Vc = dose (iv) / Cp0

Vdss = Amount of drug in the body in equilibrium conditions /  Steady-state plasma concentrations (Cpss)

Vdss = DOSE x AUMC / (AUC)²     or     Vdss = Cl x MRT

If you use a compartmental model, you should follow these steps:

first: use non-compartmental analysis for the initial estimated of Vdss and Cl and other parameters as MRT o lambdaZ.

Second: using theses estimated parameters, you can select the best model (monocomparmental, bi, tri...) using the AIC and SBC criteria.

third: for each model, select the best weighting of data (1/Cobs, 1/Cobs^2, 1/Cpred, 1/Cpre^2, etc.), and with the best model selected, make a linear regression analysis "predicted vs observed".

these steps could help you select the best model, but if there poor data fitting with all modells, you sould use non-compartmenal anaylis.

Dear Zahid,

   Why do you feel they are low, does the data appear to have been fitted well by the model otherwise?    Is it perhaps a unit issue?

   If you could post your project on http://www.certara.com/forums we could take a look at your data and method and comment withmore insight. 

   Regards,

                   Simon

For a 2-compartment model, the biexponential applies, so that:

C(t) = A*exp(ke1*t) + B*exp(ke2*t)

At t=0, C(0) = A + B

At t=0, the apparent C(0) for instantaneous complete distribution = B

Therefore,

Vc = i.v. dose/(A + B)

VD = i.v. dose/B

Thank you Simon AA Davis for your answer. I have attached the project file of WinNonlin. The study is conducted on 8 adult buffaloes with average weight of 387 kg. Let me know How can I calculate the Vc, Vdss and Vdarea in this project? Second thing I want to clear in this project is that by changing the dose of drug the results remain same, Why this happens?

Zahid, I took a qucik look at your project and it certainly looks like a good fit to the data so I have to assume there is an issue with the units.  Let's recap the inputs to your model

Time in h

Conc in ug/mL  (is this definitely correct, not e.g ug/L)

assunming the two above are correct my guess is your dose unit is off, curently you have 2.5 mg.  On a side note I personally tend to standardise the mass unit of odse to match the conc unit e.g. 2500ug but this is not strictly necessary but can save you some confusion when you get to simulations.

So I am guessing this is perhaps a dose of 2.5mg/kg? then your volume would actually be approx 700mL/kg or ~270 L for the animal, how does that sound?

If that's not the problem then you have to consider that you have some problem with you assay not capturing all the drug e.g. is it plasma and the drug is in RBC?

Let me know your matrix and actual dose  amount and let's see where we get to...

  Simon

Dear Simon,

Thank you very much for your reply. In the current project the inputs are Time in hr, Conc in ug/ml and dose is 2.5 mg/kg body weight and the data are drug plasma conc versus time. Please guide me in this scenario.

Dear Zahid:

It is not enough to say you are using WinNonlin. What specific method are you using to fit your data? What weighting scheme are you using to describe the credibility of your data? I would strongly suggest that you weight your data by the reciprocal of the assay variance at each measurement. There are easy ways to do this, but the laboratory community still thinks that CV% is the correct measure of assay precision. They are totally wrong. You might look at

Jelliffe RW, Schumitzky A, Van Guilder M, Liu M, Hu L, Maire P, Gomis P, Barbaut X, and Tahani B: Individualizing Drug Dosage Regimens: Roles of Population Pharmacokinetic and Dynamic Models, Bayesian Fitting, and Adaptive Control. Therapeutic Drug Monitoring, 15: 380-393, 1993.

In addition, most 2 compartment models usually only have observations made from the central, serum, compartment. You cannot compute the volume of an unobserved compartment without making further assumptions, which is what is usually done in the situations you describe. On the other hand, one can always calculate the amounts of drug in the central and peripheral compartments by fitting serum concentrations alone, but the volume can never be computed without making further assumptions such as that of assuming that, at the steady state, the rates of transfer are equal between the 2 compartments, and therefore that the clearance in both directions must be the same. From this one then calculated the apparent volume in the unobserved peripheral compartment. That is why hey always do this only for an assumed steady state.

Also, you might well consider using the approach taken by Dr. Michael Neely in his Pmetrics software, which has unconstrained parameter distributions. In contrast to those approaches which simply assume that the model parameter distributions have normal or lognormal shapes, the Pmetrics software makes no such assumptions. Because of this, results with Pmetrics are always more likely given the data, than those which do, as parametric approaches assume and constrain the model parameter distributions to be normal, lognormal, or some other assumed distribution. Pmetrics does not do this, and it has been shown that the results given the data are always more likely as a result.

See Bustad A, Terziivanov D, Leary R, Port R, Schumitzky A, and Jelliffe R: Parametric and Nonparametric Population Methods: Their Comparative Performance in Analysing a Clinical Data Set and Two Monte Carlo Simulation Studies. Clin. Pharmacokinet., 45: 365-383, 2006.

