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Program Set-Up - Boomer

Boomer doesn't have built-in model drawing capability. Consequently it is useful if the modeler draws the model on paper prior to starting the program. This can clarify the numbering of components and data sets. It also makes the specification of rate constants and volumes of distribution more precise. For a simple one compartment model after IV bolus administration the model is quite simple. One circle represents the central compartment and one arrow represents the elimination rate constant. The triangle, representing the apparent volume of distribution, links the amount of drug in the one compartment (circle) with the concentration of drug represented by the rectangle.

PK Model - One Compartment Oral

Figure 8.3.1 Diagram Representing a One Compartment Model after Oral Administration

The next step is to convert the parts in the model to parameters from the Boomer parameter toolbox. This could be done by notation on the diagram above or by preparing a table of parameter types. Currently the available parameter types within Boomer include:

MODEL Definition and Parameter Entry       * Allowed Parameter Types *

 -5) read model         -3) display choices      -2) display parameters

  0) Time interrupt      1) Dose/initial amount   2) First order rate
  3) Zero order          4-5) Vm and Km of Michaelis-Menten
  6) Added constant      7) Kappa-Reciprocal volume
  8-10) C = a * EXP(-b * (X-c))
 11-13) Emax (Hill) Eq with Ec(50%) & S term     14) Second order rate
 15-17) Physiological Model Parameters (Q, V, and R)
 18) Apparent volume of distribution   19) Dummy parameter for double dependence
 20-22) C = a * SIN(2 * pi * (X - c)/b)

 Special Functions for First-order Rate Constants
 23-24) k = a * X + b                  25-27) k = a * EXP(-b * (X - c))
 28-30) k = a * SIN(2 * pi * (X - c)/b)
 31,32-33) dAt/dt = - k * V * Cf (Saturable Protein Binding)
 34-36) k * (1 - Imax * C/(IC(50%) + C)) Inhibition  0 or 1st order
 37-39) k * (1 + Smax * C/(SC(50%) + C)) Stimulation 0 or 1st order
 40) Uniform [-1 to 1] and 41) Normal [-3 to 3] Probability
 42) Switch parameter                  43) Clone component
 44-47) Four parameter logistic model  48-51) Four parameter Weibull model

Figure 8.3.2 Parameter types available with Boomer, v3.4.7 (Feb 2021)

The model in Figure 8.3.1 has a dose (type 1), two first order rate constants (a type 2 parameter) and an apparent volume of distribution (type 18). These can represented in tabular form before starting the program.

Parameter NameParameter TypeFlow DirectionValueLimits
Dose1
Dose/Initial Value
Into 1100Fixed
ka2
First Order
From 1 to 21.00.0 - 10.0
kel2
First Order
From 2 to 00.10.0 - 1.0
V18
Volume
From 2 to
Data Set 1
151.0 - 100.0

Table 8.3.1 Parameter Types and Values for the Model in Figure 8.3.1

Now it is time to start the program. Boomer is a menu driven program. That is, once started the program will present the user with a set sequence of menu choices. Initially the user will select input and output options and 'Normal Fitting' for nonlinear regression analysis. The model is described to the program through a series of questions and prompts.

 Enter type# for parameter  1 (-5 to 51)      1
 Enter parameter name  Dose                                                        
 Enter Dose value     100.0    
 0) fixed, 1) adjustable, 2) single dependence
                    or 3) double dependence      0
 Enter component to receive dose      1
 Enter component for F-dependence ( 1 to - 1 or 0 for no dependence)      0

 Input summary for Dose                 (type  1)

     Fixed value is    100.0    
     Dose/initial amount added to     1

 Enter 0 if happy with input, 1 if not, 2 to start over      0

 Enter -3 to see choices, -1 or -4 (save model) to exit this section 
 Enter type# for parameter  2 (-5 to 51)       2
 Enter parameter name  ka                                                          
 Enter ka value     1.000    
 0) fixed, 1) adjustable, 2) single dependence
                    or 3) double dependence      1
 Enter lower limit     0.000    
 Enter upper limit     10.00    
 Enter component to receive flux      2
 Enter component to lose flux      1

 Input summary for ka                   (type  2)

     Initial value    1.000     float between    0.000     and    10.00    
     Transfer from     1 to     2

