Linear systems approach mathematical elements

First of all, we used this mathematical model to correlate the in vitro and in situ permeabilities of grepafloxacin and ciprofloxacin [39], and the area correction factor Sf obtained was around 4, in accord with results obtained by other authors [52]. This difference is explained by the differences in absorptive surface in the in situ versus the in vitro model, as the latter presents microvilli but not villi or folds. Now we have expanded the number of element of the correlation to all the quinolones included in Table 4.2, and the area correction factor does not suffer any variation (see Fig. 4.8, p. 104). Even if this model has been constructed using very simplistic assumptions, the results are promising and demonstrate that a good modeling approach helps to identify the system critical parameters and how the system behavior changes from the in vitro to the in situ level [39]. It is important to notice that with this linear correlation we make the assumption that the main difference between both systems is the actual effective area for transport. Nevertheless, since the plot is far from being perfect, it is probable that there are more differences in both experimental systems, such as different paracellular resistance or different expression levels of the transporter, that account for the deviation. 

In 1960, Schmit [1] set forth a rather general approach to design optimization, which has served as a conceptual foundation for the development of many modern design optimization methods. It introduced the idea and indicated the feasibility of coupling finite element analysis and non-linear mathematical progreunming to create automated optimum design capabilities for a rather broad class of design systems. 

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