volume of distribution and clearance?

[cameraGEEK]

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Clearance = volume of distribution * elimination constant

can someone explain why a greater volume of distribution would logically mean a faster clearance?

also, I am trying to fully grasp the difference between clearance and rate of elimination in imaginable terms, anyone have any good examples?

Thanks!

 

[Suncrusher]

I'm confused about this too, and I'm clearly going wrong with my logic somewhere along the line. I hope someone who enjoys puzzles will be able to find what I'm doing wrong and help me.


1) half life = ln(2) / elimination rate constant

and

2) half life = Vd*ln(2) / clearance

therefore:

ln(2) / elimination rate constant = Vd*ln(2) / clearance

1 / elimination rate constant = Vd / clearance

elimination rate constant = clearance / Vd

Vd * elimination rate constant = clearance, the same formula being used by the OP.

============

so a lower halflife is related to a high elimination rate constant (formula 1). That makes sense. A lower halflife is also related to a higher clearance (formula 2). That makes sense. A high elimination rate is related to a high clearance (final formula). That makes sense.

But the problems start when I start thinking about Vd. For instance, a low halflife related to a low Vd (formula 2)? That could make sense, since low Vd means the drug is in the plasma and therefore available for filtration in the kidneys or metabolism in the liver. However, the final formula seems to say that a low Vd should be related to a low clearance (and a high Vd should be related to a high clearance), whereas the forumlas I derived the final formula from seem to say that a low Vd should go relate to low halflife and HIGH clearance.

What went wrong 😕 I've wasted enough time on this and I'm more confused than ever 😳 Normally when stuff like this happens to me in math/logic, it's because I divided by zero or something...sigh...is it because the elimination rate constant is between zero and one? I know my logic is wrong somewhere, but I'm too stupid to find it right now. I'm also confused because sometimes a low Vd means that the drug is bound to plasma proteins and therefore LESS available for clearance due to filtration or metabolism...

 

[cameraGEEK]

bump, help!

 

[lemonade90]

“half life = Vd*ln(2) / clearance”

“…that a low Vd should go relate to low halflife and HIGH clearance.”

If Vd is down, half life is down (assuming clearance is a fixed variable/constant). If Vd is down, clearance must go down (assuming half life is the fixed variable/constant). Perhaps you were not keeping any variables fixed?

 

[notarealname]

Clearance = volume of distribution * elimination constant

can someone explain why a greater volume of distribution would logically mean a faster clearance?

also, I am trying to fully grasp the difference between clearance and rate of elimination in imaginable terms, anyone have any good examples?

Thanks!

Vd = (total drug in body)/(drug concentration in plasma)

Vd is volume of distribution

what it means is that Vd = (some total amount of drugs in body in grams) / (a unit of concentration of drug in plasma g/L)

And remember Vd is a hypothetical volume which was created for calculation of drugs physiological properties. Continue with our logic, we have Vd= (g)/(g/L) = L, so Vd = L

I hope you are following of what I did so far, if not go hit your MCAT books LOL


You question is that you want to understand why increase of clearance is related with increase of Vd. And here is your equation:

Clearance = volume of distribution * elimination constant

Do you know the unit for clearance? It is some unit volume per unit time, so you can have L/s, L/min, ml/s, or ml/min, or perhaps even ml/hr.

now I hope it is clear to you hat clearance is a flow rate ml/min, which is how much of the volume lost per unit time. Don't worry about elimination constant, just because it is a constant 😉. by just looking at Clearance = Vd, everything should starting to make sense to you.

Clearance = Vd, essentially means if you increase your hypothetical volume of drug then you have a natural increase to loss those volume at a higher rate.

also you have another simple equation to use that is in the first few pages of every pharm book... CL= (rate of elimination of the drug) / (plasma drug concentration), CL is clearance, just for the fun sake I am going to demonstrate the unit for you CL= (g/min)/(g/L)=L/min, and just as we said earlier it is unit volume per unit time.

Now to explain the difference between rate of elimination of the drug and clearance of the drug, look at the CL equation again: CL= (rate of elimination of the drug) / (plasma drug concentration), CL is volume per time L/min, and rate of elimination of the drug is amount per time g/min. You can think of CL is the the loss of volume, and rate of elimination as loss of mass or loss of amount of the drug in grams.


To make this whole thing logical to you. I give you two drugs, drug A given IV with Vd=1L, you know all the the drug are in plasma. Drug B given orally with Vd=1000 L, you know most of your drug are not in your plasma. If I give you 1 hours to eliminate both drugs. then Drug A will only have CL of 1L/hr, and Drug B because of higher Vd will need to have CL of 1000 L/ hr. My examples are not very realistic but you get the idea, if you want to eliminate a drug that is well distributed you need to loss at a greater volume per time, if you are eliminating a drug that is only in plasma then it is easy so you have a smaller CL.

I hope I am answering your question.

