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I have the following drug pk problem to analyze:
Procedure:
Drug administration: single IV bolus injection to dog
Drug dose: 1 mg/kg
Blood concentration drug units: micrograms/mL
Time units: hours
Results:
Time Conc
0.25 2.13
0.5 1.81
1 1.94
1.5 1.87
2 2.21
3 2.17
4 2.66
6 2.46
8 1.89
10 1.53
12 0.9
18 0.22
24 0.8
Below is a Windows bitmap graph of the data for those who can read it.
[db - this didn't seem to make it through the system]
Questions:
1. How can the data be analyzed? Can this data be modeled on WinNonlin?
What model should I use?
2. What does this data mean? The blood concentration of the drug
remains the same or slightly rises over the first 4 hours following IV
bolus injection to the dogs, then falls rapidly. We have dosed two
other dogs with the same results. This seems unusual to me. Is there
another example of a drug that behaves in this manner?
[db - without looking at the graph - could it be enterohepatic recyling -
any meals/food provided - what is the assay variability]
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[db - quite a few messages today]
Date: Mon, 20 Oct 1997 14:43:17 -0600
From: "Steven J. Weber"
To: PharmPK.at.pharm.cpb.uokhsc.edu
Subject: Help with unusual pk problem -Reply
Mime-Version: 1.0
I would pursue enterohepatic recirculation. You may want to perform
the initial study in rats before choosing to attempt the same more time
consuming and expensive procedure in dogs. Cannulated rats can be
purchased from several sources.
Also, a question for the group; Has anyone information regarding
hydroxyurea protein binding? Determination of protein binding of
hydroxyurea with Centrifrees yields a slightly, but constant, negative
number. We see the same over a wide range of concentrations done in
replicates of 5. Has anyone seen the same with other compounds that
exhibit little to no protein binding? References?
--
X-Sender: jelliffe.at.hsc.usc.edu
Date: Mon, 20 Oct 1997 13:57:24 -0700
To: PharmPK.-a-.pharm.cpb.uokhsc.edu
From: Roger Jelliffe
Subject: Re: Help with unusual pk problem
Mime-Version: 1.0
I realize this doesn't respond direectly to your question, but what are the
SD's of your serum level data, so that each level can be given its proper
credibility in whatever fitting process is done? It alsolooks as though you
will have to elavuate several different compartmental models before you get
an idea which model is best.
Roger Jelliffe
************************************************
Roger W. Jelliffe, M.D.
USC Lab of Applied Pharmacokinetics
CSC 134-B, 2250 Alcazar St, Los Angeles CA 90033
Phone (213)342-1300, Fax (213)342-1302
email=jelliffe.-at-.hsc.usc.edu
************************************************
Take a look at our Web page for announcements of
new software and upcoming workshops and events!!
It is http://www.usc.edu/hsc/lab_apk/
************************************************
--
From: "Robert D. Phair, Ph.D."
To: "'PharmPK.at.pharm.cpb.uokhsc.edu'"
Subject: RE: Help with unusual pk problem
Date: Mon, 20 Oct 1997 18:27:19 -0400
MIME-Version: 1.0
Tom Wallace posted a PK data set with somewhat unusual characteristics and
asked for possible interpretations. Among metabolic systems there are
several that display kinetics such as Tom describes. One with which I have
a lot of personal experience is the plasma lipoprotein delipidation
cascade. This consists of a series of metabolic conversions (catalyzed by a
pair of plasma lipases) that converts very low density lipoprotein (VLDL)
to IDL and then to the notorious LDL, which finally is cleared from the
circulation by the famous apoB receptor. In the early days of this field,
VLDL and IDL were isolated together and their combined kinetics looked a
lot like Tom's drug concentration time course. (a small peak or even a
frank plateau followed by an apparently exponential decline.
In Tom's case, a lot depends on whether you believe the point at 18 hours
or the point at 24 hours. If both are correct the system is even more
complex and David's suggestion of enterohepatic recycling could be invoked.
