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Dear all,
I have a question regarding volume of distribution that I have been
unable to solve. I have analyzed numerous sets of serum
concentration-time data for three different monoclonal antibody
products in three different primate species (including humans) and
found a central volume of distribution that is lower than plasma
volume. Two of the antibodies are targeted against cell surface
receptors and the other is against a cytokine. The analysis used to
determine central volume of distribution is model independent and
therefore does not involve extrapolation errors. A Vc markedly lower
than plasma volume can be calculated by taking the dose and dividing
by the concentration measured after an IV bolus dose. The timepoints
used for the calculation can be up to several hours after the dose,
so an argument based on incomplete mixing does not hold. The Vc
calculated this way can range from 25 to 65% of plasma volume,
assuming a plasma volume of 40 - 45 mL/kg. The data within a
particular study is tight with a CV of less than 10%. Calculating a
Vc that is higher than plasma volume can always be explained by some
type of binding phenomena or rapid extravascular distribution, but I
cannot think of a physiological reason that would explain a Vc that
is markedly lower than plasma volume. The assays used to measure the
antibodies and the doses administered are validated, so there does
not seem to be a measurement error. I was wondering if anyone has an
explanation for this observation, and/or has seen this for other
monoclonal antibody products.
Thanks
Stuart
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Date: Thu, 27 Jan 2000 02:23:54 -0700 (MST)
X-Sender: ml11439.aaa.pop.goodnet.com
To: PharmPK.-a-.boomer.org
From: ml11439.-a-.goodnet.com (Michael J. Leibold)
Subject: Re: PharmPK Vc lower than plasma volume
Stuart,
Physiologically Vd is modeled as:
i) V= Vb + Vt[Fb/Ft] equation 1
Where:
Vb= blood volume
Vt= volume in extravascular space
Fb= free fraction in blood
Ft= free fraction in extravascular space
By this model, the smallest apparent Vd is the Vb or blood volume.
However, methods for calculating Vd, whether model dependent or
model independent, assume a linear system. So that equations such as
the following are based on linear pharmacokinetics where the system is
described by linear differential equations.
ii) Vd= [Dose]/[K*AUC] equation 2
iii) Vss= D[AUMC]/[AUC]2 equation 3
A system in which the drug elmination is nonlinear due to the effects
of protein binding, equations 2 and 3 would be inaccurate.
One could reason that equation 1 accurately describes the Vd of the
monoclonal antibody, but due to nonlinearities in protein binding, equations
2 and 3 might not accurately predict the Vd.
Factors affecting plasma protein binding of drugs have been
found to also affect the T1/2:
iv) High extraction drugs:
T1/2 = [Vb+ Vt(Fb/Ft)](.693)/Q equation 4
v) Low extraction drugs:
T1/2 = [Vb + Vt(Fb/Ft)](.693)/FbCli equation 5
Both of these equations are obtained from:
T1/2= (.693)(Vd/Cl)
Cl= Q or Cli
Vd= (Vb +Vt(Fb/Ft)]
Monoclonal antibodies should be highly protein bound and could be
subject to the nonlineariries described by equations 4 and 5. This could
render even model independent methods of determining Vd inaccurate, since
the uderlying assumptions require linear pharmacokinetic systems.
Perhaps a more sophisticated method of calculating Vd would be
appropriate.
Mike Leibold, PharmD, RPh
ML11439.-a-.goodnet.com
---
Date: Thu, 27 Jan 2000 08:28:02 -0500
From: "Geng, Wanping {NCDS~Nutley}"
Subject: RE: PharmPK Vc lower than plasma volume
To: "'PharmPK.-a-.boomer.org'"
Dear Stuart,
I don't know the detail of your calculation. If you use Vc=DOSEiv/Co,
Co has to be the concentration at time zero that could be calculated
from extrapolation of the first several time points. The first one or
two points might affect regression a lot. If injection of dose was
not an ideal bolus dose, Co might be under-estimated and Vc would be
over-estimated. It might be better to calculate apparent volume of
distribution (Vss=CL*MRT=DOSEiv*AUMC/AUC2). It is only for your
consideration. Good luck.
Wanping Geng
---
Reply-To: "W. Webster"
From: "W. Webster"
To:,
"Multiple recipients of PharmPK - Sent by"
Subject: Re: PharmPK Vc lower than plasma volume
Date: Thu, 27 Jan 2000 18:59:17 -0500
X-Priority: 3
Having administered monoclonal antibody or fragments to some well over 2,000
human subjects/patients and often observed the same, It was reported in the
literature (Webster et al, J. Nucl Med, 1992)
However, in thinking about it, I believe it is when we drew blood samples
from the same site as we injected the MAb that we saw it. and it was
significant enough to influence the means. The other thing to be aware of,
is if you are dealing with patients with GI cancer, they have significant
bleeding and their plasma compartment may indeed be larger. Remember also,
there is a great amount of "non-specific" MAb binding.
