# Optimization of Spray Drying Process Parameters for the Preparation of Inhalable Mannitol-Based Microparticles Using a Box-Behnken Experimental Design

^{*}

^{†}

## Abstract

**:**

^{3}can avoid protective lung mechanisms. Their suitable aerodynamic properties make them perspective formulations for deep lung deposition. This experiment studied the effect of spray-drying process parameters on LPP properties. An experimental design of twelve experiments with a central point was realized using the Box–Behnken method. Three process parameters (drying temperature, pump speed, and air speed) were combined on three levels. Particles were formed from a D-mannitol solution, representing a perspective material for lung microparticles. The microparticles were characterized in terms of physical size (laser diffraction), aerodynamic diameter (aerodynamic particle sizer), morphology (SEM), and densities. The novelty and main goal of this research were to describe how the complex parameters of the spray-drying process affect the properties of mannitol LPPs. New findings can provide valuable data to other researchers, leading to the easy tuning of the properties of spray-dried particles by changing the process setup.

## 1. Introduction

^{3}), and thus it is possible to reach desired aerodynamic parameters with a physical size greater than 10 μm [12]. That improves the flowing properties and aerosolization of the powder from the device and protects the inhaled particles from macrophage clearance [15]. One approved product containing LPPs is tobramycin inhalation powder, represented by spherical sponge-like particles manufactured by PulmoSpheres

^{TM}technology—spray drying of an o/w emulsion [16].

_{2}and feed dispersion is sprayed into the heated drying chamber. The CO

_{2}expands from the droplets and creates secondary smaller droplets. This process is ecological and suitable for (thermo)sensitive materials such as proteins [26]. For example, Du et al. incorporated lysozyme into particles of suitable size with no impact on its secondary structure [27].

^{TM}) and therapeutic (Bronchitol

^{TM}) purposes as a dry powder inhaler [10].

## 2. Materials and Methods

#### 2.1. Spray Drying Process

#### 2.2. Particle Size and Aerodynamic Diameter

#### 2.3. Bulk and Tapped Density, Hausner Ratio

^{®}model SVM102 (DE). The volumes of samples were reported after 10, 500, 1250, and 2500 taps. The Hausner ratio was calculated using tapped (after 2500 taps) and bulk density values [41].

#### 2.4. Particle Morphology

#### 2.5. Experimental Design

_{1}; in the range of 100–140 °C), pump speed (X

_{2}; in the range of 5–15 mL/min), air speed (X

_{3}; in the range of 3.0–4.2 m/s) were selected as studied input variables. Each factor was divided into three levels coded as low (−1), medium (0), and high (+1), as listed in Table 1, which were chosen based on previous experiments with the production of LPPs used in experiments on an artificial lung model to simulate particle deposition during different breath cycles [42].

_{1}, μm), MMAD (Y

_{2}, μm), NMAD (Y

_{3}, μm), relative standard deviation (RSD) of MMAD (Y

_{4}, %), particle morphology characterized by SEM (Y

_{5}; in the coded scale 1–3; higher grade is better), and flow properties (bulk density, tapped density, and Hausner ratio).

#### 2.6. Data Analysis

- Data checking; descriptive statistics; basic data visualization (histograms, box plots).
- Choosing a suitable mathematical model for the obtained data.
- Testing the assumptions required for ANOVA and regression analysis (MLR), primarily using visual assessment of graphical outputs (histograms, residual graphs); eventually, exclusion of the outliers from the analysis and subsequent building of a new model.
- Simplification of the model by gradual backward elimination of insignificant terms (assessment of their p-values in ANOVA table) while monitoring and comparing values of coefficient of determination R
^{2}, adjusted R^{2}, Akaike information criterion, and p-value of the original and simplified model to achieve the best quality of the model fit. Percentage prediction error (PPE) was assessed to ensure the validity of the generated regression equation. PPE for each experimental run was calculated as: (observed value—predicted value)/predicted value × 100 (%). - Visualization of MLR results: RSM via 3D perspective plots.
- Interpretation of obtained regression equation and graphical outputs: investigation of the effects of independent factors (process conditions) and their possible interactions on the response (quality attributes of microparticles) and the determination of optimal process conditions for the desired response.