But I'd be inclined to believe the 18 hour point and to use a model
consisting of a series of compartments with elimination from the last of
them. You would fit the data against the sum of all the compartments, and
the injection would be into the first compartment. I have no doubt that the
data set Tom supplied could be fitted to such a model.
Then the question becomes what is the physiological significance of this
cascade? Without knowing more about the compound Tom administered, it's
hard to say for sure, but a good initial hypothesis would be that the drug
is processed intravascularly and only after several steps does it become a
substrate for its clearance mechanism. To evaluate this you'd first want to
know for sure that your assay measures only the parent compound and not its
metabolic successors. A second hypothesis perhaps worth testing, is that
the compound has a high affinity for VLDL and is adsorbed onto the surface
or even dissolved in the core lipid of this lipoprotein. This would result
in kinetics that are determined by lipoprotein processing, and in effect
the drug becomes a tracer for lipoprotein metabolism. Under some
circumstances, this could be a gold mine.
The bottom line is that a likely model for the data set Tom posted is a
series cascade with the data fitted to the sum of all the compartments and
elimination from the last. Models like this are easy to build and fit to
data using compartmental analysis packages like SAAM 31, SAAM II and ACSL
BioMed to name just the ones I'm at least a little familiar with. There are
many others, for example ScoP, and it may even be that WinNonlin will do
this problem. The software is not the key. The key is recognizing the
nature of the problem, and my best shot at doing that is the cascade
mechanism described above.
Tom, there are definitely solutions to this class of problems. Let me know
if I can be of further help.
Regards,
Bob
----------
Robert D. Phair, Ph.D. rphair.-at-.bioinformaticsservices.com
BioInformatics Services http://www.bioinformaticsservices.com
12114 Gatewater Drive
Rockville, MD 20854 U.S.A. Phone: 1.301.315.8114
Partnering and Outsourcing for Computational Biology
--
X-Sender: b1psuv57.at.pop1.sympatico.ca
Mime-Version: 1.0
Date: Mon, 20 Oct 1997 20:14:44 -0400
To: PharmPK.-at-.pharm.cpb.uokhsc.edu
From: G Soon
Subject: Re: Help with unusual pk problem
Sorry, cannot comment on equations, but, could this be an example of
redistribution from another compartment? Another example might be diazepam
diffusion from blood to CNS and then diffusion back from CNS to blood.
(Reason why lorazepam is recommended over diazepam for treatment of seizures.
Greg Soon
Pharmacist - ICU/Surgery
Peterborough Civic Hospital
Peterborough, ON, Canada
(705) 876-5083
(705) 876-5110 (fax)
gsoon.at.sympatico.ca
--
Date: Tue, 21 Oct 1997 16:29:47 +0100 (MET)
From: Maria Durisova
To: PharmPK.-at-.pharm.cpb.uokhsc.edu
Subject: Re: Help with unusual pk problem
Dear colleague,
We analyzed your data using the CXT software package. Since
we did not know the weight of the dog, we estimated it as 15 kg,
so we used the total dose of 15000 micrograms.
Below please find the model function describing behavior of
your system:
C(t) = 15000*2.51E-3*{0.0459*exp(-0.0572*t)+0.0859*exp(-0.5708*t)+
-0.0558*exp(-167.6102*t)+
exp(-0.1551*t)*[-0.0738*cos(0.3372*t)+0.052*sin(0.3372*t)]+
exp(-0.0102*t)*[-2.1112E-3*cos(0.5939*t)+2.0337E-3*sin(0.5939*t)]}
You can plot this model function and compare it with the data
measured. The value of the Akaike criterion is: 10.4.
On the basis of this preliminary model, it is possible to
estimate pharmacokinetic parameters e.g.:
Clearance=(1/2.51E-3)=398.4 mL/h, AUC=37.65 microgram*h/mL,
and MRT =14.9h, AUC_residual.28%.
