# PharmPK Discussion - Variable Infusions and Dose Linearity

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• On 5 Jan 1998 at 12:02:59, "Zutshi, Anup" (zutshi.-a-.BATTELLE.ORG) sent the message

Greetings

Does anyone have a literature citation on using variable rate IV
infusions (typically a linear accelerated infusion) as a means to
determine dose linearity of a test compound?

Anup Zutshi

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• On 12 Jan 1998 at 13:25:30, Maria Durisova (exfamadu.at.savba.savba.sk) sent the message

Dear colleague,

Using the dynamic system approach, the solution of this
problem can be performed according to the procedure
consisting from the following three steps:

1. Definition of the system (1) by the measured input
function I(t) and the measured output function C(t).

2. Calculation of the frequency response of this system
under the conditions:

a) The input function I(t) is represented by any measured
variable rate IV infusion:

I(t) = R(t) for time t from the interval [0, T1]
= 0 for time > T1,

where R(t) is any function, having the value 0 for t<=0 from
below, e.g. the ramp function (to get some information on the
ramp function see e.g.
http://www.astro.virginia.edu/~eww6n/math/),
and T1 is the duration of the infusion.

b) C(t) is the drug concentration time profile. It is
measured in the time interval [0,T2], where T2>T1, and the
residual area under the C(t) profile from the last sampling
point to infinity is less than 10% of the area under the
C(t) profile from time T1 to infinity.

3. Plotting the calculated frequency response in the complex
plane.

According to one of the inherent properties of the linear
dynamic time invariant systems, if the points of the
calculated frequency response of the system under study can
be considered to lie on a continuous curve, the system can
be sufficiently approximated by a linear model (2,1). It
follows then that, the system approach offers the
dose of the drug.

This procedure can be sufficiently performed using our
software CXT (3,4). CXT requires a fair degree of modeling
expertise in the frequency domain. If you are interested, we

Maria Durisova
and

1. L. Dedik, M. Durisova, Frequency response method in
pharmacokinetics, J. Pharmacokin. Biopharm., 22, (1994)
293-307.

2. M.G. Singh, Systems and Control Encyclopedia, Theory,
Technology and Application, Pergamon Press, Oxford UK, 1987.

3. L. Dedik , M. Durisova, CXT - A programme for analysis of
linear dynamic systems in the frequency domain, Int. J.
Bio-Med. Comput., 39, (1995) 231-241.

4. L. Dedik, M. Durisova, CXT-MAIN: A software package for
determination of the analytical form of the pharmacokinetic
system weighting function, Comput. Methods Programs
Biomed.,f 51 (1996) 183-192.

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