Experimental Design
The design used a single simplex-lattice approach, where the surfactant mixture, comprising components A + B + C = 1, was utilised to produce NEs containing 10% by mass of olive oil. The design matrix generated a total of 16 runs and was statistically analysed using the Design-Expert® 13 (Stat-Ease®, Minneapolis, United states of America) as shown in Table 4.
Table 4
Surfactant compositions generated by experimental design and responses.
Run | Tween®80 (w/w) | Span®20 (w/w) | Ethanol (w/w) | DS (nm) | ZP (mv) | PDI | DC (mg/ml) |
1 | 252.339 | 402.037 | 95.6246 | 370.23 | -4.9 | 0.2024 | 3.09 |
2 | 108.6 | 491.4 | 150 | 277.96 | 4.3 | 0.125 | 2.66 |
3 | 562.727 | 137.023 | 50.25 | 263.67 | -20.2 | 0.459 | 2.50 |
4 | 446.302 | 153.698 | 150 | 170.37 | -19 | 0.5173 | 2.80 |
5 | 643.125 | 37.5 | 69.375 | 227.67 | 27.3 | 0.5267 | 1.33 |
6 | 252.339 | 402.037 | 95.6246 | 266.33 | -7.4 | 0.3104 | 3.1 |
7 | 147.35 | 565.15 | 37.5 | 229.17 | 6.6 | 0.3131 | 2.64 |
8 | 252.339 | 402.037 | 95.6246 | 248.47 | 6.8 | 0.5163 | 1.88 |
9 | 252.339 | 402.037 | 95.6246 | 204.33 | 8 | 0.3202 | 1.83 |
10 | 108.6 | 491.4 | 150 | 398.77 | 10.6 | 0.175 | 2.19 |
11 | 37.5 | 665.661 | 46.8393 | 285 | -7.3 | 0.2088 | 2.92 |
12 | 346.791 | 253.209 | 150 | 181.67 | 10 | 0.3463 | 3.0 |
13 | 643.125 | 37.5 | 69.375 | 242.8 | 31.2 | 0.2933 | 3.2 |
14 | 477.824 | 234.676 | 87.5 | 155 | -7.7 | 0.492 | 2.81 |
15 | 382.606 | 329.894 | 37.5 | 225 | 9.3 | 0.5673 | 2.63 |
16 | 537.968 | 62.0321 | 150 | 193 | 33.7 | 0.1562 | 1.64 |
The most suitable mathematical model was determined by comparing statistical parameters such as R2, adjusted R2, and Predictive Residual Error Sum of Squares (PRESS) and are summarised in Table 5.
Table 5
Summary of statistical parameters of responses.
Response | Predicted model | R2 | Adjusted R2 | Predicted R2 | Adequate Precision | PRESS |
DS | Quadratic model | 0.5610 | 0.3414 | -0.0764 | 5.0628 | 70829.84 |
PDI | Special quartic model | 0.7606 | 0.4870 | 0.3777 | 5.2695 | 0.2075 |
ZP | Special quartic model | 0.955 | 0.8404 | 0.4611 | 11.889 | 200 |
DC | Mean model | 0.0000 | 0.0000 | -0.1378 | NA | 5.57 |
The PRESS value evaluates the predictive capability of the model, with the model with the lowest PRESS being considered the best predictor for the data set. As a result, the recommended models were a special quartic model for the PDI and ZP, a quadratic model for DS and a mean model for DC.
The mean model for DC implies that variations in the independent variables tested in the study have no meaningful influence on these response variables. Any observed differences are more likely due to random variation than to the systematic effects of the predictors 28.
The negative predicted R² of -0.0760 for droplet size suggests that the overall mean may be a better predictor of the response variable than the current model. Furthermore, in some cases, a higher-order model may produce more accurate predictions 28. However, the adjusted precision of 5.0628 indicates a good signal, as it exceeds the desirable threshold of 4. This model is therefore suitable for navigating the design space.
The comparison between the predicted R² and adjusted R², along with adequate precision, is crucial in assessing the reliability and robustness of a statistical model. The predicted R² of 0.3777 for PDI is reasonably close to the adjusted R² of 0.4870, as the difference is less than 0.2. Adequate precision measures the signal-to-noise ratio, with a desirable value being > 4. The PDI ratio of 5.269 indicates an adequate signal, meaning this model is suitable for exploring the design space.
