3. RESULTS AND DISCUSSION
3.2. Experimental design to determine the effect of process parameters on the size of chitosan microspheres obtained by emulsion cross-linking method
Computational methods are more and more extensively applied in biocatalysis to orient experimental planning and avoid expensive and time-consuming experiments. Design of experiments is a set of techniques that study the influence of different variables on the outcome of a controlled experiment. Generally, the first step is to identify the independent variables or factors that affect the product or process, and then study their effects on a dependent variable or response. Experiments are run at different factor values, called levels. Each experimental run involves a combination of levels of the factors that are being investigated.
Box-Behnken designs are experimental designs for response surface methodology that require at least three levels to run an experiment. Response surface methodology is a statistical method that explores the relationships between several explanatory variables and one or more response variables. The main idea of response surface methodology is to use a sequence of designed experiments to obtain an optimal response. For experimental design with three or four factors, the Box-Behnken design has the advantage of fewer number of runs required than in case of other response surface designs. As an example, in case of a four-factor design, the central composite design needs 30 runs, whereas the Box-Behnken design needs 27 (e-Handbook of Statistical Methods, 2012).
Biocatalytic experiments, like chemical and other experiments, require a model for optimization of the most relevant operational parameters. The traditional one-factor-at-a-time design is the most frequently used investigative approach, providing an estimate of the effect of a single variable at selected fixed conditions. However, if the variables do not act additively (i.e. they interact) the obtained information could be incomplete and the real optimum of a system can be identified only with difficulty or by chance (Braiuca et al., 2006). Statistical methods, like as response surface methodology, are more efficient, studying several variables simultaneously and at multiple levels, and can provide information about the factors or their interactions that have the greatest impact on the considered parameter. They have also the advantage of reducing the number of experimental runs and the time required.
As it was presented in section 3.1, the best approach to obtain chitosan microparticles was emulsification of aqueous chitosan solution in oil phase in presence of Tween 80 surfactant
and cross-linking of the formed micro-droplets with glutaraldehyde. The particle size of the obtained microspheres was mainly influenced by four independent process variables, such as stirring rate, concentration of chitosan, concentration of Tween 80 and concentration of glutaraldehyde.
To study these effects, a 4-factorial 3-level Box-Behnken type experimental design and statistical analysis of the experimental results were carried out in three consecutive steps:
• First, to investigate the effect of process parameters, series of experiments were carried out according to a working plan proposed by factorial experimental design, using 4 factors (i.e. four independent decision variables) and 3 levels for each factor. The four independent factors were the stirring rate, Tween 80 concentration, chitosan concentration, and glutaraldehyde concentration, while composition and viscosity of the oil phase, and nature of surfactant were not modified, as they have been previously investigated (subsection 3.1.2).
• Second, the design was completed by further experiments to check the effects of some of the variables at five levels, both inside and outside the original factor intervals used in the first step. In addition, five repeated experiments at the central points of the four factors were also involved in the second step to determine the pure error.
• Third, the less significant effects were neglected, resulting in a simplified model equation that proved to be suitable for the prediction of the mean particle size as a function of the studied process parameters.
To elucidate the effects of 4 independent variables or “factors” on the mean particle size, 4-factorial 3-level experimental design was carried out by the STATISTICA® software package (StatSoft Inc.). The experimental design procedure together with the evaluation of experimental results was carried out in the 3 consecutive steps mentioned earlier.
In the first step, a 4-factorial 3-level experimental design procedure was carried out by Box-Behnken method (Kemeny and Deak, 2000) to elucidate the effects of 4 independent variables, without considering repetition of experiments. For each variable 3 different levels (their lowest, highest and central values) were taken into consideration to elucidate the possible non-linearity in their effects. One of the main advantages of experimental design is the reduction of the number of experiments N without remarkable loss of useful information. Namely, instead of all possible combinations of variables at different levels (in our case N=LK=34=81, where N is the number of experiments, L is the number of
levels, and K is the number of factors), the applied STATISTICA software package offered only N=LK-1=33=27 runs to be carried out in randomized order, listed in the first 27 data rows of Table 3.3. After accomplishing these experiments to determine the mean particle size of chitosan microspheres formed by the process, ANOVA analysis and non-linear (quadratic) regression were carried out to elucidate the linear and quadratic effects of factors F1-F4, and the effects of 2-way linear interactions between them.