_{1}, X

_{2}, and X

_{3}are independent variables; b

_{0}is an intercept/constant; b

_{1}, b

_{2}, and b

_{3}are regression coefficients for linear terms; b

_{12}, b

_{13}, and b

_{23}are regression coefficients for interaction/cross product terms; b

_{11}, b

_{22}and b

_{33}are regression coefficients for quadratic terms. Standardized regression coefficients (β) were also determined to compare the influence of individual terms on the response.

## 3. Results and Discussion

_{1}; S, μm) and mass median aerodynamic diameter (Y

_{2}; MMAD, μm) as the most pronounced parameters in the research. Numerical median aerodynamic diameter (Y

_{3}; NMAD, μm) provides important information about the numerical distribution of particles. Y

_{4}represents the RSD of MMAD. Finally, scanning electron microscopy was performed as an important indicator of surface and morphological properties (Y

_{5}; SEM, values: G—good, A—acceptable, B—bad). Other measured values are bulk density (g/cm

^{3}), tapped density (g/cm

^{3}), and Hausner ratio.

^{2}, adjusted R

^{2}, p-value), are summarized in Table 3. The mean values of each response variable for each experimental run, as well as the values predicted by MLR models (from Table 3) and errors of prediction, are reported in Table 4. This evaluation is presented for quantities for which a significant influence of the process parameters on the final value was revealed using statistical testing. The raw data, with indicated outliers excluded from the subsequent analysis, are presented in Table S1.

#### 3.1. Laser Diffraction Median Size—S (Y_{1})

^{2}value of 0.813 means that the model can clarify 81.3% of the variability, and the associated p-value of less than 0.001 indicates the model is highly significant (Table 3). PPE for most runs is in the range of several units up to tens of percent, except for run 11—in this DoE region, the predictive ability of the model sharply decreases (extremely high PPE value, 748.9%). The mean PPE value is relatively high (67.6%). If run 11 is not considered, the mean PPE value is 18.9%, which is acceptable. Based on the mentioned characteristics, the model fitting can be considered satisfactory for response determination, especially in identifying independent variables’ effects on the S value. Based on the standardized regression coefficient values (Table 3, β values), drying temperature and air speed (linear and quadratic terms in both cases) have the most considerable effect on the response. Pump speed and interactions between variables also contribute to the model (Figure 1).

_{1}) or pump speed (X

_{2}), as well as when combining the high values of these variables.

_{1}and X

_{2}seems to be the most appropriate for achieving particles of around 10 μm. The saddle shape of the response surface in Figure 1B,C suggests a more complex dependency, where low or conversely high air speed (X

_{3}) in combination with low drying temperature (X

_{1}) or low pump speed (X

_{2}) appears to be the experimental settings leading to the S less than 10 μm. The experimental region around the center point results in a response slightly above 10 μm and thus represents the optimal conditions for preparing LPPs suitable for lung deposition.

_{1}: 0, X

_{2}: 0, X

_{3}: 0), 7 (S: 11.08 ± 3.65 μm, X

_{1}: −1, X

_{2}: 0, X

_{3}: +1), 9 (S: 12.75 ± 4.03 μm, X

_{1}: 0, X

_{2}: −1, X

_{3}: −1), and 12 (S: 11.08 ± 4.10 μm, X

_{1}: 0, X

_{2}: +1, X

_{3}: +1) [12].

#### 3.2. Mass Median Aerodynamic Diameter—MMAD (Y_{2})

^{2}value, which is found to be 0.810, suggests that the model can explain 81.0% of the total variability. The detected p-value of less than 0.001 implies that the regression equation is significant (Table 3). The low mean PPE (1.9%) indicates the high predictive ability of the MLR model. Considering these facts, it can be concluded that the resulting model is adequate for MMAD response prediction under various experimental conditions within the range of the analyzed BBD. It can be seen from Table 3 that the importance of the effect of individual process parameters on MMAD decreases in the following order: drying temperature > air speed > pump speed (applies to both linear and quadratic terms of the mentioned variables).

