martin
★★

Austria,
2011-10-18 09:49
(4359 d 18:45 ago)

Posting: # 7510
Views: 19,205

## volume of distribution at steady state [PK / PD]

Dear all!

I have a questions regarding calculation of volume of distribution at steady state (Vss). After IV bolus administration Vss can be calculated based on the non-compartmental theory as doseiv x AUMC0-infinity / AUC20-infinity. Now let us assume that the concentrations over time after extra vascular administration can be adequately described by a one-compartmental model with first order absorption and first order elimination.

How can the volume of distribution at steady state be calculated under this model? Can the above formula be adjusted straightforwardly using the bioavailability F to calculate Vss = (dosepo x F x AUMC0-infinity) / AUC20-infinity?

best regards

Martin
d_labes
★★★

Berlin, Germany,
2011-10-18 13:36
(4359 d 14:58 ago)

@ martin
Posting: # 7512
Views: 17,857

## Vss

Dear Martin!

The TOPFIT2.01) manual states (in the non-compartmental section):
"Estimation of Vss is only possible following intravenous administration because:
a) the bioavailability factor f is unknown following oral administration and
b) the intrinsic MRT is needed (the intrinsic MRT is the MRT of the substance within the systemic circulation and thus corresponds to the MRT calculated from plasma data only in the case of intravenous administration)."

(Emphasis by me)

Formulas given:
iv-bolus
  Vss = CL * MRT
iv-infusion
  Vss = CL * (MRT - IT/2)       = CL * MRTintr
where CL is the clearance, IT the infusion time and MRTintr=MRT of disposition disregarding the infusion time.

If I remember the old days I had done compartmental modelling right the p.o. MRT is something like
  MRTpo = MRTiv + 1/ka + tlag
in the one-compartmental model.

Hope this helps.

1) Heinzel, Woloszczak, Thomann
"TopFit 2.0
Pharmacokinetic and Pharmacodynamic Data Analysis System for the PC"

Gustav Fisher Verlag, Stuttgart-Jena-New York 1993

Regards,

Detlew
Helmut
★★★

Vienna, Austria,
2011-10-18 18:02
(4359 d 10:32 ago)

@ d_labes
Posting: # 7517
Views: 17,925

## History

Dear D. Labes!

❝ The TopFit 2.0 manual

SCNR.

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
javier
☆

Spain,
2016-09-21 18:47
(2559 d 09:47 ago)

@ Helmut
Posting: # 16664
Views: 15,765

## History

❝ ❝ The TopFit 2.0 manual

❝ SCNR.

Hi Helmut

Do you know where is possible to buy this book (in amazon is not available, i fear)

thanks!!
yjlee168
★★★

Kaohsiung, Taiwan,
2016-09-22 13:30
(2558 d 15:04 ago)

@ javier
Posting: # 16666
Views: 15,773

## Amazon? Yes.

Nothing to fear. You really can purchase the manual from Amazon. It is just not cheap at all. Good luck.

❝ Do you know where is possible to buy this book (in amazon is not available, i fear)

All the best,
-- Yung-jin Lee
bear v2.9.1:- created by Hsin-ya Lee & Yung-jin Lee
Kaohsiung, Taiwan https://www.pkpd168.com/bear
d_labes
★★★

Berlin, Germany,
2016-09-22 14:09
(2558 d 14:25 ago)

@ yjlee168
Posting: # 16667
Views: 15,672

## Gold Letters

Dear Yung-yin,

❝ Nothing to fear. You really can purchase the manual from Amazon. It is just not cheap at all.

That's unbelievable! 429.99 bucks for an used exemplar !
Seems it is printed in gold letters.

Regards,

Detlew
yjlee168
★★★

Kaohsiung, Taiwan,
2016-09-24 22:26
(2556 d 06:08 ago)

@ d_labes
Posting: # 16671
Views: 15,609

## Gold Letters

Dear Detlew,

I am not sure if they sell the manual together with the software or not. If not, it is really expensive.

❝ Seems it is printed in gold letters.

