1) The document describes mathematical approaches to modeling drug release from hydrogel matrices. It discusses parameters like polymer volume fraction, molecular weight between crosslinks, and network mesh size that describe hydrogel structure.
2) The mechanisms that influence drug release from hydrogels include diffusion, swelling, erosion, and chemical reactions. Different geometries like thin films, spheres, and cylinders can impact release kinetics.
3) Mathematical models are described to predict drug release profiles from hydrogels. Models incorporate diffusion equations and consider different scenarios like reservoir systems, matrix systems, and whether the initial drug concentration is above or below solubility.
Polymer microspheres for controlled drug releaseDuwan Arismendy
Polymer microspheres can be employed to deliver medication in a rate-controlled and sometimes targeted manner. Medication is released from a microsphere by drug leaching from the polymer or by degradation of the polymer matrix. Since the rate of drug release is controlled by these two factors, it is important to understand the physical and chemical properties of the releasing medium. This review presents the methods used in the preparation of microspheres from monomers or from linear polymers and discusses the physio-chemical properties that affect the formation, structure, and morphology of the spheres. Topics including the effects of molecular weight, blended spheres, crystallinity, drug distribution, porosity, and sphere size are discussed in relation to the characteristics of the release process. Added control over release profiles can be obtained by the employment of core-shell systems and pH-sensitive spheres; the enhancements presented by such systems are discussed through literature examples.
This document discusses how gel networks can be used in the pharmaceutical industry to influence crystal growth of active pharmaceutical ingredients (APIs). It begins by providing background on how gels have been used for over 100 years to grow high quality crystals. Recent research interest has focused on using low molecular weight gelators (LMWGs) which can self-assemble to form reversible gel networks. These gels can slow crystal growth and produce crystals with novel habits, polymorphs, and chirality. The document discusses how gels have been used to modify the habit of asparagine monohydrate crystals and screens for new polymorphs. It suggests LMWG gels that undergo triggered gelation could be useful for growing pharmaceutical crystals
This document summarizes literature on cocrystal systems published in 2011 that are of interest to pharmaceutical scientists. It begins with an introduction to cocrystal systems and relevant review articles. It then discusses general articles on cocrystal engineering principles and characterization methods. The majority of the document summarizes literature on preparation methods for cocrystal systems and specific pharmaceutical cocrystal systems that were reported. It concludes with a discussion of regulatory guidance on pharmaceutical cocrystals.
The document discusses preformulation studies, which involve characterizing the physical and chemical properties of a drug substance before developing a dosage form. The goals are to generate stability-indicating parameters and select an appropriate dosage form. Key topics covered include the physical properties tested (such as solubility, polymorphism, particle size), chemical degradation pathways (such as hydrolysis, oxidation), and how these properties influence dosage form design and drug performance. Understanding a drug's preformulation behavior is critical for developing a safe, effective, and stable drug product.
This document summarizes a paper on nanogels: synthesis, behavior, and applications. It discusses how nanogels are nanosized hydrogels composed of cross-linked polymeric chains that can absorb water. There are two main methods for synthesizing nanogels - solution polymerization and emulsion polymerization. Nanogels have various applications including cancer drug delivery, water purification, antipyretics, and glucose biosensing due to their ability to respond to stimuli like pH, temperature, and glucose levels. Hybrid nanogels that incorporate stimuli-responsive polymers are particularly promising for biomedical uses.
Preformulation and physicochemical property of the drugSHIVANEE VYAS
“It is the study of the physical and chemical properties of the
drug prior to compounding process”.
Preformulation commences when a newly synthesized drug shows sufficient pharmacologic promise in animal models towarrant evaluation in man.
These studies should focus on physicochemical properties of new compound that affect drug performance & development of efficaciouss dosage form.
This properties may provide;
A rationale for formulation design
Support the need for molecular modification.
1) Hydrogels created through molecular imprinting have the potential to selectively filter metabolites like glucose from biological samples, improving quantification of other molecules by GC-MS metabolomics.
2) Preliminary studies show poly(allylamine) hydrochloride hydrogels imprinted with glucose-6-phosphate are selectively binding for glucose over fructose.
3) Future work will examine imprinted and non-imprinted hydrogel binding capacities for metabolites in standard solutions and complex biological mixtures to explore their utility in metabolomics analysis.
This document provides an overview of preformulation studies for drug development. It discusses the importance of characterizing key physicochemical properties of drug substances such as solubility, ionization constants, melting point, and polymorphism. It also covers the role of excipients and how drug-excipient interactions can impact stability. The document concludes with sections on stability studies, factors that influence stability, and guidelines for stability testing procedures and frequencies.
