if there was 408 mg of drug in the body, the measured concentration would be 6 mg/L. You are correct that it would be unlikely to measure 8 mg/L in a larger individual.

Thanks for the question.

I don’t understand how you determined blood volume and plasma volume. My understanding is that normal plasma volume is 0.04L/kg and blood volume 0.07L/kg. These values are 50% less than you describe. How do you explain this?

Thank you for your comment. The post has been updated with more accurate estimates of plasma and blood volumes.

why volume of distribution is greater in renal failure and hepatic failure .

Amita,

In renal failure, patients retain water because they cannot excrete salts and fluids through the kindeys. The increased amount of water in the body can increase the volume of distribution for hydrophilic drugs.

In hepatic failure, plasma protein production decreases which also leads to fluid retention. The increased fluid in the body can increase the volume of distribution for hydrophilic drugs.

Nathan

Hi Nathan,

I still not understand, maybe you can give me some reference to read?

in renal failure, more fluids was in systemic circulation, so the amount was diluted, then lower conc and higher Vd.

but in hepatic failure, more fluids was more likely retented in the tissue, so the systemic circulation actually may have less fluid, if more drug stay in the tissue, then it still should be then lower conc and higher Vd?

am I right about the mechanism?

how it is related with loading dose..?

Hi Amita,

I’m not sure I understand your question. Volume of distribution is an independent pharmacokinetic parameter that depends on the physiology of the body and the properties of the drug molecule.

Nathan

I’m trying to understand how medication dosing might change after one has a gastric bypass procedure. If one takes a drug with a large Vd, meaning the drug distributes into adipose tissue, and then loses 100 pounds of fat after bariatric surgery, how does this affect the dose?

Would this be the same with a small Vd drug since after surgery there would then be less total body fluid for distribution?

Thank you so much!

Katharine,

Excellent question. Significant physiological changes may impact the pharmacokinetics and pharmacodynamics of drugs. Before answering your question, let’s consider 2 separate situations. The first is a drug with a very large volume of distribution, but that the Vd for each patient is about the same, regardless of weight. The second drug has a large volume of distribution, however, Vd is proportional to body weight, which means as weight increases, so does Vd.

Now to answer your question. For Drug 1, a large change in weight is unlikely to affect the Vd because the drug distributes to all tissues in the body, not just fat tissue. For Drug 2, a large change in body weight would affect Vd, and you would likely decrease the administered dose.

So, you to address the problem for a specific drug, you will need to know the volume of distribution AND the relationship of that parameter to body weight.

Thanks for the question!

Nathan

Hi Nathan,

I don’t agree with you with drug 1.

If the drug evenly distributes to all tissues in the body, then a large change in body weight would still affect Vd;

if the drug only distributed to all the other tissue but not the fat, and we assume the 100 pounds they lose is pure fat after bariatric surgery, then that could be the case for drug 1.

Julia

Julia,

Thank you for your comments. I will answer both questions here. Most texts on pharmacokinetics have some discussion of volume of distribution. Some of the most well-known texts are “Pharmacokinetics” by Gibaldi and Perrier, and “Clinical Pharmacokinetics” by Rowland and Tozer.

In certain disease states, volume of distribution may change based on the fluid status of the individual. But the parameter “Volume of distribution” is still a proportionality factor between the amount of drug in the body and the concentration at the site of measurement. When the body composition changes (e.g., fluid retention or dehydration), the proportionality factor also changes. A quick way to think about this is let’s say you drink 0.5 L of water. The volume of distribution for a drug will not increase by 0.5 L because you drank the water. The Vd would only change if there was some fundamental shift in the body composition.

I’m a little unclear about your question regarding volume of distribution and weight. I agree that for some drugs, Vd is correlated with body weight. And if there is a large change in body composition (e.g., loss of fat after bariatric surgery), then the Vd for that subject will change because their body composition changed. The point of this post is that Vd is not simply volume of tissue … if that was the case, Vd could never be larger than about 40-50 L … and we know that some drugs have Vd values of 10,000 L!

In conclusion, my post does not suggest that body weight does not affect Vd, rather my post clarifies that Vd is a function of drug physiochemical properties, body composition, and body weight.

I hope that helps!

Nathan

What are the characteristics of a drug that determines the Volume of Distribution? For example, does a hydrophilic drug have a low Vd, while a lipophilic drug will have a high Vd? What other aspects of the drug molecule determines the Vd?

