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February 22nd, 2012, 01:55 PM   #1
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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
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February 23rd, 2012, 01:05 PM   #2
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Re: Drug level decay model

You have one equation with two unknowns - this can't be solved.
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February 23rd, 2012, 02:52 PM   #3
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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)
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February 24th, 2012, 12:32 PM   #4
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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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