BIOPHARMACEUTICS MODELING AND SIMULATIONS -- CONTENTS -- PREFACE -- LIST OF ABBREVIATIONS -- 1 INTRODUCTION -- 1.1 An Illustrative Description of Oral Drug Absorption: The Whole Story -- 1.2 Three Regimes of Oral Drug Absorption -- 1.3 Physiology of the Stomach, Small Intestine, and Colon -- 1.4 Drug and API Form -- 1.4.1 Undissociable and Free Acid Drugs -- 1.4.2 Free Base Drugs -- 1.4.3 Salt Form Cases -- 1.5 The Concept of Mechanistic Modeling -- References -- 2 THEORETICAL FRAMEWORK I: SOLUBILITY -- 2.1 Definition of Concentration -- 2.1.1 Total Concentration -- 2.1.2 Dissolved Drug Concentration -- 2.1.3 Effective Concentration -- 2.2 Acid-Base and Bile-Micelle-Binding Equilibriums -- 2.2.1 Monoprotic Acid and Base -- 2.2.2 Multivalent Cases -- 2.2.3 Bile-Micelle Partitioning -- 2.2.4 Modified Henderson-Hasselbalch Equation -- 2.2.5 Kbm from Log Poct -- 2.3 Equilibrium Solubility -- 2.3.1 Definition of Equilibrium Solubility -- 2.3.2 pH-Solubility Profile (pH-Controlled Region) -- 2.3.3 Solubility in a Biorelevant Media with Bile Micelles (pH-Controlled Region) -- 2.3.4 Estimation of Unbound Fraction from the Solubilities with and without Bile Micelles -- 2.3.5 Common Ionic Effect -- 2.3.6 Important Conclusion from the pH-Equilibrium Solubility Profile Theory -- 2.3.7 Yalkowsky's General Solubility Equation -- 2.3.8 Solubility Increase by Converting to an Amorphous Form -- 2.3.9 Solubility Increase by Particle Size Reduction (Nanoparticles) -- 2.3.10 Cocrystal -- References -- 3 THEORETICAL FRAMEWORK II: DISSOLUTION -- 3.1 Diffusion Coefficient -- 3.1.1 Monomer -- 3.1.2 Bile Micelles -- 3.1.3 Effective Diffusion Coefficient -- 3.2 Dissolution and Particle Growth -- 3.2.1 Mass Transfer Equations: Pharmaceutical Science Versus Fluid Dynamics -- 3.2.2 Dissolution Equation with a Lump Sum Dissolution Rate Coefficient (kdiss).

3.2.3 Particle Size and Surface Area -- 3.2.3.1 Monodispersed Particles -- 3.2.3.2 Polydispersed Particles -- 3.2.4 Diffusion Layer Thickness I: Fluid Dynamic Model -- 3.2.4.1 Reynolds and Sherwood Numbers -- 3.2.4.2 Disk (Levich Equation) -- 3.2.4.3 Tube (Graetz Problem) -- 3.2.4.4 Particle Fixed to Space (Ranz-Marshall Equation) -- 3.2.4.5 Floating Particle -- 3.2.4.6 Nonspherical Particle -- 3.2.4.7 Minimum Agitation Speed for Complete Suspension -- 3.2.4.8 Other Factors -- 3.2.5 Diffusion Layer Thickness II: Empirical Models for Particles -- 3.2.6 Solid Surface pH and Solubility -- 3.3 Nucleation -- 3.3.1 General Description of Nucleation and Precipitation Process -- 3.3.2 Classical Nucleation Theory -- 3.3.2.1 Concept of Classical Nucleation Theory -- 3.3.2.2 Mathematical Expressions -- 3.3.3 Application of a Nucleation Theory for Biopharmaceutical Modeling -- References -- 4 THEORETICAL FRAMEWORK III: BIOLOGICAL MEMBRANE PERMEATION -- 4.1 Overall Scheme -- 4.2 General Permeation Equation -- 4.3 Permeation Rate Constant, Permeation Clearance, and Permeability -- 4.4 Intestinal Tube Flatness and Permeation Parameters -- 4.5 Effective Concentration for Intestinal Membrane Permeability -- 4.5.1 Effective Concentration for Unstirred Water Layer Permeation -- 4.5.2 Effective Concentration for Epithelial Membrane Permeation: the Free Fraction Theory -- 4.6 Surface Area Expansion by Plicate and Villi -- 4.7 Unstirred Water Layer Permeability -- 4.7.1 Basic Case -- 4.7.2 Particles in the UWL (Particle Drifting Effect) -- 4.8 Epithelial Membrane Permeability (Passive Processes) -- 4.8.1 Passive Transcellular Membrane Permeability: pH Partition Theory -- 4.8.2 Intrinsic Passive Transcellular Permeability -- 4.8.2.1 Solubility-Diffusion Model -- 4.8.2.2 Flip-Flop Model -- 4.8.2.3 Relationship between Ptrans,0 and log Poct 80 -- 4.8.3 Paracellular Pathway.