All the best,
-- Yung-jin Lee
bear v2.9.1:- created by Hsin-ya Lee & Yung-jin Lee
Kaohsiung, Taiwan https://www.pkpd168.com/bear
mittyri
★★

Russia,
2016-09-25 17:04
(2555 d 11:31 ago)

@ yjlee168
Posting: # 16673
Views: 15,554

## Another quest

Dear Yung-jin,

❝ I am not sure if they sell the manual together with the software or not.

if yes, you need to pray for 2 floppy disks to be still alive and also you need to order some device for reading

Kind regards,
Mittyri
Helmut
★★★

Vienna, Austria,
2016-09-26 01:41
(2555 d 02:53 ago)

@ mittyri
Posting: # 16675
Views: 16,029

## TopFit: 16bit DOS-application

Hi Mittyri & Yung-jin,

❝ […] you need to pray for 2 floppy disks to be still alive…

The software came on only one 3½″ floppy. If you are on a 64bit OS, you need an 32bit emulator of the 16bit DOS-environment. On my Win 7 64bit TopFit (Thomae Optimized Pharmacokinetic Fitting Program) runs in XP-mode:

429.99 USD is ridiculous. I got mine for 198 DEM in 1993. Taking inflation into account it should come for 145.43 Euros (163.26 USD).

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
mittyri
★★

Russia,
2016-09-26 02:02
(2555 d 02:32 ago)

@ Helmut
Posting: # 16678
Views: 15,542

## TopFit: less than 1.44 MB

Hi Helmut,

❝ The software came on only one 3½” floppy.

Oh, you're right
I erroneously interpreted this as 2 floppies:

The app is less than 1.44 MB weight. Amazing!

Kind regards,
Mittyri
Helmut
★★★

Vienna, Austria,
2016-09-26 02:17
(2555 d 02:17 ago)

@ mittyri
Posting: # 16680
Views: 15,539

## TopFit: less than 1.44 MB

Hi Mittyri,

❝ I erroneously interpreted this as 2 floppies:

Yep:

❝ The app is less than 1.44 MB weight. Amazing!

In the last century content was more important than form. Compiled Fortran rulez!

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
ElMaestro
★★★

Denmark,
2016-09-26 11:43
(2554 d 16:51 ago)

@ Helmut
Posting: # 16683
Views: 15,441

## TopFit: less than 1.44 MB

❝ In the last century content was more important than form.

Quote of the month!

Pass or fail!
ElMaestro
yjlee168
★★★

Kaohsiung, Taiwan,
2016-09-26 02:18
(2555 d 02:16 ago)

@ Helmut
Posting: # 16681
Views: 15,565

## TopFit: 16bit DOS-application

Hi Helmut,

Thanks for sharing the picture of TopFit & "gravity duration". Great.

All the best,
-- Yung-jin Lee
bear v2.9.1:- created by Hsin-ya Lee & Yung-jin Lee
Kaohsiung, Taiwan https://www.pkpd168.com/bear
ElMaestro
★★★

Denmark,
2016-09-24 01:13
(2557 d 03:21 ago)

@ martin
Posting: # 16668
Views: 15,569

## volume of distribution at steady state

Hi all,

❝ How can the volume of distribution at steady state be calculated under this model? Can the above formula be adjusted straightforwardly using the bioavailability F to calculate Vss = (dosepo x F x AUMC0-infinity) / AUC20-infinity?

Isn't the proposal by Martin quite reasonable in its simple logic if an estimate of F is available?
I read the answers to his post, and while I gather there's possibly a sentiment towards "no can do!" the argument seems to be merely "because this book says so" where in actuality the book assumes implicitly that no estimate of F (and through that, MRT) is known.

We don't have to be sheep, right?

Pass or fail!
ElMaestro
mittyri
★★

Russia,
2016-09-24 02:38
(2557 d 01:56 ago)

@ ElMaestro
Posting: # 16669
Views: 16,429

## Vss: MIT is needed anyway...

Hi ElMaestro,

❝ We don't have to be sheep, right?

Certainly not.
But as Detlew wisely noted, we need to know MIT

I would cite another good article1

The equation for FO input is the same as given by Detlew, just another names:

So without tlag and ka you cannot calculate Vss, sorry

1. Watari, N. & Benet, L.Z. Journal of Pharmacokinetics and Biopharmaceutics (1989) 17: 593. doi:10.1007/BF01071351

Kind regards,
Mittyri
yjlee168
★★★

Kaohsiung, Taiwan,
2016-09-24 22:19
(2556 d 06:15 ago)

@ mittyri
Posting: # 16670
Views: 15,672

## it seems possible for me...

Dear mittyri and Elmaestro,

If we re-arrange the equation of Vss = (dosepo x F x AUMC0-infinity) / AUC20-infinity as Vss/F = (dosepo x AUMC0-infinity) / AUC20-infinity. For extravascular dosing, we only can calculate Vc/F, Vss/F, or Cl/F.

❝ ... we need to know MIT,..., tlag and ka

No need to know MIT (or tlag and ka). Again we can also re-arrange Vss = (F x Dose/AUC0-infinity)x MRT as Vss/F = (Dose/AUC0-infinity)x MRT = Cl x MRT.