The first column of Table 3.3 shows the sequential number of runs carried out in this order after randomization. The next four columns show the values of independent variables determined algorithmically by experimental design. As is seen, each of them was selected from three distinct values: from the two extreme (lower and upper) values and the central point of the studied interval of the given factor. It means that stirring rate was chosen from the values of 500, 1000 and 1500 rpm. The level of Tween 80 was selected from the set of 0.5, 1.5 or 2.5 v/v%. Chitosan solution and glutaraldehyde concentrations were chosen from 0.5, 1.0 or 1.5 w/w% and 1.0, 3.0 or 5.0 w/w%, respectively. The studied ranges of variables were chosen by considering the results of preliminary experiments.
The chitosan particles obtained by emulsion cross-linking method exhibited spherical shape and acceptable size distribution, exemplified in Fig. 3.12 and 3.13, respectively, except the particles obtained in Runs No. 22, 33 and 39, indicated by asterisks in Table 3.3.
The mean particle size (d ) was greatly influenced by the process variables, changing between 0.204 and 0.767 mm (see Runs No. 27 and 24, respectively).
Fig. 3.12. SEM image of chitosan microspheres obtained by the emulsion cross-linking method (Run 29 in Table 3.3)
Size, microns
0 100 200 300 400 500 600 700 800
Freqency, %
0 5 10 15 20 25 30
Fig. 3.13. Example for particle size distribution of the prepared chitosan particles.
Experimental parameters: stirring rate n = 1500 rpm, Tween 80 concentration xTw = 2.5%, v/v, chitosan concentration xCh = 1.0%, w/w, glutaraldehyde concentration xGl = 3.0%, v/v,
mean particle size d = 298 µm
In Step 2, the procedure described in Step 1 was completed with 16 additional experiments comprising 5 repetition in the central point (Table 3.3, Runs No. 28-32) of all variables, and 11 experiments to check the effects of certain variables in broader range of parameters (Table 3.3, Runs No. 33-43). From these, 6 experiments (Runs No. 33-38) were scheduled to check the effect of stirring rate, keeping all other factors at their central values. In addition, 5 further experiments (Runs No. 39-43) were carried out to check the effect of chitosan concentration, keeping all other factors at their central values again. Among the 27+16=43 experiments carried out altogether, there were 11 redundant ones, which can be considered as repetitions, thus enabling to calculate the pure error of the experiments. The order of the 16 additional runs was not randomized, as seen from Table 3.3.
After carrying out this additional experimental work, ANOVA analysis and non-linear regression was performed again considering all runs scheduled in Step 1 and Step 2 together, except the data which were out of the range of variable levels determined for Step 1, as will be explained later. The data listed in the darker grey rows in Table 3.3 (Runs No.
34, 36, 38, 42, 43) were disregarded in this analysis, because certain variables in these runs were outside of the intervals defined originally in Step 1 of the experimental design.
Therefore, the data of 38 experiments were submitted to statistical analysis.
Table 3.3. Parameters obtained by experimental design and the measured mean particle
*agglomerated tiny particles and formless larger ones, **wide size distribution, ***not spherical, aggregated particles, wide size distribution
The results of the statistical analysis are presented in Table 3.4.
Table 3.4: Estimated effects of the factors determined by statistical analysis of the experimental data, L – linear effects, Q – quadratic effects
Effect Estimates; Dependent Variable: mean particle size [mm]
4 3-level factors, 1 Block, 38 Runs; MS Pure Error = 0.0054127 Factors and their interactions
The second column of Table 3.4 lists the estimated linear (L) and quadratic (Q) effects of factors on the mean diameter of the chitosan microspheres, namely the effects of stirring rate (F1), Tween 80 (F2), chitosan (F3), and glutaraldehyde (F4) concentrations, respectively. The interactions between them were also estimated as is shown in the last six rows of Table 3.4. The pure errors calculated from the repetitions, the results of t-test and p-values, as well as the ± 95% confidence limits of these effects are listed in other columns of the Table 3.4. The p-values show the probability that the value of a given effect could have occurred by chance. Conventionally, if p is equal or less than 0.05, the effect is regarded statistically significant. As is seen here, the data rows printed in bold were automatically qualified by the applied STATISTICA software as significant ones.
The order of standardized effects is shown in Fig. 3.14 in form of Pareto chart.
