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Hello All
Could somebody share their views on this?
How can I calculate the macro constants (alpha, beta, gamma) from the
calculated microconstants (k10, k12, k21, k13, k31, k30)? I wish to
estimate the half-life etc (iv infusion study). Are there any
reported papers on these type of results?
Thanks in advance
Atul
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The following message was posted to: PharmPK
Dear Atul,
You may find the following reference useful:
JG Wagner's Fundamentals of Clinical Pharmacokinetics (1975), Drug
Intelligence Publications, pp 114-119.
Sri
Srikumaran K. Melethil, Ph.D.
Professor, Pharmaceutics and Medicine
University of Missouri- Kansas City
203B Katz Hall (School of Pharmacy)
Kansas City, MO 64110
Phone: voice- 816-235-1794; fax - 816-235-5190
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The following message was posted to: PharmPK
I have used the following equations in the past for bolus administration
using the SAAM II Software in which the rate constant are k(to,from). This
should be a start.
Hope this helps,
Ks1=k(2,1)+k(3,1)+k(1,2)+k(1,3)+k(0,1)
Ks2=k(2,1)*k(1,3)+k(3,1)*k(1,2)+k(1,2)*k(0,1)+k(1,3)*k(0,1)
Ks3=k(1,2)*k(1,3)*k(0,1)
Km1=(3*Ks2-Ks1^2)/3
Km2=(2*Ks1^3-9*Ks1*Ks2+27*Ks3)/27
Km3=2/3*sqrt(Ks1^2-3*Ks2)
theta = -sqrt((-27*Km2^2)/(4*Km1^3))
sigma = atan(sqrt(1-theta^2)/theta)
a=Km3*cos(sigma/3)+Ks1/3
b=Km3*cos(sigma/3+2*3.14/3)+Ks1/3
c=Km3*cos(sigma/3+4*3.14/3)+Ks1/3
Cl=V*k(0,1)
ta=log(2)/a
tb=log(2)/b
tc=log(2)/c
A = Dose* a^2 - a*Val /V*(a-c)*(b-c)
Val = (k(1,2)+k(1,3))+(k(1,2)*k(1,3))
B = Dose * b^2 - b*Val /V*(a-c)*(c-b)
C = Dose * c^2 - c*Val /V*(a-c)*(b-c)
AUC = A/a + B/b + C/c
AUMC = A/a^2 + B/b^2 + C/c^2
MRT = AUMC/AUC
Vss = Cl*MRT
Steven W Martin, PhD
Amgen Inc., 1-1-A.
One Amgen Center Drive
Pharmacokinetics and Drug Metabolism Group
Thousand Oaks, CA 91320-1789
* (805)-447-4541 * 1-1-A
*Fax: 805-499-4868
* swmartin.at.amgen.com
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The following message was posted to: PharmPK
The lambdas (alpha, beta, gamma) can numerically be calculated by evaluating
the Eigenvalues from the Eigenmatrix. The Eigenmatrix is constructed from
the linear DES. See Splus guide on eigen() for references.
The special case for an example of a mammilary model is given below as Splus
code, but any other linear DES could be handled in equivalently.
-
k10 <- 1.486
k12 <- 0.351
k21 <- 0.080
k13 <- 1.703
k31 <- 0.633
print(c(k10, k12, k21, k13, k31))
dg <- matrix(NA,3,3)
dg[1, ] <- c( - k10 - k12 - k13, k21, k31)
dg[2, ] <- c( k12 , - k21, 0)
dg[3, ] <- c( k13, 0, - k31)
print(dg)
print(-eigen(dg)$values)
-
Lutz Harnisch
DMPK PopKin
Aventis Pharma
Frankfurt
Germany
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Copyright 1995-2010 David W. A. Bourne (david@boomer.org)