_{1}) and air speed (X

_{3}) decreased and pump speed (X

_{2}) increased, while under other conditions within the experimental design it reached values up to 8.2–8.4 μm. Especially high X

_{1}values (Figure 2A,B) and a combination of X

_{2}low level and X

_{3}high level (Figure 2C) resulted in a quite high MMAD value. On the other hand, the center point and the region around (0, 0, 0) correspond to the appropriate process conditions leading to the small particles.

_{1}: 0, X

_{2}: 0, X

_{3}: 0), 3 (MMAD: 7.07 ± 2.71 μm, X

_{1}: −1, X

_{2}: +1, X

_{3}: 0), 9 (MMAD: 7.19 ± 6.68 μm, X

_{1}: 0, X

_{2}: −1, X

_{3}: −1), and 5 (MMAD: 7.20 ± 2.62 μm, X

_{1}: −1, X

_{2}: 0, X

_{3}: −1) (Table 2). Values were achieved at medium and low process parameter values for air speed and drying temperature, while pump speed was at a middle and high level, except in run 9, where the pump speed was at level −1.

#### 3.3. Numeric Median Aerodynamic Diameter—NMAD (Y_{3})

^{2}value, p-value, and PPE. The coefficient of determination (0.679) does not indicate a very strong goodness of fit. In contrast, the mean value of PPE is low enough (4.2%), which, on the contrary, indicates a good prediction ability (Table 3). The overall model p-value of less than 0.001 demonstrates that the regression equation is significant. Therefore, the resulting model can still be used to determine the dependencies occurring in the data matrix. Based on the regression coefficient values listed in Table 3, it can be deduced that the quadratic term of the pump speed represents the greatest influence on the NMAD. The interaction terms and linear terms of drying temperature and air speed have a lower effect on the response, but they are still significant.

_{1}) at any value of pump speed (X

_{2}). Still, this effect is most pronounced at X

_{2}medium level. A similar dependence can be observed in Figure 3C, where there was a descending response with the increment in air speed (X

_{3}) at various X

_{2}. Still, again, the steepest descent manifested at X

_{2}medium level. As shown in Figure 3B, a visual analysis of the depicted response surface plot indicates that the NMAD decreases as the X

_{1}and X

_{3}increase. For all response surfaces, the NMAD values decreased to approximately 3 μm while the upper parts of the response surface were close to 4 μm. Although the dependences determined by MLR, in this case, differ from the response surfaces for the variable Y

_{2}(compare Figure 2 and Figure 3), the center point and the region around (0, 0, 0) can again be evaluated as a suitable combination of process parameters resulting in an optimal response.

#### 3.4. Relative Standard Deviation of Mass Median Aerodynamic Diameter—MMAD RSD (Y_{4})

^{2}value of 0.775 implies that 77.5% of the variability can be interpreted by the model, which is acceptable. The statistical significance of the model was confirmed by the p-value (p < 0.001) (Table 3). Predicted errors of all runs within 5% (the mean value of 2.2%) demonstrate the excellent fit of the MLR model. All the results mentioned above clearly show that the quality of the model is satisfactory and reliable, especially for examining data dependencies in the DoE region. As presented in Table 3, the linear and quadratic coefficients of drying temperature were the terms that most affected the response. Other quadratic terms and interactions between pump speed and air speed contribute less to the model but are still statistically significant, as can also be inferred from Figure 4.

_{1}) at any pump speed (X

_{2}) or any air speed (X

_{3}), a decrease in MMAD RSD to values approaching 30% can be observed. From Figure 4C, an interaction between X

_{2}and X

_{3}can be deduced. High values of MMAD RSD are achieved, especially at high levels of both independent variables. A decrease in MMAD RSD can be obtained with a combination of experimental conditions: high X

_{2}at the low level of X

_{3}or, conversely, low X

_{2}at the high level of X

_{3}. Therefore, the region around the central point (0, 0, 0) appears less suitable for particle size variability.

