[Traumatic Acid]

Hi all, I'm pretty new to (the mathematical aspect of) pharmacology.
Question about the asthma medication aminophylline word for word as follows:



Ms. Nicholls is a 30 year old, 65 kg non-smoker who is to receive intravenous aminophylline for treatment of her asthma.

The bioavailability of aminophylline, F = 1; Vd = 0.5 L/kg; Cl = 40 ml/hr/kg

Each ml of the drug contains 25 mg aminophylline, which dissociates to form 21 mg of theophylline.  The pharmacological effects of aminophylline are entirely attributed to that of theophylline.

The patient is administered a loading dose of 6 mg/kg of aminophylline, i.v.  Calculate the anticipated plasma concentration of theophylline following this dose.

I somehow managed to conclude that Cp = 0.655 mg / kg but It doesn't look quite right to me.

6 mg/kg aminophylline = 15.6 ml drug solution.
15.6 x 21 = 327.6 mg aminophylline.
C = D/Vd
C = 327.7 / 500

0.655 mg/ kg

Any help would be much appreciated.
Cheers

[Mitch]

How did you get to 15.6 mL of drug solution? Out of my own curiosity, which book are they teaching this from?

[Traumatic Acid]

That was quick.

Well the patient weighs 65 kg, so in order to get a dose of 6 mg per kg you would need to administer a total of 390 mg. 390 / 25 mg per ml = 15.6 ml?

I'm not sure if this question came from a book or if the professor made it up himself.

[Mitch]

Shouldn't plasma concentration (Cp) be in units of mass over volume? You got mass (mg) over mass (kg).

[Traumatic Acid]

Ahhh, yeah I get you.

I asked the exact same question on a different forum and a reply I got was:

"Vd should be in just liters, not L/kg. So your numbers are right, but the concentration will be in mg/L."

So 0.655 mg / L

Still seems a little low to me?

[Mitch]

Something seems off about Vd in the problem. The units of Vd should only be in Liters. I think your professor made a typo, but I think your answer is fine.

[Traumatic Acid]

I think he was just abbreviating.
To calculate Vd you multiply the concentration of the drug per kg by the Vd.

Aaaaaaand as soon as I typed that I question my own answer again  
If the patient is 65 kg then that is a conc of 5 mg /L  Theophylline?
therefore Cp = 5mg L / 500 L = 0.01 mg / L

I don't know which is correct now.

[Mitch]

I think you only use the 65 kg to find the mass of drug (dose) you need to give.

[Traumatic Acid]

Okay to the answer I came to is very incorrect, the actual answer was more along the lines of 10 grams / Litre. I am still in the process of getting the correct working out from the professor. To anyone reading this for help, don't do it like that haha

[Traumatic Acid]

Rightio, attached is a copy of the correct working out

[Mitch]

Thanks for sharing the right answer Traumatic Acid.