The predicted R² of 0.4611 for ZP is not as close to the adjusted R² of 0.8404 as one might normally expect i.e. the difference is more than 0.2. The adjusted result indicates that the model fits the experimental data well, accounting for a significant portion of the variability in the response variable. A high adjusted R² indicates a good fit as it takes into account the number of predictors. A low Predicted R² value indicates the inability of the model to accurately predict new data. Predicted R², derived from cross-validation, assesses how well the model generalises to new data points 29.
A composition residual analysis was performed to ensure that the ANOVA assumptions were met. To accomplish this, diagnostic plots such as Box-Cox residual plots were generated for each of the four monitored responses. Data transformation was not required for DS, ZP, PDI, or DC and the Box-Cox plots are shown in Fig. 1.
Quadratic Model Droplet Size
The resultant DS of the dispersed phase ranged between 155.00 nm and 398.77 nm. The plot shows that increasing Tween® 80 concentration generally resulted in smaller droplet sizes however larger droplet sizes are seen with increasing Span® 20 concentration (Fig. 2).
The unsaturation of the Tween® 80 non-polar tails resulted in molecular packing, which facilitated the formation of ultrafine droplets at the oil-water interface of nanoemulsions. This phenomenon was also observed in a previous study involving Tween® 80 30.
The ratio of effective cross-sectional areas of the tail and head groups of a surfactant influences its unique molecular geometry. When surfactant molecules are present in adequate quantities, they can produce an ideal monolayer curvature during spontaneous emulsification. The combination of Span® 20 and Tween® 80 can create a synergistic effect, where the balance between hydrophilic and lipophilic properties leads to the formation of smaller, more stable droplets. Higher concentrations of Tween® 80 with an HLB value of 15 combined with Span® 20 with an HLB value of 8.6 results in high overall HLB-mixture value which is suitable for the formulation of an oil in water NE, promoting smaller droplets 31,32.
The ANOVA results for the quadratic model are listed in Table 6. The Lack of Fit F-values for the model shows that the lack of fit is not significant in comparison to the pure error, which is a ideal because it indicates that the models fit well. The F-value for droplet size is 2.56, with a 9.70% chance the outcome occurring due to noise.
Table 6
ANOVA for quadratic model for DS.
Source | Sum of Squares | df | Mean Square | F-value | p-value |
Model | 0.0000 | 6 | 1.988 x 10− 6 | 2.26 | 0.1306 |
Linear Mixture | 4.223 x 10− 6 | 2 | 2.111 x 10− 6 | 2.40 | 0.1460 |
AB | 1.179 x 10− 7 | 1 | 1.179 x 10− 7 | 0.1341 | 0.7226 |
AC | 2.682 x 10− 6 | 1 | 2.682 x 10− 6 | 3.05 | 0.1147 |
BC | 3.503 x 10− 6 | 1 | 3.503 x 10− 6 | 3.98 | 0.0770 |
ABC | 5.766 x 10− 7 | 1 | 5.766 x 10− 7 | 0.6558 | 0.4389 |
Residual | 7.913 x 10− 6 | 9 | 8.792 x 10− 7 | | |
Lack of Fit | 3.192 x 10− 6 | 4 | 7.981 x 10− 7 | 0.8453 | 0.5521 |
Pure Error | 4.721x 10− 6 | 5 | 9.441x 10− 7 | | |
Cor Total | 0.0000 | 15 | | | |
The coded equation (Eq. 1) allows for predictions about the response based on specified levels of each factor. The first two terms of the Equation, A and B suggest that the individual excipients Span® 20 and Tween® 80 significantly influence droplet size, with B having the greatest positive impact. The correlation between independent factors and DS is provided in Eq. 1.
$$\:Droplet\:size=244.69A+270.44B-3555.48C-251.31AB+4049.48AC+5409.57BC$$
Equation 1
PDI
The contour plot for the PDI reveals the NEs in the design space ranged between 0.125 and 0.5673. The red regions, which represent higher PDI values, are observed with increased concentration of Tween® 80. Conversely, there appears to be a direct effect of lowering PDI values with increasing amounts Span® 20 and lower Tween® 80 concentrations. This could be due to particle aggregation, which results in the formation of micelles or other varying-sized structures. This can lead to a broader size distribution, increasing the PDI 33. Increasing ethanol concentration reduced the PDI in nanoemulsions due to its impact on the solubility, interfacial tension, and stabilisation mechanisms of the system 34. The rest of the region showed no particular pattern as indicated in the 3D surface and contour plot in Fig. 3.
The ANOVA results for the special quartic model are listed in Table 7.