 Enter 0 if happy with input, 1 if not, 2 to start over      0

 Enter -3 to see choices, -1 or -4 (save model) to exit this section 
 Enter type# for parameter  3 (-5 to 51)       2
 Enter parameter name  kel                                                         
 Enter kel value    0.1000    
 0) fixed, 1) adjustable, 2) single dependence
                    or 3) double dependence      1
 Enter lower limit     0.000    
 Enter upper limit     1.000    
 Enter component to receive flux      0
 Enter component to lose flux      2

 Input summary for kel                  (type  2)

     Initial value   0.1000     float between    0.000     and    1.000    
     Transfer from     2 to     0

 Enter 0 if happy with input, 1 if not, 2 to start over      0

 Enter -3 to see choices, -1 or -4 (save model) to exit this section 
 Enter type# for parameter  4 (-5 to 51)      18
 Enter parameter name  V                                                           
 Enter V value     15.00    
 0) fixed, 1) adjustable, 2) single dependence
                    or 3) double dependence      1
 Enter lower limit     1.000    
 Enter upper limit     100.0    
 Enter data set (line) number      1
 Enter line description  Cp                                                          
 Enter component number (0 for obs x)      2

 Input summary for V                    (type 18)

     Initial value    15.00     float between    1.000     and    100.0    
     Component     2 added to line     1


 Enter 0 if happy with input, 1 if not, 2 to start over      0

 Enter -3 to see choices, -1 or -4 (save model) to exit this section 
 Enter type# for parameter  5 (-5 to 51)      -1

Figure 8.3.3 Defining Parameters and Initial Estimates using Boomer, v3.4.7 (Feb 2021)

Fitting and optimization algorithms are selected.

Method of Numerical Integration

 0) Classical 4th order Runge-Kutta
 1) Runge-Kutta-Gill
 2) Fehlberg RKF45
 3) Adams Predictor-Corrector with DIFSUB
 4) Gears method for stiff equations with PEDERV
 5) Gears method without PEDERV

 Enter choice (0-5) 2

 Enter Relative error term for
     Numerical integration (0.0001) 

 Enter Absolute error term for
     Numerical integration (0.0001) 

 FITTING METHODS

 0) Gauss-Newton
 1) Damping Gauss-Newton
 2) Marquardt
 3) Simplex
 4) Simplex->Damping GN

 Enter Choice (0-4) 4

 Enter PC for convergence (0.00001) 

Figure 8.3.4 Defining Numerical Integration and Optimization using Boomer, v3.4.7 (Feb 2021)

Finally the data and weighting schemes are entered.

Enter data from

 0) Disk file      2) ...including weights
 1) Keyboard       3) ...including weights

 Enter Choice (0-3) 1

 Enter data for Cp             
      Enter x-value (time) = -1 to finish data entry


 X-value (time) 0.0
 Y-value (concentration) 0.0

 X-value (time) 0.5
 Y-value (concentration) 1.89

 X-value (time) 1
 Y-value (concentration) 2.9

 X-value (time) 1.5
 Y-value (concentration) 3.38

 X-value (time) 2
 Y-value (concentration) 3.56

 X-value (time) 3
 Y-value (concentration) 3.46

 X-value (time) 4
 Y-value (concentration) 3.12

 X-value (time) 6
 Y-value (concentration) 2.38

 X-value (time) 9
 Y-value (concentration) 1.52

 X-value (time) 12
 Y-value (concentration) 0.97

 X-value (time) 18
 Y-value (concentration) 0.40

 X-value (time) 24
 Y-value (concentration) 0.16

 X-value (time) -1
 
...
 
 Weighting function entry for Cp             

 0) Equal weights
 1) Weight by 1/Cp(i)
 2) Weight by 1/Cp(i)^2
 3) Weight by 1/a*Cp(i)^b
 4) Weight by 1/(a + b*Cp(i)^c)
 5) Weight by 1/((a+b*Cp(i)^c)*d^(tn-ti))

 Data weight as a function of Cp(Obs)

 Enter choice (0-5) 2

Figure 8.3.5 Entering the Data and Defining the Weighting Scheme using Boomer, v3.4.7 (Feb 2021)

Refer to the Boomer manual for more detail. Boomer (Reference https://www.boomer.org/boomer/BoomerManual.pdf)


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