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Dear all,
Can anyone help me about equations to calculate plasmatic
concentrations employing a three compartment open model after ORAL
administration and IV administration?
I would like to use Scientist PK software for modeling the data.
Thanks in advance.
Regards,
Prof. Dr. Tasso
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The following message was posted to: PharmPK
letasso wrote:
> PharmPK - Discussions about Pharmacokinetics
> Pharmacodynamics and related topics
>
> Dear all,
>
> Can anyone help me about equations to calculate plasmatic
> concentrations employing a three compartment open model after ORAL
> administration and IV administration?
Dear Dr Tasso,
Below are Scientist code for three compartment models with i.v. or oral
doses. If you copy each of these into a Scientist model window, they
should compile OK. Scientist is very sensitive to "stray" characters
like spaces and tabs in the code, so if the cutting and pasting adds
these you will need to remove them. Like most things on the internet,
you should also check this code carefully with a few simulations to make
sure there are no inadvertant mistakes on my behalf and the code behaves
as advertised. Hopefully the parameter names are self-explanatory.
Regards, Richard Upton
// A classical 3 compartment model with intravenous doses
// Parameterised as intercompartmental clearances
IndVars: t
DepVars: C1
Params: V1,CL,V2,Q2,V3,Q3
//Provision for 2 constant rate infusion
dose1 = 10
start1=0
tau1 = 10
doserate1 = pulse(dose1,start1, tau1)
dose2 = 10
start2=60
tau2 =10
doserate2 = pulse(dose2,start2, tau2)
doserate=doserate1+doserate2
//3 compartment model
V1*C1' = doserate + Q2*(C2-C1) + Q3*(C3-C1) -CL*C1
V2*C2' = Q2*(C1-C2)
V3*C3' = Q3*(C1-C3)
//Parameters
0 < t < 1200
V1 = 5
CL = 0.5
V2 = 9
Q2 = 3
V3 = 200
Q3 = 0.8
//Initial conditions
t=0
C1=0
C2=0
C3=0
***
// A classical 3 compartment model with single oral dose
// Parameterised as intercompartmental clearances
IndVars: t
DepVars: C1
Params: V1,CL,V2,Q2,V3,Q3, ka,F
//Dose set as an initial condition
//Agut is amount of drug in the gut, absorbed at rate ka with
bioavailability F
Agut' = -ka*Agut
//3 compartment model
V1*C1' = ka*Agut*F + Q2*(C2-C1) + Q3*(C3-C1) -CL*C1
V2*C2' = Q2*(C1-C2)
V3*C3' = Q3*(C1-C3)
//Parameters
0 < t < 1200
V1 = 5
CL = 0.5
V2 = 9
Q2 = 3
V3 = 200
Q3 = 0.8
ka=0.02
F=0.5
//Initial conditions
t=0
C1=0
C2=0
C3=0
//Dose is 100 mg
Agut=100
***
--
Dr Richard Upton
Principal Medical Scientist/Senior Lecturer
Discipline of Anesthesia and Intensive Care
Royal Adelaide Hospital/University of Adelaide
North Tce, SA 5000, Australia
richard.upton.at.adelaide.edu.au
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Dear Dr Upton,
Thank you very much for yor reply.
I have just worked with Scientist PK software with simple equations
employing 1 and 2 intravenous and oral administration.
What are the terms V1, V2, V3 and Q1, Q2 and Q3 described in your e-
mail?
What do you think about the following equation to calculate plasmatic
concentration in a 3 comp. open model after oral administration?
Cp= A*exp(-alpha*T)+B*exp(-beta*T)+C*exp(-gama*T)-D*exp(-ka*T)
Could you send me some reference, paper where the equations are
described?
Best regards,
Prod. Dr. Tasso.
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The following message was posted to: PharmPK
letasso wrote:
>
> Dear Dr Upton,
>
> Thank you very much for yor reply.
>
> I have just worked with Scientist PK software with simple equations
> employing 1 and 2 intravenous and oral administration.
>
> What are the terms V1, V2, V3 and Q1, Q2 and Q3 described in your
e- mail?
V1, V2 & V3 are the volumes of the first, second and third compartments
of a three compartment model. CL is the clearance from the first
compartment, and Q2 and Q3 are the inter-compartmental clearances
between compartments 1 & 2 and 1 & 3, respectively. The models can be
expressed in terms if micro-rate constants as well, but I think the
above parameterisation is more intuitive and is predominant in the
anaesthetic literature.
