My Math Forum Drug level decay model

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 February 22nd, 2012, 01:55 PM #1 Newbie   Joined: Feb 2012 Posts: 2 Thanks: 0 Drug level decay model There is a known equation to model the drug levels over time. C = (D1/Vd)*e^(-ke*t1) + (D2/Vd)*e^(-ke*t2) + (D3/Vd)*e^(-ke*t3) Where... C = Drug concentration D1 = Dose in mg (eg 1000) D2 = Dose in mg (eg 750) D3 = Dose in mg (eg 1250) t1 = Time from drug administration till level draw in hours (eg. 4 t2 = Time from drug administration till level draw in hours (eg. 27) t3 = Time from drug administration till level draw in hours (eg. 17) Vd = Volume of distribution in Liters (eg. 50) ke = elimination rate constant (eg. 0.035) I have the above equation correctly working in excel, but I want to be able to solve for ke & vd when I have "C" I've been trying to figure this out for a while, but I cant seem to get it to come out right and math has never been my strong suit. Thanks in advance
 February 23rd, 2012, 01:05 PM #2 Global Moderator   Joined: May 2007 Posts: 6,556 Thanks: 600 Re: Drug level decay model You have one equation with two unknowns - this can't be solved.
 February 23rd, 2012, 02:52 PM #3 Newbie   Joined: Feb 2012 Posts: 2 Thanks: 0 Re: Drug level decay model I should have been more clear. I don't want to solve for ke AND vd at the same time. I want to solve for only one at a time. (sometime ke, sometimes vd)
 February 24th, 2012, 12:32 PM #4 Global Moderator   Joined: May 2007 Posts: 6,556 Thanks: 600 Re: Drug level decay model vd is easy - multiply through by vd/c. ke is much harder - can be done readily under special circumstances, like only one D non-zero or all t's the same.

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