This model function is a solution of the seventh-order
differential equation, indicating a time delay in your
pharmacokinetic system. It follows then that, your system
cannot be described by a multiexponential model. We would
recommend you to add the following sampling points: 5,
10 min., 15, 21, 27, and 30 h.
Sincerely,
Maria Durisova
and
Ladislav Dedik
--
Priority: Normal
X-MSMail-Priority: Normal
X-Priority: 3
To: PharmPK.-at-.pharm.cpb.uokhsc.edu
MIME-Version: 1.0
From: "Steve Duffull"
Subject: Re: Help with unusual pk problem
Date: Tue, 21 Oct 97 16:39:59 PDT
To Tom Wallace
Interesting problem...
> Procedure:
> Drug administration: single IV bolus injection to dog
> Drug dose: 1 mg/kg
> Blood concentration drug units: micrograms/mL
> Time units: hours
This raises further questions:
1) what was the drug? (I seem not to be able to find it in your note.)
2) what was the salt of the drug?
3) was it inadvertantly administered SC or intradermally?
4) how was it administered IV (?via a cannula or other tubing, was the
tubing flushed?)
5) how were the blood samples taken (via the same cannula?, how much blood
was discarded from the sample before the remainder was kept for assay...?)
6) what condition was the dog in? (any relevant pathology?)
I am interested to hear the comments of others.
Steve Duffull
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[a collection of responses - db]
Date: Tue, 21 Oct 1997 12:46:15 -0400 (EDT)
Sender: Jian-hua Liu
From: Jian-hua Liu
X-Sender: jliu.aaa.login3.isis.unc.edu
To: PharmPK.-at-.pharm.cpb.uokhsc.edu
cc: Multiple recipients of PharmPK - Sent by
Subject: Re: Help with unusual pk problem
MIME-Version: 1.0
What is your detection limit? The noisy data may due to the concentration
closed to or below the detection limit.
--
From: "Joseph Balthasar"
To:
Subject: Re: Help with unusual pk problem &&&& Negative value for protein
bound drug
Date: Tue, 21 Oct 1997 14:56:45 -0600
X-MSMail-Priority: Normal
X-Priority: 3
MIME-Version: 1.0
Dear Steve:
How are you measuring the hydroxyurea? If you are using radioactivity, it
is possible that the Centrifree tubes are removing a quenching substance.
You may wish to verify your quench curve for ultrafiltrated and
non-filtered samples. Occasionally, investigators rely too heavily on
external quench correction, perhaps forgetting that the underlying
efficiency relationships are matrix dependent.
If you are using HPLC, are you observing a fixed increase in assayed
concentration (i.e., ultrafiltrated recovery = control recovery + some
intercept) or a fractional increase in assayed concentration (e.g.,
ultrafiltrated recovery = 110% of control)? If you observe a fixed
increase, you may be extracting an interfering substance with your
ultrafiltration step. If you see a fractional change (i.e., a matrix
effect), you may wish to check for increased post-filtration extraction of
hydroxyurea, decreased post-filtration extraction of an internal standard,
extraction of a substance which interferes with an internal standard).
************************************************************
Joseph P. Balthasar, PhD
Assistant Professor
Department of Pharmaceutics
and Pharmaceutical Chemistry
University of Utah
Telephone: 801-585-5958
Fax: 801-585-3614
************************************************************
--
Date: Wed, 22 Oct 1997 21:39:48 -0400 (EDT)
From: "Susan E. Shoaf"
Sender: "Susan E. Shoaf"
Reply-To: "Susan E. Shoaf"
Subject: Re: Help with unusual pk problem
To: PharmPK.at.pharm.cpb.uokhsc.edu
Mime-Version: 1.0
Problem: sustained concentrations following iv bolus administration
You don't mention any of the drug characteristics, particularly its
solubility.
