Bioequivalence and Bioavailability Forum

Dear AA!

Please see my suggestion above about your user name.

❝ 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 Ae_0-24 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^-λ_z·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^-λ_z·t) and would get λ_z 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 Ae_0-t only.

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