Pareto Chart of Standardized Ef f ects; Variable: mean particle size 4 3-lev el f actors, 1 Blocks, 38 Runs; MS Pure Error=0.005413
-,160661
Standardized Ef f ect Estimate (Absolute Value) Stirring rate rpm (Q)
Fig. 3.14. Pareto chart of the standardized effects of the studied factors and their interactions
The columns extending over the dotted vertical line at p=0.5 indicate the effects, which are qualified as significant, while other effects not reaching that line are regarded not significant. At the first sight, it can be thought that only three factors and two interactions, namely chitosan concentration (F3), glutaraldehyde concentration (F4) and Tween 80 concentration (F2), and 1L by 4L and 2L by 4L have significant influence. It can be seen in Fig. 3.14 that linear effects (L) of these factors are much higher than the quadratic (Q) ones. As regards stirring intensity (F1), it was a surprise that the primary effect of this factor was only on the 7th place, and was qualified as not significant.
The statistical analysis of experimental data involved a non-linear regression to reveal the dependence of mean particle size on process variables. The results are summarized in Table 3.5.
Table 3.5. Regression coefficients determined by non-linear regression analysis, L – linear effects, Q – quadratic effects
Regression Coefficients; Dependent Variable: mean particle size [mm];
4 3-level factors, 1 Block, 38 Runs; MS Pure Error=0.0054127 Factors and their interactions Intercept (b) 1.116185 0.2226 5.0127 0.0010 0.6027 1.6295 (F1) Stirring rate n,
min-1 (1L) -0.000083 0.0002 -0.3421 0.7411 -0.0006 0.0005 (F1) Stirring rate n,
min-1 (1Q) 0.000000 0.0000 0.1607 0.8763 -0.0000 0.0000 (F2) Tween 80 concentration
xTw, v/v% (2L) -0.077946 0.1076 -0.7241 0.4896 -0.3262 0.1703 (F2) Tween 80 concentration
xTw, v/v% (2Q) -0.018862 0.0266 -0.7099 0.4979 -0.0801 0.0424 (F3) Chitosan concentration
xCh, w/w% (3L) -0.437166 0.2416 -1.8092 0.1080 -0.9944 0.1201 (F3) Chitosan concentration
xCh, w/w% (3Q) 0.040755 0.1012 0.4028 0.6976 -0.1926 0.2741 (F4) Glutaraldehyde
concentration xGl, w/w% (4L) -0.109551 0.0538 -2.0355 0.0762 -0.2337 0.0146 (F4) Glutaraldehyde
concentration xGl, w/w% (4Q) 0.005493 0.0066 0.8269 0.4323 -0.0098 0.0208 interaction 1L by 2L 0.000024 0.0000 0.5491 0.5979 -0.0001 0.0001 interaction 1L by 3L 0.000117 0.0001 1.3322 0.2195 -0.0001 0.0003 interaction 1L by 4L -0.000051 0.0000 -2.3352 0.0478 -0.0001 -0.0000 interaction 2L by 3L -0.043111 0.0439 -0.9827 0.3545 -0.1443 0.0581 interaction 2L by 4L 0.029944 0.0110 2.7303 0.0258 0.0047 0.0552 interaction 3L by 4L 0.046844 0.0219 2.1356 0.0653 -0.0037 0.0974
The factor names and their interactions are listed again in the first column, while the intercept of the regression surface and the regression coefficients are shown in the second column. The standard errors, the results of t-test, the p-values, and the ± 95% confidence limits are listed in the other columns, similarly to Table 3.4. Data rows referring to statistically significant dependences are set in bold again. Note that apart from the estimated intercept only one factor (F4) and two interactions (1L by 4L and 2L by 4L) were qualified here as significant. This rating forced us to further examination.
On the other hand, the results of regression analysis were in good agreement with the experimental data: the mean square of residuals was 0.047 mm2, and the average deviation of the measured and predicted data was 11.4% (Fig. 3.15).
Observed vs. Predicted Values
4 3-lev el f actors, 1 Blocks, 38 Runs; MS Pure Error=,005413
0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9
Predicted mean particle size, mm Mean deviation: 11.4 %
Fig. 3.15. Comparison of the measured and predicted mean particle size
The normal probability plot of residuals showed nearly Gaussian distribution as can be seen in Fig. 3.16.
Normal Prob. Plot; Raw Residuals
4 3-lev el f actors, 1 Blocks, 38 Runs; MS Pure Error=0,005413
-0,20 -0,15 -0,10 -0,05 0,00 0,05 0,10 0,15 0,20 0,25 Residual
Fig. 3.16. The normal probability plot of raw residuals shows nearly Gaussian distribution
Plotting the predicted mean particle size in function of the studied variables provided useful tool to check their importance independently from the results of the mechanistic evaluation shown in Tables 3.4 and 3.5, and to gain information on the possible particle size control or optimization during the process. The results of this study are discussed below.
