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The following message was posted to: PharmPK
Dear All,
Not so long ago I posted a message asking for help, Now I am posting it
again. In case someone can help me I will really appreciate it.
I have a question related to PK modeling.
I am recently working with PK models. Now I am studying the
"ELIMINATION OF PHOSPHATE DURING HEMODIALYSIS". I found an article by
Spalding,Chamney and Farrington (2002). They did something similar and
they propose 3 models based on 2, 3 and 4 compartments. In their
article they present the differential equations. The three models are
bellow:
Model A: Passive diffusion
dCi=(Ci-Ce)Kie
dt Vi
dCe=(Ci-Ce)Kie - CeKd - CeQu
dt Ve
dVe=Qu
dt
Model B: Passive Diffusion + regulated intracellular phosphate
They assumed that from the third compartment the flux (F3) is:
F3 = (Ci - Ciset) G3
Ciset: desired set point
Thus the differential equation for the extracellular compartment needs
to be modified and it is
dCe=(Ci-Ce)Kie - CeKd - CeQu + F3
dt Ve
Model C: Passive Diffusion + regulated intracellular + immediate action
Consider an aditional mechanism that is invoked when phosphate falls
bellow a critical level
If Ci < Cicrit AND F4 off, then F4 on
If Cicrit < Ci < Cihighlimit AND F4 on, then F4 off
My question is the following. I would like to use this model, but I
would like to have the solutions for this equation for the 3 models, if
someone can help me I will appreciate it very much.
Thanks in advance,
Jose Cortinas Abrahantes
jose.cortinas.-at-.luc.ac.be
[You may be able to derive the equations using Laplace transforms, see
http://www.boomer.org/c/p3/c02/c0208.html and
http://www.boomer.org/c/p3/c07/c0701.html - db]
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