4.8.4 Relationship between log Doct, MW, and Fa% -- 4.9 Enteric Cell Model -- 4.9.1 Definition of Papp -- 4.9.2 Enzymatic Reaction: Michaelis-Menten Equation -- 4.9.3 First-Order Case 1: No Transporter and Metabolic Enzymes -- 4.9.4 First-Order Case 2: Efflux Transporter in Apical Membrane -- 4.9.5 Apical Efflux Transporter with Km and Vmax -- 4.9.6 Apical Influx Transporter with Km and Vmax -- 4.9.7 UWL and Transporter -- 4.9.7.1 No Transporter -- 4.9.7.2 Influx Transporter and UWL -- 4.9.7.3 Efflux Transporter -- 4.10 Gut Wall Metabolism -- 4.10.1 The Qgut Model -- 4.10.2 Simple Fg Models -- 4.10.3 Theoretical Consideration on Fg -- 4.10.3.1 Derivation of the Fg Models -- 4.10.3.2 Derivation of the Anatomical Fg Model -- 4.10.4 Interplay between CYP3A4 and P-gp -- 4.11 Hepatic Metabolism and Excretion -- References -- 5 THEORETICAL FRAMEWORK IV: GASTROINTESTINAL TRANSIT MODELS AND INTEGRATION -- 5.1 GI Transit Models -- 5.1.1 One-Compartment Model/Plug Flow Model -- 5.1.2 Plug Flow Model -- 5.1.3 Three-Compartment Model -- 5.1.4 S1I7CX (X = 1-4) Compartment Models -- 5.1.5 Convection-Dispersion Model -- 5.1.6 Tapered Tube Model -- 5.2 Time-Dependent Changes of Physiological Parameters -- 5.2.1 Gastric Emptying -- 5.2.2 Water Mass Balance -- 5.2.3 Bile Concentration -- 5.3 Integration 1: Analytical Solutions -- 5.3.1 Dissolution Under Sink Condition -- 5.3.1.1 Monodispersed Particles -- 5.3.1.2 Polydispersed Particles -- 5.3.2 Fraction of a Dose Absorbed (Fa%) -- 5.3.3 Approximate Fa% Analytical Solutions 1: Case-by-Case Solution -- 5.3.3.1 Permeability-Limited Case -- 5.3.3.2 Solubility-Permeability-Limited Case -- 5.3.3.3 Dissolution-Rate-Limited Case -- 5.3.4 Approximate Fa% Analytical Solutions 2: Semi-General Equations -- 5.3.4.1 Sequential First-Order Kinetics of Dissolution and Permeation -- 5.3.4.2 Minimum Fa% Model.

