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Explore the cutting-edge of dissolution testing in an authoritative, one-stop resource In Pharmaceutical Dissolution Testing, Bioavailability, and Bioequivalence: Science, Applications, and Beyond, distinguished pharmaceutical advisor and consultant Dr. Umesh Banakar delivers a comprehensive and up-to-date reference covering the established and emerging roles of dissolution testing in pharmaceutical drug development. After discussing the fundamentals of the subject, the included resources go on to explore common testing practices and methods, along with their associated challenges and issues, in the drug development life cycle. Over 19 chapters and 1100 references allow practicing scientists to fully understand the role of dissolution, apart from mere quality control. Readers will discover a wide range of topics, including automation, generic and biosimilar drug development, patents, and clinical safety. This volume offers a one-stop resource for information otherwise scattered amongst several different regulatory regimes. It also includes: * A thorough introduction to the fundamentals and essential applications of pharmaceutical dissolution testing * Comprehensive explorations of the foundations and drug development applications of bioavailability and bioequivalence * Practical discussions about solubility, dissolution, permeability, and classification systems in drug development * In-depth examinations of the mechanics of dissolution, including mathematical models and simulations * An elaborate assessment of biophysiologically relevant dissolution testing and IVIVCs, and their unique applications * A complete understanding of the methods, requirements, and global regulatory expectations pertaining to dissolution testing of generic drug products Ideal for drug product development and formulation scientists, quality control and assurance professionals, and regulators, Pharmaceutical Dissolution Testing, Bioavailability, and Bioequivalence is also the perfect resource for intellectual property assessors.
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Cover
Title Page
Copyright
Dedication
Foreword
Foreword
Preface
Acknowledgments
Reference
1 Pharmaceutical Dissolution Testing:
Fundamentals and Essential Applications (An Overview)
1.1 Introduction and Objective(s)
1.2 Science of Dissolution Over Past 120+ Years
1.3 Fundamentals of Dissolution Testing (An Overview)
1.4 Factors Influencing Dissolution Test(ing)
1.5 Pharmaceutical Product Life Cycle:
Role of Dissolution (An Overview)
1.6 Dissolution Test(ing):
What It Is and What It Is Not!
1.7 Need for This Textbook
1.8 Summary and Concluding Remarks
References
2 Bioavailability (BA) and Bioequivalence (BE):
Fundamentals and Applications in Drug Product Development
2.1 Introduction and Objective(s)
2.2 Definitions
2.3 Bioequivalence (BE) Testing:
Basics, Advances, and Global Perspectives
2.4 Current Challenges and Solutions (
Insight into Chapter 14
)
2.5 Summary and Concluding Remarks
References
3 Solubility, Dissolution, Permeability, and Classification Systems
3.1 Introduction and Objective(s)
3.2 Definitions
3.3 Solubility Versus Solubilization:
What Is Critical in Development?
3.4 Dissolution: Intrinsic Versus Apparent!
3.5 Permeability Versus Permeation (Process): What Is Critical for Bioefficacy!
3.6 Classification Systems: Theoretical Versus Pragmatic Considerations!
3.7 Summary and Concluding Remarks
References
4 Understanding the Mechanics of Dissolution:
Mathematical Models and Simulations
4.1 Introduction and Objective(s)
4.2 Mechanics of Dissolution:
Theories, Presumptions, and Reality Check
4.3 Dissolution Theories/Models
4.4 Dissolution Mechanics (Model-Dependent Methods)
4.5 Dissolution Mechanics (Model-Independent Methods)
4.6 Relevance of Mathematical Modeling of Dissolution
4.7 Purposeful Modeling and Simulation
4.8 Summary and Concluding Remarks
References
5 Dissolution Testing Methods:
Necessity Is the Mother of Invention!
5.1 Introduction and Objective(s)
5.2 Need for Dissolution Testing Method
5.3 Dissolution Testing Methods
5.4 Necessity Is the Mother of Invention!
5.5 The Perpetual Struggle
5.6 Concluding Remarks
References
6 Essentials of Dissolution Testing of Pharmaceutical Systems
6.1 Introduction and Objective(s)
6.2 Objectives of Dissolution Testing of Pharmaceutical Systems
6.3 Oral Solid Dosage Forms (SDFs)
6.4 Oral Liquid Dosage Forms
6.5 Non-oral Dosage Forms
6.6 Nanotechnology-Based Pharmaceutical Systems
6.7 Nutraceuticals and Natural Products
6.8 Concluding Remarks:
Need for Purposeful Dissolution/Release Testing!
References
7 Dissolution/Release Test Data (Profile):
Requirements, Analyses, and Regulatory Expectations
7.1 Introduction and Objective(s)
7.2 Academic Curiosity
7.3 Early Development
7.4 Product Development Stage
7.5 Comparative Analyses
7.6 Summary and Concluding Remarks
References
8 Automation in Dissolution Testing:
Recent Advances and Continuing Challenges!
8.1 Introduction and Objective(s)
8.2 Automated Dissolution Testing:
Why and What to Automate?
8.3 Challenges in Automation of Dissolution Test(ing)
8.4 Automation in Dissolution Testing: Looking Forward!
8.5 Concluding Remarks
References
9
In vitro–In vivo
Correlations (IVIVCs):
What Makes Them Challenging!
9.1 Introduction and Objective(s)
9.2 Basic Model, Scheme, and Assumptions
9.3 Mechanics for Determination of IVIVC
9.4 BCS and IVIVC
9.5 IVIVC in New Drug Development
vis-à-vis
Generic Drug Development
9.6 IVIVCs in Topical/Transdermal Drug Delivery Systems (TDDSs)
9.7 Nonlinear IVIVCs
9.8 Validation of IVIVC Prediction Error (PE)
9.9 IVIVC in Drug Product Life Cycle: What Is the Ultimate Objective?
9.10 Summary and Conclusions
References
10 Biorelevant Dissolution/Release Test Method Development for Pharmaceutical Dosage Forms
10.1 Introduction and Objective(s)
10.2 General Considerations in BDM Development
10.3 Oral Drug Delivery Systems
10.4 Inhalation Drug Delivery Systems
10.5 Parenteral Drug Delivery Systems
10.6 Other Drug Delivery Systems
10.7 The Roadmap
10.8 Summary and Concluding Remarks
References
11 Bioavailability Prediction Software:
Hype or Reality!
