Experiments of 3-level factorial design
Response data for all the 13 experimental runs of 3-level factorial design, performed in accordance with
Table 2, are presented in
Table 3.
| Run | Response
|
|---|
| Y1= bioadhesion (gf) | Y2= Consistency Index(in dyne/cm2) | Y3 = CPR at 2 (h) | Y4= CPR at 8 (h) |
|---|
| 1 | 53 | 8881 | 27.57 | 53.8 |
| 2 | 60 | 10127 | 22.81 | 50.86 |
| 3 | 61 | 10154 | 22.81 | 50.86 |
| 4 | 92 | 20653 | 16.66 | 38.17 |
| 5 | 37 | 5139 | 21.82 | 53.56 |
| 6 | 70 | 13001 | 17.74 | 44.21 |
| 7 | 61 | 10092 | 22.97 | 51.14 |
| 8 | 59 | 10198 | 22.45 | 50.56 |
| 9 | 85 | 20356 | 19.82 | 44.56 |
| 10 | 62 | 10154 | 22.34 | 50.38 |
| 11 | 68 | 16368 | 24.19 | 47.95 |
| 12 | 15 | 3556 | 39.67 | 66.98 |
| 13 | 20 | 4563 | 29.78 | 60.53 |
Mathematical modeling
Mathematical relationship was generated between the factors (independent variables) and responses (dependent variables) using the statistical package Design-Expert. First step in mathematical modeling was fitting the experimental data to appropriate model. A suitable model was selected by software on the basis of different parameter obtained from regression analysis such as p-value, adjusted R
2, predicted R
2 and Predicted Residual Sum of Square (PRESS) value (
Tables 4 and
5).
Table 3 lists the values of various response parameters of the prepared batches. ANOVA was applied for estimating the significance of model, at 5% significance level. If more than one model was significant (p < 0.05) for the response, the adjusted R
2 and PRESS value of the model were compared to select the best mathematical model for that response. Focus on maximizing the value of adjusted R
2 and predicted R
2. Low PRESS value indicated adequate fitting of model (
31). General quadratic equation for two independent variables is as follow:
Y = β0 + β1X1 + β2X2 + β3X1 X2 + β4X12 + β5X22
Where: β0 is the intercept representing the arithmetic averages of all the quantitative outcomes of 13 runs. β1 to β5 are all coefficients calculated from the observed experimental values of Y. X1 and X2 are the coded levels of factors. The terms X1X2 and Xi2 (i є {1, 2}) represent the interaction and quadratic terms, respectively. Coefficients with one factor represent the effect of that particular factor while the coefficients with more than one factor and those with second order terms represent the interaction between those factors and the quadratic nature of the phenomena, respectively. Synergistic effect and antagonistic effect of factor were indicated by positive sign and negative sign in front of that factor term, respectively.
| Source | Y1
| Y2
| Y3
| Y4
|
|---|
| f-value | p-value | f-value | p-value | f-value | p-value | f-value | p-value |
|---|
| Linear vs Mean | 105.39 | < 0.0001 | 144.02 | < 0.0001 | 34.06 | < 0.0001 | 148.46 | < 0.0001 |
| 2 FI vs Linear | 0.034 | 0.8584 | 1.64 | 0.2323 | 9.00 | 0.0127 | 1.76 | 0.2178 |
| Quadratic vs 2 FI | 12.71 | 0.0047 | 6.07 | 0.0295 | 23.09 | 0.0008 | 18.21 | 0.0017 |
| Source | | Linear
| 2 FI
| Quadratic
|
|---|
| Adj. R2 | Pred. R2 | PRESS | Adj. R2 | Pred. R2 | PRESS | Adj. R2 | Pred. R2 | PRESS |
|---|
| Response | Y1 | 0.9456 | 0.9104 | 529.8 | 0.9398 | 0.8264 | 1027.58 | 0.9833 | 0.9085 | 541.08 |
| Y2 | 0.9597 | 0.9382 | 2.183 E + 007 | 0.9622 | 0.9346 | 2.309 E + 007 | 0.9822 | 0.9165 | 2.948 E + 007 |
| Y3 | 0.8464 | 0.6812 | 132.59 | 0.9147 | 0.6934 | 127.53 | 0.9856 | 0.9239 | 31.67 |
| Y4 | 0.9609 | 0.9338 | 41.21 | 0.9637 | 0.9290 | 44.22 | 0.9925 | 0.9630 | 23.04 |
Drug content uniformity study of topical bioadhesive gels of Aceclofenac
All prepared gels were analyzed for aceclofenac content and the content of drug in each prepared TBG ranged from 96% to 104%. The drug content of the prepared TBG was within desired range of 90% to 110% (
21).
