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Hi all,
I have a modeling question for the list's collective soul. Let's say
that I have profiles of a drug given at several doses and that those
profiles are increasingly "convex" in shape as dose increases. Let's
also say that upon multiple dosing, accumulation is more than what
would be predicted from linear kinetics. Below is an example of the
profiles I observe (totally fictious but that illustrate well what I
try to express).
time dose1 dose2 dose3
0 0 0 0
0.5 0 19 4
1 62 340 200
2 480 950 1215
3 870 1790 2530
4 1200 2270 3500
5 1530 2600 4520
6 1430 2650 4550
7 1370 2700 4575
8 1325 2680 4580
10 1300 2675 4600
12 1135 2670 4500
16 970 2590 4400
20 750 2490 4300
24 540 2355 4200
30 380 2175 4100
36 175 1770 3900
48 30 890 2900
72 0 325 1000
96 0 80 260
120 0 0 30
I figured that elimination probably follows M-M kinetics. Now, I'm
not too familiar with nonlinear kinetics and I was wondering if some
of you could point me in the right direction.
If I try a single M-M elimination process (or parallel M-M and linear
elimination for that matter), I'm not even getting close to such
concentration-time profiles (I haven't tried fitting yet, I just
wanted to get an appropriate signature profile first).
Is it because I badly estimate parameters? Or should I be looking at
a different way of expressing elimination (like something resembling
ODEs of indirect response models)? Or have I got this all wrong in
the first place?
Many thanks in advance :o)
Pierre-Olivier Tremblay
SFBC Anapharm
P.S.: Just in case you wondered, I'm not trying to get a quick fix
for a term exam question here ;o)
[A quick semi-log plot looks like MM elimination. What were the
doses, all three oral? - db]
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The following message was posted to: PharmPK
First it's difficult to draw any conclusions without knowing the
nature of
the data. It this from one individual administered 3 different doses, 3
individuals given a single dose, or the means from many individuals
given 3
different doses? I would say looking at the graph that MM kinetics is
occurring and that the data are 1-compartment. My guess is that your
starting values are way off. I would try the following.
Put Km somewhere in the x-axis around where the curves start to appear
linear on a log scale. 50 seems to be about right. Then using a
noncompartmental estimate for clearance of the middle curve, multiply
this
value by your estimate of Km. This then becomes your estimate of Vmax.
Start from here.
If you fit the data and you still run into trouble, try modeling CL
Vmax/(exp(Km) + C) as this has been shown to result in better estimation
than the standard Vmax/(Km + C). I have also found that sometimes
Vmax is so
large relative to Km that you should try CL = (Vmax/1000)/(exp(Km + C).
Next time, when you put data on the list serve you need to send the
doses as
well.
Good luck,
Pete Bonate
Peter L. Bonate, PhD, FCP
Director, Pharmacokinetics
Genzyme Corporation
4545 Horizon Hill Blvd
San Antonio, TX 78229
phone: 210-949-8662
fax: 210-949-8219
email: peter.bonate.aaa.genzyme.com
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Sometimes a increasing convex curvature with increased dose can be
related with a saturable protein binding rather than nonlinear
elimination kinetics. A tentative model could be a Michaelis-Menten
elimination kinetic model associated simultaneously to a saturable
protein binding kinetic model.
Wong, H et al. Drug. Metabol. Disp. 29: 664-675. 2001.
Relling, MV et al. J. Pharmacokin. Biopharm. 21: 639-651. 1993.
Regards,
Jose M. Lanao
Dpt. Pharmacy and Pharmaceutical Technology
Faculty of Pharmacy.
University of Salamanca
Spain.
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The following message was posted to: PharmPK
Let's not put the cart before the horse.
Start with the PK definition of nonlinearity: Plot AUC (or Css) vs.
dose.
What does it look like?
If you have Css vs. dose, can you use something simple (like the Mullen
method used for phenytoin) to get a reasonable estimate of what Vmax
and Km
might be?
What do you know about the elimination of the drug (hepatic vs. renal,
active renal secretion vs. GFR)?
--Larry
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Pierre-Olivier,
I have seen several examples of non-linear kinetic profiles
resembling M-M, however impossible to fit properly with any M-M
model, when the non-linear component was in fact in the absorption
process. This is typically the case for subcutaneous injections of a
peptide, but I can imagine that it may happen as well with oral
dosing of a xenobiotic. In such situations you have to elaborate a
non-linear model for absorption; an i-v period may be of great help.
Best regards
Thierry Buclin
Div of clinical pharmacology and toxicology, CHUV Lausanne
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The following message was posted to: PharmPK
Larry Bauer wrote:
>
> PharmPK - Discussions about Pharmacokinetics
> Pharmacodynamics and related topics
>
> The following message was posted to: PharmPK
>
> Let's not put the cart before the horse.
>
> Start with the PK definition of nonlinearity: Plot AUC (or Css) vs.
> dose.
IMHO the definition of PK non-linearity is more fundamental than the
relation between dose and a PK statistic such as AUC. PK non-linearity
arises when the fundamental PK parameters of clearance and volume of
distribution are non-stationary e.g. they change with concentration.
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New
Zealand
email:n.holford.-a-.auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/
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The following message was posted to: PharmPK
Hi Nick- How many physiologic possibilities are there for clearance or
volume to be "nonstationary" if the AUC (or Css) vs. Dose relationship
is linear? I can't think of many, but, then again, it is bedtime in
Seattle. :)
I believe the original post (long since erased, on my account, so I
can't double check) jumped to the conclusion that a curvilinear decline
on a ln C vs. t plot was MM kinetics--which to my mind is jumping way
ahead without doing some simple preliminary analysis (a few plots that
actually help define MM) and some simple thought (do the routes of
elimination lend themselves to MM). This seems to me to be most
unwise.
--Larry
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The following message was posted to: PharmPK
Hello again and thank you all for your quick responses. From your
answers, I see that I inadvertently omitted important information.
- Doses were 200, 600 and 1200 mg (all oral).
- The data are mean concentration-time profiles of three groups of
individuals receiving each one dose. Individual concentration-time
profiles show little variation from the mean.
- Plotting AUC/dose (and Cmax/dose) against dose suggested more than
proportional increase as dose increases.
- Multiple dosing produced higher exposure than predicted by
superposition.
- A good proportion of the product's elimination is through metabolic
pathways to an active metabolite.
PO :o)
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The following message was posted to: PharmPK
Larry,
Any concentration or dose dependence of Vss will not influence AUC0-
inf or Css... Only CL (or F) can affect AUC and Css.
My point is try and think more physiologically about PK and not fall
into the trap that the statisticians are in when they develop ever
more bizarre ways to 'prove dose proportionality' using empirical ad
hoc models and hypothesis tests. I know full well that *you* know
about the physiology :-)
Nick
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New
Zealand
email:n.holford.-at-.auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/
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