11.1 Introduction and Objective(s)
11.2 The Need for Simulations and Predictions in Drug Product Development
11.3 Simulation and Prediction of
In Vivo
Performance:
The Catch-22 Situation!
11.4 Bioavailability (BA)/Bioequivalence (BE) Simulation Software:
What They Do and Do Not!
11.5 Appreciating and Depreciating Potential Utility of BA Prediction Software
11.6 Concluding Remarks
References
12 Challenges and Unique Applications of IVIVC in Drug Development
12.1 Introduction and Objective(s)
12.2 USP <1088> and US FDA Guidance for Industry (1997): Operational Challenges
12.3 Applications of IVIVC(s)
12.4 Prospective IVIVC(s)
12.5 Retrospective IVIVC(s): Responding to Agency Queries!
12.6 Summary and Concluding Remarks
References
13 Dissolution Testing in Generic Drug Development:
Methods, Requirements, and Regulatory Expectations/Requirements
13.1 Introduction and Objective(s)
13.2 Generic Drug Development Process: Role of Dissolution Testing
13.3 Generic Pharmaceutical Systems: Role of Dissolution
13.4 Generics: Finished Products – Role of Dissolution Testing
13.5 Summary and Concluding Remarks
References
14 Successful Bioequivalence Investigations:
Current Challenges and Possible Solutions!
14.1 Introduction and Objective(s)
14.2 Understanding Challenges and Approaches to Overcome Them!
14.3 Concluding Remarks
References
15 Beyond Guidance(s):
Convincing Regulatory Authorities Through Creative Dissolution Data Interpretation
15.1 Introduction and Objective(s)
15.2 Regulatory Guidance(s):
Reading Versus Understanding!
15.3 Regulatory Submission:
Premise and Expectation(s)
15.4 Handling Regulatory Query/Deficiency:
Efficient and Satisfying Response
15.5 Winning an Argument:
Three Cs to Succeed!
15.6 Sample Case Study(ies)
15.7 Summary and Concluding Remarks
References
16 Biosimilars: The Emerging Frontier for Generics –
Role of Dissolution Testing!
16.1 Introduction and Objective(s)
16.2 Generics, (Bio)betters, and Biosimilars:
What Are They?
16.3 Regulatory Approval Process (Brief):
Focus on Efficacy!
16.4 Role of Solubility and Dissolution
16.5 Concluding Remarks
References
17 Patentability of Drug Product Based on Dissolution Data:
Intellectual Property Considerations!
17.1 Introduction and Objective(s)
17.2 Patentability and the Patent Process (Brief):
Scientist's Perspective
17.3 Pharmaceutical Product: Patentability and Role of Dissolution Testing
17.4 Patentability:
Double-Edged Sword!
17.5 Concluding Remarks
References
18 Setting Up Clinical Therapeutics Safety-Based QC Specifications for Dissolution Testing of a Finished Product
18.1 Introduction and Objective(s)
18.2 Critical Quality Attributes (CQA):
Role of In vitro Dissolution as a QC Test!
18.3 Clinical Drug Product Performance:
Adequate or Predictable!
18.4 Clinically Relevant Specifications (CRS):
Basics and Challenges!
18.5 Idealism and Pragmatism Versus
Realism!
18.6 Concluding Remarks
References
19 Unlocking the Mystery(ies) While Predicting Bioavailability from Dissolution
19.1 Introduction and Objective(s)
19.2 The IVIVC Model and Objective(s) of IVIVC
19.3 Challenges Encountered in Predicting Bioavailability from Dissolution
19.4 What Are We Doing Now?
19.5 What We Should Be Doing! The Way Forward:
The Missing Link!
19.6 Advent of IVRT, IVPT, PBPK, and PBAM
19.7 Summary and Concluding Remarks
References
Index
End User License Agreement
Chapter 1
Table 1.1 Factors that influence drug dissolution/release testing.
Table 1.2 Physical factors that affect the dissolution apparatus (Agilent 20...
Chapter 2
Table 2.1 Factors that influence the selection of the study design of a BE i...
Table 2.2 Categories of BE investigation/study designs.
Table 2.3 Sample size,
n
, based on BE acceptance criteria (US-FDA 2001).
Table 2.4 Conditions to be complied with when dissolution test is employed w...
Table 2.5 Pharmacodynamic endpoint-based BE study guidelines from various dr...
Table 2.6 Organizations from various regions of the world and regulatory aut...
Table 2.7 Selected criteria for conducting BE investigations.
Chapter 3
Table 3.1 Generalized and dimensionless definition of solubility without reg...
Table 3.2 Domain of solubilization and solubility in drug development.
Table 3.3 Approaches employed in drug delivery to overcome poor aqueous solu...
Table 3.4 Particle technologies to improve water solubility of drug substanc...
Table 3.5 Proposed topical drug classification system (TCS).
Chapter 5
Table 5.1 Drug dissolution/release testing apparatuses as classified in vari...
Table 5.2 Classification of various types of pharmaceutical systems (dosage ...
Table 5.3 Applications of compendial methods with respect to various types o...
Table 5.4 Comparison of sink volume and hydrodynamics parameters.
Table 5.5 Specifications and tolerances for various parameters for mechanica...
Table 5.6 Biophysiological factors that influence the
in vivo
dissolution/rel...
Table 5.7 Typical (average) pH value of various regions of the GIT.
Table 5.8 “Biorelevant” dissolution media (partial listing) used for drug di...
Table 5.9 Predictive testing and “biorelevant dissolution” methods (partial ...
Chapter 6
Table 6.1 Classification of matrix-type solid drug delivery systems (Basak e...
Table 6.2 Types of osmotically controlled modified release drug delivery sys...
Table 6.3 Drug release profiles of three rapid dissolving tablet formulation...
Table 6.4 Pharmaceutical systems administered by routes other than the oral ...
Table 6.5 The various dosage forms used to deliver the drug via various otic...
Table 6.6 Types of parenteral formulations.
Table 6.7
In vitro
cumulative percent iloperidone release from optimized in situ ...
Table 6.8 Regulations for dissolution testing of herbal (natural) drugs in E...
Table 6.9 The USP classifications with respective dissolution test requireme...
Chapter 7
Table 7.1 Categories of pharmaceutical systems.
Table 7.2 Theories/models/approaches to characterize process of solubilizati...
Table 7.3 Summary of critical considerations while employing the
f
2
test.
Table 7.4 Experimental factors that may adversely influence the outcome of t...