Polymer microspheres for controlled drug releaseDuwan Arismendy
Polymer microspheres can be employed to deliver medication in a rate-controlled and sometimes targeted manner. Medication is released from a microsphere by drug leaching from the polymer or by degradation of the polymer matrix. Since the rate of drug release is controlled by these two factors, it is important to understand the physical and chemical properties of the releasing medium. This review presents the methods used in the preparation of microspheres from monomers or from linear polymers and discusses the physio-chemical properties that affect the formation, structure, and morphology of the spheres. Topics including the effects of molecular weight, blended spheres, crystallinity, drug distribution, porosity, and sphere size are discussed in relation to the characteristics of the release process. Added control over release profiles can be obtained by the employment of core-shell systems and pH-sensitive spheres; the enhancements presented by such systems are discussed through literature examples.
This document discusses how gel networks can be used in the pharmaceutical industry to influence crystal growth of active pharmaceutical ingredients (APIs). It begins by providing background on how gels have been used for over 100 years to grow high quality crystals. Recent research interest has focused on using low molecular weight gelators (LMWGs) which can self-assemble to form reversible gel networks. These gels can slow crystal growth and produce crystals with novel habits, polymorphs, and chirality. The document discusses how gels have been used to modify the habit of asparagine monohydrate crystals and screens for new polymorphs. It suggests LMWG gels that undergo triggered gelation could be useful for growing pharmaceutical crystals
This document summarizes literature on cocrystal systems published in 2011 that are of interest to pharmaceutical scientists. It begins with an introduction to cocrystal systems and relevant review articles. It then discusses general articles on cocrystal engineering principles and characterization methods. The majority of the document summarizes literature on preparation methods for cocrystal systems and specific pharmaceutical cocrystal systems that were reported. It concludes with a discussion of regulatory guidance on pharmaceutical cocrystals.
The document discusses preformulation studies, which involve characterizing the physical and chemical properties of a drug substance before developing a dosage form. The goals are to generate stability-indicating parameters and select an appropriate dosage form. Key topics covered include the physical properties tested (such as solubility, polymorphism, particle size), chemical degradation pathways (such as hydrolysis, oxidation), and how these properties influence dosage form design and drug performance. Understanding a drug's preformulation behavior is critical for developing a safe, effective, and stable drug product.
This document summarizes a paper on nanogels: synthesis, behavior, and applications. It discusses how nanogels are nanosized hydrogels composed of cross-linked polymeric chains that can absorb water. There are two main methods for synthesizing nanogels - solution polymerization and emulsion polymerization. Nanogels have various applications including cancer drug delivery, water purification, antipyretics, and glucose biosensing due to their ability to respond to stimuli like pH, temperature, and glucose levels. Hybrid nanogels that incorporate stimuli-responsive polymers are particularly promising for biomedical uses.
Preformulation and physicochemical property of the drugSHIVANEE VYAS
“It is the study of the physical and chemical properties of the
drug prior to compounding process”.
Preformulation commences when a newly synthesized drug shows sufficient pharmacologic promise in animal models towarrant evaluation in man.
These studies should focus on physicochemical properties of new compound that affect drug performance & development of efficaciouss dosage form.
This properties may provide;
A rationale for formulation design
Support the need for molecular modification.
1) Hydrogels created through molecular imprinting have the potential to selectively filter metabolites like glucose from biological samples, improving quantification of other molecules by GC-MS metabolomics.
2) Preliminary studies show poly(allylamine) hydrochloride hydrogels imprinted with glucose-6-phosphate are selectively binding for glucose over fructose.
3) Future work will examine imprinted and non-imprinted hydrogel binding capacities for metabolites in standard solutions and complex biological mixtures to explore their utility in metabolomics analysis.
This document provides an overview of preformulation studies for drug development. It discusses the importance of characterizing key physicochemical properties of drug substances such as solubility, ionization constants, melting point, and polymorphism. It also covers the role of excipients and how drug-excipient interactions can impact stability. The document concludes with sections on stability studies, factors that influence stability, and guidelines for stability testing procedures and frequencies.
Nanogels are nanosized hydrogels that can be synthesized through various polymerization techniques. They have potential applications in drug delivery, tissue engineering, and bionanotechnology due to their 3D structure, mechanical properties, and biocompatibility. Hybrid nanogels are smart materials that can swell or collapse in response to physical or chemical stimuli like pH, temperature, or electric fields. This makes them useful for applications like cancer treatment by releasing drugs only in acidic tumor environments, water purification by absorbing contaminants, and glucose biosensing through a volume change signal.
The document discusses various physicochemical properties that can affect bioequivalence studies, including crystal morphology, polymorphism, solvates, hydrates, complexation, surface activity, hygroscopicity, particle size, solubility and dissolution. It explains how these properties can influence parameters like raw material characteristics, reproducibility, performance of the dosage form, absorption rate and extent. Factors like ionization, partitioning, distribution coefficient, chemical structure and salt forms are also covered in relation to their effects on solubility, dissolution and absorption of drug substances and products.
This document discusses co-crystals, which are crystalline materials composed of two or more components in the same crystal lattice. It outlines several advantages of co-crystals such as increased stability and solubility compared to amorphous forms. Common preparation methods include solution methods, grinding, and antisolvent techniques. Key characterization techniques are X-ray powder diffraction, infrared spectroscopy, and solubility analysis. Several marketed drug formulations utilizing co-crystals are also mentioned.
