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Re: Simplified Bateman equation where Ka=Ke

From: Jakob Ribbing <jakob.ribbing>
Date: Mon, 15 May 2017 17:05:56 +0200

Dear Rik,

Thanks, theses were indeed convenient equations!

For multiple dosing Matt Hutmacher derived the explicit equation for the =
ka=ke case of the Bateman function, and this effort is available as =
supplemental material here:
=
https://static-content.springer.com/esm/art%3A10.1007%2Fs10928-012-9274-0/=
MediaObjects/10928_2012_9274_MOESM1_ESM.docx

I am sure this was not easy to derive, but it is still just a tiny =
example among the vast number of contributions that Matt patiently made =
to the community.
I will always miss him for that, and for being a friendly face and a =
good chat.
However, it is good to see that his spirit lives on in so many others.

Sincerely

Jakob


PS.

The above link is one of the online supplements to this publication, on =
a KPD model that used the ka=ke assumption for (single and) multiple =
dosing:
J Pharmacokinet Pharmacodyn. 2012 Dec;39(6):619-34. doi: =
10.1007/s10928-012-9274-0. Epub 2012 Sep 23.
Longitudinal FEV1 dose-response model for inhaled PF-00610355 and =
salmeterol in patients with chronic obstructive pulmonary disease.
Nielsen JC, Hutmacher MM, Cleton A, Martin SW, Ribbing J.
DS.


Jakob Ribbing, Ph.D.

Senior Consultant, Pharmetheus AB



Cell/Mobile: +46 (0)70 514 33 77

Jakob.Ribbing

www.pharmetheus.com



Phone, Office: +46 (0)18 513 328

Uppsala Science Park, Dag Hammarskjölds väg 52B

SE-752 37 Uppsala, Sweden



This communication is confidential and is only intended for the use of =
the individual or entity to which it is directed. It may contain =
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immediately. Please do not copy it or disclose its contents to any other =
person.





On 15 May 2017, at 16:08, Rik Schoemaker <rik.schoemaker
wrote:

> Dear fellow NMusers,
>
> My previous submission to the forum had Word equations, and I think =
the email 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 system breakdown. The consequence however is a =
very useful equation governed only by Cmax and Tmax. The Bateman =
function describes the biexponential equation associated with a kinetic =
system with first order absorption and linear 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 biexponential equation breaks down to a single exponential equation =
(see Eqn 25 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 and 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 published 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 compartment body model as a function of time =
with first-order invasion and first-order elimination. J Pharmacokinet =
Biopharm (1994) 22(2):103-128.
> [2] Bialer M. A simple method for determining whether absorption and =
elimination 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 - 11:05:56 EDT

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