Chapter 8
Table 8.1 Merits and limitations associated with automation of dissolution t...
Table 8.2 General workflow for a validated dissolution test conducted manual...
Chapter 9
Table 9.1 Potential limitations in determining IVIVC (partial listing).
Table 9.2
In vitro
and
in vivo
parameters commonly used in the three levels of IV...
Table 9.3 Mathematical models (partial listing) for describing/defining
in vi
...
Table 9.4 Empirical statistical models to demonstrate relationship between
in
...
Table 9.5 Prospects of Achieving IVIVC for immediate release oral solid dosa...
Chapter 10
Table 10.1 Physiological factors that influence
in vivo
drug dissolution/rele...
Table 10.2 Gastrointestinal (GI) pH values under fasted and fed states (Flei...
Table 10.3 Factors that influence GI motility and GI hydrodynamics.
Table 10.4 List of dissolution media used for drug dissolution/release testi...
Table 10.5 List of surfactants used in dissolution/release testing (not in a...
Table 10.6
In vitro
drug dissolution/release testing methods.
Table 10.7 Drug dissolution/release media used in evaluation of
in vitro
diss...
Table 10.8 Drug dissolution/release media used in
in vitro
drug dissolution/r...
Table 10.9 Drug dissolution/release media used in
in vitro
drug dissolution/r...
Table 10.10 Development of a biorelevant dissolution test (general scheme).
Chapter 11
Table 11.1 A list (not all inclusive) of BA/BE prediction and simulation sof...
Chapter 12
Table 12.1 Levels of IVIVC per USFDA Guidance for Industry.
Table 12.2 Regulatory
a)
and other applications of IVIVC.
Table 12.3 Comparison of
in vitro
drug release parameters.
Table 12.4 Regression curve fitted expressions for the 3 unique formulations...
Table 12.5 Comparison of PK parameters between the 3 unique formulations.
Table 12.6 IVIVC – linear regression analysis-based coefficient of determina...
Table 12.7 Absolute % PE for predicted PK parameters (
C
max
, AUC) for each fo...
Table 12.8 Similarity factor,
f
2
, values for various reference lots.
Table 12.9 Similarity factor,
f
2
, values for various test lots.
Table 12.10 Predicted ratios
a)
for
C
max
and for AUC for various test lots.
Table 12.11
f
2
a)
values for T1 and T2 formulations when compared with RLD employi...
Table 12.12 Predicted ratios
a)
for
C
max
and for AUC for formulations T1 and ...
Chapter 13
Table 13.1 Product development guide for an abbreviated new drug application...
Table 13.2 Enhancement of solubility and intrinsic dissolution rate (IDR) of...
Table 13.3 Approved 505(b)(2) applications (products) in 2019.
Table 13.4
In vitro
dissolution performances of bupropion IR tablets and bupropio...
Table 13.5 Global comparison of
f
2
criteria.
Table 13.6 Levels of formulation changes and required tests for immediate re...
Table 13.7
In vitro
dissolution test medium/media recommended by various regulato...
Chapter 14
Table 14.1 List of criteria for BE in descending order of accuracy, sensitiv...
Table 14.2 Roots and/or sources (not limited to) that emanate difficulties a...
Table 14.3 General approaches to overcome challenges in successful BA/BE inv...
Table 14.4 Partial listing of orally administered drug products that act loc...
Table 14.5 Methods to demonstrate BE of topical formulations.
Table 14.6 Essential testing of ophthalmic formulations during development.
Table 14.7 Comparison of PK-based BE study recommendations from the US FDA, ...
Table 14.8 PD-based BE study recommendations from Health Canada and the EMA.
Table 14.9 Representative examples of complex drugs per GDUFA II Commitment ...
Chapter 16
Table 16.1 Differences between biosimilar drug products and generic drug pro...
Table 16.2 Approved biosimilars during 2015 through December 2020 in the Uni...
Table 16.3 Multilevel building block modular approach for development of bio...
Chapter 17
Table 17.1 What can and cannot be patented.
Table 17.2 Overview of the steps involved in the patent process (USPTO 2020)...
Table 17.3 Factors that influence the dissolution testing results.
Chapter 18
Table 18.1 Approaches to set CRDS or CRS for drug products based on BCS of t...
Table 18.2 Critical steps essential to establish CRDS or CRS employing QbD.
Chapter 19
Table 19.1 Summary of potential limitations in determining IVIVC.
Table 19.2 Different biophysiologically relevant dissolution media (partial ...
Table 19.3 Required
in vitro
testing criteria for topical formulations per US...
Chapter 1
Figure 1.1 Dissolution studies in the life cycle of a pharmaceutical product...
Figure 1.2 Progressive application of the drug dissolution test and/or the d...
Chapter 3
Figure 3.1 Schematic depiction of the interplay of the element of solubiliza...
Figure 3.2 Schematic representation of solubilization from a planar surface ...
Figure 3.3 Schematic representation of the boundary layer adjacent to the su...
Figure 3.4 Schematic depiction of Danckwerts model (surface renewal theory),...
Figure 3.5 Schematic representation of a pH-solubility profile of a basic dr...
Figure 3.6
In vitro
dissolution profiles of pure drug and various nanoformul...
Figure 3.7 Schematic representation of dissolution of drug from formulation ...
Chapter 4
Figure 4.1 Interplay between solute (drug substance – API) and solvent (medi...
Figure 4.2 Schematic representation of the dissolution process of SDF (Banak...
Figure 4.3 Schematic dissolution profiles.
Figure 4.4 Schematic representation of a typical drug dissolution/release pr...
Figure 4.5 Schematic drug dissolution/release profile where
A
= 0.
Chapter 5
Figure 5.1 Schematics of the intrinsic dissolution testing assembly as descr...
Figure 5.2 USP/BP Apparatus 1 EP/IP Apparatus 2.
Figure 5.3 USP/BP Apparatus 2 EP/IP Apparatus 1.
Figure 5.4 USP Apparatus 3.
Figure 5.5 (a) USP Apparatus 4 and BP/EP Apparatus 3 [open loop]. (b) Flow-t...
Figure 5.6 USP Apparatus 5 (paddle over disk).
Figure 5.7 USP Apparatus 6 (rotating cylinder).
Figure 5.8 (a) USP Apparatus 7 (reciprocating holder). (b): Non-compendial m...
Figure 5.9 Modified baskets with different mesh and design.
Figure 5.10 Commonly used sinkers in USP Apparatus 2.