Table 7
ANOVA data for special quartic model for PDI.
Source | Sum of Squares | df | Mean Square | F-value | p-value |
Model | 0.2536 | 8 | 0.0317 | 2.78 | 0.0978 |
Linear Mixture | 0.1259 | 2 | 0.0629 | 5.52 | 0.0364 |
AB | 0.0360 | 1 | 0.0360 | 3.16 | 0.1189 |
AC | 0.0241 | 1 | 0.0241 | 2.11 | 0.1894 |
BC | 0.0268 | 1 | 0.0268 | 2.35 | 0.1692 |
A²BC | 0.0006 | 1 | 0.0006 | 0.0525 | 0.8253 |
AB²C | 0.0347 | 1 | 0.0347 | 3.05 | 0.1245 |
ABC² | 0.0131 | 1 | 0.0131 | 1.15 | 0.3188 |
Residual | 0.0798 | 7 | 0.0114 | | |
Lack of Fit | 0.0001 | 2 | 0.0000 | 0.0022 | 0.9978 |
Pure Error | 0.0797 | 5 | 0.0159 | | |
The significance of the linear mixture term implies that the primary effects of the factors are important in influencing the response. The other interaction and quadratic terms (AB, AC, BC, A2BC, AB2C, ABC2) are not significant, as indicated by their high p-values. This suggests that the inclusion of these terms does not substantially improve the model’s ability to explain the variation in the response, and the response is primarily driven by the linear effects of the factors. The Lack of Fit F-values for the model show that the lack of fit is not significant in comparison to the pure error, which is good because it indicates that the models fit well. The F-value for PDI is 2.78 indicating that there is only a 9.78% chance of the data obtained being due to noise. Eq. 2 reveals that an increase in Tween® 80, Span® 20 slightly decreased PDI, however an increase in ethanol significantly decreased PDI as indicated by the larger value of ethanol.
$$\:PDI=-0.0299A-0.0422B-58.81C+2.45AB+71.12AC+77.21BC-10.01{A}^{2}BC-118.31A{B}^{2}C+186.62AB{C}^{2}$$
Equation 2
ZP
The 3D surface and contour plot (Fig. 4) reveals the presence of a significant region in blue indicating that as the concentration of Tween® 80 in the surfactant mixture increases with increase in concentration of ethanol, the ZP becomes more negative. Furthermore, the contour plot shows the upper positive point occurring when ethanol and Span® 20 are used at the upper limit. This suggests that higher concentrations of Span® 20, with lower concentrations of Tween® 80 and Ethanol, result in higher ZP values. Design points located in the central region show a mix of Tween® 80, Span® 20, and Ethanol. The ZP in these areas varies significantly, with the more negative values seen around the Tween 80®-rich region, and the more positive values in the span® 20-rich areas. BDQ is a weakly basic compound, implying that it can exist in both ionised and non-ionised states depending on the pH of the environment.
As the pH rises, BDQ becomes more likely to ionise, producing positively charged molecules 35. The positively charged molecules interact with the Tween® 80, resulting in a more negative overall zeta potential because the interactions alter the surface charge distribution 36.
The overall model is statistically significant, indicating that the model's factors and interactions explain the variation in the response variable. The linear combination of Tween® 80, Span® 20, and ethanol has a significant effect on the response variable, indicating that the factors' primary or direct effects play an important role in determining the response. The terms A²BC and ABC² were significant, indicating that complex interaction has a substantial impact on the response variable. The terms AB, AC, BC, AB²C were not significant and suggest that these interactions do not significantly affect the response.
The ANOVA results for the special quartic model are listed in Table 8. The Lack of Fit F-values for the model shows that the lack of fit is not significant in comparison to the pure error, which is a good result because it indicates that the models fit well. The F-value for ZP is 10.87 which is significant, with a 0.25% chance of occurring due to noise.
Table 8
ANOVA for special quartic model for ZP.
