Notes on Lab #3
In this lab we'll apply some of our newly-acquired modeling techniques to
a real-world situation: the spread of drugs in the body.
To get started, copy the OneCompartmentAspirin.mdl
and href="OneCompartDilantin.mdl files from the
zipped folder you downloaded last time.
Then read in Module 2.5 pp. 45 - 54, in which you will use these pre-built models to get
familiar with the overall approach. These two models will also serve as templates for
the more complicated models you will build for your turnin.
These more complicated models are described in Projects 1 and 3 on
p. 55. For these projects, you will turn in three model files, named
appropriately. For example, my
files would be levys_TwoCompartmentAspirin1a.mdl,
levys_TwoCompartmentAspirin1b.mdl, and levys_OneCompartmentDilantin3.mdl.
You will also turn in a single writeup in PDF format.
To get started, build the compartment for the digestive system first. This
should be like the population model from the first lab, except
Test this digest-system compartment model by itself first, looking for
exponential decay in the concentration of aspirin in the intestines. Once this
is working, connect the other end of the absorption flow into the
aspirin in plasma stock (you may have to delete the old flow and rebuild
it). Change the aspirin in plasma stock to have an initial value of
- Instead of population you have aspirin in intestines, whose
initial value is the same as the initial value of the aspirin in plasma
- Instead of a growth flow going into the box, you have an
absorption flow coming out.
- Instead of growth rate you have absorption rate.
Now, think about what should happen to aspirin in plasma in
this simple two-compartment model. Run the model and test your predictions by
plotting aspirin in plasma. In your writeup, include labeled plots for
the one-compartment plot for this variable, as well as its plot under two
different values of absorption rate. For each of the plots, write
a brief description of how the plots characterize the differences
between the successive models.
Once you're satisfied with username_TwoCompartmentAspirin1a, save it as
username_TwoCompartmentAspirin1b and make the indicated modifications:
Add a few labeled plots and comments to your
writeup, showing some runs from the 1b version.
- Add intestinal volume as a variable and factor it into
absorption (it can just replace absorption rate). For
simplicity, you can normalize its range to the
interval [0,1]. Test with different intestinal volumes (a slider would be
- Add an arrow from aspirin in plasma to absorption, and
make absorption also be proportional to the difference in aspirin
concentrations between the intestines and plasma. (You
may want to make this a separate variable.)
Next, copy the Dilantin model and rename the copy appropriately.
An easy way to do Project 3 is to one more flow into
drug in system, and then connect into it
one variable for each loading dosage and time (use a PULSE function
for each varible, experimenting with the PULSE parameters to get a single spike
at the correct time.) Then the new flow is just the sum of the three pulses.
Before you do that, you can change the normal (entering) flow
to start at 28 hours (24 hours after the final loading dose at 4 hours).
Run the model, then plot drug in system to make sure this initial
Then add the new flows for the loading doses, by mimicking what's in
entering. Each of these loading-dosage flows will use a pulse at a given time
(400 mg at 0 hours, 300 mg at 2 hours, 300 mg at 4 hours, but check the
original dosage variable to determine the actual magnitudes).
As with the aspirin model, show a labeled plot contrasting this
version with the original, and briefly comment on the effect of the loading
dose. If you have time, you might want to rename the variables to distinguish
between the normal and loading flows. You may also be able to reduce the three loading-dosage
flows to a single flow, using a pulse train, combined with a dosage that uses an IF-THEN-ELSE
that is sensitive to time. This would simplify the appearance of the model.