Figure 5.11 Peak vessel used to eliminate formation of cone of particles at ...
Figure 5.12 Schematic representation of Stricker model (refined Sartorius ab...
Figure 5.13 Schematic representation of the GI pH gradient model: A, SIF res...
Figure 5.14 Schematics of the dynamic processes (a) and the assembly of the ...
Figure 5.15 Schematic representation of FloVitro dissolution testing assembl...
Figure 5.16 Schematics of TNO TIM-1 dissolution testing assembly: A, stomach...
Figure 5.17 Biphasic drug release testing assemblies. (a) Hoa and Kinget (19...
Figure 5.18 Schematic representation of biphasic dissolution testing device ...
Figure 5.19 Schematic representation of the drug dissolution/release testing...
Figure 5.20 Schematic depiction of drug release testing cell modified to pos...
Figure 5.21 Drug release testing assembly for DES. (a) Modified USP Apparatu...
Figure 5.22 Schematic depiction of a capillary bioreactor device. (a) Top vi...
Figure 5.23 Schematic representation of a drug release test setup. (a) The m...
Figure 5.24 Schematics of drug release/dissolution testing method for sublin...
Figure 5.25 Schematics of drug release/dissolution testing method for mucoad...
Figure 5.26 Schematic of
in vitro
dissolution method for sublingual tablets:...
Figure 5.27 Schematic depiction of the dissolution testing device for MCG as...
Figure 5.28 Schematic depiction of drug release testing method for SGC: I, o...
Figure 5.29 Illustration of a modified flow-through cell for assessment of d...
Figure 5.30 Soft gelatin rectal capsule disintegration testing assembly (Ash...
Figure 5.31 Schematic representation of twin stage impinger to collect parti...
Figure 5.32 Schematic depiction of (A) dissolution station and (B) impaction...
Figure 5.33 Schematics of a typical Franz diffusion cell: (a) vertical and (...
Figure 5.34 Schematics of drug release testing devices for semisolid product...
Figure 5.35 Schematic representations of flow-through diffusion cells (a, b)...
Figure 5.36 Schematic illustration of drug dissolution/release testing of na...
Figure 5.37 Schematic representation of a continuous flow-through cell USP A...
Figure 5.38 Schematic representation of a drug release testing setup incorpo...
Figure 5.39 Schematic depiction of a special flow-through cell used in the E...
Chapter 6
Figure 6.1 Schematic representation of an
in vitro
drug dissolution/release ...
Figure 6.2 Schematic representation of an
in vitro
drug dissolution/release ...
Figure 6.3 Schematic representation of the process of dissolution/release of...
Figure 6.4 Percent drug dissolved at (a) 90 minutes and at (b) 60 minutes (P...
Figure 6.5 Drug dissolution profiles of tacrolimus from capsules containing ...
Figure 6.6 Dissolution profiles of nine SLM formulations: (a) Formulations F...
Figure 6.7
In vitro
dissolution profiles of drug: Pluronic F127 ratios and p...
Figure 6.8
In vitro
dissolution profiles of various SMEDDS-chewable tablets ...
Figure 6.9 Schematic representation of modified European Pharmacopoeia Appar...
Figure 6.10
In vitro
drug release profiles of two nicotine chewing gum produ...
Figure 6.11 Frontal view (left) and bottom view (right) of the four-cusped m...
Figure 6.12 Photograph of a chewing simulator. Source: Stamberg et al. (2017...
Figure 6.13
In vitro
dissolution profiles of soft chewable formulations of p...
Figure 6.14
In vitro
dissolution profiles of soft chewable formulations of p...
Figure 6.15 Schematic illustration of pH-adjusted biphasic dissolution appar...
Figure 6.16
In vitro
release profile of (a) dipyridamole pellet formulation ...
Figure 6.17 Drug release profiles of conventional and extended release produ...
Figure 6.18 Drug release profiles of novel metoprolol extended release produ...
Figure 6.19 Drug release profile of Azukon MR® when tested using USP Apparat...
Figure 6.20 3D model of DCM tube using ANSYS SpaceClaim 2015. The DCM tube i...
Figure 6.21 Schematic representation of the biorelevant Dynamic Gastric Mode...
Figure 6.22 Drug release profiles of Seroquel® extended release tablets (50 ...
Figure 6.23 Drug release profile of Coral® retard 60 mg and Adalat OROS® 60 ...
Figure 6.24 Cumulative release profile of venlafaxine from controlled porosi...
Figure 6.25 Release rate profile of paliperidone double-layered controlled r...
Figure 6.26 Combined percent cumulative drug release profile of a formulatio...
Figure 6.27 Bimodal release profile of adinazolam tablet. (a) Percentage of ...
Figure 6.28 Bimodal drug release profile form matrix tablets (Streubel et al...
Figure 6.29 Drug release rate profile of a push–pull osmotically controlled ...
Figure 6.30 Cumulative
in vitro
release profile of an MR oral SDF comprising...
Figure 6.31 Drug release profiles of each of the three groups of drug pellet...
Figure 6.32 Percent cumulative release as a function of time for six fast-me...
Figure 6.33
In vitro
dissolution profile of zolpidem lozenge and conventiona...
Figure 6.34 Percent cumulative drug release (%CDR) of levocetrizine from two...
Figure 6.35 Percent cumulative drug release (% CDR) of montelukast from two ...
Figure 6.36 Fraction of chlorpropamide HCl released in buffer (pH 5.5) as a ...
Figure 6.37
Ex vivo
permeation profiles of various drug chitosan/pectin comp...
Figure 6.38
In vitro
release of ciprofloxacin as a function of time from lip...
Figure 6.39
Ex vivo
permeation profiles of ciprofloxacin from liposomal hydr...
Figure 6.40
In vitro
release of metronidazole from liposomal hydrogel vagina...
Figure 6.41
In vitro
release of drug using the traditional USP Apparatus 2 (...
Figure 6.42
In vitro
release of drug using a biophysiologically relevant dua...
Figure 6.43 Permeation profiles of 5-fluorouracil through various regions of...
Figure 6.44
In vitro
release of immunoreactive TT from parenteral depot form...
Figure 6.45 Release of iron from intravenous injectable formulations: (a) by...
Figure 6.46 Variety of factors that influence dissolution (testing) of inhal...
Chapter 7
Figure 7.1 Drug dissolution/release profiles of hypothetical controlled rele...