3.2.1. Effect of stirring rate
From Tables 3.4 and 3.5 it is seen that the effect of stirring rate was qualified as non significant. Repeated experiments carried out with the central values of other factors (xCh=1.0%, w/w, xTw=1.5%, v/v, xGl=3.0%, w/w) (see Runs 34-38 in Table 3.3) seemingly also confirmed this rating. However, results obtained at different combinations of variables made this evaluation questionable.
Fig. 3.17. Influence of stirring rate and surfactant concentration at the centre of other factors
According to a more detailed study, at certain combinations of variables it was seen indeed that stirring rate has only modest influence on particle size, or has no effect at all, as is seen in Fig. 3.17 at maximal Tween 80 concentration (xTw=2.5%, v/v), or in Fig. 3.18 at maximal chitosan concentration (xCh=1.5%, w/w), keeping the other variables at their central values.
Fig. 3.18: Influence of stirring rate and chitosan concentration at the centre of other factors Fig. 3.19 gives also evidence that stirring has not remarkable effect at medium Tween 80, medium chitosan and medium glutaraldehyde concentrations.
Fig. 3.19. Influence of stirring rate and glutaraldehyde concentration at the centre of other factors
However, at minimal Tween 80 (xTw=0.5%, v/v), medium chitosan (xCh=1.0%, w/w) and medium glutaraldehyde (xGl=3.0%, w/w) concentrations d definitely decreases with increasing stirring rate (Fig. 3.17). Similar tendency is observed at minimal chitosan (xCh=0.5%, w/w), medium Tween 80 (xTw=1.5%, v/v) and medium glutaraldehyde
(xGl=3.0%, w/w) concentrations, too (Fig. 3.18). Applying medium chitosan and medium Tween 80 concentrations (Fig. 3.19), strong dependence on the stirring rate at low and high glutaraldehyde concentrations can be revealed. It is very interesting that at high glutaraldehyde concentration (xGl=5.0%, w/w), the mean particle size decreases with increasing stirring rate, similarly to the examples mentioned above. However, lowering the glutaraldehyde concentration, the slope of this tendency diminishes, and later on it reverses: at the lowest glutaraldehyde concentration (xGl=1.0 w/w%) the size of particles steeply increases with increasing stirring rate. The most probable explanation of this phenomenon can be the higher susceptibility of chitosan microspheres to coagulate by vigorous stirring. It might be caused by the lower quantity of glutaraldehyde cross-linking agent resulting in softer and sticky particles. This reverse effect indicates strong interaction between the two factors, which is also confirmed by the relatively high effect of 1L by 4L seen in Fig. 3.14 and its high significance (p=0.0478) shown in Tables 3.4 and 3.5.
3.2.2. Effect of surfactant concentration
The increase of Tween 80 concentration during the preparation of chitosan microspheres generally decreased the mean particle size (see Fig. 3.17 and 3.20), due to the dispersing effect of this surfactant. This effect is the third highest one among other factors as is seen in Fig. 3.14.
Fig. 3.20. Influence of the surfactant and chitosan concentrations at the centre of other factors
However, at certain combinations of other variable values, especially at higher glutaraldehyde levels, the concentration of Tween 80 has minor influence on the particle size or can be reversed as is seen in Fig. 3.21.
Fig. 3.21. Influence of the surfactant and glutaraldehyde concentrations at the centre of other factors
This is probably caused by the combined effect of Tween 80 and glutaraldehyde (effect of 2L by 4L), which is the fourth highest effect as seen in Fig. 3.14, also clearly indicated in Fig. 3.21.
3.2.3. Effect of chitosan concentration
According to Fig. 3.14, chitosan concentration has the most significant effect on the mean particle size. Namely, this latter is generally decreasing with increasing chitosan level (see Fig. 3.18 and 3.20). However, this effect depends on other factors, too. In case of high glutaraldehyde concentration, at medium stirring rate and medium Tween 80 concentration practically no dependence was revealed as can be seen in Fig. 3.22 at xGl=5.0%, w/w. In the same diagram it is well observable that at minimal glutaraldehyde concentration (xGl=1.0%, w/w) the influence of chitosan concentration is much stronger.
