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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: 6,607 Thanks: 616  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: 6,607 Thanks: 616  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 nonzero or all t's the same.


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