#### 3.5. Particle Morphology Characterized by SEM (Y_{5})

^{2}value, p-value, and PPE. The value of the determination coefficient (0.866) shows that the model fitting is relatively good. The mean PPE (13.7%) indicates acceptable magnitudes of differences between experimental and calculated data (Table 3). The results may also be affected by the relatively low number of experimental values (absence of repeated measurements for each run), given the nature of the discussed microparticles’ properties. The model p-value of 0.012 proves the statistical significance of the identified dependencies. Therefore, the found equation can be used to display the regression equation and to explain these relationships. From Table 3, it can be seen that the air speed has a considerable influence on the response. The lower magnitude of other terms indicates their lower effects; however, some are still statistically significant.

_{2}) and air speed (X

_{3}), irrespective of the drying temperature (X

_{1}), as can be seen in Figure 5A,B. From Figure 5C, it can be interpreted that the combination of medium-to-high levels of X

_{2}and X

_{3}leads to the maximum particle morphology grade, shown in the plot as a peak value of 3. Thus, it can be concluded that the experimental conditions corresponding to the region around the center point (0, 0, 0) result in the microparticles with the best particle morphology.

_{1}: −1, X

_{2}: 0, X

_{3}: +1), 9 (X

_{1}:0, X

_{2}: −1, X

_{3}: −1), 12 (X

_{1}: 0, X

_{2}: +1, X

_{3}: 01), 13 a, b, c (X

_{1}: 0, X

_{2}: 0, X

_{3}: 0) have process parameters set to provide particle sizes S (parameter Y

_{1}, μm) in the range 11.08 ± 3.65 μm–13.34 ± 4.26 μm, which is the closest to ten targeted micrometers. Particle morphology provided by SEM pointed out spherical, polydisperse particles with minimal damage. These particles are marked as good (G) except for sample 9. In Figure 6, sample 9 (X

_{1}: 0, X

_{2}: −1, X

_{3}: −1) spherical particles with a larger size distribution, locally wrinkled with few holes present, and very few fragments can be seen. Similar observations were observed in samples 2 (X

_{1}: +1, X

_{2}: −1, X

_{3}: 0), 4 (X

_{1}: +1, X

_{2}: +1, X

_{3}: 0), and 8 (X

_{1}: +1, X

_{2}: 0, X

_{3}: +1). These particles are marked as acceptable—A. Spherical polydisperse particles, with a small presence of holes, with suitable shapes were observed in samples 1 (X

_{1}: −1, X

_{2}: −1, X

_{3}: 0), 3 (X

_{1}: −1, X

_{2}: +1, X

_{3}: 0), 6 (X

_{1}: +1, X

_{2}: 0, X

_{3}: −1), 7 (X

_{1}: −1, X

_{2}: 0, X

_{3}: +1),12 (X

_{1}: 0, X

_{2}: −1, X

_{3}: +1), and 13 a, b, c (X

_{1}: 0, X

_{2}: 0, X

_{3}: 0), these samples are classified as good (G). In samples 5, 10, and 11, particles with an irregular shape, a high proportion of damage, wide size distribution, a high fragment content, and a tendency to agglomerate can be observed. These are marked as bad (B).

^{3}, which fulfills the requirement for LPPs according to current knowledge (Table 2). Bulk density values ranged between 0.25 and 0.31 g/cm

^{3}and tapped densities were between 0.34 and 0.41 g/cm

^{3}. These small differences are not considered statistically significant. The Hausner ratio values as the parameter of powder flow (important for processing powders into capsules for DPI filling) ranged from 1.25 to 1.47, which corresponds to acceptable to bad flow behavior [1,41,49].

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Three-dimensional (3D) perspective plots: response surface of S (Y

_{1}, μm) as a function of drying temperature (X

_{1}, °C), pump speed (X

_{2}, mL/min), and air speed (X

_{3}, m/s).

**Figure 2.**Three-dimensional (3D) perspective plots: response surface of MMAD (Y

_{2}, μm) as a function of drying temperature (X

_{1}, °C), pump speed (X

_{2}, mL/min), and air speed (X

_{3}, m/s).

**Figure 3.**Three-dimensional (3D) perspective plots: response surface of NMAD (Y

_{3}, μm) as a function of drying temperature (X

_{1}, °C), pump speed (X

_{2}, ml/min), and air speed (X

_{3}, m/s).