Source | Sum of Squares | df | Mean Square | F-value | p-value |
Model | 3584.42 | 8 | 448.05 | 10.87 | 0.0025 |
⁽¹⁾Linear Mixture | 520.79 | 2 | 260.40 | 6.32 | 0.0270 |
AB | 61.95 | 1 | 61.95 | 1.50 | 0.2598 |
AC | 125.28 | 1 | 125.28 | 3.04 | 0.1247 |
BC | 61.84 | 1 | 61.84 | 1.50 | 0.2602 |
A²BC | 1661.01 | 1 | 1661.01 | 40.31 | 0.0004 |
AB²C | 1.82 | 1 | 1.82 | 0.0443 | 0.8394 |
ABC² | 746.64 | 1 | 746.64 | 18.12 | 0.0038 |
Residual | 288.43 | 7 | 41.20 | | |
Lack of Fit | 73.53 | 2 | 36.77 | 0.8554 | 0.4792 |
Pure Error | 214.90 | 5 | 42.98 | | |
Cor Total | 3872.84 | 15 | | | |
According to Eq. 3, an increase in Tween® 80 concentration results in a more negative ZP, an increase in Span® 20 concentration also results in the ZP also becoming slightly negative, but the effect is much smaller than that of Tween® 80 or ethanol. An increasing concentration of ethanol also resulted in a negative ZP and had the largest effect compared to the other factors. Ethanol can have a significant impact on the zeta potential by changing the medium's dielectric constant, influencing ion distribution, and potentially dehydrating the particle surface layer. As the concentration of ethanol increases, it may reduce electrostatic repulsion by compressing the double layer, resulting in a more negative ZP 37.
$$\:ZP=-30.79A-5.34B-3701.50C+101.49AB+5128.59AC+3710.40BC-16669.47{A}^{2}BC+857.36A{B}^{2}C+44496.93AB{C}^{2}$$
Equation 3
DC
The resultant DC of the dispersed phase ranged between 1.33 mg/ml and 3.20 mg/ml. Given that this is a mean model as illustrated in Fig. 5, which represents average responses rather than specific experimental values, we can interpret the contour plot for DC based on trends and overall behaviour across the composition space. The surfactant compositions do not have any significant effects on the DC therefore the model was not significant.
The mean model indicates that the factors being tested do not significantly impact the response variable. The ANOVA results for the mean model are listed in Table 9. The Lack of Fit F-values for the model shows that the lack of fit is not significant in comparison to the pure error, which is a good result because it indicates that the models fit well.
Table 9
ANOVA for mean model for DC.
Source | Sum of Squares | df | Mean Square | F-value | p-value |
Model | 0.0000 | 0 | | | |
Residual | 4.90 | 15 | 0.3266 | | |
Lack of Fit | 1.50 | 10 | 0.1502 | 0.2210 | 0.9796 |
Pure Error | 3.40 | 5 | 0.6796 | | |
Cor Total | 4.90 | 15 | | | |
Optimisation of the BDQ-NE
The optimised BDQ-NE (OPT-BDQ-NE) was produced based on the desirability function and the formulation composition for the solutions is reported in Table 10.
Table 10
Optimised surfactant solutions based on the desirability function.
No | Tween® 80 | Span® 20 | Ethanol | DS | PDI | ZP | DC | Desirability |
1 | 631.425 | 81.075 | 37.500 | 230.446 | 0.125 | -22.583 | 2.513 | 0.813 |
2 | 675.000 | 37.500 | 37.500 | 244.689 | -0.030 | -30.785 | 2.513 | 0.795 |
3 | 59.419 | 653.081 | 37.500 | 261.214 | 0.039 | -2.848 | 2.513 | 0.701 |
4 | 281.889 | 376.538 | 91.573 | 260.515 | 0.392 | -11.131 | 2.513 | 0.587 |
5 | 359.359 | 240.641 | 150.000 | 206.834 | 0.387 | 3.215 | 2.513 | 0.582 |
Based on the optimal design, the optimum levels of the studied factors were estimated for BDQ-NE preparation. The goal was to minimise DS, PDI and ZP and maximise DC to ensure optimal drug release after oral administration. Thus, simultaneous optimisation of all four responses was performed, and the desirability value was used to select the optimal formulation.
The highest desirability value represented the best ideal formulation. The optimal BDQ-NE selected by the optimal design was prepared and characterized for their DS, PDI, ZP and DC. The optimal selected formulation produced an observed DS, ZP, PDI and DC of 191.6 ± 2.38 nm, and PDI 0.1176 ± 1.69, -25.9 ± 3.00 mV, and 3.14 ± 0.82 mg/ml, respectively. As a result of these findings, the optimal BDQ-NE formulation, proposed by the design expert, offered a promising formulation of small particle size and uniformity, good stability, and maximum DC; subsequently, it was selected for in vitro drug release studies.
