topic Re: solving an integral for pharmacokinetics work in Discussions

solving an integral for pharmacokinetics work

tvkmez11 — Thu, 03 Nov 2016 07:28:33 GMT

Hi,

Pharmacokinetics: mathematically characterizing how a drug enters and leaves the body

In pharmacokinetics experiments the influence of the stomach is ignored in most data analyses, which is not appropriate. Stomach emptying can be described with the equation (in which t=time):

Plateau×(1-e^(-Ks × t))^ß (Ks=rate, beta =lag phase)

Subsequently, the absorption kinetics of a test component can be described with the equation:

Plateau ×(Ka× (Exp^(-Ke × t)-Exp^(-Ka × t)))/(Ka-Ke) (Ka=absorption rate, Ke=elimination rate, Plateau is cummulative absorption)

Combining both gives:

∫ Plateau×(1-e^(-Ks × t))^ß * Plateau ×(Ka× (Exp^(-Ke × t)-Exp^(-Ka × t)))/(Ka-Ke)

Does anybody know how to solve such an equation in JMP, or is someone smart enough to integrate them (I am not)? I can only solve it in Excel, but then I don't get statistics.

Happy to include you as a co-author in a publication on the topic if we end with publishable outcomes.

thanks

Theo

Re: solving an integral for pharmacokinetics work

Steven_Moore — Thu, 03 Nov 2016 13:14:32 GMT

There are many sirtes on the internet that will solve derivatives and integrals for you. See this link for one of my favorites:

http://www.integral-calculator.com/

Re: solving an integral for pharmacokinetics work

tvkmez11 — Thu, 03 Nov 2016 15:27:59 GMT

Hi Steven,

Thanks for pointing this out to me; learning every day. I have tried the link you supplied, and this site can't find an answer, same answer I got from a couple of professors in mathematics.

Theo

Re: solving an integral for pharmacokinetics work

MRB3855 — Thu, 03 Nov 2016 15:40:36 GMT

Wolfram Alpha...maybe?

http://www.wolframalpha.com/examples/Integrals.html

Re: solving an integral for pharmacokinetics work

tvkmez11 — Thu, 03 Nov 2016 15:43:12 GMT

came across the wolfram site, and this one did yield an integral. Something to try tonight ;)

Re: solving an integral for pharmacokinetics work

Byron_JMP — Tue, 24 Sep 2024 19:11:58 GMT

I think you could use JSL to solve the problem

pl=1;
ka=1;
ke=.5;
pk=expr(pl*(ka*(exp(-ke*t)-exp(-ka*t)))/(ka-ke));
integrate(pk, t, 0, 12);