Chapter 8
Figure 8.1 Schematic depiction of an ideal totally automated dissolution tes...
Figure 8.2 Levels of automation envisaged in dissolution/release testing (Ha...
Figure 8.3 Automated dissolution testing systems over the past 4 decades. (a...
Figure 8.4 Schematic representation of the automated dissolution system comb...
Figure 8.5 Schematic representation of a modular dissolution test combining
Figure 8.6 Schematic representation of an
in vitro
biphasic drug dissolution...
Chapter 9
Figure 9.1 Schematic representation of an IVIVC model.
Figure 9.2 Schematic depiction of the potential utility of IVIVC in drug dev...
Chapter 11
Figure 11.1 Schematic representation of progressive application of
in vitro
...
Figure 11.2 Schematic depiction of drug product development process, general...
Chapter 12
Figure 12.1 (a)
In vitro
dissolution profiles. (b)
In vivo
BA profiles of ph...
Figure 12.2 IVIVC for phenobarbital tablet formulations.
Chapter 13
Figure 13.1
In vitro
drug release profile for certain preferred dosage form(...
Chapter 14
Figure 14.1 Schematics representation of the Strawman decision tree.
Figure 14.2 Schematic depiction on the decision tree for determination of th...
Figure 14.3 Stepwise approach to establish TE of OIDPs per EMA (Health Canad...
Figure 14.4 BE for generic OIDPs based on totality of the “weight of evidenc...
Chapter 15
Figure 15.1 Three Cs to win an argument.
Chapter 17
Figure 17.1 Primary review criteria for determination of patentability of a ...
Figure 17.2 Schematic representation of the process of solubilization/dissol...
Figure 17.3 Schematic representation of how a pharmaceutical dosage form com...
Chapter 18
Figure 18.1 Schematic depiction of interrelationship between QC, biophysiolo...
Figure 18.2 Schematics of the decision tree to develop CRDS or CRS (Hermans ...
Figure 18.3 Schematic representation of the general process followed to arri...
Figure 18.4 Schematic representation of CRDS or CRS based on idealistic, pra...
Chapter 19
Figure 19.1 The IVIVC model. A, drug in dosage form; B, drug dissolved in th...
Figure 19.2 Schematic combination of
in vitro
dissolution and
in vitro
perme...
Cover Page
Table of Contents
Title Page
Copyright
Dedication
Foreword
Foreword
Preface
Acknowledgments
Begin Reading
Index
End User License Agreement
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Umesh V. BanakarBanakar Consulting ServicesWestfield, IN, USA
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To all the frontline healthcare providers, first responders, service providers, mothers, fathers, spouses, brothers, sisters, empathetic and compassionate well-wishers, gods, deities, spirits, faiths, and above all the love and affection shared by everyone in the combat to survive and overcome the SARS COVID-19 pandemic of 2020.
I am pleased that you are currently reading this text. This must mean you have an active interest in the science of dissolution. I spent almost 30 years of my working life in the field and found it profoundly rewarding. My dissolution experience began with The VanKel Technology Group, which later became part of Varian Inc. and subsequently part of Agilent Technologies. While on the surface, it appears to be a simple, perfunctory test. In fact, it is quite complex and essential to the pharma industry.
I first met Dr. Banakar in 1996 when our company initiated an educational program for our customers. At that time, I was working for a manufacturer of dissolution equipment. It became clear to us that our customers were looking for both practical and theoretical knowledge pertaining to dissolution. As we saw it, it was not enough to produce solid instrumentation. People needed to know the proper way to use the apparatus and interpret the results. This led to the creation of an educational initiative within our Laboratory Services business unit. Our instructors were internal staff supplemented by experts in various fields. Dr. Banakar was one of these experts. He brought a level of expertise to our customers that combined his teaching skills from the University along with analytical skills from his many years of consulting for industry.
In those days (obviously pre-COVID), we hopped on a plane and delivered seminars around the world. Over the years, we spent many hours traveling to both mature and developing markets, trying to “spread the word” about dissolution. We found that it was common for many dissolution analysts to first learn about dissolution when they were thrust into performing the test. Our goal was to supplement their practical knowledge with the underlying science so they could more fully understand the intricacies of how and why the test was performed. Based on the positive reviews over the many seminars that were delivered, I believe we achieved our objective.
The book you have provides a complete, comprehensive, and an up-to-date review of the how and why the dissolution test is performed. From the fundamentals of the test to method development of NDAs and ANDAs and bioavailability to bioequivalence, it is all here. Your challenge is how to absorb this material. Dr. Banakar has done a wonderful and commendable job of presenting the essential details in such a way that they can be easily understood and adapted to your applications.
I hope you are entertained and enlightened and find the answers you are looking for.
Good reading.
Allan Little, ESQDirector of MarketingDissolution SystemsAgilent TechnologiesSanta Clara, CaliforniaUSA
I began working on pharmaceutical patent infringement litigations about 25 years ago. For those of you who do not know much about patent law, it is a wonderful field that combines both the law and science. Most of my work in those early case involved sustained release pharmaceutical dosage forms. As a relative neophyte in the area, and although I had a background in chemical engineering, I had much to learn. Fortunately, in my early cases, I worked with Dr. Banakar as an expert on dissolution technology, learning the principles of pharmacokinetics (absorption, dissolution, metabolism, and elimination) and in vitro–in vivo correlation (IVIVC). I could not have had a better teacher for these topics. Dr. Banakar patiently and thoroughly taught me much of the basic concepts regarding this science. One of my first litigations had patent claims that included a sustained release of a medicament defined in terms of its dissolution profiles. Dr. Banakar spent hours to help me understand the nuanced differences between the paddle and basket methods, calibration of the equipment, the importance of the dissolution media and volume, stirring speeds, and other dissolution methods, as well as how the dissolution apparatus setup was essential to obtaining consistent and repeatable results and how even small changes that could introduce a wobble to the stirrer or a change in the type or volume of the dissolution media could affect those results. I was fascinated and hooked on dissolution science. Dr. Banakar inevitably had all the answers.
Later cases involved new concepts, such as pharmacokinetics. Again, there was no better teacher for me than Dr. Banakar, who quickly related those principles to what I knew from the chemical engineering concepts of a mass balances. I became enamored with pharmacokinetics. As new litigations involved new aspects of pharmacokinetics, I came across the topic of deconvolution and IVIVC. Once again, I was hooked on these fascinating fields, as well as the concepts of Cmax, AUC, Cmin, and how they were implicated in determining bioequivalence. Again, Dr. Banakar was with me every step of the way on my journey, and I will always be thankful to him for that.