Model independent or not, volumes are proportionality constants that
function to balance the equation where you measure a concentration in mass
per volume from the subject but you administered mass. The Volume of
distribution term is necessary to put a volume term on both sides of the
equation. Veng-Pederson is fond of referring to "theoretical
pharmacokinetic space" in model independent work.
So anyway, since you calculated dose/concentration and you are sure of your
dose, then it has to be the concentration term is "too high" for some
reason. That reason could be the MAb still in the vessel and not mixed in
the circulation well.
Having looked at many radiolabeled MAb Planar and SPECT scans after bolus
administration, I can see and report with some certainty that the MAb
radioactivity does remain in the vessel where it is administered for some
time. We always, (NOW) use a contralateral limb for sampling.
WW
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To Mike Leibold,
Would you please explain how nonlinear protein binding effects the
calculation of V using equations 2 or 3? That is, would the
calculation of V be overestimated or underestimated?
Also is equation 5 supposed to have the second Fb?
Thanks,
Art Straughn
Memph
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Art,
The textbook equations I was referring to show that changes in
protein binding can change the Vd, which in turn can change the
T1/2 and Ke:
iv) High extraction drugs:
T1/2 = [Vb+ Vt(Fb/Ft)](.693)/Q equation 4
v) Low extraction drugs:
T1/2 = [Vb + Vt(Fb/Ft)](.693)/FbCli equation 5
Both of these equations are obtained from:
T1/2= (.693)(Vd/Cl)
Cl= Q or Cli
Vd= (Vb +Vt(Fb/Ft)]
Equation 4 and 5 predict a decrease in Vd with a decrease in the
free fraction (Fb) in the blood volume, which in turn would cause a
decrease in T1/2. Similarly, an increase in free fraction in the
extravascular space (Ft) would cause a decrease in Vd, and a decrease
in T1/2.
The corresponding increase in Ke during the elimination of the
drug from the body would make the linear assumptions of the following
equations invalid, since the assumptions include linear "constants"
of elimination:
ii) Vd= [Dose]/[K*AUC] equation 2
iii) Vss= D[AUMC]/[AUC]2 equation 3
Extrapolating plasma concentrations to time zero for a plasma
concentration curve which is not log-linear, could result in various
calculated Vd's depending on what portion of the curve is used, and
whether the Ke is decreasing of increasing as a result of protein binding.
In a simplified sense, if the Ke is estimated in an increasing phase,
then equation 2 would predict an decreased Vd.
Mike Leibold, PharmD, RPh
ML11439.-a-.goodnet.com
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I have been following this thread with some interest. I have
clinical case that may throw a wrench in all of this.
An 8 week old male child with documented VSD and ASD presents
to our ED. Patient is in respiratory failure. Bagged, tubed and
sent to our PICU. Blood and urine cultures are positive for Gram
Positive Staph Coagulase positive. Staph aureus sepsis suspected.
MD starts patient on Vancomycin 10mg/kg q 6hr. Pt. has pertinent hx
of 31 week preemie.
Vancomycin levels ordered, pharmacy consult.
Based on prior experience I would anticipate the levels to be
low. Nurse calls me last night around 9:00pm with the lab results.
Vanco Tr= 12.9
Vanco PK= 19.8
Chem-7 as follows. Na.135, K 4.2, Cl 105, CO2 25, BUN 6, CrS
0.3. Urine output = 4.57ml/kg/hr via foley. CBC: WBC 16.8, left
shift and significant bandemia.
I checked the lab times and the dosing times. Also checked
the nursing notes for documentation of med administration, rate of
administration and total volume used for infusion.
Everything is in order.
Point to make...
All of the equations in the world will not predict what
individual patients do on any given day. Equations were based on
healthy males 19 to 25 yrs old, not 31 week old preemies with heart
problems leading to poor renal perfusion.
I have been following levels and doses of various drugs for
several years in a busy PICU. Kids and sick people in general, do
not follow the rules.
If any of you can give me the set of equations to treat this
kind of patient, I will send you six of my best white camels and
dance at your next wedding.
Please don't interpret this post as a knock on what you guys
do. We need the work. But please temper any pronouncement with a
grain of salt to consider the clinical picture of the target audience.
