Q: How can I use data to simulate a function?
A: A function can be approximated by knowing
values along its curve, and the SAAM II Compartmental application can
use linear interpolation on these values to simulate the original function.
The first step is to enter the known points into the Compartmental Data
window as data. A data weight must be entered to satisfy the Data window
syntax, even though it is not used. The example data and plotted values
for the data (f1) are shown in Figures 1 and 2, respectively.
Figure 1
Figure 2
Once the data has been entered it can be used for almost any purpose
in the model to simulate the original unknown function. One common
use is to specify a Forcing Function. The Forcing Function is useful
where a large model is split into two or more sections, and the interfaces
between the sections are simulated by ‘forcing” the contents
of a compartment to be the same as it would have been prior to removing
that section of the model. To use data for that purpose, double-click
on the compartment where the Forcing Function is to be applied to open
the Compartment Attributes dialog box, and click on
the Forcing Function button. In the Forcing
Function box, click the Associate with Data radio
button and enter the name of the data element in the adjacent entry
area. When the model is Solved or Fitted,
the application uses linear interpolation on the specified data to
calculate the quantity in the compartment at any time during the experiment.
A Forcing Function is an advanced feature of the Compartmental application.
More details on how to use it are beyond the scope of this discussion.
A more common use is to assign the data values to a variable to simulate
the original function. For this example, the data for f1 will
be used to specify the exogenous input in the one compartment model
shown in Figure 3.
Figure 3
To do this, double-click the input object ex1 to open the Exogenous
Input dialog box. For the Input Type, click
the Equation radio button. Enter 0.0 for
the Event Start time, and 388.0 for Event
Stop. For the equation, enter ex1 = lin(f1). The
lin() function invokes the SAAM II linear interpolator to calculate
the infusion rate at points other than where a value is specified
in the data. Without this feature, the application would not be able
to calculate the intermediate values needed for the integration.
Note that the infusion times cannot extend beyond the first or last
data point since the linear interpolator does not extrapolate. If
the infusion is to run throughout the experiment, the end of the
experiment must be specified at or prior to the last data point;
otherwise the infusion will shut down before the experiment ends
(in this example it would stop at time 388.0).
After the model has been Solved, a plot of the interpolated ex1 infusion
curve superimposed on the original f1 data would appear as
shown in Figure 4. Depending upon the other characteristics of
the model, the contents of compartment q1 during the experiment
would appear similar to Figure 5.
Figure 4
Figure 5
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