Effect of formulation variables on bioadhesion
From the p-values presented in
Table 4, linear model and quadratic model was found to be significant for bioadhesion. Quadratic model was selected on the basis of maximum value of adj. R
2 and low PRESS value indicating adequate fitting of model (
Table 5). Quadratic model was significant with model f-value of 142.32 (p-value < 0.0001). The quadratic equation generated by software is as follows:
Y1 = 60.66 + 10.50X1 + 28.83X2 + 0.50X1X2 + 0.71X12 - 8.29X22
Equation reveals that both factors (X
1 and X
2) affect bioadhesion characteristics of gel significantly. Equations also indicated that the effect of the change in HPMC concentration seems to be more pronounced in comparison with that of the change in PL-407 concentration since the coefficient of factor X
2 has a larger value than that of factor X
1. The combined effect of factors X
1 and X
2 can further be elucidated with the help of response surface plots (
Figure 1A ), which demonstrated that Y
1 varies in a linear fashion with the amount of both the polymers. However, the steeper ascent in the response surface with HPMC (X
2) – instead of Poloxamer (X
1) – is clearly discernible from response surface plots, indicating that the effect of HPMC is comparatively more pronounced than that of Poloxamer. From this discussion, one can conclude that the bioadhesion may be changed by appropriate selection of the levels of
X1 and
X2.
Figure 1B shows a linear relationship between the observed response values and the predicted values indicating the correctness of the model.
(A) Response surface plot showing the effect of PL-407 and HPMC on Bioadhesion (Y1); (B) Linear plot between observed and predicted value of Y1
Effect of formulation variables on rheological properties (consistency index)
It is essential for any formulation to study its rheological behavior to be used for topical drug delivery applications. It is important for its efficacy in delivering molecules onto or across the skin. Rheological studies of all the gels were done to study the effect of polymer proportion on the viscosity. Consistency index and flow index were calculated for all the batches. Consistency index (CI) was a measure of consistency and equivalent to apparent viscosity at a shear rate of 1 sec
-1. The flow index (FI) was a measure of the deviation of a system from Newtonian behavior (n = 1). Value of n < 1 indicates pseudoplastic flow or shear thinning system whereas n > 1 indicates dilatant flow or shear thickening system (
28). All the gels showed a flow index of less than 1 (data not shown), indicating pseudoplastic flow behavior. Thus, gel becomes thin when applied on the skin and provide better spreadability. Values of consistency index (Y
2) were summarized in
Table 3. Mathematical modeling was applied to result obtained for the consistency index to evaluate the effect of independent variable (HPMC and Poloxamer content in gel) and interaction of two independent variables on rheological properties of gel. From the p-values presented in
Table 4, linear contribution and quadratic contribution were found to be significant as p-value is less than 0.05 for both sources. To further fit the data to suitable model, the software was used to analyze the value of adjusted R
2, predicted R
2 and Predicted Residual Sum of Square (PRESS). Low PRESS value indicates adequate fitting of quadratic model (
31). PRESS value for Y
2 response (consistency index) showed no significant difference between the linear model and quadratic model (
Table 5). The value of Adj. R
2 of quadratic model was more than that of linear model (
Table 5). Moreover, quadratic model was selected by software because of the highest order of polynomial model. Quadratic model was significant with model f-value of 133.53 (p-value < 0.0001). The quadratic equation generated by software is as follows:
Y2 = 10396.93 + 1664.6X1 + 7353.17X2 + 675.50X1X2 - 85.76X12 + 1432.74X22
In this case, X
1, X
2 and X
22 are significant model terms. The equation represents the quantitative effect of factors (X
1 and X
2) upon the consistency index (Y
2 response). Increased concentration of polymers resulted in a stronger gel structure as reflected by equation generated for quadratic model. Equation also reveals that HPMC has more pronounced effect than PL-407 on the consistency index of gel. Surface (
Figure 2A) showed a steeper ascent in the response surface with HPMC (X
2) than with Poloxamer (X
1). It was in accord with equation generated by software showing pronounced effect of HPMC on consistency index. Model term X
22 was also found to be significant (
Table 6). This can be explained on the fact that HPMC swells in water and forms three disordered dimensional-physical networks. Tightly oriented gel structures are formed within poloxamer micelle pathways by HPMC-molecule entanglement and extensive hydrogen binding (
32).
