RE: backward integration from t-a to t

From: Pavel Belo [email protected] Date: Thu, 16 Jan 2014 13:05:54 -0500 (EST) To: [email protected], [email protected] Subject: RE: [NMusers] backward integration from t-a to t Hello Leonid, Thank you bein helpful. You got the main point. AUC is a better predictor than concentration, but it has to disppear very slowly but surely. A potential challenge is biological meaning of this approach. It will be necessary to explain it to the biologists, who ask question like "Why do you use 2 compartment in PK model while human body has so many compartments?". We will see! Thanks, Pavel On Wed, Jan 15, 2014 at 01:19 AM, [email protected] wrote: > Pavel, > I think one can use equation > DADT(2)=C-K0*A(2) > > where C is the drug concentration. When K0=0, A2 is cumulative AUC. > When > k0>0, A2 would represent something like AUC for the interval prior to > the current > time > The length of the interval would be proportional to 1/K0 (and equal to > infinity when k0=0). Conceptually, K0 is the rate of "AUC elimination" > from the > system. PD then can be made dependent on A2, and the model would > select optimal > value of K0. One interesting case to understand the concept is when C > is constant. > Then A2=C/K0 while AUC over some interval TAU is AUC=C*TAU. So > roughly, A2 can > be interpreted as AUC over the interval of 1/K0. Leonid > > > Original email: > ----------------- > From: Pavel Belo [email protected] > Date: Tue, 14 Jan 2014 13:45:18 -0500 (EST) > To: [email protected], [email protected] > Subject: [NMusers] backward integration from t-a to t > > > > > > Dear Robert, > > > > >  > > Efficacy is frequently considered a function of AUC. (AUC is just > an integral. It is obvious how to calculate AUC any software which can > solve ODE.) A disadvantage of this model of efficacy is that the > effect is irreversable because AUC of concentration can only > increase; it cannot decrease. In many cases, a more meaningful model > is a model where AUC is calculated form time t -a to t (kind of > "moving average"), where t is time in the system of differential > equations (variable T in NONMEM).  There are 2 obvious ways to > calculate AUC(t-a, t). The first is to do backward integration, which > looks like a hard and resource consuming way for NONMEM. The second > one is to keep in memory AUC for all time points used during the > integration and calculate AUC(t-a,t) as AUC(t) - AUC(t-a), there > AUC(t-a) can be interpolated using two closest time points below and > above t-a. > >  > > Is there a way to access AUC for the past time points (> integration > routine? It seems like an easy thing to do.   > >  > > Kind regards, > > > Pavel  > > > -------------------------------------------------------------------- > mail2web - Check your email from the web at > http://link.mail2web.com/mail2web > > > -------------------------------------------------------------------- myhosting.com - Premium Microsoft® Windows® and Linux web and application hosting - http://link.myhosting.com/myhosting