pharm question on Loading dose ? help plz

[sadaca]

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hey guys, I have uploaded a question , and the answer is there and explanation. I am poor with math and these type of questions. I don't understand it even after many tries. Could someone plz explain how they got the answer to this?

I would greatly appreciate it.
thank you

 

[Nephronlearner]

The half life is 3 hours -> 6h = 2 half lives

current level: 1 mg/L -> one half life ago it was 2 mg/L and 2 half lives ago it was 4 mg/L (or looking backwards: started with 4 mg/L -> after 3 hours (1 half life) 2 mg/L -> after 6 hours (2 half lives) 1 mg/L)

volume of distribution is 200 L and current concentration is 1 mg/L
mass concentration = m/V => m=conc * V = 200 mg currently in his body

n half lives ago it was 200 mg * 2^n
since you need what happened 2 half lives ago: 200 mg * 2^2 = 200 mg * 4 = 800 mg

I believe this is the simplest way to look at it and I tried to explain every step. If someone is more knowledgeable, feel free to correct me.

 

[sadaca]

hey! Thanks alot. I am a bit confused on how you knew to do 2^2 ?

 

[sadaca]

also could u tell me how u calculated the t 1/2 plz?

 

[Fatalis]

here is a tip man, just cancel out the units if you are unsure.
plasma is 1mg/L and we are told the vd is 200L. So lets multiply them. We get 200mg. Now, we are told the kid did this 6 hours ago and the drug has a t1/2 of 3 hours so we know there are 2 half lives. Therefore we work backwards starting with 200mg; so one half life ago we are at 400 and another half life ago we are at 800mg. Which is the right answer.

 

[sadaca]

oooh! Fatalis to the rescue again!Thanks alot.
Thank you both of you! Much appreciated =)

 

[Nephronlearner]

hey! Thanks alot. I am a bit confused on how you knew to do 2^2 ?

Fatalis is correct. You are just calculating the half-lives.
Maybe you missed the definition of half-life. It is the time required for one half of the amount of drug to disappear (so one half remains). That being said if you have 800 mg then after one half life you have 400 mg (800/2) and after 2 half lives you have 200 mg (800/4 = 800/(2*2)) after 3 half lives you have 100 mg (800/(2*2*2)) after 4 half lives you have 50 mg (800/2*2*2*2) and so on
and those 2*2*2*2*.... = 2^n and since the question was about 2 half lives then you have 2^2=2*2

Working in the opposite direction, you just multiply by 2 for each half life.

 

[sadaca]

Okay, that makes sense now. Thanks for the clarification buddy