“Central composite design” (CDD)
As explained in the Introduction section, the 23 “full factorial
design” was expanded to a “central composite design” (CDD),
adding a “star design” and a “central point” to find the formulation
of optimized composition.
CDD is a symmetrical response surface design, that covers a
symmetrical experimental domain, and is useful to determine the
optimal conditions for each factor. A CDD contains a two-level “full
factorial design” (2f
experiments), a “star design” (2*f experiments)
and a “central point”; the model requires N experiments (N = 2f
+
(2*f) + 1) to examine f factors (Fig. 2). For three variables, the total
number of formulations to be tested is 15. The points of the 23 “full
factorial design” are situated at the levels 1 and +1, those of the
star design at the levels 0, a and +a (a= 1.73), and the central
point at the level 0 as indicated in Fig. 2 (Dejagher and Vander
Heyden, 2011). The factors and the response variables considered
in the CDD were the same of the screening phase. Five levels for
each factor were considered and seven additional mini-capsule
formulations were investigated with respect to the “full factorial
design” (Table 2).
A polynomial model (Eq. (1)), describing the relation between
each response variable and the considered factors, was build using
the experimental results