We can get the values of all parameters (Dose, AUC0-infinity, AUMC0-infinity and MRT) on the right-hand sided both equations after NCA. So I wonder why we can not calculate Vss.

All the best,
-- Yung-jin Lee
bear v2.9.1:- created by Hsin-ya Lee & Yung-jin Lee
Kaohsiung, Taiwan https://www.pkpd168.com/bear
mittyri
★★

Russia,
2016-09-24 23:33
(2556 d 05:01 ago)

@ yjlee168
Posting: # 16672
Views: 15,559

## Leslie disagrees

Dear Yung-jin,

That's kind of incorrect.

Vss/F = (dosepo x AUMC0-infinity) / AUC20-infinity.

This equation was derived from the original one (please see equation (7) in my previous post) using assumption which is hold only for bolus:
MRT = AUMC0-infinity/AUC0-infinity

❝ Again we can also re-arrange Vss = (F x Dose/AUC0-infinity)x MRT as Vss/F = (Dose/AUC0-infinity)x MRT = Cl x MRT.

That's right, and now please see equation (8) from my previous post.

Kind regards,
Mittyri
yjlee168
★★★

Kaohsiung, Taiwan,
2016-09-26 01:27
(2555 d 03:07 ago)

@ mittyri
Posting: # 16674
Views: 15,585

## OK! we cannot calculate Vdss with dataset from extravascular dosing alone

Dear mittyri,

Thanks for your response. You are correct. Apparently Vdss cannot be calculated using NCA with BE dataset alone. In WNL manual of the old version (v5.3), it said: (quoted) "An estimate of the volume of distribution at steady state. Vss = MRTINF*Cl, where MRT = Mean Residence Time and CL= total body clearance. For steady-state date (a typo? data?), Vss = MRTINF*Clss. Not computed for model 200, as calculating MRT from oral data requires estimating Mean Input Time, which requires compartmental methods." about Vdss. It is easy to calculate Vdss with IV or IV infusion since MRTiv is ready to use. For extravascular dosing (po for example), MRTpo = MRTiv + MITpo. Thus we not only require MIT (ka and tlag) but also MRTiv to calculate Vdss. BTW, I just find this R package PKNCA seems interesting. It calculates Vdss too.

Finally, I have a question: when using NCA to analyze a BE dataset, we can obtain MRT. Apparently this MRT is not what we call MRTpo. What is it?

All the best,
-- Yung-jin Lee
bear v2.9.1:- created by Hsin-ya Lee & Yung-jin Lee
Kaohsiung, Taiwan https://www.pkpd168.com/bear
mittyri
★★

Russia,
2016-09-26 01:45
(2555 d 02:49 ago)

@ yjlee168
Posting: # 16676
Views: 15,771

## MRTINF includes Mean Input Time

Dear Yung-jin,

❝ Finally, I have a question: when using NCA to analyze a BE dataset, we can obtain MRT. Apparently this MRT is not what we call MRTpo. What is it?

I checked the last version of WNL

So in PHX interpretation
MRTINFpo = MRTINF + MIT = AUMCINF/AUCINF

Kind regards,
Mittyri
Helmut
★★★

Vienna, Austria,
2016-09-26 01:47
(2555 d 02:47 ago)

@ yjlee168
Posting: # 16677
Views: 15,574

## “Gravity Duration”

Hi Yung-jin,

❝ Finally, I have a question: when using NCA to analyze a BE dataset, we can obtain MRT. Apparently this MRT is not what we call MRTpo. What is it?

See this post. IIRC, AUMC/AUC for ev administration was sometimes called in the “old days” of PK the Gravity Duration (GD).

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
yjlee168
★★★

Kaohsiung, Taiwan,
2016-09-26 02:13
(2555 d 02:22 ago)

@ mittyri
Posting: # 16679
Views: 15,492

## Was Leslie wrong about Eq (8)?

Dear mittyri,

Should Eq. (8) be written as MRT = AUMC/AUC + MIT?

All the best,
-- Yung-jin Lee
bear v2.9.1:- created by Hsin-ya Lee & Yung-jin Lee
Kaohsiung, Taiwan https://www.pkpd168.com/bear
mittyri
★★

Russia,
2016-09-26 02:23
(2555 d 02:11 ago)

@ yjlee168
Posting: # 16682
Views: 15,475

## Leslie cannot be wrong

Dear Yung-jin,

❝ Should Eq. (8) be written as MRT = AUMC/AUC + MIT?

Well, to cut to the chase: no.

I sent the article on your mobilepk mailbox, so you can see all derivations

Kind regards,
Mittyri