Generating an Effect-Time plot

First step is to generate a Concentration - Time plot. We know that in its simplest form, an IV dose of a drug will be eliminated by a mono-exponential process. The plamsa concentration at any time, C, can be described by an equation using the starting concentration C0, elimination rate constant, k, and the time, t.

C = C0exp-kt

Secondly, we know that the effect at any concentration can be described by an 'Emax model', which is similar to a Michaelis Menten equation, using Emax (max effect), ED50 (concentration producing 50%) effect, and E0 (residual effect when there is no drug).

Effect = E0 + Emax. C/(ED50+ C)

It is then a simple matter to link those the above two relationships in an EXCEL spreadsheet and generate a plot of Effect vs Time. You can arbitrarily use the following constants: C0=100, k=0.015, E0=10, Emax=100, ED50=5

Here is the output using the above method. This plot assumes the concentrations begin at a point associated with Emax and reduces down to zero.