>
> What do you think about the following equation to calculate plasmatic
> concentration in a 3 comp. open model after oral administration?
>
> Cp= A*exp(-alpha*T)+B*exp(-beta*T)+C*exp(-gama*T)-D*exp(-ka*T)
Actually, that is a pretty old way of fitting pharmacokinetic data, and
is only good for a single oral dose. I couldn't say that it is correct
without doing a few sums. You have Scientist, why not write your model
as differential equations? If you really want to interpret you data as
half-lifes (via macro-rate constants alpha, beta etc) the following
paper is a way to convert between macro and micro rate constants:
Upton RN. Calculating the hybrid (macro) rate constants of a three
compartment mamillary pharmacokinetic model from known micro-rate
constants. J Pharmacol Toxicol Methods. 2004;49:65-8.
By the way, I suspect you will need very good data over a wide
concentration range to estimate all the parameters for your 3
compartment model, and there may be a need to constrain ka in some
biologically plausible range. Absorption models may have more than one
unique solution (google "flip-flop model").
Hope this helps.
regards, Richard
--
Dr Richard Upton
Principal Medical Scientist/Senior Lecturer
Discipline of Anesthesia and Intensive Care
Royal Adelaide Hospital/University of Adelaide
North Tce, SA 5000, Australia
richard.upton.at.adelaide.edu.au
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The following message was posted to: PharmPK
Dear Richard and Letasso,
In his excellent answer to Letasso, Richard stated:
> By the way, I suspect you will need very good data over a wide
> concentration range to estimate all the parameters for your 3
> compartment model, and there may be a need to constrain ka in some
> biologically plausible range. Absorption models may have more than
> one unique solution (google "flip-flop model").
Please note that there are always two solution for the absorption
model (i.e. for ka and the other rate constants, volumes and
intercompartmental clearances(not for clearance!)), irrespective of
the number of exponentials (i.e. for a 1-, 2-, or 3-compartment
model). I do not have a formal proof for this, but I'm not aware of
any exception.
Assume the following equation, with alpha > beta > gamma:
Cp= A*exp(-alpha*T)+B*exp(-beta*T)+C*exp(-gamma*T)-D*exp(-ka*T)
If A, B, C, and D are all positive, ka is either larger than alpha, or
between alpha and beta (two solutions).
If A is negative, ka is either between alpha and beta, or between beta
and gamma (two solutions).
If A and B are negative, ka is either between beta and gamma, or
smaller than gamma (two solutions).
Other situations will lead to 'invalid' solutions, i.e. solutions that
cannot be converted to a compartmental model, e.g. if only B or C is
negative.
Please note that there isn't any reason that A, or A and B are
positive. Constraining these values to positive values is incorrect.
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.aaa.rug.nl
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The following message was posted to: PharmPK
Hans,
Although the method you describe is sometimes useful, it is
fundamentally
incorrect in that Ka is never a constant, but varies with time. It is
best
used as an approximation when a drug is absorbed quickly at a high
rate, and
is not limited by low permeability and/or slow dissolution. But for
low-solubility compounds or formulations with slow dissolution, where
absorption occurs over a large expanse of the intestinal tract,
treating Ka
as a constant is an oversimplification.
With today's state-of-the-art in computer simulations, mechanistic
models
run in seconds, accounting for the interactions among such phenomena as
pH-dependent solubility, regionally dependent permeability,
transporters and
enzymes in various tissues, etc. The old 1-, 2-, or 3-compartment
pharmacokinetics were mathematical conveniences necessary in a time when
mechanistic models were not available. We still use them sometimes for
quick
estimates, but more often with iv data rather than oral doses.
I believe that universities should encourage students to learn about
and use
the best state-of-the-art methods in order to better prepare them for
the
real world. Companies like ours will provide software for free for
student
use (with limited capabilities, but sufficient for students to gain
insight
into how various parameters affect results).
Best regards,
Walt Woltosz
Chairman & CEO
Simulations Plus, Inc. (NASDAQ: SLP)
42505 10th Street West
Lancaster, CA 93534-7059
U.S.A.
http://www.simulations-plus.com
E-mail: walt.aaa.simulations-plus.com
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