From: Rik Schoemaker <*rik.schoemaker*>

Date: Mon, 15 May 2017 14:08:42 +0000

Dear fellow NMusers,

My previous submission to the forum had Word equations, and I think the ema=

il server choked on that so I'm submitting a new text-only version :-)

I've been going insane trying to search for a reference to which I assumed =

was a very common equation. It is the simplification of a Bateman function =

where absorption cannot be distinguished from elimination, resulting in sys=

tem breakdown. The consequence however is a very useful equation governed o=

nly by Cmax and Tmax. The Bateman function describes the biexponential equa=

tion associated with a kinetic system with first order absorption and linea=

r elimination [1,2]:

C(Time)=(F*Dose*Ka/(V*(Ka-Ke)))*(exp(-Ke*Time)- exp(-Ka*Time))

In the case where Ka and Ke cannot be distinguished (Ka=Ke=K), this bie=

xponential equation breaks down to a single exponential equation (see Eqn 2=

5 in Garret [1] or Eqn 2 in Bialer [2])

C(Time)=(F*Dose*K*Time/V)*(exp(-K*Time))

For this equation, Tmax can be derived to be given by 1/K and Cmax is given=

by F*Dose/(V*e) where e is the base of natural logarithms (see Eqn 26 and =

27 in Garret [1] or Eqn 3 and 4 in Bialer [2]). Substituting K by 1/Tmax an=

d V by F*Dose/(Cmax*e) gives:

C(Time)=(Cmax*e*Time/Tmax)*(exp(-Time/Tmax))

Extremely useful for describing disease progression profiles, and I assumed=

it to be widely know. Perhaps it still is, but then someone must have publ=

ished it somewhere: can anyone help me out?

Cheers and thanks,

Rik

[1] Garrett ER. The Bateman function revisited: a critical reevaluation of =

the quantitative expressions to characterize concentrations in the one comp=

artment body model as a function of time with first-order invasion and firs=

t-order elimination. J Pharmacokinet Biopharm (1994) 22(2):103-128.

[2] Bialer M. A simple method for determining whether absorption and elimin=

ation rate constants are equal in the one-compartment open model with first=

-order processes. J Pharmacokinet Biopharm (1980) 8(1):111-113

Rik Schoemaker, PhD

Occams Coöperatie U.A.

Malandolaan 10

1187 HE Amstelveen

The Netherlands

http://www.occams.com

+31 20 441 6410

mailto:rik.schoemaker

Received on Mon May 15 2017 - 10:08:42 EDT

Date: Mon, 15 May 2017 14:08:42 +0000

Dear fellow NMusers,

My previous submission to the forum had Word equations, and I think the ema=

il server choked on that so I'm submitting a new text-only version :-)

I've been going insane trying to search for a reference to which I assumed =

was a very common equation. It is the simplification of a Bateman function =

where absorption cannot be distinguished from elimination, resulting in sys=

tem breakdown. The consequence however is a very useful equation governed o=

nly by Cmax and Tmax. The Bateman function describes the biexponential equa=

tion associated with a kinetic system with first order absorption and linea=

r elimination [1,2]:

C(Time)=(F*Dose*Ka/(V*(Ka-Ke)))*(exp(-Ke*Time)- exp(-Ka*Time))

In the case where Ka and Ke cannot be distinguished (Ka=Ke=K), this bie=

xponential equation breaks down to a single exponential equation (see Eqn 2=

5 in Garret [1] or Eqn 2 in Bialer [2])

C(Time)=(F*Dose*K*Time/V)*(exp(-K*Time))

For this equation, Tmax can be derived to be given by 1/K and Cmax is given=

by F*Dose/(V*e) where e is the base of natural logarithms (see Eqn 26 and =

27 in Garret [1] or Eqn 3 and 4 in Bialer [2]). Substituting K by 1/Tmax an=

d V by F*Dose/(Cmax*e) gives:

C(Time)=(Cmax*e*Time/Tmax)*(exp(-Time/Tmax))

Extremely useful for describing disease progression profiles, and I assumed=

it to be widely know. Perhaps it still is, but then someone must have publ=

ished it somewhere: can anyone help me out?

Cheers and thanks,

Rik

[1] Garrett ER. The Bateman function revisited: a critical reevaluation of =

the quantitative expressions to characterize concentrations in the one comp=

artment body model as a function of time with first-order invasion and firs=

t-order elimination. J Pharmacokinet Biopharm (1994) 22(2):103-128.

[2] Bialer M. A simple method for determining whether absorption and elimin=

ation rate constants are equal in the one-compartment open model with first=

-order processes. J Pharmacokinet Biopharm (1980) 8(1):111-113

Rik Schoemaker, PhD

Occams Coöperatie U.A.

Malandolaan 10

1187 HE Amstelveen

The Netherlands

http://www.occams.com

+31 20 441 6410

mailto:rik.schoemaker

Received on Mon May 15 2017 - 10:08:42 EDT