**Figure 4.**Three-dimensional (3D) perspective plots: response surface of MMAD RSD (Y

_{4}, %) as a function of drying temperature (X

_{1}, °C), pump speed (X

_{2}, ml/min), and air speed (X

_{3}, m/s).

**Figure 5.**Three-dimensional (3D) perspective plots: response surface of particle morphology (Y

_{5}, the scale 1–3, the higher grade is better) as a function of drying temperature (X

_{1}, °C), pump speed (X

_{2}, mL/min), and air speed (X

_{3}, m/s).

**Figure 6.**SEM images of samples divided into 3 categories: G—good; A—acceptable; B—bad (magnification 5k×).

Input Variable (Process Parameter) | Unit | Code Level | ||
---|---|---|---|---|

Low (−1) | Medium (0) | Hight (+1) | ||

Drying temperature (X_{1}) | °C | 100 | 120 | 140 |

Pump speed (X_{2}) | mL/min | 5 | 10 | 15 |

Air speed (X_{3}) | m/s | 3.0 | 3.6 | 4.2 |

Run | Drying Temperature (X_{1}) | Pump Speed (X_{2}) | Air Speed (X_{3}) | S (Y _{1}) | MMAD (Y_{2}) | NMAD (Y_{3}) | MMAD RSD (Y_{4}) | SEM (Y _{5}) | Bulk Density | Tapped Density | Hausner Ratio |
---|---|---|---|---|---|---|---|---|---|---|---|

[°C] | [mL/min] | [m/s] | [μm] | [μm] | [μm] | [%] | [Grade] | [g/cm^{3}] | [g/cm^{3}] | ||

1 | 100 | 5 | 3.6 | 9.13 ± 3.40 | 7.67 ± 2.69 | 3.60 ± 3.24 | 35.2 | G | 0.31 | 0.39 | 1.28 |

2 | 140 | 5 | 3.6 | 26.33 ± 3.98 | 8.28 ± 2.67 | 3.65 ± 3.60 | 32.3 | A | 0.29 | 0.38 | 1.32 |

3 | 100 | 15 | 3.6 | 39.39 ± 4.81 | 7.07 ± 2.71 | 3.48 ± 3.19 | 38.4 | G | 0.25 | 0.34 | 1.39 |

4 | 140 | 15 | 3.6 | 35.80 ± 5.32 | 8.27 ± 2.68 | 3.22 ± 4.51 | 32.4 | A | 0.29 | 0.37 | 1.28 |

5 | 100 | 10 | 3.0 | 5.60 ± 3.45 | 7.20 ± 2.62 | 3.70 ± 3.59 | 36.4 | B | 0.30 | 0.41 | 1.37 |

6 | 140 | 10 | 3.0 | 32.07 ± 5.10 | 8.42 ± 2.89 | 2.68 ± 4.93 | 30.0 | G | 0.28 | 0.35 | 1.25 |

7 | 100 | 10 | 4.2 | 11.08 ± 3.65 | 7.34 ± 2.66 | 3.20 ± 1.14 | 36.3 | G | 0.27 | 0.39 | 1.43 |

8 | 140 | 10 | 4.2 | 18.34 ± 3.88 | 8.33 ± 2.87 | 3.02 ± 3.70 | 34.8 | A | 0.27 | 0.40 | 1.47 |

9 | 120 | 5 | 3.0 | 12.75 ± 4.03 | 7.19 ± 2.68 | 3.47 ± 3.43 | 37.2 | A | 0.25 | 0.35 | 1.39 |

10 | 120 | 15 | 3.0 | 8.22 ± 3.23 | 7.33 ± 2.58 | 4.14 ± 2.78 | 35.2 | B | 0.26 | 0.38 | 1.46 |

11 | 120 | 5 | 4.2 | 7.80 ± 3.97 | 8.68 ± 2.63 | 3.34 ± 4.99 | 30.3 | B | 0.26 | 0.35 | 1.32 |

12 | 120 | 15 | 4.2 | 11.08 ± 4.10 | 7.59 ± 4.25 | 2.98 ± 4.35 | 42.5 | G | 0.27 | 0.37 | 1.39 |

13a | 120 | 10 | 3.6 | 15.54 ± 4.74 | 7.14 ± 2.73 | 3.03 ± 4.24 | 38.5 | G | 0.26 | 0.36 | 1.39 |