Zeta potential values greater than + 30 mV or less than − 30 mV are generally regarded as good stability due to electrostatic repulsion between particles, which prevents aggregation. A zeta potential of -25.9 mV ± 3.00 mV indicates moderate stability suggesting that the optimised nanoemulsion is likely to be stable 38.
Characterisation of OPT-BDQ-NEs
Transmission Electron Microscopy
The smaller DS observed in TEM when compared to DLS were due to the deterioration of liquid droplets under vacuum while DLS measures samples in their hydrated forms, in the presence of water or solvents. DLS determines the hydrodynamic diameter of droplets in emulsions based on intensity, typically resulting in larger values than those measured by TEM. Since TEM measures droplet sizes in a dried state, the samples often shrink, explaining the lower droplet sizes observed for optimised samples measured using TEM 39.
FTIR
The FTIR spectra in Fig. 7 demonstrate no detectable interactions between the BDQ and the excipients used following the optimisation process.
The spectra show the presence of the same functional groups of the payload in the optimised NE and those that have been previously reported in BDQ NE preformulation studies 20. The spectrum reveals the presence of -OH group observed at peak 3083 cm− 1. Similarly, chemical shifts associated with the aromatic region are visible at 2960 cm− 1 and 1631 cm− 1 and as well as C = C stretch in aromatic ring at wavenumber 1546 cm− 1. Importantly, there are no new peaks or unexpected functional groups present. This lack of spectral alterations indicates the absence of any chemical interactions.
Viscosity, pH, Conductivity
The viscosity of the optimised formulation was found to be 327 ± 3.05 cP. The optimised BDQ-NE exhibited low viscosity. Low viscosity values ensure easy handling, smoother administration, and swallowing, particularly for paediatrics 23,40.
The pH of the formulation was found to be 5.63 ± 1.78. Formulations for paediatric use should have a pH close to neutral to prevent irritation to the gastrointestinal tract. A pH of 5.63 is generally satisfactory 41.
The conductivity of the formulation was 53.1 µScm− 1. The conductivity indicates that it is an o/w NE 42. This demonstrates that the API was dissolved into the oil phase and uniformly dispersed in the aqueous phase.
In vitro release studies
NEs are designed to increase the solubility and bioavailability of lipophilic drugs such as BDQ. In vitro drug release studies aid in determining the release kinetics of BDQ from the nanoemulsion and provide insight on how the NE improves BDQ solubility and bioavailability, both of which are critical for its therapeutic effectiveness 43. These studies also contribute to a better understanding of the mechanisms by which BDQ is released from the NE, such as diffusion through the oil phase, micellar solubilisation, or erosion of nanoemulsion droplets using kinetic modelling 44,45.
OPT-BDQ-NE exhibited over 97.5% drug release. However, no detectable drug release was observed from the pure BDQ drug suspension over the given time points. The drug release profile from OPT-BDQ-NE as shown in Fig. 8.
There was no detectable drug release from the drug suspension over the test period which is attributable to the low aqueous solubility of BDQ. The suspended BDQ would require to first go into solution prior to diffusion into the release medium. This initial dissolution step is the rate limiting step and is likely responsible for the undetectable BDQ levels from the pure drug suspension.
Surfactants and co-surfactants can improve the solubility of poorly water-soluble drugs such as BDQ. The increased solubility in the nanoemulsion results in a higher concentration gradient, resulting in faster drug release. The small particle size and presence of surfactants may facilitate better drug absorption. In contrast, the pure drug suspension has a larger particle size, poor solubility, and a small surface area, resulting in minimal drug release 46.
The drug release from the BDQ-NE was delayed as drug release was only observed from 2 hours. This could have resulted from the API partitioning between the oil and water phases which influences its release rate. BDQ has greater affinity for the oil phase and, subsequently, requiring time for adequate partitioning into the aqueous phase for detectable release. There is also a possibility that within the first 2 hours the API released was undetectable. There may be an initial period when the NE distributes and equilibrates in the dissolution medium. This can cause a lag period before significant drug release occurs 47,48.
Determination of Best Fit Drug Release Model
BDQ release data from the BDQ-NEs was fitted to different kinetic models with consideration given to the time lag for drug release (tlag) and then the best fit was selected based on the calculated adjusted R2, MSE and AIC value for each model as depicted in Table 11.
Table 11
R2 values of different drug release models studied.
