# Bioequivalence and Bioavailability Forum

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AA
Junior

2010-04-07 07:01

Posting: # 5028
Views: 12,391

## Pk parameter: Urine study (WinNonlin) [Software]

Hi, All...

Can anyone clear my doubt regarding the urine study?

One of the pk parameters of urine study is:

Ae(0-t)-Total amount of drug excreted unchanged in the urine over the entire period of sample collection (0-t hours).

is calculation of Ae(0-t)=AURClast in WinNonlin?

Edit: Category changed. Please give a (nick-)name in your profile/signature. Your initials carries ambiguity in some languages… [Helmut]
Helmut
Hero

Vienna, Austria,
2010-04-07 18:26

@ AA
Posting: # 5033
Views: 11,295

## Ae-inf based on rate

Dear AA!

» Ae(0-t)-Total amount of drug excreted unchanged in the urine over the entire period of sample collection (0-t hours).
»
» is calculation of Ae(0-t)=AURClast in WinNonlin?

No! I haven't used WinNonlin for urinary data for ages, but let's see. According to the User's Guide, Table B-6:

AURC_last: Area under the urinary excretion rate curve from time 0 to the last measurable rate.

Not sure what's the use of this (only nice to know). But here we are:

Amount_ Recovered: Cumulative amount eliminated. = Sum(Concentration × Volume)

WinNonlin uses following data structure for urinary models (NCA 210-212): Lower, Upper, Concentration, Volume; where lower/upper denote the sampling interval. See file ‘Urine.pwo’ (which according to the Examples Guide is extravascular data - model 210), dose 10 mg:
```Lower Upper Concentration Volume (hr) ( hr)     (ug/mL)     (mL)   0     2        4         105   2     4        8.7       110   4     6       12.8       234   6    10       10.2       179  10    18        6.7       309  18    24        1.6       234```
Analysis of urinary data is based on the midpoint time (upper-lower) and the length of the interval when it comes to the rate, and the end of the sampling interval when amount excreted is concerned. We get
```  MP Delta   Ae    Ae-cum    Rate         AURC-t (hr) (hr)   (ug)   (ug)     (ug/hr)       (ug)   1    2    420     420     210           105   3    2    957    1377     478.5         793.5   5    2   2995.2  4372.2  1497.6    *   2769.6   8    4   1825.8  6198     456.45   *   5700.675  14    8   2070.3  8268.3   258.7875 *    7846.3875  21    6    374.4  8642.7    62.4    *    8970.54375```
The cumulative amount excreted Ae0-24 is 8642.7 µg (or 86.4% of the dose). WinNonlin calculates AURC_last based on the MP and the linear trapezoidal. For drugs which are renally unchanged cleared, the time course of Rate vs. MP reflects the (fictive) plasma profile. WinNonlin (up to the current version 5.3) fits the rate from 5 h - 21 h, whereas Phoenix (6.x) doesn’t include the data point at the maximum rate, and fits in the interval 8 h - 21 h.

WinNonlin 5.x
```Final Parameters --------------- Rsq                                           0.9552 Rsq_adjusted                                  0.9329 Corr_XY                                      -0.9774 No_points_lambda_z                            4 Lambda_z                         1/hr         0.1824 Lambda_z_lower                     hr         5.0000 Lambda_z_upper                     hr        21.0000 HL_Lambda_z                        hr         3.8000 Tlag                               hr         0.0000 Tmax_Rate                          hr         5.0000 Max_Rate                  mL*ug/mL/hr      1497.6000 Mid_Pt_last                        hr        21.0000 Rate_last                 mL*ug/mL/hr        62.4000 AURC_last                    mL*ug/mL      8970.5438 Vol_UR                             mL      1171.0000 Amount_Recovered             mL*ug/mL      8642.7000 Percent_Recovered                   %        86.4270 AURC_all                     mL*ug/mL      8970.5438 AURC_INF_obs                 mL*ug/mL      9312.6347 AURC_%Extrap_obs                    %         3.6734 AURC_INF_pred                mL*ug/mL      9314.6705 AURC_%Extrap_pred                   %         3.6945```

Phoenix WinNonlin 6.x
```Final Parameters --------------- Rsq                                           0.9610 Rsq_adjusted                                  0.9220 Corr_XY                                      -0.9803 No_points_lambda_z                            3 Lambda_z                         1/hr         0.1545 Lambda_z_lower                     hr         8.0000 Lambda_z_upper                     hr        21.0000 HL_Lambda_z                        hr         4.4878 Tlag                               hr         0.0000 Tmax_Rate                          hr         5.0000 Max_Rate                  mL*ug/mL/hr      1497.6000 Mid_Pt_last                        hr        21.0000 Rate_last                 mL*ug/mL/hr        62.4000 AURC_last                    mL*ug/mL      8970.5438 Vol_UR                             mL      1171.0000 Amount_Recovered             mL*ug/mL      8642.7000 Percent_Recovered                   %        86.4270 AURC_all                     mL*ug/mL      8970.5438 AURC_INF_obs                 mL*ug/mL      9374.5528 AURC_%Extrap_obs                    %         4.3096 AURC_INF_pred                mL*ug/mL      9420.5265 AURC_%Extrap_pred                   %         4.7766```

