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The following message was posted to: PharmPK
Hello all,
A colleague of mine is attempting to fit a 0-order absorption profile to
some data where the length of infusion is not known. I regret, that I
don't
know anything about that software so I can not help him. If you could
let
us know how to model this in SAAM it would be greatly appreciated.
Matt
[I'm not sure that SAAM II will do this (by design) but happy to be
corrected...however Boomer can ;-) I have put a .BAT (control) files in
various formats at http://www.boomer.org/pkin/pk/infit.sit - db]
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The following message was posted to: PharmPK
You can use the XUF function in SAAM.
For example :IC(7)=10
L(1,7)=1
l(0,7)=-1
The negative on l(0,7) is to maintain mass balance. This results in a
constant amount of 10 units /time being delivered to compartment 1.
Under HDAT set XUF=1.
If you want to solve for the infusion rate you need to give an initial
estimate with upper and lower limits.
This example is presented in the online manual on the WINSAAM web site
http://www.winsaam.com/
[This seems to allow a zero order infusion (I seem to remember an
F-dependence in the old SAAM-23/25 that would do this as well) but can
you make the duration of the infusion adjustable? Fitting across a
discontinuity (when the infusion stops) seemed to upset some ;-) - db]
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The 0-th order absorption is not built in in the current SAAM II
version but this empirical solution works well.
You need to define (in the exogenous input equation ) a function that
is 1 before time t1 and 0 afterwards. For instance this is the
possibility I will suggest:
ex1=Rate*(1-t^n/(t^n+T50^n))
In this case fixing a high value for n (n= 50 or more) enables a sharp
transition. Therefore the estimated T50 will be an excellent
approximation of the infusion time. Of course it is possible to use
other 100 fantasy equations doing exactly the same things.
Needless to say that the total dose is known and therefore you may want
to put the constraint
Rate = Dose / T50
in the equation canvass.
Hope this helps,
Gianluca Nucci
GlaxoSmithKline
CPK-Modeling & Simulation
Psychiatry - Verona
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The following message was posted to: PharmPK
You can adjust the rate either by using T-interrupts see example 12 on
the
web site(Infusions with T-interrupts). In the example instead of
changing
UF(1)=0 one sets it to another value.
Also in my previous reply I should have categorized the methods as:
1.using the XUF function ie XUF(1)=1 gives a constant infusion of 1
unit/time
2.Alternative method:
IC(7)=10
L(1,7)=1
l(0,7)=-1
which results in 10 units per time
Your question related to function dependence may be addressed by
example 13
on the web site which shows how to use QO functions to control infusions
H DAT
XUF(1)=F(2)*p(1)/p(3)
102QO
0 1
2 0
What happens is that the infusion is terminated at 2 hours with the rate
being p(1)=150000. One can also use the QO to change infusion rates.
I do not believe that there is a problem fitting across a
discontinuity (when the infusion stops). However if you require a
rigorous
explanation you can contact Ray Boston whose E-mail address is
available at
the web site.
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The following message was posted to: PharmPK
> I do not believe that there is a problem fitting across a
> discontinuity (when the infusion stops).
Neither do I.
An example of the model of the drug behavior in the body
during both the infusion and post-infusion time period
can be found for example in our study:
DedĚk, L., Durisov·, M., B·torov·, A. Weighting function used for
adjustment of multiple-bolus drug dosing.
Meth Find Exper Clin Pharmacol 2000, 22: 543-549.
The model mentioned above was not determined using the
software SAAM, but using the software CTDB. A version of the latter
software can be found at the www site accessible from the link
given in my signature.
Regards,
Maria Durisova, PhD, D.Sc,
Head of Department of Pharmacokinetics
and Scientific Secretary
Institute of Experimental Pharmacology
Slovak Academy of Sciences
842 16 Bratislava
Slovak Republic
http://www.uef.sav.sk/durisova.htm
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GastroPlus handles this effortlessly - discontinuities and all. You can
mix dosage forms as well, such as an IV bolus at time zero, with an IV
infusion starting also at time zero, then an oral dose at some later
time, and a different oral dose at another later time, etc. And you can
fit PK and PD parameters across such combinations. It's quite easy to
do.
Walt Woltosz
Chairman & CEO
Simulations Plus, Inc. (SIMU)
1220 W. Avenue J
Lancaster, CA 93534-2902
U.S.A.
http://www.simulations-plus.com
E-mail: walt.-at-.simulations-plus.com
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The following message was posted to: PharmPK
Further to the discussion of zero order input and optimizing the
duration of
an input.
If we assume a 2 pool model, comp 1 to comp 2, impulse input into comp
1 at
zero time. The input into comp 2 is a zero order function with can be
defined as
k(2,1)=k21/q1, where k21 is a new parameter and q1 is the mass in
compartment 1
If the input into comp 2 runs for an unknown duration the heaviside
function, below, can be used to switch off the input at time tlag, a
parameter that can be optimized during fitting. The function and its
integration into the transfer between comp 1 and comp 2 is given below.
heaviside=0.5*(1+atan(lambda*(t-tlag))*2/3.141592653)
k(2,1)=(1-heaviside)*k21/q1
k(0,2) 0.100000
k21 1.000000
lambda 100.000000
tlag 50.000000
If anyone would like the SAAM II model file with this capability please
email me at pbarrett.-a-.cyllene.uwa.edu.au
Hugh
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The following message was posted to: PharmPK
Dear colleagues,
With respect to problems in fitting and discontinuities: Please note
that the plasma concentration profile is continuous (of course!), but
the derivatives are discontinuous at the time point of stopping an
infusion or true 0-order input (and, e.g., at the start of input after
a lag-time). Many optimization algorithms use these derivatives for
finding the best solution. This may cause a problem in 'crossing' a
time point of measurement, but not necessarily so. This depends on the
typical problem and, of course, on the software.
As an example: assume measurements at each time point 1, 2, 3, etcetera
(arbitrary time units). The best fitting duration of the infusion is
3.5 time units. If you start the analysis with an initial estimate for
this duration between 3 and 4, you will most probably get the correct
result. But if you start with an initial estimate of, e.g., 2.5 or 4.5,
you may get a different solution; either a local minimum with an
infusion time of, say, 2.84, or a value very close to, e.g., 3, i.e.
at the point of the discontinuous derivative. The latter may be
recognized easily, but the former may be unnoticed.
In my experience the problem does not occur always, but you should be
aware of it.
Best regards,
Hans Proost
Johannes H. Proost
Dept. of Pharmacokinetics and Drug Delivery
University Centre for Pharmacy
Antonius Deusinglaan 1
9713 AV Groningen, The Netherlands
Email: j.h.proost.-a-.farm.rug.nl
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Copyright 1995-2010 David W. A. Bourne (david@boomer.org)