13b | 120 | 10 | 3.6 | 12.40 ± 3.97 | 6.99 ± 2.74 | 2.97 ± 4.26 | 38.8 | G | 0.28 | 0.39 | 1.42 |

13c | 120 | 10 | 3.6 | 12.09 ± 4.08 | 6.93 ± 2.79 | 3.18 ± 3.29 | 40.2 | G | 0.27 | 0.37 | 1.40 |

**Table 3.**MLR models for selected variables: estimated regression coefficients (b) with p-values, standardized regression coefficients (β) and the basic model characteristics.

Regression Coefficient (Constant)/Model Parameter | ${Y}_{1}$ | ${Y}_{2}$ | ${Y}_{3}$ | ${Y}_{4}$ | ${Y}_{5}$ | |||||
---|---|---|---|---|---|---|---|---|---|---|

Coefficient | p-Value | Coefficient | p-Value | Coefficient | p-Value | Coefficient | p-Value | Coefficient | p-Value | |

${\mathrm{b}}_{0}$ ${\mathsf{\beta}}_{0}$ | −93.3966 0.0178 | 0.361 (ns) | 30.9155 −0.0015 | <0.001 *** | 11.3003 0.0000 | <0.001 *** | −64.8662 0.0246 | 0.144 (ns) | −45.0000 0.0000 | 0.005 ** |

${\mathrm{b}}_{1}\left({\mathrm{X}}_{1}\right)\phantom{\rule{0ex}{0ex}}{\mathsf{\beta}}_{1}\left({\mathrm{X}}_{1}\right)$ | −4.2188 −8.6415 | <0.001 *** | −0.2635 −6.2616 | <0.001 *** | −0.0725 −0.3614 | 0.001 ** | 1.6284 7.6038 | <0.001 *** | 0.2188 −0.1157 | 0.011 * |

${\mathrm{b}}_{2}\left({\mathrm{X}}_{2}\right)\phantom{\rule{0ex}{0ex}}{\mathsf{\beta}}_{2}\left({\mathrm{X}}_{2}\right)$ | 1.3080 −0.6524 | 0.653 (ns) | −0.1182 −1.8881 | 0.491 (ns) | 0.0149 −2.7110 | 0.885 (ns) | −1.8425 1.5110 | 0.118 (ns) | −0.4750 1.9670 | 0.169 (ns) |

${\mathrm{b}}_{3}\left({\mathrm{X}}_{3}\right)\phantom{\rule{0ex}{0ex}}{\mathsf{\beta}}_{3}\left({\mathrm{X}}_{3}\right)$ | 185.4160 6.2569 | <0.001 *** | −5.3053 −4.8503 | 0.023 * | −1.5371 −0.3748 | 0.043 * | 10.3711 3.8965 | 0.485 (ns) | 20.4167 8.5640 | 0.004 ** |

${\mathrm{b}}_{11}\left({\mathrm{X}}_{1}^{2}\right)\phantom{\rule{0ex}{0ex}}{\mathsf{\beta}}_{11}\left({\mathrm{X}}_{1}^{2}\right)$ | 0.0271 9.1212 | <0.001 *** | 0.0012 6.8800 | <0.001 *** | – | (ns) | −0.0083 −8.0185 | <0.001 *** | – | (ns) |

${\mathrm{b}}_{22}\left({\mathrm{X}}_{2}^{2}\right)\phantom{\rule{0ex}{0ex}}{\mathsf{\beta}}_{22}\left({\mathrm{X}}_{2}^{2}\right)$ | 0.1386 0.9664 | 0.038 * | 0.0134 1.6753 | 0.002 ** | 0.0145 2.7490 | <0.001 *** | −0.0566 −1.1837 | 0.037 * | −0.0200 −1.8780 | 0.057 (ns) |