Now for the interesting question: Why is WNL/PHX not calculating Ae? I would say that the extra­polated fictive plasma profile is nice to know only - I would be primarily interested in knowing the amount excreted at t=∞. Remaining amount at t=1-ℯ-λz·t, that’s 2.455% at t=24 → Ae 8960.3 µg (quick and dirty!).
In my old studies I fitted the last Ae-values vs. the end of the interval. Model: Ae=Ae(1-e-λz·t) and would get λz 0.1093/h, Ae 9425.86 µg, which is pretty close to WNL’s AURC_INF_pred.
WinNonlin’s term ‘Area under the urinary excretion rate curve’ (an amount!) - is valid, but semantically confusing. Extrapolation of urine data in NCA is a nasty business anyhow - whatever method you apply. If ever possible, stay with Ae0-t only.

You may consider registering at Pharsight’s Extranet for software-specific questions.

Regards,
Helmut Schütz

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AA
Junior

2010-04-08 14:08

@ Helmut
Posting: # 5041
Views: 10,450

## Ae-inf based on rate

» Dear AA!
»

ok will change initial to nick name.

Thanks for your prompt reply. What all i understand it is Ae(0-t) is not same as AURClast.

Correct me if i'm wrong...

Thanks...
Helmut
Hero

Vienna, Austria,
2010-04-08 14:27

@ AA
Posting: # 5043
Views: 10,460

## Amount_ Recovered = Ae(0-t)

Dear AA!

» ok will change initial to nick name.

» What all i understand it is Ae(0-t)is not same as AURClast.

Yes. If extrapolation to t=∞ is not required (what I hope), I would use WinNonlin’s ‘Amount_Recovered’ (Ae0-t in common PK terminology) for simplicity.

Regards,
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. ☼
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H_Rotter
Regular

Germany,
2010-04-08 20:07

@ Helmut
Posting: # 5051
Views: 10,431

Dear Helmut!

» In my old studies...

How old?

» ...I fitted the last Ae-values vs. the end of the interval. Model: Ae=Aeinf(1-e-lambdaz·t)

As far as I know your model is correct for any renally cleared drug (regardless how many compartments are 'upstream' of the excretion process). But you can't linearize this function?! You do need some nonlinear fitting software. Comes close to 'compartmental models are not acceptable'.
Maybe that's the reason behind Far Side's method - ready to be checked by the assessor's pocket calculator.

» Pharsight's Extranet...

Not a very crowed place yet.

Regards,
Hermann
Helmut
Hero

Vienna, Austria,
2010-04-08 20:47

@ H_Rotter
Posting: # 5053
Views: 10,463

Dear Hermann,

welcome back; nice to see a veteran posting again!

» » In my old studies...
» How old?

Very old. Actually in the age of the 5¼”-floppy. A few studies later on, but never extrapolated.

» But you can't linearize this function?!

According to my highschool-math: no. Maybe I’ll ask my personal friend Maxima later on – but I’m not very optimistic.

» You do need some nonlinear fitting software. […] Maybe that’s the reason behind Far Side’s method – ready to be checked by the assessor’s pocket calculator.

Probably.

» » Pharsight's Extranet
» Not a very crowed place yet.

Regrettably, yes. WinNonlin-users waited for such a site for years. David’s PKPD-list and this forum were meeting sites for the Dazed and Confused. Needs some time, I would say. Here it took eight months for the first 100 posts. Now it takes a little bit more than two weeks for 100 posts (or sometimes only twelve hours for twenty like today).

Regards,
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. ☼
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d_labes
Hero

Berlin, Germany,
2010-04-09 09:31

@ Helmut
Posting: # 5063
Views: 10,472

## Dinosaurs solution.

Dear Helmut, dear Hermann,

» Very old. Actually in the age of the 5¼"-floppy.

That must be BC or in the times of dinosaurs .

