# PharmPK Discussion - Conversion of micro constants to macro constants

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• On 14 Aug 2001 at 14:55:55, "bvatul" (bvatul.aaa.ufl.edu) sent the message
`Hello AllCould somebody share their views on this?How can I calculate the macro constants (alpha, beta, gamma) from thecalculated microconstants (k10, k12, k21, k13, k31, k30)? I wish toestimate the half-life etc (iv infusion study). Are there anyreported papers on these type of results?Thanks in advanceAtul`
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• On 14 Aug 2001 at 22:12:23, "Melethil, Srikumaran K." (MelethilS.at.umkc.edu) sent the message
`The following message was posted to: PharmPKDear Atul,You may find the following reference useful:JG Wagner's Fundamentals of Clinical Pharmacokinetics (1975), DrugIntelligence Publications, pp 114-119.SriSrikumaran K. Melethil, Ph.D.Professor, Pharmaceutics and MedicineUniversity of Missouri- Kansas City203B Katz Hall (School of Pharmacy)Kansas City, MO 64110Phone:  voice-  816-235-1794; fax - 816-235-5190`
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• On 14 Aug 2001 at 22:15:08, "Martin, Steven W." (swmartin.at.amgen.com) sent the message
`The following message was posted to: PharmPKI have used the following equations in the past for bolus administrationusing the SAAM II Software in which the rate constant are k(to,from). Thisshould 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)/3Km2=(2*Ks1^3-9*Ks1*Ks2+27*Ks3)/27Km3=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)+Ks1/3b=Km3*cos(sigma/3+2*3.14/3)+Ks1/3c=Km3*cos(sigma/3+4*3.14/3)+Ks1/3Cl=V*k(0,1)ta=log(2)/atb=log(2)/btc=log(2)/cA = 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/cAUMC = A/a^2 + B/b^2 + C/c^2MRT = AUMC/AUCVss = Cl*MRTSteven W Martin, PhDAmgen Inc., 1-1-A.One Amgen Center DrivePharmacokinetics and Drug Metabolism GroupThousand Oaks, CA 91320-1789* (805)-447-4541    * 1-1-A*Fax: 	805-499-4868* swmartin.at.amgen.com`
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• On 15 Aug 2001 at 10:37:17, Lutz.Harnisch.-at-.aventis.com sent the message
`The following message was posted to: PharmPKThe lambdas (alpha, beta, gamma) can numerically be calculated by evaluatingthe Eigenvalues from the Eigenmatrix. The Eigenmatrix is constructed fromthe linear DES. See Splus guide on eigen() for references.The special case for an example of a mammilary model is given below as Spluscode, 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 HarnischDMPK PopKinAventis PharmaFrankfurtGermany`
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