Basic Applied Pharmacokinetics (need help.. newbie)

[selenew]

I'm a newcomer to the world of Pharmacology and I am hoping you guys would help familiarize with this subject :l
Here are some of the questions I have a hard time of answering. If this is too basic for you, please help me in finding the answers to these problems.

1) A dose of 2000mg of a drug is administered to a patient and the following blood levels result at the indicated times:

Plasma Conc (ug/ml) Time after dose (hr)
100 ..................................2
50 .................................. 4
30 .................................. 6
What is the estimated volume of distribution?

-i know the formula volume distribution = dose/ concentration but how does this apply to the above question?


2) Provide the predicted resulting concentration at the time of measurement

initial plasma conc (ug/ml) = 120 ; t1/2 = 3 ; time after initial conc (hr) 12 ; predicted plasma conc =?


3) the plasma concentration achieved after oral administration of 80mg propranolol is equivalent to IV administratio of 2 mg Propranolol. Explain the difference in the required dosage.

-how do i prove this?

4) Four different drug products containing the same antibiotic were given to 18 volunteer adult males in a 4 way cross over design. the volunteers were fasted 12 hours prior to taking the drug product. Blood samples werecollected up to 72 hours after the administration of the drug. the following are obtained

drug product dose (mg/kg) AUC (ug/ml x hr)
IV sol 4 58
oral sol 20 300
oral tablet 20 230
oral capsule 20 250

determine the following:

a. apparent volume distribution
b. halflife
c. elimination rate constant
d. total body clearance


-can you provide the formulas to be used in these problems?
-i've looked on different pharmacology books but i can't apply the formulas stated in them.
-any comment will be appreciated
-thanks

[Catarro]

I dont have a lot of time. Im going to help you with the first one, but please understand this is very hard to explain via internet.

1) For this first question, you need to know HOW was it administrated. That is the first question: was it IV? IM? Oral?

I guess its IV-bolus otherwise it would be very hard to calculate the Vd (volume of distribution). Vd = DOSE administrated / Concentration at the exact time it was given by IV.

You have to plot the results they give you, and by looking at it, I can say the drug follows a first-order kinetic elimination behaviour. This means that for each half-life that passes (this is specific for every drug), you lose half of the concentration you have at the moment. A zero-order kinetics means you always lose a fixed mass of drug/time, so by two half-lifes you will lose all the drug you have in the organism.

SO what you need to do, is use the formula of 1º order kinetics in order to find out, what was the blood concentration when the drug was administered (time 0).

C=Co x e ^ (-Ke . t)

What we have is the drug concentration (C) at a given time (t) but we lack the elimination constant (Ke).

This is easy to calculate: Lets consider Co as 100. Notice that 100 is not the Co that we are after (the real Co at the time where the drug was administered (time 0)), but we have to consider it in order to calculate Ke. So Co = 100 at time 0, and C = 50 at time 2.
Notice what i did: i defined time 2 as 0 and by the time we get to time 4, only 2 hours have passed:

50 = 100. e^ - (ke . 2)
ln 50 = - 2ke x ln 100
Just solve it to find out Ke.

Now after we get Ke, we can use it to calculate the concentration at the real time 0:

100 = Co. e^ - (ke . 2)

Solve it to find Co. After you find Co you can use it to calculate the Vd.

Vd = dose/Co
Vd = 2000mg/Co

Hope it helps.