From the same times (but a tick later) originates the TOPFIT solution, a program running under MS-DOS:
1. Calculate regression line of the terminal part of excretion rates to obtain lambdaZ (like Far side solution)
2. calculate excretion rate at tlast from that regression line
3. Ae(inf) := Ae(tlast) + excretion_rate((tlast)/lambdaZ

Regards,

Detlew
Helmut
Hero

Vienna, Austria,
2010-04-09 17:25

@ d_labes
Posting: # 5067
Views: 10,390

## Youngster's solution

Dear D. Labes!

» From the same times (but a tick later) originates the TOPFIT solution, a program running under MS-DOS:

Oh, TopFit (like billards it required a combination of imagination, skill, patience, and devotion). I wouldn’t call it a dinosaur – at sweet seventeen has not reached adolescence yet.
• Heinzel G, Woloszczak R, Thomann P. TopFit Version 2.0: Pharmacokinetic and Pharmacodynamic Data Analysis System for the PC. Stuttgart, Jena, New York: Gustav Fischer; 1993.
• Tanswell P, Koup J. TopFit: a PC-based pharmacokinetic / pharma­co­dynamic data analysis program. Int J Clin Pharmacol Ther Toxicol. 1993;31(10):514–20.
What I really liked, was the ingenious method of running any model without initial estimates – even the most ambitious user defined ones. At that time PCNONLIN drove my crazy because I couldn’t find suitable ones in many cases. When I switched to the first version of WinNonlin (mainly for the graphical capabilities) I still (mis)used TopFit to get initial estimates for tricky models.

» 1. Calculate regression line of the terminal part of excretion
» `  `rates to obtain lambdaZ (like Far side solution)
» 2. calculate excretion rate at tlast from that regression line
» 3. Ae(inf) := Ae(tlast) + excretion_rate((tlast)/lambdaZ

Are you sure?

Step 1 gives lambdaZ 0.1545, t½ 4.49
Step 2 gives 69.50 (measured 62.40) * see my edit at the end
Step 3 gives 8642.7+69.5/0.1545=9092.68 but I can't find it in TopFit:``` ============================================================================ TopFit V 2.0                                                     Page 2 of 3                      *** NON-COMPARTMENTAL ANALYSIS *** File : WNLURINE                                              9.04.2010 16:56 ============================================================================ Formulation no                                                             1 Type of formulation                                      Absorption (Tablet) Name of formulation                                            WNL Urine.pwo ----------------------------------------------------------------------------                             *** DOSING TABLE ***              No           Time           Dose       Duration          Entry                         [hour][mg/individual]                   compartment ----------------------------------------------------------------------------               1        0.00000       10.00000        0.00000              0 ---------------------------------------------------------------------------- Data set no                                                                1 Sample matrix                                                          Urine ----------------------------------------------------------------------------              No           Time          Value              R                         [hour]           [mg] ----------------------------------------------------------------------------               1        0.00000        0.00000               2        2.00000      420.00000               3        4.00000     1377.00000               4        6.00000     4372.20000               5       10.00000     6198.00000               6       18.00000     8268.30000               7       24.00000     8642.70000 ----------------------------------------------------------------------------              No           Time      Excretion              R                                         Rates                         [hour]      [mg/hour] ----------------------------------------------------------------------------               1        1.00000      210.00000               2        3.00000      478.50000               3        5.00000     1497.60000               4        8.00000      456.45000              *               5       14.00000      258.78750              *               6       21.00000       62.40000              * ---------------------------------------------------------------------------- * in column R marks values which are used for regression ============================================================================ TopFit V 2.0                                                     Page 3 of 3                      *** NON-COMPARTMENTAL ANALYSIS *** File : WNLURINE                                              9.04.2010 16:56 ============================================================================              No           Time         (Ui-U)              R                         [hour]           [mg] ----------------------------------------------------------------------------               1        0.00000     8642.70000               2        2.00000     8222.70000               3        4.00000     7265.70000               4        6.00000     4270.50000              *               5       10.00000     2444.70000              *               6       18.00000      374.40000              * ---------------------------------------------------------------------------- * in column R marks values which are used for regression                 *** MRT mean residence time (excretion) ***                         Lambda             t½            MRT                       [1/hour]         [hour]         [hour] ---------------------------------------------------------------------------- excretion rates        0.15445        4.48778        8.74997            Ui-U        0.20737        3.34248        8.77977 Ui extrapolated        0.14621        4.74068        8.74836 ---------------------------------------------------------------------------- Total amount excreted                                   [mg]      8925.8```

There’s another fit – corresponding to the table above:

According to the documentation 2-58:

The amount excreted at tlast is assumed to be the Aeinf-value.