${\mathrm{b}}_{33}\left({\mathrm{X}}_{3}^{2}\right)\phantom{\rule{0ex}{0ex}}{\mathsf{\beta}}_{33}\left({\mathrm{X}}_{3}^{2}\right)$ | −20.6202 −6.3651 | <0.001 *** | 0.9863 5.1313 | <0.001 *** | – | (ns) | −4.4550 −3.8149 | 0.019 * | −2.0833 −8.3460 | 0.011 * |

${\mathrm{b}}_{12}({\mathrm{X}}_{1}{\mathrm{X}}_{2})\phantom{\rule{0ex}{0ex}}{\mathsf{\beta}}_{12}({\mathrm{X}}_{1}{\mathrm{X}}_{2})$ | −0.0520 −0.2600 | 0.004 ** | 0.0015 0.1380 | 0.101 (ns) | – | (ns) | −0.0077 −0.1199 | 0.192 (ns) | – | (ns) |

${\mathrm{b}}_{23}({\mathrm{X}}_{2}{\mathrm{X}}_{3})\phantom{\rule{0ex}{0ex}}{\mathsf{\beta}}_{23}({\mathrm{X}}_{2}{\mathrm{X}}_{3})$ | 0.8419 0.1291 | 0.115 (ns) | −0.1025 −0.2833 | 0.002 ** | −0.0856 −0.3589 | <0.001 *** | 1.1762 0.5370 | <0.001 *** | 0.2500 0.5249 | 0.009 ** |

${\mathrm{b}}_{13}\left({\mathrm{X}}_{1}{\mathrm{X}}_{3}\right)\phantom{\rule{0ex}{0ex}}{\mathsf{\beta}}_{13}\left({\mathrm{X}}_{1}{\mathrm{X}}_{3}\right)$ | −0.4000 −0.2513 | 0.003 ** | −0.0032 −0.0346 | 0.684 (ns) | 0.0174 0.2926 | 0.005 ** | 0.0905 0.1613 | 0.099 (ns) | −0.0625 −0.5249 | 0.009 ** |

${\mathrm{R}}^{2}$ | 0.813 | 0.810 | 0.679 | 0.775 | 0.866 | |||||

$\mathrm{adjusted}{R}^{2}$ | 0.761 | 0.756 | 0.625 | 0.708 | 0.732 | |||||

p-value | <0.001 *** | <0.001 *** | <0.001 *** | <0.001 *** | 0.012 * |

**Table 4.**Box–Behnken experimental design, observed (O) * and predicted (P) responses for each experimental run, along with their percentage prediction errors (PPE).

Run | Pattern of Coded Factors (X _{1}, X_{2}, X_{3}) | Y_{1} | Y_{2} | Y_{3} | Y_{4} | Y_{5} | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

O (μm) | P (μm) | PPE (%) | O (μm) | P (μm) | PPE (%) | O (μm) | P (μm) | PPE (%) | O (%) | P (%) | PPE (%) | O (Grade) | P (Grade) | PPE (%) | ||

1 | −1, −1, 0 | 9.1 | 11.4 | −20.3 | 7.67 | 7.65 | 0.2 | 3.60 | 3.69 | −2.3 | 35.2 | 34.2 | 2.7 | 3.0 | 2.5 | 20.0 |

2 | +1, −1, 0 | 26.3 | 35.2 | −25.1 | 8.28 | 8.38 | −1.2 | 3.65 | 3.30 | 10.8 | 32.3 | 31.5 | 2.3 | 2.0 | 2.3 | −11.1 |

3 | −1, +1, 0 | 39.4 | 30.6 | 28.9 | 7.07 | 6.96 | 1.5 | 3.48 | 3.65 | −4.6 | 38.4 | 39.1 | −1.9 | 3.0 | 2.8 | 9.1 |

4 | +1, +1, 0 | 35.8 | 33.5 | 6.9 | 8.27 | 8.29 | −0.2 | 3.22 | 3.26 | −1.2 | 32.4 | 33.4 | −2.8 | 2.0 | 2.5 | −20.0 |