Fig. 3.22. Influence of the chitosan and glutaraldehyde concentrations at the centre of other factors
It means that characteristic interaction exists between these factors, also seen in Fig. 3.14 where the effect of 3L by 4L is the sixth significant one.
This interaction at other combination of factors is also pronounced: e.g. in case of maximal stirring rate and minimal Tween 80 concentration (Fig. 3.23) the effect of chitosan concentration is reversed by the change of glutaraldehyde concentration, namely: at low xGl the mean particle size decreases with increasing xCh, while at high xGl opposite dependence takes place.
0.25 0.35 0.45 0.55 0.65 0.75
0.5 0.7 0.9 1.1 1.3 1.5
Chitosan concentration [%]
Particle size [mm]
xGl=1%
xGl=3%
xGl=5%
Fig. 3.23. The effect of the concentration of chitosan solution at n = 1500, xTw = 0.5%, and different glutaraldehyde concentrations
Interaction between chitosan concentration and stirring rate (1L by 3L) is seen in Fig. 3.18, where the gradient of the mean particle size as a function of chitosan concentration decreases with increasing stirring rate.
There is a weak interaction between the chitosan and Tween 80 concentrations in Fig. 3.14 (2L by 3L). It can also be revealed from Fig. 3.20 where the gradient of the mean particle size along the chitosan concentration axis depends on the ratio of the applied surfactant, namely: the slope of the regression surface is somewhat increasing with increasing Tween 80 concentration.
0.25 0.30 0.35 0.40 0.45 0.50 0.55
0.5 0.7 0.9 1.1 1.3 1.5
Chitosan concentration [%]
Particle size [mm]
xGl=1%
xGl=3%
xGl=5%
Fig. 3.24. The effect of the concentration of chitosan solution at n = 1500, xTw = 2.5%, v/v, and different glutaraldehyde concentrations
Due to the interactions between different factors, we have found certain parameter combinations (e.g. n=1500 rpm, xGl=5.0%, w/w, xTw = 2.5%, v/v, Fig. 3.24) where the influence of chitosan concentration on the mean particle size is negligible.
3.2.4. Effect of glutaraldehyde
According to the Pareto plot in Fig. 3.14, the concentration of glutaraldehyde has the second highest influence among the studied factors. Increasing this concentration at medium Tween 80 and medium chitosan concentrations at the highest stirring rate, the size of chitosan microspheres steeply decreases as can be seen in Fig. 3.19. This tendency is also obvious at medium stirring rate and at medium chitosan and minimal Tween 80
concentration (see Fig. 3.21), or at medium stirring rate, and medium Tween 80 and minimal chitosan concentrations (Fig. 3.22). Fig. 3.19 shows a characteristic interaction between the stirring rate and glutaraldehyde concentrations as was already explained in Section 3.1. Fig. 3.21 also reveals strong interaction between the glutaraldehyde and Tween 80 concentrations (2L by 4L also seen in Fig. 3.14), because the applied surfactant level essentially influences the particle size decreasing the effect of glutaraldehyde. At low Tween 80 concentration the mean particle size is steeply diminishing with increasing glutaraldehyde concentration, but at high Tween 80 concentration (xTw=2.5%, v/v) this tendency is not recognisable, only a slight minimum appears at medium glutaraldehyde concentration. Similar interaction between the chitosan and glutaraldehyde concentrations (3L by 4L) can be revealed in Fig. 3.22, where the gradient of the surface is high at minimal chitosan concentration, but almost negligible at high chitosan concentration. A slight minimum is also recognisable around 3.5-4.5%, w/w glutaraldehyde concentration.
3.2.5. Prediction of the mean particle size
In Step 3 of the experimental design, considering the order of magnitudes of all linear and quadratic effects of the factors and their interactions determined in Steps 1 and 2, the less significant effects were eliminated. Carrying out new ANOVA process and regression, the corrected effects and correlation coefficients have been determined to obtain simpler equation to predict the mean particle size at various combinations of process variables.
It was seen that, as a result of statistical analysis a set of regression coefficients have been determined. According to 4 independent (factors F1-F4) and 1 dependent variables (d ), using these coefficients in Eqn. 3.1 specifies a 5 dimensional surface giving the best fit to the experimental data.
b x x a x
a x
a
d =
∑
iL i +∑
iQ⋅ i2 +∑
( iL,jL⋅ i⋅ j)+ (3.1)where d is the mean particle size, xi is the ith independent variable (namely n is the stirring
where d is the mean particle size, xi is the ith independent variable (namely n is the stirring