Monte Carlo simulation of the release data

The general problem that we will focus on in this section is the escape of drug molecules1 from a cylindrical vessel. Initially, theoretical aspects are presented demonstrating that the Weibull function can describe drug release kinetics from cylinders, assuming that the drug molecules move inside the matrix by a Fickian 

Mhe terms drug molecule and particle will be used in this section interchangeably. 

A simple approximate solution is sought for the release problem, which can be used to describe release even when interacting particles are present. The particles are assumed to move inside the vessel in a random way. The particle escape rate is expected to be proportional to the number n (t) of particles that exist in the vessel at time t. The rate will also depend on another factor, which will show how freely the particles are moving inside the vessel, how easily they can find the exits, how many of these exits there are, etc. This factor is denoted by g. Hence, a differential equation for the escape rate can be written 

It stands to reason to assume that the factor g should be a function of time since as time elapses a large number of drug molecules leave the vessel and the rest can move more freely. Thus, in general one can write that g = g(t) and the previous differential equation becomes 

We are interested in supplying a short-time approximation for the solution of the previous equation. There are two ways to calculate this solution. The direct way is to make a Taylor expansion of the solution. The second, more physical way, is to realize that for short initial time intervals the release rate n(t) will be independent of n(t). Thus, the differential equation (4.13) can be approximated by n (t) = — ag (t). Both ways lead to the same result. 

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