Description
This activity can be used to introduce compartmentalized models for a 2 by 2 system of linear differential equations.
Typically when a drug is administered to an individual, the concentration of the drug $C(t)$ in the body changes over time. The drug is gradually eliminated from the body. The concentration is usually amount per unit volume, though we will see an alternative idea of concentration. A first-order drug reaction is one in which the rate of change is proportional to the concentration of the drug in the body.
Sometimes it is useful to think of how drugs distribute throughout the various parts of the body, particularly tissues (like fat and muscle where proteins might bind to the drug) and the plasma. Even though there are many tissues throughout the body, and they are all different, we can make a simplification of treating some as a single compartment. Two main compartments of interest are the ``tissue compartment'' and the ``plasma compartment.''
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