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
possibility to  answer your question  even after one  single
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
can help you in the evaluation of your data.

Maria Durisova
and
Ladislav Dedik

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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