5.3.5 Approximate Fa% Analytical Solutions 3: FaSS Equation -- 5.3.5.1 Application Range -- 5.3.5.2 Derivation of Fa Number Equation -- 5.3.5.3 Refinement of the FaSS Equation -- 5.3.5.4 Advantage of FaSS Equation -- 5.3.5.5 Limitation of FaSS Equation -- 5.3.6 Interpretations of Fa Equations -- 5.3.7 Approximate Analytical Solution for Oral PK Model -- 5.4 Integration 2: Numerical Integration -- 5.4.1 Virtual Particle Bins -- 5.4.2 The Mass Balance of Dissolved Drug Amount in Each GI Position -- 5.4.3 Controlled Release of Virtual Particle Bin -- 5.5 In Vivo FA From PK Data -- 5.5.1 Absolute Bioavailability and Fa -- 5.5.2 Relative Bioavailability Between Solid and Solution Formulations -- 5.5.3 Relative Bioavailability Between Low and High Dose -- 5.5.4 Convolution and Deconvolution -- 5.5.4.1 Convolution -- 5.5.4.2 Deconvolution -- 5.6 Other Administration Routes -- 5.6.1 Skin -- References -- 6 PHYSIOLOGY OF GASTROINTESTINAL TRACT AND OTHER ADMINISTRATION SITES IN HUMANS AND ANIMALS -- 6.1 Morphology of Gastrointestinal Tract -- 6.1.1 Length and Tube Radius -- 6.1.2 Surface Area -- 6.1.2.1 Small Intestine -- 6.1.2.2 Colon -- 6.1.3 Degree of Flatness -- 6.1.3.1 Small Intestine -- 6.1.3.2 Colon -- 6.1.4 Epithelial Cells -- 6.1.4.1 Apical and Basolateral Lipid Bilayer Membranes -- 6.1.4.2 Tight Junction -- 6.1.4.3 Mucous Layer -- 6.2 Movement of the Gastrointestinal Tract -- 6.2.1 Transit Time -- 6.2.1.1 Gastric Emptying Time (GET) -- 6.2.1.2 Small Intestinal Transit Time -- 6.2.1.3 Colon Transit Time -- 6.2.2 Migrating Motor Complex -- 6.2.3 Agitation -- 6.2.3.1 Mixing Pattern -- 6.2.3.2 Agitation Strength -- 6.2.3.3 Unstirred Water Layer on the Intestinal Wall -- 6.3 Fluid Character of the Gastrointestinal Tract -- 6.3.1 Volume -- 6.3.1.1 Stomach -- 6.3.1.2 Small Intestine -- 6.3.1.3 Colon -- 6.3.2 Bulk Fluid pH and Buffer Concentration.

6.3.2.1 Stomach -- 6.3.2.2 Small Intestine -- 6.3.2.3 Colon -- 6.3.3 Microclimate pH -- 6.3.3.1 Small Intestine -- 6.3.3.2 Colon -- 6.3.4 Bile Micelles -- 6.3.4.1 Stomach -- 6.3.4.2 Small Intestine -- 6.3.4.3 Colon -- 6.3.5 Enzymes and Bacteria -- 6.3.6 Viscosity, Osmolality, and Surface Tension -- 6.4 Transporters and Drug-Metabolizing Enzymes in the Intestine -- 6.4.1 Absorptive Drug Transporters -- 6.4.1.1 PEP-T1 -- 6.4.1.2 OATP -- 6.4.2 Efflux Drug Transporters -- 6.4.2.1 P-gp -- 6.4.3 Drug-Metabolizing Enzymes -- 6.4.3.1 CYP3A4 -- 6.4.3.2 Glucuronyl Transferase and Sulfotransferase -- 6.5 Intestinal and Liver Blood Flow -- 6.5.1 Absorption Sites Connected to Portal Vein -- 6.5.2 Villous Blood Flow (Qvilli) -- 6.5.3 Hepatic Blood Flow (Qh) -- 6.6 Physiology Related to Enterohepatic Recirculation -- 6.6.1 Bile Secretion -- 6.6.2 Mass Transfer into/from the Hepatocyte -- 6.6.2.1 Sinusoidal Membrane (Blood to Hepatocyte) -- 6.6.2.2 Canalicular Membrane (Hepatocyte to Bile Duct) -- 6.7 Nasal -- 6.8 Pulmonary -- 6.8.1 Fluid in the Lung -- 6.8.2 Mucociliary Clearance -- 6.8.3 Absorption into the Circulation -- 6.9 Skin -- References -- 7 DRUG PARAMETERS -- 7.1 Dissociation Constant (pKa) -- 7.1.1 pH Titration -- 7.1.2 pH-UV Shift -- 7.1.3 Capillary Electrophoresis -- 7.1.4 pH-Solubility Profile -- 7.1.5 Calculation from Chemical Structure -- 7.1.6 Recommendation -- 7.2 Octanol-Water Partition Coefficient -- 7.2.1 Shake Flask Method -- 7.2.2 HPLC Method -- 7.2.3 Two-Phase Titration Method -- 7.2.4 PAMPA-Based Method -- 7.2.5 In Silico Method -- 7.2.6 Recommendation -- 7.3 Bile Micelle Partition Coefficient (Kbm) -- 7.3.1 Calculation from Solubility in Biorelevant Media -- 7.3.2 Spectroscopic Method -- 7.3.3 Recommendations -- 7.4 Particle Size and Shape -- 7.4.1 Microscope -- 7.4.2 Laser Diffraction -- 7.4.3 Dynamic Laser Scattering (DLS).

7.4.4 Recommendations.