Mary,

There isn’t a set list of molecular characteristics that determine the Vd for a drug. In general, you are correct that hydrophilic drugs tend to have low volume of distribution and lipophilic drugs have a high volume of distribution. But the specific Vd for a molecule cannot be predicted (in my opinion) from pysiochemical properties alone. The Vd is a proportionality factor between the amount of drug in the body and the concentration of drug measured in some fluid in the body. Thus Vd can be different for each fluid that is measured. Additional aspects that can affect Vd are transporter systems, tissue binding, and sequestration of the drug. Ultimately the best way to determine Vd is to measure the concentration-time profile.

Nathan

Hi! I think it was a good description but i am confused over one thing.

How can you determine the volume of distribution for certain drugs? For example drugs with a volume of distribution of 10 000, that means that they have been distributed to the tissues to a large extent. But isn’t the concentration of the drug in the plasma the only thing that we can measure? So based on the concentration of the drugs concentration in plasma, how is it possible to know if it has been distributed to the tissues or not? (With the volume of distribution of course, but i dont understand how it is possible to found such a value for different drugs).

Thanks in advance!

Best regards

Alexander

Alexander,

Thanks for the question. Volume of distribution is simply a proportionality factor relating the amount of drug in the body to the concentration you measure in a biological fluid (e.g., plasma). As you correctly state, you cannot be certain that a drug enters tissues unless you measure it in those tissues. The volume of distribution makes the assumption that the drug distributes evenly and instantaneously through the body. By measuring the concentration in one location, we assume that the same concentration occurs throughout the body. Using those assumptions and the single measurement, we can calculate a theoretical volume. Again, this is simply a proportionality factor to help us with calculations that relate dose to concentration.

Nathan

Thank you for this great explanation, Nathan.

I want to ask about the difference between Distribution and Volume of Distribution. For instance, Vancomycin is widely distributed in most tissues and fluids (except poor CSF and lung penetration). But it is also my understanding that Vancomycin has a small Volume of Distribution due to its hydrophilicity, i.e. it likes to be in body fluids and not fatty tissues.

I believe the same could be said of the Aminoglycosides. Gentamicin is widely distributed, but has a small Volume of Distribution.

So it seems that widely distributed drugs have a small Volume of Distribution? Am I missing something?

Thank you very much for your help with this!

Michael

Michael,

Thank you for your question. It can be very confusing when the same word is used multiple times for different things. The PK parameter “Volume of Distribution” is a proportionality factor that relates the amount of drug in the body to the concentration measured in some biological fluid. It is simply a math term that helps us with our equations. The “distribution” of a drug generally refers to either the process or extent to which a specific drug molecule moves through tissues in the body. Thus, you can have a drug the “distributes” to a specific organ, yet has a small volume of distribution. This is common with agents that might take advantage of some targeting moiety.

With respect to Vancomycin, it has a volume of distribution of approximately 0.7 L/kg (or 49 L for a 70 kg person). That is larger than total body water (42 L), which means that it distributes to more than just the total body water. It gets into the tissues. The volume of distribution for Vancomycin is not considered small, although it is much less than some other drugs (e.g., Digoxin has a Vd of 500 L). I believe a “small volume of distribution” would be less than 15 L (<0.2 L/kg). Anything larger than 42 L (>0.6 L/kg) would be considered large. Thus, aminoglycosides would fall into the moderate to large volume of distribution category for me … which is consistent with their distribution to most of the tissues of the body.

I hope that helps!

Nathan

what is the difference between Vd and Vdss.In single dose PK study which is more approprite to use.

Here’s a link to a journal article on Vdss and Vdarea, two methods of estimating the volume of distribution (Vd): http://www.ncbi.nlm.nih.gov/pubmed/6355205

Dear Michel,

Thanks for sharing the article. I want to understand for oral dose, which is the most suitable volume of distribution to be presented (Vd/Vz).Also while calculating volume of distribution by non-compartmental we use dose*F/Kel*AUC.But some of the software(e.g Winnonlin) does not consider ‘F’ in their calculation. is it correct?

regards

Raja

Here are some equations for estimates of volume of distribution:

Vz = CL/kel

Vss = D*AUMC/(AUC^2)

Vdarea = FD/AUC/kel

Many of these are simply manipulations of each other (Vz and Vdarea are different ony by substitution of FD/AUC for CL).

Most software packages calculate V/F if the value for F is not known for an extravascular dose administration. So F is considered, it just isn’t calculated. At that point, you will be reporting the “apparent” volume of distribution. The only way to accurately estimate the real volume of distribution is to administer an IV dose.