As I look through this textbook, I can only think of what a wonderful asset it will be to the patent lawyer practicing in the field of pharmaceutical science. Whether in a litigation or in determining how to claim a particular feature of a new invention, an understanding of the science is essential. This book takes the reader from the fundamental principles to advanced techniques and complicated issues relating to the science and applications of dissolution testing to predict in vivo bioavailability in a systematic manner that is understandable and practical to a pharmaceutical scientist. Last, but necessarily not the least, the topics covered in this book are precisely the ones needed for the aspiring pharmaceutical patent practitioner.
Alan Clement, ESQChair, Intellectual Property DepartmentLocke Lord, LLPBrookfield Place, 200 Vesey StreetNew York, NY 10281USA
An active pharmaceutical ingredient (API) is seldom administered alone to a subject (human or an animal) for evaluation of its biological efficacy, i.e., bioefficacy. It is invariably combined with excipients and processed into a formulation that is ultimately administered as a dosage form (pharmaceutical product) that meets the required attributes of quality with respect to performance, both in vitro and in vivo. Without regard to the type of the dosage form – solid (powders, tablet, capsule, etc.,), liquids (suspensions, creams, etc.,), and semisolids (ointments, creams, lotions, etc.,) – administered to a subject (human and/or animal) for determination of its resultant systemic availability (in vivo absorption, i.e., bioavailability [BA]), if the API exists in its solid state, it has to dissolve out of the formulation into the biological medium – in vivo dissolution. The dissolved drug is subsequently absorbed across the biological absorption surface (in vivo absorption). It results in the appearance of the drug in the systemic circulation, thus effecting BA. Such a process, comprehensively, is commonly referred to as the overall bioefficacy of the administered dosage form. Thus, it has been realized that in vivo dissolution is a prerequisite to in vivo absorption and thereby the resulting bioefficacy of the administered formulation (drug product/dosage form).
Pharmaceutical product design and development is still considered more of an art than science! Nonetheless, a clear and comprehensive understanding of the multitude of factors influencing formulation design and development including evaluation, both in vitro and in vivo, is pivotal to succeed in the development of a pharmaceutical formulation. The constant quest of a pharmaceutical scientist and formulation scientist, in particular, is to implement appropriate steps during the development process such that the resultant formulation (product) meets the preset criteria for bioefficacy and ultimately clinical efficacy.
The development of pharmaceutical dosage forms often requires a multidisciplinary approach taking advantage of sound science and the technical skills required to combine these approaches. While the primary target of formulation development is to meet the preset and/or expected requirements of BA (bioefficacy), each and every formulation cannot be evaluated for BA for obvious reasons of cost, time, and availability of limited resources. Hence, there are numerous prospective tests, such as in vitro dissolution tests, presumably biophysiologically relevant (biorelevant), employed to screen the formulations during the various stages of drug development process. In so doing, the potential for success of the various formulations designed, developed, and evaluated can be substantially enhanced if such surrogate tests are appropriately used. As a result, a bioefficacy-centered pharmaceutical product design, development, and evaluation especially focusing on the role of dissolution testing in drug product development is of paramount significance.
Generic drug development, in particular, leading to the successful demonstration of bioequivalence (BE) relies heavily on in vitro dissolution test, right from screening of formulations to deciding which formulation proceeds to evaluation of BE. Additionally, the in vitro dissolution test is employed to demonstrate compliance with the criteria for biowaivers for dose-proportionate formulations and various levels of changes employed in the manufacturing process of the product post approval. Furthermore, in vitro dissolution test is often employed to respond and satisfy regulatory queries about the quality performance, both in vitro dissolution and in vivo efficacy, of the product.
Two pharmaceutical formulations are considered BE when their respective rate and extent of BA following administration of a unit dose under standard clinical conditions are substantially similar. Statements regarding bioavailability and bioequivalence appear to be simple and straightforward but have given rise to considerable controversy in pharmaceutical and clinical circles for many years that are compounded by economic factors associated with establishing bio- and therapeutic equivalence. Numerous rules and global regulations have been issued, and equal, if not more, number of interpretations and opinions have been reported primarily due to our insufficient understanding of the scope and depth of fundamental considerations associated with pharmaceutical bioequivalence.
Challenges, more than often, surface while designing bioequivalence investigations for complex generic formulations. While generic bioequivalence that is strictly based on similar bioefficacy between two formulations and their respective clinical and therapeutic equivalence is more desirable, thus, designing a bioequivalence investigation with clinical endpoint assessment seems to be emerging as an assessment tool for generic equivalence between two products. Despite complying with the regulatory requirements, various regulatory agencies seek further clarifications in the submissions in the data of a “successful” bioequivalence investigation. To address such challenges, one has to adopt an “out-of-the-box” approaches that are scientifically sound yet are convincing and compelling.
Global perspectives – regulatory and technical – addressing the various challenges in designing, conducting, and presenting successful BA/BE investigations including providing satisfactory and convincing rationale for queries from various regulatory agencies pose submission of results/data through a judicial blend of technical information and case studies. Special attention is warranted to stand the intricacies associated with BE of complex generics!
Dissolution testing, of course, is a regular quality control procedure in good manufacturing practice. However, the dissolution test can be employed prospectively – while developing a formulation with appropriate drug release characteristics and retrospectively – to assess whether a dosage form is releasing the drug at prescribed/predetermined rate and extent. The common principal assumption underlying these two uses of this test is that the dissolution test is able to adequately represent, if not predict, the biological performance, i.e., BA, of the drug.
As of date, in vitro dissolution tests seem to be the most reliable predictors of in vivo availability. Although official tests have great practical value, the fact that there is still a need for test more directly related to bioavailability has been recognized. Numerous attempts have been made to understand, develop, and potentially quantify the correlation between dissolution and bioavailability. Additionally, several compendial descriptions and regulatory guidelines are available that provide assistance and direction in establishing and demonstrating such correlations. However, accomplishing an in vitro–in vivo correlation (IVIVC) still appears to be elusive and potentially comprehensible only in a handful of circumstances. As a result, a concerted focus on how to overcome such challenges, both in the conceptual and the practical understanding of IVIVC and its applications in drug development and approval through case studies, yet ensuring that such an attempt results in its simplified workable approach, is not only essential but also overdue.
