Drug half life

[deleted500612]

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I thought I understood the concept of half life pretty well, but having a hard time understanding the logic behind the equation to calculate half life based on volume of distribution and clearance. Just got a UWorld question with the following drug properties:

- Metabolized via first order kinetics
- Volume of distribution: 10L
- Rate of clearance: 7L/hr

How many hours will it take to eliminate 75% of the drug?

Now of course I did not have the proper equation memorized, so I just tried to logic through it. If the volume of distribution is 10L and you are clearing 7L/hr, wouldn't you be clearing 7/10L of the volume of distribution = 70% of the drug cleared in an hour?? The UWorld explanation doesn't really explain it, and just gives the equation of

t1/2 = (0.7vd)/CL

t1/2 = half life, vd = volume of distribution, CL = rate of clearance

Where is the 0.7 coming from? I really don't understand the logic of this equation, maybe someone better at pharm kinetics can explain why apparently if you clear 7/10L of the volume of distribution of a drug in an hour only 50% of the drug is cleared and not 70%?!

 

[pacman2018]

I haven't done any UWorld questions yet, but I'm assuming they were using the equation t1/2 = 0.693/k. Looks like they just rounded 0.693 to 0.7. I don't remember the derivation of the equation from pharm school, but 0.693 comes from ln(2). Elimination constant (k) is equal to Cl/Vd so that is substituted in. Just remember the first equation for half life and you should be able to substitute in the other factors as needed.

 

[Prince090]

I thought I understood the concept of half life pretty well, but having a hard time understanding the logic behind the equation to calculate half life based on volume of distribution and clearance. Just got a UWorld question with the following drug properties:

- Metabolized via first order kinetics
- Volume of distribution: 10L
- Rate of clearance: 7L/hr

How many hours will it take to eliminate 75% of the drug?

Now of course I did not have the proper equation memorized, so I just tried to logic through it. If the volume of distribution is 10L and you are clearing 7L/hr, wouldn't you be clearing 7/10L of the volume of distribution = 70% of the drug cleared in an hour?? The UWorld explanation doesn't really explain it, and just gives the equation of

t1/2 = (0.7vd)/CL

t1/2 = half life, vd = volume of distribution, CL = rate of clearance

Where is the 0.7 coming from? I really don't understand the logic of this equation, maybe someone better at pharm kinetics can explain why apparently if you clear 7/10L of the volume of distribution of a drug in an hour only 50% of the drug is cleared and not 70%?!

It's just the formula . Memorize it.