Figure 2B represented the observed response value compared with that of predicted values indicating the correctness of model.
(A) Response surface plot showing the effect of PL-407 and HPMC on Consistency Index (Y2) (B) Linear plot between observed and predicted value of Y2
| Model/Model term | Y1
| Y2
| Y3
| Y4
|
|---|
| f-value | p-value | f-value | p-value | f-value | p-value | f-value | p-value |
|---|
| Model | 142.32 | < 0.0001 | 133.53 | < 0.0001 | 164.78 | < 0.0001 | 317.22 | < 0.0001 |
| X1 | 80.33 | < 0.0001 | 31.79 | 0.0008 | 412.77 | < 0.0001 | 458.46 | < 0.0001 |
| X2 | 605.74 | < 0.0001 | 620.23 | < 0.0001 | 311.76 | < 0.0001 | 1082.71 | < 0.0001 |
| X1X2 | 0.12 | 0.7377 | 3.49 | 0.1040 | 53.19 | 0.0002 | 8.47 | 0.0226 |
| X12 | 0.17 | 0.6945 | 0.039 | 0.8494 | 0.75 | 0.4159 | 12.55 | 0.0094 |
| X22 | 23.07 | 0.0020 | 10.84 | 0.0133 | 34.85 | 0.0006 | 34.43 | 0.0006 |
Effect of formulation variables on cumulative percentage release in 2 h
For this response, all the models (linear, 2FI and quadratic) are found to be significant with p-value < 0.05 (
Table 4). Among all the models, lowest PRESS value was found for quadratic model. Therefore, quadratic model was selected to fit the data of this response (
Table 5). Quadratic model was significant with model f-value of 164.78 (p-value < 0.0001).
The quadratic equation generated by software is as follows:
Y3 = 22.56 - 5.87X1 - 5.10X2 + 2.58X1X2 + 0.37 X12 + 2.51X22
In this case, X
1, X
2, X
1X
2 and X
22 were found to be significant model terms (
Table 6)
. Equation reveals that both factors have antagonistic effect on the drug release.
Figure 3A displayed a non-linear relationship for CPR in 2 h at high levels of the polymers. This can be attributed to the occurrence of potential interaction between the two polymers at the corresponding factor levels, construing that each polymer tends to modify the effect of the other one toward the drug release. Model term X
1X
2 was found to be significant which indicating the potential effect of this interaction on the drug release in 2 h.
Figure 3A also displayed the non-linearity of the response at high concentration of HPMC supported by the model term X
22 which is found to be significant for the response. This could be due to the rigid gel structure formation due to the interaction between HPMC and PL-407 as already explained in consistency index.
Figure 3B represented the observed response values compared with that of predicted values indicating the correctness of the model.
(A) Response surface plot showing the effect of PL-407 and HPMC on cumulative percentage release of drug in 2h (Y4); (B) Linear plot between observed and predicted value of Y3.
Effect of formulation variables on cumulative percentage release in 8 h
From the p-values presented in
Table 4, linear contribution and quadratic contribution were found to be significant since p-value is less than 0.05 for both sources. In this case, A, B, AB, A
2 and B
2 are significant model terms. PRESS value for quadratic model (23.04) was found lower than that of linear model (41.
21) as indicating in
Table 5. Therefore, quadratic model was selected to fit the data of this response. Quadratic model was significant with model f-value of 317.22 (p-value < 0.0001). The quadratic equation generated by software is as follows:
Y4 = 50.64 - 5.47X1 - 8.40X2 + 0.91X1X2 - 1.33X12 + 2.21X22
In this case, all the model terms (X
1, X
2, X
1X
2, X
12 and X
22) were found to be significant (
Table 6)
. The equation reveals that both factors have antagonistic effect on the drug release. CPR of the drug in 8 h with highest polymer content (30% Poloxamer and 4% HPMC) was found to be lowest. However, in this equation, it was clearly indicating that the retarding effect of HPMC was more prominent than PL-407. Coefficient of interactions shown in above equation was also significant which confirms the formation of rigid gel structure of PL-407 with HPMC. At high concentration of HPMC and PL-407, a very thick gel (highest consistency index value) was formed which provide a very slow release of drug.
Figure 4A represented the response surface indicating the more pronounced effect of HPMC than PL-407 on Y
4.
Figure 4B represented the observed response value compared with that of predicted values indicating the correctness of model.
(A) Response surface plot showing the effect of PL-407 and HPMC on cumulative percentage release of drug in 8h (Y4); (B) Linear plot between observed and predicted value of Y4.