# List of figures

1.1. QbD approach, combining design space development and risk management tools 4

3.1. Three-level full factorial design for 3 factors, 3^{3} designs with 27 experiments 37

3.2. Experimental points for the mixture design 43

3.3. Three most commonly used mixture designs for three- component mixtures supporting linear (left), quadratic (center), and special cubic (right) models 44

3.4. Response surface plot showing effect of chitosan and sodium alginate concentration on encapsulation efficiency 54

4.1. PCA of the 4 sample 2 variables data set 61 Score and score contributions plot 79

4.2. Loading plot representing relationships among variables 80

4.3. Scores and loadings plot 82

4.4. Different arrangements of the data 84

4.5. Batch control chart 85

5.1. Schematic representation of an artificial neuron that receives inputs x_{i} of varying weights w_{i}, and after summation applies activation function that produces its output y_{k} 94

5.2. Organization of the neural network consisting of an input layer, one hidden layer, and an output layer 95

5.3. Schematic representation of the Gamma memory 106

5.4. Topology of the ENN 106

5.5. The most important steps in ANN construction and testing 108

5.6. Decision trees generated using tree induction methodology for selection among (a) lipidic/surfactant and solid dispersion formulation classes; (b) conventional and nonconventional formulation classes 129

5.7. J48 decision tree for predicting loading efficiency based on loading conditions and drug properties 131

5.8. Decision tree for tablet tensile strength 133

5.9. Decision tree of tablet disintegration time 134

5.10. Multivariate linear equations for tablet tensile strength generated by model trees 135

5.11. Multivariate linear equations for tablet disintegration time generated by model trees 135

5.12. Decision tree for medium particle size determined by dynamic light scattering method 137

5.13. Decision tree for median particle size determined by dynamic light scattering method 138

5.14. Two randomly selected parents form offspring in the next generation 146

5.15. U-matrix and SOMs of three-dimensional data set 153

5.16. Self-organizing feature maps of the formulation factors (a–c), the latent variables (d–f), and the DTZ release properties (g–i) 155

5.17. SOM feature maps of response variables (A) flux, (B) TIS, and causal factors (C) IPA, (D) /-menthol, and (E) NMP 157

5.18. SOMs developed for fluid-bed granulation process 159

5.19. Proceeding of a successful granulation in self-organized map through regions A (mixing phase), B (spraying phase), and C (drying phase) 160

5.20. Product and process properties 162

6.1. ACAT model interpretation of *in vivo* drug behavior 181

6.2. GI simulation: general modeling and simulation strategy 184

6.3. GastroPlus™ Model 1 and Model 2 predicted and *in vivo* observed mean NIM plasma profiles following administration of a single 100 mg nimesulide IR tablet (a); predicted dissolution and absorption profiles (b) 187

6.4. GastroPlus™ predicted and observed mean GLK plasma C_{p}–time profiles following administration of a single 80-mg GLK IR tablet 191

6.5. Compartmental absorption of GLK 192

6.6. Effects of dosage forms on CBZ regional absorption: (a) fasted; (b) fed 196

6.7. Parameter sensitivity analysis: dependence of the percentage of drug absorbed (a), C_{max} (b), and t_{max} (c) on different input parameters 200

6.8. Parameter sensitivity analysis: dependence of fraction CBZ absorbed on different input parameters 201

6.9. Parameter sensitivity analysis: oral bioavailability (%) as a function of reference solubility at pH 6.5 (mg/mL), and effective particle radius (*μ*m) at a dose of 160 mg R1315 203

6.10. Virtual BE study: (a) Weibull controlled release profiles; (b) fasted state; (c) fed state 206

6.11. PBPK prediction strategy for oral absorption prediction 209

6.12. (a) Virtual GLK dissolution profiles, and (b) the corresponding simulated *in vivo* profiles, along with the actual *in vivo* data 212

6.13. IVIVC plot for GLK IR tablets: (a) convolution approach; (b) deconvolution approach 213

6.14. CBZ IR (a–d) and CR tablets (e–f) dissolution profiles in various dissolution media and the corresponding simulated *in vivo* profiles 215

6.15. Comparative dissolution data for generic and reference CBZ tablets in water and 1% SLS 216

6.16. IVIVC plot for CBZ tablets in (a) water and (b) 1% SLS 217

6.17. Comparison of *in vitro* dissolution, Weibull CR profiles, and *in vivo* dissolution profiles for different dosage forms 218

6.18. Etoricoxib: (a) comparison of dissolution profiles in the USP Apparatus 2 (n = 3); (b) comparison of simulated profiles and observed *in vivo* data (60 mg tablet) using dissolution data as input function in GastroPlus 219

7.1. Illustration of finite difference grid 237

7.2. Example of: (a) triangular; (b) tetrahedral; and (c) prismatic element 238

7.3. Illustration of: (a) cell-centered; and (b) node-centered control volume 239

7.4. Illustration of: (a) structured; and (b) unstructured grid 240

7.5. Schematic representation of different grid structures: (a) full grid case; (b) grid case 1; and (c) grid case 2 242

7.6. CFD simulated particle tracks of dispersed powder: full grid case; (b) grid case 1; and (c) grid case 2 242

7.7. Turbulence kinetic energy across the center plane of a grid aperture at 140 L/min: (a) 1999 μm, and 532 μm grid aperture size 244

7.8. Carrier particle trajectory inside the inhaler at 60 L/min 245

7.9. CFD simulations of fluid flow: (a) below the paddle in the USP dissolution apparatus at 50 rpm; and (b) in the USP dissolution apparatus with a compact of 8.5 mm height situated at the base of the vessel 247

7.10. Path-lines of fluid flow tracked with time for 5 seconds from an initial plane 0.5 mm above the base of the USP paddle dissolution vessel at 25, 50, 100, and 150 rpm 248

7.11. Photograph of compact after undergoing dissolution for 1 h in: (a) position 1 and (c) position 2. Velocity vectors surrounding the compact in: (b) position 1 and (d) position 2 249

7.12. Contours of velocity magnitude around the basket at 50 rpm 250

7.13. CFD simulations of the airflow in cases of different equipment designs: (a) pre-distributor; (b) ceramic ball packing; and (c) bottom plenum air inlet 252

7.14. Schematic representation of a Wurster processor 253

7.15. Moisture content after 50 s simulation in: (a) particle phase; and (b) gas phase 254

7.16. Particle positions and velocity distributions inside: (a) Wurster-coater; and (b) top-spray granulator, at the simulation time t = 1.4 s 255

7.17. CFD simulations of the flow dynamics in fluidized bed: (a) granular temperature; (b) solid velocity magnitude; and (c) solid concentration 256