Robert
Robert Aucoin, RPh 1-888-765-7428 (Toll free)
Senior Clinical Pharmacist/Operations fax: 225-765-8410
The Children's Center at Office: 225-765-7652
Our Lady of the Lake RMC pager: 225-237-6564 (digital)
Baton Rouge, LA 70808 e-mail: RAucoin.-a-.ololrmc.com
web site: www.mraucoin.com (new,
under constru)
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[A few replies - db]
Date: Thu, 3 Feb 2000 21:48:02 PST
From: Walter Wolf
To: PharmPK.aaa.boomer.org
Cc: Multiple recipients of PharmPK - Sent by
Subject: Re: PharmPK Re: Vc lower than plasma volume
On Thu, 3 Feb 2000 21:40:39 -0600 Robert Aucoin wrote:
>All of the equations in the world will not predict what individual
>patients do on any given day.
How true!.
>Equations were based on healthy males 19 to 25 yrs old, not 31 week old
>preemies with heart problems leading to poor renal perfusion.
And this is specially relevant in special populations (e.g., infants), or in
acute diseases (e.g., cancer), where each patient presents a unique set of
pathophysiological characteristics.
In all those patients, one must measure, and then attempt to individually
optimized dosages.
There is one additional critical issue. What does one measure? When blood
levels of drugs are the rate determining step, then it is possible to use
blood measurements. But when the critical site to measure is a tissue (e.g.,
a tumor), that is what one must measure. But repetitive and sequential
measurements in tissues and organs must be done noninvasively. Not only for
ethical considerations, but also because only those measurements that do not
perturb the system being studied will have any meaning.
| Professor Walter Wolf, Ph.D. E-Mail: wwolfw.-a-.hsc.usc.edu |
| Distinguished Professor of Pharmaceutical Sciences |
| Director, Pharmacokinetic Imaging Program |
| Department of Pharmaceutical Sciences, School of Pharmacy |
| University of Southern California Telephone:323-442-1405|
| 1985 Zonal Ave., Los Angeles, CA 90089-9121 Fax: 323-442-9804|
| |
|Center for Noninvasive Pharmacology, Los Angeles Oncologic Institute|
| MRI at St. Vincent Medical Center Telephone: 213-484-7235 |
| 2131 Third St., Los Angeles, CA 90057 Fax: 213-484-7447 |
---
Date: Fri, 4 Feb 2000 03:49:04 -0700 (MST)
X-Sender: ml11439.-a-.pop.goodnet.com
To: PharmPK.aaa.boomer.org
From: ml11439.aaa.goodnet.com (Michael J. Leibold)
Subject: Re: Vc lower than plasma volume
Robert,
The pharmacy staff at our "geriatric" hospital has been using Datakinetics
for vancomycin and gentamicin dosing for ~10 years. The equations used
in the Datakinetics program are Sawchuk-Zaske like equations. Steady-state
is assumed for each calculation and the peak and trough are inserted into
the equations as if the trough was actually taken after the reported peak
[a steady-state assumption].
NOTE: STEADY-STATE IN YOUR PATIENT WOULD AROUND THE 5TH DOSE[ie 24 HOURS].
LEVELS DRAWN BEFORE THIS WOULD NOT BE AT STEADY-STATE.
The mathematical model assumed is a one compartment intermittent
infusion, and the equations are as follows:
1) Steady-state peak plasma concentration:
Cpkss= [Ko/KVd][(1-e-KT)/(1-e-KTau)]e-Kt'
Ko= infusion rate in mg/hr
K= elimination constant (hr-1)
Vd= volume of distribution (liters)
T= infusion time in hours
Tau= dosage interval (hours)
t'= time after intusion (hours)
2) Steady-state trough plasma concentration
Ctrss= Cpkss[e-ke(Tau-T)]
3) Elimination Constant (hr-1)
K= [Ln (Cpkss)- Ln (Ctrss)]/(Change in time)
4) Volume of distribution
Vd= [Ko/KCpkss][(1-e-kT)/(1-e-KTau)]e-Kt'
5) Dosage interval (hours)
Tau= (1/K)[Ln(Cpkss/Ctrss)] + T
6) Infusion rate or dose (mg/hr)
Ko= [(KVd)(Cpkss)(1-e-KTau)]/[(1-e-KT)(e-Kt')]
Assuming steady-state conditions in your patient's data:
8 week old male
pertinent hx of 31 week preemie.
