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The following message was posted to: PharmPK
Dear collegues,
I seek where I can find mathematical formulas for calculating micro rate constants for a typical three-compartment model: k(1,2), k(2,1), k(1,3), k(3,1), k(el.) and compartment apparent volumes, from fit parameters of the time-course of the amount of drug in the first compartment:
C(t) = A*exp(-a*t) + B*exp(-b*t) + C*exp(-g*t)
May anyone suggest me a scientific publication about this topic?
Thank very much in advance.
Yours sincerely,
Sandro Ridone
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The following message was posted to: PharmPK
The book Pharmacokinetics for the Pharmaceutical Scientist by John G. Wagner will have the equations you need. You can purchase the book at amazon.com
http://www.amazon.com/Pharmacokinetics-Pharmaceutical-Scientist-John-Wagner/dp/1566760321/ref=sr_1_1?ie=UTF8&s=books&qid=1269018012&sr=8-1
Good luck!
Nathan Teuscher
[Other books can be found at
http://www.boomer.org/pkin/book.html
- db]
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The following message was posted to: PharmPK
I suggest any the book authored by Milo Gibaldi.
Stanley Cotler
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Hello,
There is an Excel spread sheet convert.xls for doing this, developed by Dr. Steven Shafer. Please see this NMusers posting to download the spread sheet: http://cognigencorp.com/nonmem/nm/97aug142001.html
Best wishes,
MNS
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The following message was posted to: PharmPK
The responses you have received concerning the Wagner and Gibaldi books are correct with respect to the relationship between the exponentials and the microconstants.
However, you are asking how to calculate the microconstants from the three exponentials. It can not be done.
If you look back at my old J Pharm Sci paper in 1972 (vol. 61, page 236) I point out that the number of solvable rate constants in a multicompartment mamillary model is 2(n-1)+ 1, where n is the number of driving force compartments in a disposition model (3 in your case) and only one of the constants may be an exit constant from the model, k(el)in your case. Therefore, since the answer would be 5, you might suspect that these can be calculated and they can but not uniquely. You can solve for k(el) since CL = Dose/[(A/a) + (B/b) + (C/c)]; V1 = Dose/(A+B+C); and k(el) = CL/V1.You can also get k(2,1) and k(3,1) (E2 and E3 in my terminology, the sum of the exit rate constants for compartments 2 and 3, respectively)assuming elimination is only from the central compartment, since they can be determined from the quadradic equations in the numerators of A, B and C, knowing Dose, V1 and a, b and g. But you can not determine unique solutions for k(1,2) and k(1,3) since you end up with relationships with more unknowns t
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Dear Les and colleagues:
The spreadsheet convert.xls (written at Atlanta airport after missing a
connection about 15 years ago) can run the calculation in both directions:
microrate constants from exponents and exponents from microrate constants.
I've attached it. [See below - db]
What Les says below is correct: you can calculate 3 parameters (exponents)
from 5 parameters (microrate constants), but you cannot calculate 5
parameters (microrate constants) from 3 parameters (exponents) alone.
However, if you know the coefficients for each exponent, then you are
calculating 6 parameters (3 exponents + 3 coefficients) from 6 parameters (5
microrate constants + V1). That can be uniquely solved on the assumption
that clearance only occurs from the central compartment.
This applies to every transformation calculated by convert.xls: it requires
the same number of parameters to be entered as are generated in the output:
2 for a 1 compartment model, 4 for a 2 compartment model, and 6 for a three
compartment model.
Best regards,
Steve Shafer
[The spreadsheet is available at the link provided earlier
http://cognigencorp.com/nonmem/nm/97aug142001.html
Steve, is that the same version? - db]
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