List of figures – Computer-Aided Applications in Pharmaceutical Technology

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, 33 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 xi of varying weights wi, and after summation applies activation function that produces its output yk94

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 Cp–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), Cmax (b), and tmax (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 (μm) 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