Vancomycin 10mg/kg q 6hr
Vanco Tr= 12.9
Vanco PK= 19.8
Assumed time change between peak and trough: 3.5 hours
Assumed time peak occured after completion of infusion: 1 hour
Assumed infusion time: 1 hour
Assume time trough drawn before dose: 0.5 hour
1) K= .1224156 hr-1
2) T1/2= (.693)/(.1224156)= 5.66 hours
Literature value is ~4.1-6.7 hours
3) Vd= .8084 liters/kg
Literature value is ~.595-.964 liters/kg
4) Clearance= (KVd)= .098961 liter/hr/kg
Literature value is ~.0714-.1629 liter/hr/kg
5) Tau (calculated)= 15.63 hours
6) Tau (rounded)= 12 hours
7) Ko (calculated) = 19.837 mg/hr/kg (one hour infusion)
8) Ko (rounded) =20.0 mg/hr/kg (one hour infusion)
9) Predicted steady-state peak plasma concentration= 30.236 ug/ml
10) Predicted steady-state trough plasma concentration= 7.868 ug/ml
11) Summary
The calculated regimen is a 20mg/kg/hr one hour infusion every 12 hours
for a predicted steady-state peak of 30.3 ug/ml and trough of 7.9 u/ml. The
literature suggests the following regimens:
i) 10mg/kg every 6 hours
ii) 22.5mg/kg every 12 hours
iii) 10mg/kg every 12 hours
The calculated pharmacokinetic values do not deviate significantly
from the literature values, and the calculated regimen agrees with one of
the literature suggested regimens. Changing renal/cadiovascular function
requires frequent monitoring of vancomycin levels for further dosage
adjustments.
Use your clinical judgement.
Mike Leibold, PharmD, RPh
ML11439.-at-.goodnet.com
Reference
1) Schumacher, G.E., Therapeutic Drug Monitoring, Norwalk, Appleton&
Lange 1995; pp 587-632
---
From: "Aucoin, Robert"
To: 'Walter Wolf', PharmPK.-a-.boomer.org
Cc: "Aucoin, Robert"
Subject: Re: Vc lower than plasma volume
Date: Fri, 4 Feb 2000 12:10:07 -0600
Please do not misconstrue my remarks in the earlier post. On many
occasions I use standard equations to predict levels and guide
therapy. The work of the pharmacokineticist is invaluable here. They
set the baseline against which we measure/compare those patients who
fall outside the standard parameters. (I know what the drug should
do, but this is what it is doing.... Scratch head, look puzzled.)
The problems arise in treating specific diseases and
pathophysiological conditions that alter the regular physiology in
ways we have yet to determine. The most common confounding states
being ARDS, MOSD, Sepsis, Multiple Trauma, Sickle Cell and many types
of cancers.
These are the train wrecks that turn up on our doorstep where
clinical knowledge/experience coupled with a firm grasp of harder
science comes into play.
If it were easy, I would be selling popcorn in St. Martin.
Keep up the good work ladies and gentlemen. We need you, the patients need us.
robert
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Dear Robert:
You are absolutely right. All population models are like yesterday's
newspaper. Even if your patient was an adult, the use of population models
alone is usually NOT enough, because of the diversity in the population.
But they are all one has. Any initial dosage regimen, based on any
population model, NEEDS to be followed up by measuring levels and making an
individualized model of how that drug is behaving in that particular
patient. That is the whole purpose of getting feedback. That is what Bayes'
theorem is all about. The set of equations you need is simply obtained by
fitting the model to your patient's data, and using that patient's
individualized model to compute the regimen to achieve the desired target
goal(s). Most software, including our own USC*PACK Bayesian software, is
designed to do just this. Put in the dosage regimen. Put in the levels. Fit
the model. See the plot. Compare the behavior of the plot with the clinical
behavior of the patient. That is the only way I know to really evaluate the
patient's clinical sensitivity to a drug. Then consider your target goals,
and find the best combination of dose and dose interval to best hit your
target goals. Also, what does your patient weigh?
After this is over, you will get experience with patients such as this
one, and you then can store your experience by making a population model of
the patients you have studied, in exactly the clinical situations which are
relevant. This will help you get a better Bayesian prior for use in
designing the initial regimen to hit your target goals. Yo might also
consider looking at our web site (see below) for more info, especially in
our technical reports and other publications.
Hope this helps. I look forward to talking with you further.
Roger Jelliffe
Roger W. Jelliffe, M.D. Professor of Medicine, USC
USC Laboratory of Applied Pharmacokinetics
2250 Alcazar St, Los Angeles CA 90033, USA
Phone (323)442-1300, fax (323)442-1302, email= jelliffe.at.hsc.usc.edu
Our web site= http://www.usc.edu/hsc/lab_apk
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