RE: backward integration from t-a to t
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:
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Quoted reply history
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,
Â
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.Â
Â
Is there a way to access AUC for the past time points (<t) from the
integration routine? It seems like an easy thing to do.  Â
Â
Kind regards,
Pavel Â
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