Biologics Price Competition and Innovation () Act creates an abbreviated licensure pathway for biological products shown to be biosimilar to or interchangeable with an Food and Drug Administration (FDA)-licensed (approved) reference product (Section 351(k) of Public Health Service [PHS]). The biological product is highly similar to the reference product notwithstanding minor differences in clinically inactive components, and there are no clinically meaningful differences between the biological product and the reference product in terms of safety, purity, and potency of the product. As a consequence, biosimilarity is judged on demonstrated “Totality of Evidence” that is expected to integrate various types of information – scope and extent of development plan and, ultimately, an overall assessment that a biological product is (or is not) biosimilar to an approved reference product. One of the primary criteria is the structural and functional characterization of the proposed biosimilar product. The role of dissolution in this context can play a critical role in the functional characterization, among others, of the proposed biosimilar product. Hence, biosimilars, which is considered as the emerging frontier for generics, and the role of dissolution testing in their development and evaluation should be explored.
Over the past decade, the dissolution test in drug development has matured from a simple convenient test for routine testing to assure batch-to-batch quality of the product to extremely complex application to predict bioefficacy of the product through demonstration of IVIVC. This test has now forayed into the discipline of intellectual property (IP) wherein the novel and innovative considerations of the invention have been secured. Often these inventions are worth “multimillion dollars,” and their ratification through (in)validity and/or (non)infringement focuses on convincing and compelling rationale based on principles of dissolution science and applications. The emerging and fascinating role of dissolution testing in has translated into securing exclusive rights to the inventor(s), i.e., a patent, based on dissolution performance of the product through specifications defining the invention.
The fundamental question needs to be addressed: Can dissolution, process, and result(s) individual or in combination provide sufficient information with respect to novelty and innovation that are the prerequisites for securing a patent? Additionally, it is generally accepted that the “new” product is patentable, but the patentability of this “new” product is more than often based on its some unique aspect – functional and/or outcome. As a result, the patentability of the product and underlying dissolution data needs to be explored.
Last but necessarily not the least, the drug development process is more than often governed by demonstrating compliance with regulatory expectations. The regulatory Agency(ies), on the other hand, are continually attempting to streamline this very process through harmonizing requirements. One such attempt is providing guidance(s) to the industry whereby the so-called “mystery” and/or the complexity of regulatory expectations is minimized. While the primary objective of the Agency(ies) is to ensure safety and efficacy of the applications (products) for approval, the pathway to demonstrate and secure such an approval is, at times, very daunting – thus the guidances in general and those pertaining to dissolution testing! They have value, and they come with disclaimers. However, complying with the guidance(s), both in dissolution data interpretation and data integrity, is often challenging. Thus, it is essential to focus on how to overcome such challenges, both in data interpretation and data integrity, through case studies, yet ensuring that such an attempt does not result in yet another guidance! In so doing, one has to peer beyond “Agency recommendations and guidances” while providing a convincing, if not compelling, rational interpretation of dissolution data that is acceptable to the regulatory agency/authority.
Finally, there are the primordial questions that have been the focus while exploring the role of the in vitro dissolution test in predicting in vivo (bio)availability of a drug delivered from a formulation: Where do we come from? Where are we going? A plethora of information focusing on attempts to predict effective IVIVC of various solid dosage forms exists. It is often observed that when such a correlation does exist between an in vitro parameter and an in vivo parameter, it is of limited value, for there is no unequivocal relationship between such parameters. Thus, good correlations being elusive, one settles for acceptable correlations!
The past three decades have witnessed diverse multidisciplinary approaches to address the challenges associated with such an IVIVC-based prediction of bioavailability, through mathematical modeling, biorelevant (medium) dissolution testing, and compendial and/or Agency recommendations/guidances, among others, with varying degrees of success. It is essential to realize and appreciate that dissolution is a prerequisite to bioavailability and not bioavailability itself! The need is to understand that solubility and permeability of a drug are equally crucial in understanding the in vivo dissolution of drug to comprehensively understand the so-called IVIVC. In so doing, with the rich experience combined with the current practices employed to enhance the bioavailability predictive power(s) of the dissolution test, the primordial question of the hour is: What we should be doing? In this pursuit, thinking “out of the vessel” is essential to enhance possibilities of progressing toward accomplishing acceptable, if not truly good, correlations based on an introspection-centered proactive pathway in predicting bioavailability from in vitro dissolution testing of a drug product.
The science and applications of “Pharmaceutical Dissolution Testing” have been recognized, beyond doubt, as an integral part of the drug development process while demonstrating bioefficacy (bioavailability and bioequivalence) and quality performance of the pharmaceutical product. Over the past century, the understanding of the science of dissolution technology and its applications in pharmaceutical drug development, from molecular basis to advanced levels while simulating bioefficacy a priori, to the clinical evaluations of the drug product have been reported in the literature. Additionally, the role of dissolution testing in the discipline of development of biosimilars has been explored. Furthermore, creative and innovative approaches in the analyses and interpretation of the dissolution test data (results) to satisfactorily demonstrate quality, with respect to safety and efficacy, of the pharmaceutical product to the regulatory authorities worldwide. This book comprehensively addresses the established and well-demonstrated role and the emerging role(s) of dissolution testing in pharmaceutical drug development. In so doing, this will be a valuable, current, ready-to-use reference resource for product development (formulation) scientists, quality control and quality assurance professionals, regulatory affairs personnel, and assessors, among others. Additionally, this will be a crucial addition to the libraries of academic and other healthcare institutions, organizations and corporations (industry).
There will be some who will quickly denounce and criticize this effort, and there will be those who will find this book very timely and helpful. This book is not intended to be a recipe text as a turnkey problem solver. To the contrary, this is a serious monumental effort/attempt to provide a wholesome understanding of the multidisciplinary considerations that need to be considered while developing and using a dissolution test in various, if not all facets, of the life cycle of a pharmaceutical product. Additionally, and most importantly, a compilation of 19 chapters with a collection of over 1100 references should enrich the scientist in understanding the role of dissolution beyond just quality control and provide the necessary toolkit to think out of the box with respect to its utility in bringing forth affordable, conventional and advanced, medications that are safe and effective.