5 | −1, 0, −1 | 5.6 | 6.9 | −18.8 | 7.20 | 7.06 | 2.0 | 3.70 | 3.70 | 0.1 | 36.4 | 37.0 | −1.6 | 1.0 | 2.6 | −61.9 |

6 | +1, 0, −1 | 32.1 | 29.8 | 7.6 | 8.42 | 8.16 | 3.2 | 2.68 | 2.89 | −7.2 | 30.0 | 30.6 | −1.9 | 3.0 | 2.6 | 14.3 |

7 | −1, 0, +1 | 11.1 | 13.3 | −17.0 | 7.34 | 7.60 | −3.5 | 3.20 | 2.92 | 9.8 | 36.3 | 35.9 | 1.1 | 3.0 | 3.4 | −11.1 |

8 | +1, 0, +1 | 18.3 | 17.0 | 7.6 | 8.33 | 8.55 | −2.5 | 3.02 | 2.94 | 2.5 | 34.8 | 33.9 | 2.6 | 2.0 | 1.6 | 23.1 |

9 | 0, −1, −1 | 12.7 | 9.1 | 39.6 | 7.19 | 7.35 | −2.2 | 3.47 | 3.42 | 1.5 | 37.2 | 37.6 | −0.9 | 2.0 | 2.1 | −5.9 |

10 | 0, +1, −1 | 8.2 | 12.8 | −35.8 | 7.33 | 7.58 | −3.2 | 4.14 | 3.90 | 6.3 | 35.2 | 33.9 | 3.9 | 1.0 | 0.9 | 14.3 |

11 | 0, −1, +1 | 7.8 | 0.9 | 748.9 | 8.68 | 8.43 | 2.9 | 3.34 | 3.57 | −6.5 | 30.3 | 31.6 | −4.2 | 1.0 | 1.1 | −11.1 |

12 | 0, +1, +1 | 11.1 | 14.7 | −24.6 | 7.59 | 7.43 | 2.2 | 2.98 | 3.02 | −1.2 | 42.5 | 42.0 | 1.2 | 3.0 | 2.9 | 4.3 |

13a | 0, 0, 0 | 15.5 | 13.3 | 16.5 | 7.14 | 7.01 | 1.9 | 3.03 | 3.11 | −2.5 | 38.5 | 39.3 | −2.1 | 3.0 | 3.0 | 0.0 |

13b | 0, 0, 0 | 12.4 | 13.3 | −7.1 | 6.99 | 7.01 | −0.3 | 2.97 | 3.11 | −4.6 | 38.7 | 39.3 | −1.4 | 3.0 | 3.0 | 0.0 |

13c | 0, 0, 0 | 12.1 | 13.3 | −9.4 | 6.93 | 7.01 | −1.1 | 3.18 | 3.11 | 2.2 | 40.2 | 39.3 | 2.3 | 3.0 | 3.0 | 0.0 |

Goal | >10 μm; Minimize | Minimize | Minimize | Minimize | Maximize |

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## Share and Cite

**MDPI and ACS Style**

Karas, J.; Pavloková, S.; Hořavová, H.; Gajdziok, J.
Optimization of Spray Drying Process Parameters for the Preparation of Inhalable Mannitol-Based Microparticles Using a Box-Behnken Experimental Design. *Pharmaceutics* **2023**, *15*, 496.
https://doi.org/10.3390/pharmaceutics15020496

**AMA Style**

Karas J, Pavloková S, Hořavová H, Gajdziok J.
Optimization of Spray Drying Process Parameters for the Preparation of Inhalable Mannitol-Based Microparticles Using a Box-Behnken Experimental Design. *Pharmaceutics*. 2023; 15(2):496.
https://doi.org/10.3390/pharmaceutics15020496

**Chicago/Turabian Style**

Karas, Jakub, Sylvie Pavloková, Hana Hořavová, and Jan Gajdziok.
2023. "Optimization of Spray Drying Process Parameters for the Preparation of Inhalable Mannitol-Based Microparticles Using a Box-Behnken Experimental Design" *Pharmaceutics* 15, no. 2: 496.
https://doi.org/10.3390/pharmaceutics15020496