Discrete, reaction-limited dissolution process

Defining Sj and yi as the populations of the drug molecules in the solid state and in solution in the ith generation (i = 0,1, 2.), respectively, the following finite difference equation describes the change of j/j between generations i and 

This equation can be normalized in terms of dose by dividing both sides by qo and written more conveniently using yi/qo = yi+i/qo = an  

Since difference equations exhibit dynamic behavior [124,125], the stability of the fixed points of (5.24) is explored according to the methodology presented in Appendix A. The absolute value of the derivative of the right-hand side of (5.24) is compared with unity for each fixed point. There are the following cases  

The population growth model of dissolution utilizes the usual information available in dissolution studies, i.e., the amount dissolved at certain fixed intervals of time. The time points of all observations need to be transformed to 

However, the use of (5.24) should not be considered as a panacea for modeling nonmonotonic dissolution curves. Obvious drawbacks of the model (5.24) are  

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Figure 5.6 A discrete, reaction-limited dissolution process interpreted with the population growth model of dissolution.

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