Umesh Banakar, PhD; Professor and President, Banakar Consulting Services, Westfield, IN 46074 USA
This is the fourth textbook on this topic that I have authored solely or have edited since the publication of my first textbook in 1992 (Banakar 1992). Since then, while the fundamentals of dissolution science have not changed, there have been incremental advances and improvements in their applications in virtually all phases of the life cycle of a drug product. Additionally, dissolution testing has forayed into disciplines of nutraceuticals and natural products, intellectual property, and biosimilars, among others, over the past three decades. I am thankful that I have witnessed and participated and contributed to these developments.
I acknowledge with gratitude the invitation and opportunity extended by Mr. Jonathan Rose, Senior Editor, Academic Publishing Group, John Wiley & Sons, Hoboken, NJ, and for his expression of interest in my contribution in the disciplines of dissolution, bioavailability, and bioequivalence.
I would like to express my heartfelt sincere gratitude to my wife, Suneeta, for her continuous unselfish support. Without her, this project would not have been completed.
I am indebted to Ms. Rajashree Gude, PhD, Associate Professor, Goa College of Pharmacy, for her invaluable and continued support in literature searches, editing, formatting, and structuring of each and every chapter of this textbook.
I would like to thank our son, Mr. Kapil Banakar, ESQ, for the timely and thoughtful gift of a 24-inch screen monitor that helped me immensely while structuring, writing, and editing the manuscript of every section, chapter, and portion of this book.
I am profoundly indebted to all the professionals that I have interacted with at all the platforms such as national and international conferences, webinars, scientific advisory boards, doctoral dissertation and master of science theses committee memberships, and numerous research and development groups from academia and industry, among others, which provided me opportunities to present my ideas and motivated me to develop, construct, and pursue new ones.
Last, but not the very least, I would like to thank all the well-wishers for their support that is often taken for granted but needs to be recognized.
Banakar, U. (1992).
Pharmaceutical Dissolution Testing
, Drugs and the Pharmaceutical Sciences, vol. 49. New York, NY: Marcel Dekker, Inc.
It has now been accepted, as well as recognized beyond doubt, that the dissolution test(ing) and the resulting drug release testing data are crucial tests that interface all phases of the life cycle of a pharmaceutical product. It is one of the key tests that can provide valuable information about the functional performance of the product, an insight into the potential in vivo behavior of the product, the quality control (QC) requirements of the product, and much more. The importance of dissolution studies in the various aspects of the product's life cycle is aptly depicted in Figure 1.1 (Scheubel 2010).
Thus, broadly speaking, the scope of dissolution testing extends right from the identification of a lead compound as a potential active pharmaceutical ingredient (API) through the stages of preclinical development, followed by development of a prototype formulation (early pre-formulation and formulation) encompassing development of an in vitro–in vivo correlation (IVIVC)-based assessment to identify the pilot formulation for early-phase clinical trials. Subsequently, dissolution testing plays key role in the progress to the scale-up of the pilot formulation to pivotal formulation for assessment in definitive clinical trials. The collective information from all these assessments often forms critical mass of information that leads to setting the QC specifications of the product. The resulting data forms the critical mass of data sufficient for the regulatory authorities to assess the functional performance characteristics of the product during the decision-making process for grant of provisional and/or tentative approval of the product. The scale-up of the “tentatively and/or provisionally approved” product to commercial scale thereby validating the manufacturing process is demonstrated by dissolution/release studies whereupon a final approval is granted by the regulatory agency. There are other considerations, such as scale-up and post-approval changes (SUPAC), biowaivers for scale-up/scale-down dose strengths, bioequivalence (BE) with respect to generics, and 505(b)(2) new drug applications (NDAs), among others, in the life cycle of a pharmaceutical product where drug dissolution test(ing) and drug release testing play a critical role. Suffice it here to say, drug dissolution/release testing (studies) interfaces virtually all aspects of the life cycle of a pharmaceutical product.
Figure 1.1 Dissolution studies in the life cycle of a pharmaceutical product.
Source: Based on Scheubel (2010).
The interest in dissolution testing of solid chemical compounds exploring the functional aspects of solubilization of the solid solute independently and in combination with other chemical compounds – excipients or otherwise – and finally from a carefully prepared composition (formulation) can be traced over a century. Substantial mass of critical information relating to the physicochemical considerations that directly or indirectly influence the process of dissolution has been acquired. Similarly, with the realization that drug dissolution/release testing can be potentially exploited to predict bioavailability (BA) of the drug from the formulation, the physiological considerations that directly or indirectly influence the process of dissolution has been acquired. As the technology incorporated during the development of the formulation advanced, so did the scope and thereby the role of dissolution testing of these formulations. Quite akin to this, as the formulations became more complex, the role of the dissolution test emerged as one of the key determinants that could be relied upon with respect to the functional characterization of such advances and “complex formulations.” The realization of IVIVCs – demonstrated adequately and appropriately – opened the possibilities of reduced and often duplicative unnecessary testing in humans and animals. The drug dissolution/release test was overwhelmingly identified as the (bio)physiologically relevant surrogate test that could potentially predict in vivo performance of the product with reasonable accuracy, predictability, and reliability. As a result, the knowledgebase in the discipline of dissolution science has grown phenomenally over the past few decades.
While the role of dissolution test(ing) and thereby release testing in drug product development and in demonstrating the quality considerations of the product has grown, numerous challenges have surfaced, and numerous new applications of this test(ing) have been explored. The primary objective of this chapter is to present an introductory overview of the fundamentals of the scientific considerations underlying the dissolution/release test(ing) sufficient to set up the baseline for this textbook. The secondary objective of equal, if not more, importance is to provide the rationale for bringing forth this textbook along with the format followed therein as exemplified through the flow of information presented in the various parts of this textbook.
The interest in understanding and characterizing the process of dissolution dates back to late nineteenth century where physical chemists studied the rate of solubilization of solid substances in their own solution (Noyes and Whitney 1897; Bruner and Tolloczko 1900). The basic physicochemical principles and laws that helped in describing the process of dissolution of solid chemical compounds, i.e., solutes, were already in place. Nernst and Brunner (1904), first, provided a mathematical expression describing the process of dissolution based on the diffusion layer concept combined with Fick's second law of diffusion. Early to mid-twentieth century witnessed the elaboration of the factors that influence the process of dissolution through presentation of a series of mechanistic mathematical models, such as the diffusion layer model, interfacial barrier model, surface renewal model, and the like (Hixson and Crowell 1931; Wilderman 1909; Miyamoto 1933; Zdanovskii 1946; Danckwerts 1951; Higuchi 1961; Levich 1962; among others). While the advances in in vitro