You might also look at Neely M, van Guilder M, Yamada W, Schumitzky A, and Jelliffe R: Accurate Detection of Outliers and Subpopulations with Pmetrics, a Nonparametric and Parametric Pharmacometric Modeling and Simulation Package for R. Therap. Drug Monit. 34: 467-476, 2012.

I hope these references and comments might be helpful to you. All the best for the Holidays!

Roger Jelliffe

Dear Roger Jelliffe

Thank you very much for your reply. Can you guide/provide me the Pmetrics software?

Dear Zahid:

It is not enough to say you are using WinNonlin. What specific method are you using to fit your data? What weighting scheme are you using to describe the credibility of your data? I would strongly suggest that you weight your data by the reciprocal of the assay variance at each measurement. There are easy ways to do this, but the laboratory community still thinks that CV% is the correct measure of assay precision. They are totally wrong. You might look at

Jelliffe RW, Schumitzky A, Van Guilder M, Liu M, Hu L, Maire P, Gomis P, Barbaut X, and Tahani B: Individualizing Drug Dosage Regimens: Roles of Population Pharmacokinetic and Dynamic Models, Bayesian Fitting, and Adaptive Control. Therapeutic Drug Monitoring, 15: 380-393, 1993.

In addition, most 2 compartment models usually only have observations made from the central, serum, compartment. You cannot compute the volume of an unobserved compartment without making further assumptions, which is what is usually done in the situations you describe. On the other hand, one can always calculate the amounts of drug in the central and peripheral compartments by fitting serum concentrations alone, but the volume can never be computed without making further assumptions such as that of assuming that, at the steady state, the rates of transfer are equal between the 2 compartments, and therefore that the clearance in both directions must be the same. From this one then calculates the apparent volume in the unobserved peripheral compartment. That is why they always do this only for an assumed steady state.

Also, you might well consider using the approach taken by Dr. Michael Neely in his Pmetrics software, which has unconstrained parameter distributions. In contrast to other approaches which simply assume that the model parameter distributions have normal or lognormal shapes, the Pmetrics software makes no such assumptions. Because of this, results with Pmetrics are always more likely given the data, than those which do, as parametric approaches assume and constrain the model parameter distributions to be normal, lognormal, or some other assumed distribution. Pmetrics does not do this, and it has been shown that the results given the data are always more likely as a result.

See Bustad A, Terziivanov D, Leary R, Port R, Schumitzky A, and Jelliffe R: Parametric and Nonparametric Population Methods: Their Comparative Performance in Analysing a Clinical Data Set and Two Monte Carlo Simulation Studies. Clin. Pharmacokinet., 45: 365-383, 2006.

You might also look at Neely M, van Guilder M, Yamada W, Schumitzky A, and Jelliffe R: Accurate Detection of Outliers and Subpopulations with Pmetrics, a Nonparametric and Parametric Pharmacometric Modeling and Simulation Package for R. Therap. Drug Monit. 34: 467-476, 2012.

I hope these references and comments might be helpful to you. All the best for the Holidays!

Roger Jelliffe

Dear Zahid:

     You can access the Pmetrics software by going to www.lapk.org, and downloading it by following the instructions there. Hope this helps,

Roger

So is ~270 L too small for your Volume?  what do you expect it to be, and why?

Dear Simon,

Thank you very much for your reply. I was confused about the unit of volume of distribution obtained in WinNonlin. As it is in ml/L but Vc or Vss are mostly described in L/kg in the research papers.  I have converted the obtained volume (ml) into ml/kg and the resulting volume was too small. that's why I was confused to see these low values. Now I am clear by your reply, The only thing I would like to ask you is that how can we calculate the Vbeta for this project?

With Phoenix WinNonlin or any other modelling tool for that matter I would pay special attention that I enter my units in a consistent way e.g. standardising dose to the same mass unit as the concentration.  Then I am much more confident in what order of magnitude my output parameters are in.

In the WNL classic model you made you cna find V2 in the Secondary parameter sheet e.g. for Subject 1 it is V2 ml/kg 473

.  Alternatively you could have parametised it as a clearance model from the beginning.  If you have upgraded to Phoenix WinNonlin 6.4 I cna send you a project file where I also built the equivalent model in a Phoenix model and ran it both in individual and populaton mode;

tvV 908.127 ml/kg 24.964975 2.7490621

tvV2 782.045 ml/kg 86.743299 11.091855

tvCl 227.52 ml/hr/kg  17.781732 7.8154589

tvCl2 80.7089 ml/hr/kg 25.37814 31.444042

stdev0 0.144469 0.006123806 4.2388374

Dear Simon,

Thank you very much for your reply.