PHAR 7632 Homework #6 1999
Numerical Integration, Optimization, One Compartment IV Bolus Urine Data, and another Laplace Transform
DUE 27th April 1999
Question 3.
Round the numbers you calculated in Question 2 to two digits. For example, take 2.3456 as 2.3 or 0.3456 as 0.35. Now use a nonlinear regression program (Boomer, SAAM II, etc.) to fit these data using two different fitting algorithms. Turn in the two printouts which include final parameter values and a graph of observed and calculated data versus time.
The Data
| Time (hr) |
U (mg) |
| 0 |
0 |
| 2 |
39 |
| 4 |
71 |
| 6 |
96 |
| 9 |
130 |
| 12 |
150 |
| 24 |
190 |
Using Boomer - Damping Gauss-Newton
** FINAL OUTPUT FROM Boomer (v2.7.8) ** 28-Apr-1999 --- 2:01:55 pm
Title: Homework #6 Question #3
Input: From HW9906a3.BAT
Output: To HW9906a3.OUT
Data for U came from keyboard (or ?.BAT)
Fitting algorithm: Damping Gauss-Newton Method
Weighting for U by Equal weight
Numerical integration method: 2) Fehlberg RKF45
with 2 de(s)
With relative error 0.1000E-03
With absolute error 0.1000E-03
DT = 0.1000E-02 PC = 0.1000E-04 Loops = 3
Damping = 1
** FINAL PARAMETER VALUES ***
# Name Value S.D. C.V. % Lower <-Limit-> Upper
1) ke 0.88302E-01 0.123E-02 1.4 0.00 1.0
2) km 0.18526E-01 0.143E-02 7.7 0.00 1.0
AIC = 18.4474 Final WSS = 11.1106
R-squared = 0.9993 Correlation Coeff = 0.9997
Model and Parameter Definition
# Name Value Type From To Dep Start Stop
1) Dose = 250.0 1 0 1 0 0 0
2) ke = 0.8830E-01 2 1 2 0 0 0
3) km = 0.1853E-01 2 1 0 0 0 0
4) V = 1.000 18 2 1 0 0 0
Data for U :-
DATA # Time Calculated Observed (Weight) Weighted residual
1 0.0000 0.000000 0.000000 0.000000 0.000000
2 2.000 39.7530 39.0000 1.00000 -0.752953
3 4.000 71.8585 71.0000 1.00000 -0.858490
4 6.000 97.7878 96.0000 1.00000 -1.78777
5 9.000 127.637 130.000 1.00000 2.36342
6 12.00 149.301 150.000 1.00000 0.699249
7 24.00 190.732 190.000 1.00000 -0.732025
WSS for data set 1 = 11.11
R-squared = 0.9993 Correlation Coeff = 0.9997
Plots of observed (*) and calculated values (+)
versus time for U . Superimposed points (X)
190.7 Linear 190.7 Semi-log
| + | +
| * | *
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| X | X
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|X | X
|_____________________________________ |X____________________________________
0.0000 39.00
0 <--> 24. 0 <--> 24.
Plot of Std Wtd Residuals (X) Plot of Std Wtd Residuals (X)
versus time for U versus calcd Cp(i) for U
1.585 1.585
| X | X
| |
| |
| |
| |
| |
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| X | X
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0X==================================== 0X====================================
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| X | X
| X X | X X
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| X | X
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-1.199 -1.199
0.00 <--> 24. 0.00 <--> 0.19E+03
Using Boomer - Simplex
** FINAL OUTPUT FROM Boomer (v2.7.8) ** 28-Apr-1999 --- 2:00:52 pm
Title: Homework #6 Question #3
Input: From HW9906a3.BAT
Output: To HW9906a3.OUT
Data for U came from keyboard (or ?.BAT)
Fitting algorithm: Simplex Method
Weighting for U by Equal weight
Numerical integration method: 2) Fehlberg RKF45
with 2 de(s)
With relative error 0.1000E-03
With absolute error 0.1000E-03
PC = 0.1000E-04
** FINAL PARAMETER VALUES ***
# Name Value S.D. C.V. % Lower <-Limit-> Upper
1) ke 0.88309E-01 0.00 1.0
2) km 0.18532E-01 0.00 1.0
AIC = 18.4474 Final WSS = 11.1107
R-squared = 0.9993 Correlation Coeff = 0.9997
Model and Parameter Definition
# Name Value Type From To Dep Start Stop
1) Dose = 250.0 1 0 1 0 0 0
2) ke = 0.8831E-01 2 1 2 0 0 0
3) km = 0.1853E-01 2 1 0 0 0 0
4) V = 1.000 18 2 1 0 0 0
Data for U :-
DATA # Time Calculated Observed (Weight) Weighted residual
1 0.0000 0.000000 0.000000 0.000000 0.000000
2 2.000 39.7557 39.0000 1.00000 -0.755695
3 4.000 71.8626 71.0000 1.00000 -0.862640
4 6.000 97.7924 96.0000 1.00000 -1.79240
5 9.000 127.641 130.000 1.00000 2.35915
6 12.00 149.304 150.000 1.00000 0.696045
7 24.00 190.730 190.000 1.00000 -0.729874
WSS for data set 1 = 11.11
R-squared = 0.9993 Correlation Coeff = 0.9997
Plots of observed (*) and calculated values (+)
versus time for U . Superimposed points (X)
190.7 Linear 190.7 Semi-log
| + | +
| * | *
| |
| |
| |
| | X
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| X |
| | X
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| X |
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| | X
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| X |
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| X | X
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| X |
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|X | X
|_____________________________________ |X____________________________________
0.0000 39.00
0 <--> 24. 0 <--> 24.
Plot of Std Wtd Residuals (X) Plot of Std Wtd Residuals (X)
versus time for U versus calcd Cp(i) for U
1.583 1.583
| |
| X | X
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| |
| |
| |
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| X | X
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0X==================================== 0X====================================
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| X | X
| X X | X X
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| X | X
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-1.202 -1.202
0.00 <--> 24. 0.00 <--> 0.19E+03