 

[cameraGEEK]

Vd = (total drug in body)/(drug concentration in plasma)

Vd is volume of distribution

what it means is that Vd = (some total amount of drugs in body in grams) / (a unit of concentration of drug in plasma g/L)

And remember Vd is a hypothetical volume which was created for calculation of drugs physiological properties. Continue with our logic, we have Vd= (g)/(g/L) = L, so Vd = L

I hope you are following of what I did so far, if not go hit your MCAT books LOL


You question is that you want to understand why increase of clearance is related with increase of Vd. And here is your equation:

Clearance = volume of distribution * elimination constant

Do you know the unit for clearance? It is some unit volume per unit time, so you can have L/s, L/min, ml/s, or ml/min, or perhaps even ml/hr.

now I hope it is clear to you hat clearance is a flow rate ml/min, which is how much of the volume lost per unit time. Don't worry about elimination constant, just because it is a constant 😉. by just looking at Clearance = Vd, everything should starting to make sense to you.

Clearance = Vd, essentially means if you increase your hypothetical volume of drug then you have a natural increase to loss those volume at a higher rate.

also you have another simple equation to use that is in the first few pages of every pharm book... CL= (rate of elimination of the drug) / (plasma drug concentration), CL is clearance, just for the fun sake I am going to demonstrate the unit for you CL= (g/min)/(g/L)=L/min, and just as we said earlier it is unit volume per unit time.

Now to explain the difference between rate of elimination of the drug and clearance of the drug, look at the CL equation again: CL= (rate of elimination of the drug) / (plasma drug concentration), CL is volume per time L/min, and rate of elimination of the drug is amount per time g/min. You can think of CL is the the loss of volume, and rate of elimination as loss of mass or loss of amount of the drug in grams.


To make this whole thing logical to you. I give you two drugs, drug A given IV with Vd=1L, you know all the the drug are in plasma. Drug B given orally with Vd=1000 L, you know most of your drug are not in your plasma. If I give you 1 hours to eliminate both drugs. then Drug A will only have CL of 1L/hr, and Drug B because of higher Vd will need to have CL of 1000 L/ hr. My examples are not very realistic but you get the idea, if you want to eliminate a drug that is well distributed you need to loss at a greater volume per time, if you are eliminating a drug that is only in plasma then it is easy so you have a smaller CL.

I hope I am answering your question.

Thanks for these great answers to both of you 🙂 I understand your logic and what you have done, except for one issue. I guess my confusion lies in what clearance is telling us realistically. In your example, you mention that for Drug B, because of higher Vd, will need to have CL of 1000 L/ hr ... how can the body know or be able to do this faster clearance. When I think of it in practical terms it seems like it should be harder for the body to extract the volume in needs to excrete from this wider more dispersed volume? Do you mean that clearance is just a theoretical value for what the body would need to do to maintain functioning (but may not necessarily be able to do in real life)? Or, is it that the body somehow knows it must compensate for the less concentrated volume by clearing much, much faster, and is able to do this. I hope my point of confusion makes sense. Thanks so much for your time & help, would love to hear any thoughts on this issue.

 

[notarealname]

Thanks for these great answers to both of you 🙂 I understand your logic and what you have done, except for one issue. I guess my confusion lies in what clearance is telling us realistically. In your example, you mention that for Drug B, because of higher Vd, will need to have CL of 1000 L/ hr ... how can the body know or be able to do this faster clearance. When I think of it in practical terms it seems like it should be harder for the body to extract the volume in needs to excrete from this wider more dispersed volume? Do you mean that clearance is just a theoretical value for what the body would need to do to maintain functioning (but may not necessarily be able to do in real life)? Or, is it that the body somehow knows it must compensate for the less concentrated volume by clearing much, much faster, and is able to do this. I hope my point of confusion makes sense. Thanks so much for your time & help, would love to hear any thoughts on this issue.

You welcome, make sure you know that CL is volume over time, a larger volume just means it has a lower concentration. In another words, a drug with higher Vd need a lot of volume to have the same amount of drug as a drug with lower Vd. But honestly you don't need to relearn physics, just stick with the facts and know roughly how it works then you should be fine.

 

[SeventhSon]

This was probably already answered by the posts above, but succinctly...

Clearance is the amount of equivalent plasma cleared of some substance, X.

Consider fixed amounts of substance X and Y administered to two different patients, say in mg/kg, and assume they are eliminated by first-order kinetics and have the same half-life. Their excretion rates from the body are the same , but the clearance of X is twice that of Y, not because of some deep, confusing concept, but simply because X was diluted by a factor of two in the plasma to begin with, meaning the equivalent amount of plasma cleared was greater, though the absolute amount of drug excreted was the same. This might be kind of tricky to wrap your head around but I think you'll get it after some thought.

Note to be precisely correct in this specific example you have to make some additional assumptions about the kinetics of the additional compartments of the volume of distribution but I won't go into those assumptions.