How Do You Model Drug Absorption in a Patient Using Differential Equations?

[Bogus_Roads]

Fluid is entering a patient at a rate r, given in cm^3/hr, and a drug is present at some amount of mg/cm^3, m. The drug is absorbed or leaves at a rate given in h^(-1), c, proportional to the amount of the drug.

I want to write a differential eq describing amount, a, in terms of t.

I thought something like da/dt=r*m-c made sense, but I really have no idea. Should c be multiplied by the amount, if it is prop to it and given in h^(-1)? Could anyone show me an analog to this situation in terms of velocity and distance?

This is my first dif eq problem sets, so I'm not really sure how to approach it-any general tips would be much appreciated.

 

[lippyka]

The differential equation you have written is correct. Think of it this way: the rate of change in the amount of drug, a, is equal to the rate of fluid entering (r) times the amount of drug per volume of fluid (m) minus the rate of absorption or leaving of the drug (c) times the amount of drug (a). An analogy to this situation would be a car traveling along a road. The rate of change of the distance from the starting point, d, is equal to the car's velocity v minus the rate at which it slows down due to friction c times the total distance it has traveled (d). This can be written as: dd/dt = v - cd