Release Models | R2 | Adjusted R2 | MSE | AIC |
Zero-order | 0.7916 | 0.7655 | 393.2183 | 84.5381 |
First-order | 0.9264 | 0.9172 | 138.8004 | 74.1248 |
Higuchi | 0.9126 | 0.9017 | 164.85 | 75.85 |
Korsmeyers-Peppas | 0.9098 | 0.8840 | 194.57 | 78.17 |
Weibull | 0.9919 | 0.9896 | 17.403 | 54.03 |
Hixson-Crowell | 0.9478 | 0.9413 | 98.40 | 70.68 |
Hopfenberg | 0.9877 | 0.9842 | 26.480 | 58.22 |
Baker-Lonsdale | 0.9649 | 0.9605 | 66.28 | 66.73 |
Makoid-Banakar | 0.9925 | 0.9888 | 18.83 | 55.27 |
From the data obtained, the Makoid-Banakar model had the highest R2 value of 0.9925 for the BDQ-NE followed by the Weibull model. The Weibull and Makoid-Banakar models are the best fits for the drug release dataset. They both have high R² and adjusted R² values, low MSE, and low AIC, suggesting they accurately describe the drug release kinetics with minimal complexity. However, the Weibull model has a slightly better performance overall, with the lowest AIC and MSE values, making it the best choice for this dataset. The best-fit values for all the drug release models are illustrated in Table 12.
Table 12
Best fit values for kinetic model parameters.
Model | Parameter | Data value |
Zero-order | k0 | 0.083 |
| Tlag | -84.328 |
First-order | k1 | 0.002 |
| Tlag | 51.237 |
Higuchi | kH | 3.383 |
| Tlag | 198.052 |
Korsmeyer-Peppas | kKP | 3.487 |
| N | 0.481 |
| Tlag | 112.678 |
Hixson-Crowell | KHC | 0.001 |
| Tlag | 53.580 |
Hopfenberg | kHB | 0.002 |
| N | 0.718 |
| Tlag | 40.665 |
Baker-Lonsdale | KBL | 0.000 |
| Tlag | 231.666 |
Makoid-Banakar | kMB | 0.000 |
| N | 2.536 |
| K | 0.002 |
| Tlag | -3.810 |
Weibull | α | 1336648035.667 |
| β | 3.266 |
| Ti | -142.258 |
The empirical Weibull model characterises drug release with a sigmoidal curve, with the aim of establishing a linear relationship between the logarithms of drug release and time 49. Q∞ represents the total amount of the drug released. The scale parameter T indicates the lag time before the dissolution or release process begins, which is typically zero. The scale parameter α refers to the process time, while β influences the shape of the dissolution curve. Specifically, when β = 1, the dissolution curve corresponds to an exponential profile with a consistent rate. If β > 1, the curve takes on a sigmoidal shape with a distinct turning point. Conversely, when β < 1, the curve exhibits a parabolic shape 49. The mathematical equation is shown in Eq. 5.
\(\:{\varvec{Q}}_{\varvec{t}}\mathbf{}={\varvec{Q}}_{\mathbf{\infty\:}}\mathbf{}\left(1-{\varvec{e}}^{-\left(\frac{\varvec{t}}{\varvec{\tau\:}}\right)\varvec{\beta\:}}\right)\:\) Eq. 5
At 120 minutes, detectable drug release begins with approximately 12%, and by 240 minutes, 14% of the drug had been released. This indicates the onset of the drug release process, possibly due to the activation of diffusion mechanisms. During this phase, the release rate is relatively slow, which aligns with the characteristics expected of a NE formulation designed for sustained drug release.
The Weibull value of β = 3.266 indicates a significant sigmoidal release profile, beginning slowly, then accelerating and slowing down again. There is a significant increase in release between 240 and 720 minutes. This phase is characterised by accelerated release, which signals a shift from initial barrier overcoming to a more dominant diffusion-controlled release mechanism. The accelerating release implies that the main mechanism during this phase is the diffusion process becoming more efficient as the drug concentration gradient increases. The plateau at 1440 minutes, where nearly all of the drug has been released, indicates that the release process is approaching completion, with any remaining drug being released slowly, seemingly from less accessible regions of the formulation or due to medium saturation.
The large α value indicates that the time required for significant release is long. This is typical for controlled-release formulations where the drug is designed to be released gradually 50. The mechanism of drug release from the BDQ-NE is best described as biphasic, as it effectively releases the drug in two separate phases: an initial, burst release, and a subsequent, slower release that ensures sustained drug release over a longer period of time. Through rapid achievement of the targeted drug levels and subsequent maintenance of those levels to provide prolonged treatment benefits, this dual-phase release profile improves therapeutic efficacy 51.