The mathematical model generated for each response Y was a quadratic model with first-order interactions, built according to the following equation:
in which X
represent the levels of the factors; a
0 is the intercept representing the mean of the measured response data; and a
, and a
correspond to the coefficients of first-order terms, the coefficients of second-order quadratic terms, and the coefficient
of second-order interaction terms, respectively. The coefficient corresponding to a factor or interaction shows its importance
on the studied response. The symbol ε represents pure error. For the multilevel categoric factors presenting more than two
levels (i.e., factor E), the software calculates two coefficients, E(1) and E(2), of the difference between the overall average
and the high and low levels, respectively. To simplify the design-of-experiments interpretation, the coefficients of second-order
quadratic terms were not presented in this study. The coefficient values were expressed in coded units to compare their relative
effect to that of the others.
Analysis of variance (ANOVA) was performed to determine the significance of the model. A probability value lower than 0.05
was considered significant. A probability value greater than 0.10 was regarded as not significant. The effects of factors
and main interactions between the factors, deduced from the analysis of the experimental design, are summarized with bar graphs
on Figure 3. The red bars correspond to the factors that significantly influenced the response Yx.
Figure 3: Effects of factors and main interactions on various responses.
Influence of formulation.
As deduced from the analysis of the experimental design (see Figure 3), the drug substance solubility (D) and concentration (A) had significant influence on all the responses except pellet elongation and roughness index for the drug concentration.
Some of these effects can be explained by the different water quantities required for different formulations.
Decreases in drug concentration and solubility both led to a lower extrusion rate and yield. The corresponding water quantity
increase should nevertheless facilitate extrusion by an extrusion force decrease due to a lubricant effect (1–3, 5, 10, 28,
32, 37, 38). The observed effect is more likely linked to raw materials properties and facilities to extrude than to associated
water quantities. Decreases in drug concentration and solubility also decreased pellet size and the usable yield fraction,
and increased true density, friability, and hardness. The drug-solubility decrease also increased pellet elongation and rugosity
by decreasing the solidity index. These effects can be explained by the corresponding water quantity increase. Many authors
reported that water evaporation from wet pellets during the oven-drying step caused a mechanical shrinkage phenomenon (15,
39–44). Shrinkage proportional to the water-quantity increase led to a particle size reduction (and thus a decrease in usable
yield fraction), a decrease in circularity decrease, a roughness increase and subsequent friability increase by attrition,
and densification leading to an increase in hardness.
Drug concentration and solubility thus had a similar influence on the responses, including an important effect on drug solubility.
Except for pellet friability, an interaction between the two formulation variables was observed for all the responses. Some
authors also indicated an interaction between the two formulation variables and observed higher impact of drug solubility
on the different responses, because it led to greater differences between the corresponding water quantities than for DS concentration
(3, 4). Moreover, drug concentration had more influence for the highly soluble drug, where large changes in water quantity
are required for different concentrations, than for the poorly soluble drug, where water quantities remain very similar.
Influence of the extrusion system.
The extrusion system had a significant effect on all responses. Significant interactions between the extrusion system and
drug substance solubility and concentration and their effect on the responses necessitated that formulations were analyzed
as distinct designs of experiments. This method enabled identification of the extruder type that gave the best results in
terms of process and pellet quality, according to the formula (see Table I).
Table I: Analysis of the influence of extrusion system on responses to drug substance solubility and concentration.
For example, in the formulation constituting 36% DS1, the dome system had the highest extrusion rate, and the axial system
had the lowest extrusion rate. Analysis of the extrusion system influence showed different results according to the formulation
tested. The extrusion systems presented more significant differences for DS2 than for DS1 on pellet properties. Overall, the
axial system presented the best results in terms of pellet yield, mechanical properties, and roughness, followed by the dome
system for productivity and pellet circularity. The radial system produced the worst results irrespective of the formulation.
Influence of spheronization conditions.
The design of experiments showed a significant effect of spheronization speed and time on some pellet characteristics, as
shown on Figure 3. An increase in spheronization speed influenced the pellet usable yield fraction, roughness index, and hardness,
whereas spheronization time influenced pellet size, elongation, roughness index, true density, and hardness. Both factors
increased pellet hardness to the same degree, as observed previously (26, 46–48). This result most likely can be explained
by pellet densification caused by the pellet water migration during spheronization, which decreases pellet porosity after
drying (21). An increase in spheronization speed decreased the usable yield fraction, probably because of the phenomenon of
attrition linked to increases in rugosity (28, 35). On the other hand, as reported by other authors, spheronization time increased
pellet size and quality by improving pellet roundness and decreasing pellet rugosity (17, 22, 26, 28, 34, 36, 49). Nevertheless,
spheronization time decreased the pycnometric density, which can be explained by pores closing on the surface during spheronization,
thus creating internal porosity.