- On 26 Jan 2000 at 23:53:51, "Stuart Friedrich" (SFriedrich.-at-.genetics.com) sent the message

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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 - On 27 Jan 2000 at 22:52:41, David_Bourne (david.aaa.boomer.org) sent the message

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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 - On 31 Jan 2000 at 11:40:34, Art Straughn (ASTRAUGHN.-a-.utmem1.utmem.edu) sent the message

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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 - On 1 Feb 2000 at 21:39:46, ml11439.-a-.goodnet.com (Michael J. Leibold) sent the message

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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 - On 3 Feb 2000 at 21:40:39, "Aucoin, Robert" (RAucoin.-a-.ololrmc.com) sent the message

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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) - On 4 Feb 2000 at 23:45:48, David_Bourne (david.at.boomer.org) sent the message

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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 - On 16 Feb 2000 at 21:56:56, Roger Jelliffe (jelliffe.-a-.usc.edu) sent the message

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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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