- On 17 Jul 2006 at 00:28:39, "Peter CMAlt" (petercmalt.-at-.hotmail.com) sent the message

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Dear friends

I need some help regarding the solution of the 2 compartment open

model with iv infusion input. I cannot find the way to pass from the

form =[(K0/s)(s+K21)]/[(s+a)(s+b)] to the time equation, also there

seems to be some different solutions. Can anyone help me with the

solution or with some books where I can go and find the solution

Thanks to all

Best regards

PeterCmalt

[Have you tried the fingerprint method - see http://www.boomer.org/c/

p3/c07/c0702.html and references listed - db] - On 17 Jul 2006 at 14:33:57, "Porzio, Stefano" (Stefano.Porzio.aaa.ZambonGroup.com) sent the message

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The following message was posted to: PharmPK

Dear PeterCmalt,

if I correctly understand your problem, you need the solution for

the two-open model with central compartment elimination (I suppose)

and zero-order input (infusion is a zero order input).

If you need peripheral elimination, obviously the solution is different.

You can find the solution for central compartment elimination and, if

required a lot solutions for many other compartmental models, in

Pharmacokinetics for the Pharmaceutical Scientists

John G. Wagner, PhD

Technomic Publishing Company Inc. (1993)

In the case of the two-open model with central compartment

elimination (I suppose) and zero-order input, I tray to report the

Wagner solution (it's difficult to write equation in plain test....):

"During the zero-order input, such as intravenous infusion, the

concentration C in the central compartment at the time t, during the

interval 0 < t < T where T is the duration of the zero-order input,

is given by the equation

C= Ko (K21-L1)(1-exp(-L1t))/L1(L2-L1)Vc + K0(K21-L2)(1-exp(L2t))/L2

(L1-L2)Vc

After the zero-order input ceases (i.e. when t >T), the concentration

is given by the equation

C= Ko (K21-L1)(exp(L1T)-1)exp(-L1t)/L1(L2-L1)Vc + Ko (k21-L2) (exp

(L2T)-1)exp(-L1t)/L2(L1-L2)Vc

In the previous two equations

Ko ist the zero-order input constant,

K21 is the transfer rate constant from peripheral compartment to the

central compartment

L1 is the first elimination constant ( the first macro-constant of

the bi-exponential disposition)

L2 is the second elimination constant ( the second macro-constant of

the bi-exponential disposition)

Vc is the volume of the central compartment"

I hope this is useful!

Best regards

Stefano - On 17 Jul 2006 at 12:10:40, "MONZANI VALMEN" (V.MONZANI.at.italfarmaco.com) sent the message

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The following message was posted to: PharmPK

Dear Peter

The book I found to treat the argument deeply is Pharmacokinetics

second edition by M.Gibaldi and D.Perrier.

Hope this help

Valmen - On 21 Jul 2006 at 12:26:39, "Peter CMAlt" (petercmalt.at.hotmail.com) sent the message

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Dear Friends

Thanks a lot for your answers, however I should say that my question

continues. I probably should be more specific (let's see if i can

write the problem with the equations in plain text).

The solution of the two compartmet open model with iv infusion input

will provide the following equation:

mass1=[(K0/s)(s+K21)]/[(s+a)(s+b)] .

Using the fingertip method as sugested by David Bourne (or using

direct Laplace transformations) to pass for the time order gives the

equation:

(1) M(t)=(K0K21/ab)+[(K0(K21-a)/a(a-b))e(-at)]+[(K0(K21-b)/b(b-a))e(-

bt)] (i hope i didn't miss anything)

The final equation provided by Wagner and other authors is

(2) M(t)= K0(K21-a)(1-exp(-at))/a(b-a) + K0(K21-b)(1-exp(-bt))/b(a-b)

So my problem starts in the passagem from (1) to (2). I think this is

only a problem of mathemathical simplication, or lack of personal

mathemathical knowledge, but can anyone has the kind to help me (i

know that this is too much but with much detail as possible!!!)?

Thak you very much for your help

Best regards

PeterCmalt - On 15 Aug 2006 at 19:10:46, "Peter CMAlt" (petercmalt.-at-.hotmail.com) sent the message

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Dear Friends

Regarding the solution of the two compartment open model with

perfusion there still are some questions:

After applying the fingertip method to the equation:

[(K0(s+K21)]/[s(s+a)(s+b)]

I obtain the equation:

(K0K21/ab)+{[K0(K21-a)]/[a(a-b)]}exp(-at)-{[K0(K21-b)]/[b(a-b)]}exp(-bt)

My problem is that I cannot pass from the previous equation to the

one presented in the Wagner book:

{[K0(K21-a)]/[a(a-b)]}(1-exp(-at))+{[K0(K21-b)]/[b(a-b)]}(1-exp(-bt))

Can anyone help me?

Thanks in advance for your kind help

PeterCmalt - On 17 Aug 2006 at 10:43:40, Rakesh.2.Nagilla.at.gsk.com sent the message

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Peter,

The actual equation from Wagner's book is

k0(k21-a) k0(k21-b)

--------- x [1-exp(-at] + --------- x [1-exp(-bt)]

a(b-a) b(a-b)

[retyped from submitted figure - db]

which when simplified would lead to the equation you obtained. - On 17 Aug 2006 at 15:46:27, "Shawn D. Spencer" (shawn.spencer.aaa.famu.edu) sent the message

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Peter,

It is apparent to me, that J. Wagner used the Laplace tables in

arriving at his function, whereas heaviside expansion and partial

fraction theorems would arrive at a different, albeit it equivalent,

function. Not every function with two or more exponential terms can

be manipulated algebraically, as some are transcendental. I do not

know if this is the case here, however if you can simulate both

equations, then you have a suitable endpoint to move forward.

Regards,

Shawn D. Spencer, Ph.D., R.Ph.

Assistant Professor of Biopharmaceutics and Pharmacokinetics

College of Pharmacy and Pharmaceutical Sciences

Florida A&M University

Tallahassee, FL 32307

shawn.spencer.-at-.famu.edu

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