When I was injecting Tribrissen, a suspension of Trimethoprim and
solution of sulfadiazine, into 1 day old calves we found that
Trimethoprim (TMP) seemed to adhere to the walls of the vein (jugular)
and give us a prolonged "distribution phase". It was not as dramatic as
the data presented here but it may be the same phenomenon. Also, are you
sampling from the same vein as you injected from? This can really "inflate"
your plasma values.
Susan
shoaf.at.clinpharm.niaaa.nih.gov | National Institute on Alcohol Abuse and
I don't speak for NIAAA, | Alcoholism
that's for the PR office. |
--
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Dear PharmPK Folks:
About detection limits. This is an interesting issue. It relates in
general to the problem of assigning the correct weight to a serum level (or
any other) data point when fitting it by almost any method, and in optimal
population modeling.
The really important thing is to KNOW the error with whith each serum
level is measured. Often people choose weighting by the reciprocal of the
concentration, or its square. The best, I think, is to know the standard
deviation (SD) with which each and every serum level is measured. Then one
can correctly weight each level by its Fisher information, the reciprocal
of its variance, in the modeling process.
Unfortunately, most labs have not done this. Once the error,
usually the
coefficient of variation, has been shown to be within socially aceptable
limits, then the actual errors are too often ignored, and not realistically
incorporated into the fitting process.
We suggest that one determine, empirically, in at least
quadruplicate, the
SD of representative concentrations over the working range of the assay -
for example, of a blank, a low, a medium, a high, and a very high level.
Now, fit the relationship of SD to concentration with a polynomial to
capture this usually nonlinear, convex upward, relationship, so that you
can estimate the SD from the serum concenreation that is measured. Having
done this, one now has a pretty good, and cost-effective way to get an
estimate of the SD with which any single level is measured.
These issues are discussed in more detail in
Jelliffe R: Explicit Determination of Laboratory Assay Error Patterns - A
Useful Aid in Therapeutic Drug Monitoring. The Americal Society of Clinical
Pathologists CHECK SAMPLE continuing education program, Drug Monitoring and
Toxicology, 10: No. DM 89-4 (DM-56), 1990, and
Jelliffe R, Schumitzky A, Van Guilder M et al: Individualizing Drug Dosage
Regimens: Roles of Population Pharmacokinetic and Dynamic Models, Bayesian
Fitting, and Adaptive Control. Ther. Drug Monit. 15; 380-393, 1993.
The point of this is that for toxicology, one MUST have lower
detectable
limits, as there is no other way tomake a decision as to whether the drug
is present or not. However, for TDM or for PK studies, one usually knows
quite well how long after each dose the semple was measured, and we also
know that for most linear systems, at least, one never gets rid of the last
molecule, so to speak. We therefore have the answer as to whether the drug
is actually there or not - it clearly IS. The only question remaining is
what concentration, and with what error.
It has been common to think that when the levels get very low that the
coefficient of variation approaches infinity. True enough, but what about
the SD and the variance, and therefore, the Fisher information? All this is
knowable right down through low levels, all the way down to the blank.
Because of this, there is actually NO LOWER DETECTION LIMIT for samples
measured when the time after the last dose is known, at least for drugs
having linear models. Using such polynomials, fron which the SD of each
level can be estimated usually easily and quite well, the correct weight
appropriate to its credibility can be given. For TDM at least, this whole
question of lower detection limits has been a cultural problem derived from
toxicology, not from TDM. Look at the articles and let me kow what you guys
think, and let's continue to talk about it.
Very best regards,
Roger Jelliffe
************************************************
Roger W. Jelliffe, M.D.
USC Lab of Applied Pharmacokinetics
CSC 134-B, 2250 Alcazar St, Los Angeles CA 90033
Phone (213)342-1300, Fax (213)342-1302
email=jelliffe.-at-.hsc.usc.edu
************************************************
Take a look at our Web page for announcements of
new software and upcoming workshops and events!!
It is http://www.usc.edu/hsc/lab_apk/
************************************************
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