Hi! A question about large Vd (1100L – 3800L) and half life (12hrs).

It would seem to me that drugs with a large Vd will redistribute to plasma for a very very long time, therefore making effective half-life of a very long duration.

The med in question is duloxetine (Vd up to 3800L) which was discontinued 2 months ago. I’m suspecting interaction with mirtazapine (clinical picture of serotonin syndrome), even though duloxetine has not been ingested for 2 months!

Thanks for this great site! – Michelle

How does volume of distribution relate to weight loss?

I don’t think there is a single answer to that question. Volume of distribution is a theoretical volume that is a proportionality factor between the amount of drug in the body and the concentration of drug measured in some fluid. Thus volume of distribution may change with weight, and it may not. It depends on the physiochemical properties of the drug in question and the type of weight loss.

How does Volume of distribution relate to Loading Dose?

Thanks.

There is no relationship between loading dose and Vd. One is a specific measurable item (loading dose), and the other is an experimentally determined PK parameter (Vd).

I have to mix 10 mg of LPS (E. coli lippopolysaccharides) in 1 ml of PBS (phosphate buffer solution). and inject it @4 micro liter (0.004 ml) into mice. i don’t have small syringe, so i want to increase the solute and solvent such that it is equivalent (concentration) to previous solution (10 mg in 100 ml). can you help me how much LPS should be added to PBS, so that If I inject 0.25 ml into mice, the effect would be same as if it were injected as previous dose.

Dinesh,

The original solution is 10 mg LPS/1 mL PBS or 10 mg/mL. You inject 0.004 mL. Thus you have injected 0.04 mg of LPS (0.004 mL * 10 mg/mL = 0.04 mg). If you want to inject 0.25 mL at the same dose of LPS, you would calcuate the target concentration (0.04 mg / 0.25 mL = 0.154 mg/mL). That means you can add 0.154 mg of LPS to 1 mL of PBS to get the 0.154 mg/mL solution. Alternatively, you can add 1.54 mg of LPS to 10 mL of PBS to achieve the same final concentration.

Nathan

Dear Nathan,

Really good job!!!!

I have reas somewhere that there are various types of volume of distribution. is it so?? and if yes then kindly elaborate each

Thanks!!!

hi Nathan, how does the volume of distribution of a drug relate to its ability to cross the blood brain barrier?

There is no direct correlation, but generally, compounds with large volumes of distribution have good penetration across the blood brain barrier. This relationship generally occurs because lipophilic molecules have good BBB penetration, and they have large volumes of distribution.

– Nathan

Dear Nathan,

How can we calculate the Vc and Vdss of an i.v. administered drug which obey two compartmental model?

For a 2-compartment IV model, Vc = V1 and Vss = V1 + V2.

Does the volume of distribution tell you about the characteristics of the drug administered. For example, can you determine if the drug is basic or acidic based off the volume of distribution?

Andrea,

Thank you for your question. The volume of distribution does not tell you much about the physiochemical properties of a drug. In general, drugs with large volume of distribution are more lipophilic than drugs with small volumes of distribution; however, that is not always true.

Nathan

Nathan, I’m a first year PharmD student and I am stumped on a homework problem…I have a chart of “data” with Time (hrs) and Concentration (ng/mL) for an hypothetical drug administered via IV. I have graphed the data on a log-linear scale. Can you give me some pointers on how to take the information I have and use it to calculate the volume of distribution of the drug? If Vd=IV dose/plasma drug concentration, how do I use and interpret “plasma drug concentration”?

Hi Beth,

If you extrapolate the concentration-time curve from the first data points back through the origin (y-axis), you can estimate the concentration at time zero (also called C0). Then you can determine the Volume of distribution using the following equation:

Vd = Dose/C0

Nathan

Dear professor,

I am a cardiac surgeon. You made it so easy to understand the concept of Vd . So nice of you for your patient teaching. thanks a million. Actually I wanted to learn this concept in relation to the drug amiodarone which was bothering me for a long time.

Thank you for posting this article, it helps me to learn this subject at a comfortable pace. Are there online resources which can give specific pk/pd details to aid personal analysis, particularly datasets of hourly readings of plasma concentrations from individual subjects? I was thinking of using such data to create my own tables and charts which I can then try to interpret first-hand.

I am not aware of PK datasets available for that purpose. I generally create my own … but for people new to the area, that can be difficult. I will add this to my list of to-do items and it should show up on my website soon. Thanks for the suggestion.

– Nathan

very nice and easy