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                    |                                     
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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====================================
 |                                       |                                     
 |                                    X  |                                    X
 |   X  X                                |       X     X                       
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 |         X                             |                  X                  
 |                                       |                                     
   -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                    |                                     
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 |             X                         |                                     
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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              

    1.583                                  1.583    
 |                                       |                                     
 |             X                         |                        X            
 |                                       |                                     
 |                                       |                                     
 |                                       |                                     
 |                                       |                                     
 |                                       |                                     
 |                  X                    |                            X        
 |                                       |                                     
 |                                       |                                     
 0X====================================  0X====================================
 |                                       |                                     
 |                                    X  |                                    X
 |   X  X                                |       X     X                       
 |                                       |                                     
 |                                       |                                     
 |         X                             |                  X                  
 |                                       |                                     
   -1.202                                 -1.202    
     0.00       <-->             24.         0.00       <-->            0.19E+03