My emphasis. Nice assumption. Why try to extrapolate, if we already ‘know’ the value - because we have sampled until complete excretion). That's corresponding to Gabriels­son’s/Weiner’s ARE-method (Amount Remaining to be Recovered).
From this fit we get lambdaZ 0.2074, t½ 3.34; now what?
Never try to ‘understand’ software you haven’t written yourself.

Edit: Now I got it. tlast = 24 - not the last midpoint time (21). You stated this in your step 2 (Lesen bildet). Therefore the estimated last rate 43.27, 8642.7+43.27/0.1545=8925.82, matching TopFit.

Regards,
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. ☼
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d_labes
Hero

Berlin, Germany,
2010-04-12 09:39

@ Helmut
Posting: # 5082
Views: 10,239

## Some youngsters may be very old

Mark Twain: "Age is an issue of mind over matter. If you don't mind, it doesn't matter."

Dear Helmut!

» Oh, TopFit (like billards it required a combination of imagination, skill, patience, and devotion). I wouldn’t call it a dinosaur - at sweet seventeen has not reached adolescence yet.

Seventeen is rather young for NLYW but may be very old for software.
Considering the life cycles of some other pieces of software (1993: M\$-W for Workgroups 3.11, 1994: M\$-W NT Workstation 3.5, 1995: M\$-W 95, 1996: M\$-W NT Workstation 4.0, 1998: M\$-W 98, 1999: M\$-W 98 SE, and so on, and so on ...) I estimate that TopFit had now reached at least version 18.0 .

Unfortunately it had not evolved after 1993 but for me it was very useful up to the year 2007 (!) as the main NCA tool. So my judgment is that it was adolescent and reliable from the beginning.

Regards,

Detlew
SDavis
Regular

UK,
2010-04-09 13:10

@ Helmut
Posting: # 5065
Views: 10,424

## Ae-inf based on rate

Hi Helmut,

Just following up on this discussion here, although as you say
Pharsight's Extranet is probably the better location, note my high-lighting of the last statement.

» Now for the interesting question: Why is WNL/PHX not calculating Aeinf?

and also

» Extrapolation of urine data in NCA is a nasty business anyhow - whatever method you apply. If ever possible, stay with Ae0-t only.

I would concur that extrapolation of urine data using NCA is extremely tricky due in major part to the difficulty of obtaining sufficient quality collection volumes to actually plot a useful profile. In my experience the use of urinary data has decreased markedly in Phase I trials over the last 10+ years, presumably as analytical techniques have become that much more sensitive to lower concentrations in plasma etc. This leads me to two questions:
1. beyond assessing metabolism pathways, is there a use for NCA of urine data; wouldn't this be more appropriate to model and fit if you truly want to understand your compound better?
2. the more important one, when wearing a Pharsight hat, is whether there is any benefit to the WNL user / general PK community of Phoenix implementing the extrapolation Herr Doktor Rotter described in TopFit if experience of real data shows us that this is rarely possible with confidence?

» 1. Calculate regression line of the terminal part of excretion rates to obtain lambdaZ
» 2. calculate excretion rate at tlast from that regression line
» 3. Ae(inf) := Ae(tlast) + excretion_rate((tlast)/lambdaZ

If people believe it is, it can be written up as an enhancement request.

Simon
Senior Scientific Consultant
Pharsight - A Certara™ Company
Forthcoming meetings and training
Problems are not stop signs, they are guidelines. Robert H. Schuller
Helmut
Hero

Vienna, Austria,
2010-04-09 17:47

@ SDavis
Posting: # 5068
Views: 10,678

## Replicate design studies in Phoenix/WinNonlin

Dear Simon!

Agree with all your points. The original post dealt with Ae0-t; in bioequivalence only NCA is acceptable to regulators – so I was asking the heretic question about extrapolation. But let sleeping dogs lie.

And you are right, in development of an NCE everybody would model anyway.

» […] whether there is any benefit to the WNL user / general PK community of Phoenix implementing the extrapolation Herr Doktor Rotter described in TopFit

Well, the post was D. Labes’, not Hermann’s.
I don’t consider it of any importance at all.

We have bigger problems – no mixed effects model in BE according to the new European Guideline. That’s really a problem – right now

I don’t see any possibility to evaluate a replicate design study with PHX/WNL!

Or as our Indian friends use to say: Please correct me if I am wrong.

Regards,
Helmut Schütz

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