Understanding transport phenomena and degradation of bioresorbable medical polymers - Durability and Reliability of Medical Polymers - page 88

in this context, mathematical modelling can be seen as a powerful tool,
enabling a reduction in the number of experiments and their necessary
assessments. Thus, many time-consuming experiments with a trial-and-
error approach are replaced by the selection of a small number to confirm
or reject hypotheses from the experimental evidence. Model building can
be extremely difficult, especially in selecting the best model to describe a
particular phenomenon. Figure 4.3 shows a schematic representation of the
actions required to achieve a reliable model. starting from the phenomenon
analysis, the first step is the identification of the single mechanisms ruling
the chosen phenomenon. Following that, validation of the hypothesis is
translated into a mathematical equation. If the model is then able to fit the
experimental data, its ability to predict new situations is tested to see if a
reliable model has been obtained. Thus, we decided to focus our attention
on two typical topics of biodegradable polymeric devices: modelling their
ability to deliver the drugs loaded within them, and their biodegradability.

Phenomenon
analysis

Identification of the
mechanisms ruling the
phenomenon

Definition of proper
experiments aimed to
check the hypothesis

Physical mechanisms
translation into math equations and
assembling into the model

￿ ￿ ￿ ￿ ￿ ￿

Model comparison
with experimental
data: fitting

No

Model comparison
with experimental data:
prediction

Ye s

No

Reliable model

4.3 Schematic representation of the process for obtaining a reliable
mathematical model.