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RE: Parallel first order and Michaelis-Menten elimination

From: Han, Kelong <keh45>
Date: Sun, 28 Mar 2010 14:38:46 -0400

Dear Dr. Holford:

Please correct me if I am wrong, but I think the DV may not have been log t=
ransformed. If the DV was log transformed, the residual error model may hav=
e been coded as


Dear Dr. Gibiansky:

I think you may have used DV in the original units with an residual error m=
odel for log transformed DV, which is equivalent to an additional+proportio=
nal residual model. Please correct me if I am wrong. But would you please c=
larify a little bit why you used this error model instead of a regular addi=
tional+proportional residual model?

Kelong Han
PhD Candidate

University of Pittsburgh
School of Pharmacy

From: owner-nmusers
 Of Nick Holford [n.holford
Sent: Sunday, March 28, 2010 1:44 PM
To: nmusers
Cc: chenyuhong
Subject: Re: [NMusers] Parallel first order and Michaelis-Menten eliminatio=


Thanks for the code example which illustrates one side of a religious debat=
e which took place a few weeks ago on PharmPK. The essence of this debate w=
as should one normalize PK parameters to a unit volume or to a unit body.

The unit volume believers feel that the rate constant is the 'natural' way =
to describe pharmacokinetics while the unit body believers feel that cleara=
nce is more 'natural'. Both groups agree that the two systems are just repa=
rameterizations and make identical numerical predictions.

Your coding of Vmax for the mixed order elimination process has the implici=
t units of mass/time per unit volume e.g. mg/h/L. This is the unit volume b=
elief system.

I am a unit body believer so I would code this system differently with a ve=
ry simple change- substituting A(1) with C1 to multiply the mixed order exp=
ression. I have also changed VM to VMUB to indicate that the dimensions of =
the Vmax parameter are per unit body i.e. mg/h per body.

DADT(1) = -K10*A(1)-C1*VMUB/(KM+C1)-K12*A(1)+K21*A(2)

It could also be written like this to emphasize that the mixed order proces=
s has the same units as CL (for unit body believers) when C1 tends to 0:

DADT(1) = -C1*(CL+VMUB/(KM+C1) - K12*A(1)+K21*A(2)

I note also that your residual error model implies that the DV has been log=
 transformed. This reflects yet another belief system which I think you hav=
e shown has little, if any, practical merit. I prefer to keep the DV in the=
 original units.

Best wishes,


Leonid Gibiansky wrote:
ADVAN6 ADVAN8 or (nm7) ADVAN13

The code is below



   NCOMP = 2
   COMP = (CENTRAL) ;1
   COMP = (PERIPH) ;2

V1= THETA(2)*EXP(ETA(2))
Q = THETA(3)*EXP(ETA(3))
V2= THETA(4)*EXP(ETA(4))

K10 = CL/V1
K12 = Q/V1
K21 = Q/V2
S1 = V1
S2 = V2

C1 = A(1)/S1
DADT(1) = -K10*A(1)-A(1)*VM/(KM+C1)-K12*A(1)+K21*A(2)
DADT(2) = K12*A(1)-K21*A(2)

TY = A(1)/V1
W = SQRT(THETA(7)**2/TY**2+THETA(8)**2)



1 FIX ; ~ERR

Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
e-mail: LGibiansky at
tel: (301) 767 5566

Dear All,

I am working with a Biologic and would like to have a PK model with paralle=
l first order and Michaelis-Menten elimination. Any suggestion about which =
subroutine I am supposed to use? If you can share an example for the contro=
l stream, that will be a great help.



Nick Holford, Professor Clinical Pharmacology
Dept Pharmacology & Clinical Pharmacology
University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand
tel:+64(9)923-6730 fax:+64(9)373-7090 mobile:+64(21)46 23 53
email: n.holford
Received on Sun Mar 28 2010 - 14:38:46 EDT

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