The document discusses co-crystals, which are crystalline materials composed of an active pharmaceutical ingredient and a co-crystal former. Co-crystals can improve properties like dissolution rate and stability. They are formed through hydrogen bonding, pi-stacking, or van der Waals forces between components. Common preparation methods include solution crystallization, grinding, and antisolvent crystallization. Co-crystals are characterized using techniques like infrared spectroscopy, X-ray crystallography, and thermal analysis. Examples of co-crystallized drugs discussed include itraconazole, caffeine, and carbamazepine.
In recent years, robustness and surface engineering of dosage form made improvement in pharmacokinetics with decrease in dose of drug. Specificity with adherence of ligands has now become the reality as surface modifi cation can easily deceive phagocytic system. Lipid molecules ensures the
release of drug at lymphatic system, entrapment of polymeric nanoparticles in lipoidal core led to the
avoidance of disadvantage of low entrapment effi ciency if use of hydrophobic drug with hydrophobic polymer becomes essential. Various studies have been published and the best formulations with optimal In vitro and In vivo results are highlighted in this paper. In this review most advanced researches and accepted patents were discussed so to act as a medium for getting everything regarding lipid polymer hybrid particles under one umbrella.
This document discusses characterization methods for hydrogels. Hydrogels are crosslinked polymeric networks that can absorb large amounts of water due to hydrophilic functional groups. The document outlines various physical and chemical characterization techniques to determine a hydrogel's structure, mechanical properties, porosity, water content, and chemical composition. Physical techniques include stress-strain tests, microscopy, atomic force microscopy, and mercury intrusion. Chemical techniques involve Fourier transform infrared spectroscopy, nuclear magnetic resonance, and differential scanning calorimetry. These characterization methods provide insights into a hydrogel's properties and structure-property relationships.
This document discusses preformulation studies, which examine the physicochemical properties of drugs and excipients before formulation to optimize the dosage form design. It covers fundamental properties like spectroscopy, solubility, melting point and assay. Derived properties include microscopy, flow properties, drug-excipient compatibility and drug stability studies. Preformulation helps ensure quality, uniformity and minimize costs and errors in product development and regulatory filings.
This document discusses mucoadhesive drug delivery systems, which use bioadhesive polymers that adhere to mucosal membranes to increase drug residence time and bioavailability. It covers the basics of mucosal membranes and theories of mucoadhesion, as well as the mechanisms, types of polymers, formulations, and targets for bioadhesive drug delivery. The goal of these systems is to deliver drugs through mucosal routes and potentially bypass first-pass metabolism through prolonged adhesion to the site of administration.
The document presents a research project on preparing and evaluating co-crystals of atorvastatin calcium with saccharin and urea. The objectives are to prepare the co-crystals using solvent drop grinding and solvent evaporation methods, characterize them using various techniques, and evaluate their solubility. The document outlines the materials, methods, results and discussion sections of the project including pre-formulation studies of atorvastatin calcium and the co-formers, characterization of the prepared co-crystals using FTIR, DSC and solubility testing, and evaluation of drug-excipient compatibility. The project aims to develop co-crystal formulations to improve the solubility and dissolution rate of the poorly soluble at
In this slide, you will learn about what is polymorphism, types, and properties of polymorphism, the application of polymorphism in pharmaceutical industries, polymorphism of several drugs. Hope you will like it.
Biodegradable polymers based transdermal drug delivery systemDeepanjan Datta
Friends..me and my best buddy miss.pragya paramita pal prepared this presentation during the last semester of our graduation.I am just uploading this so that this can help you to prepare better presentations based on such topics.Thanks to my guide and my friend miss.pragya.Enjoy friends & best of luck..
This document discusses polymorphism as part of a preformulation study seminar. It defines polymorphism as the ability of a substance to exist in two or more crystalline forms that have different molecular arrangements. The key points covered include:
- The need to study polymorphism to select the most stable and soluble form for formulations. Metastable forms often have better bioavailability.
- Various methods to identify and characterize polymorphs such as X-ray diffraction, thermal analysis techniques like DSC and TGA, and microscopy.
- Factors that can influence polymorphic transitions like temperature, humidity, solvents, grinding, and compression during tableting.
- The importance of understanding polymorphism for properties like
Abstract
Niosomes, non-ionic surfactant vesicles (NSVs), are the hydrated lipids composed mainly of different classes of non-ionic surfactants, introduced in the seventies as a cosmetic vehicle. Nowadays, niosomes are used as important new drug delivery systems by many research groups and also they are effective immunoadjuvants which some commercial forms are available in the market. These vesicles recently used as gene transfer vectors as well. This review article presents a brief report about the achievements in the field of nanoscience related to NSVs. Different polar head groups from a vast list of various surfactants with one, two or three lipophilic alkyl, perfluoroalkyl and steroidal moieties may be utilized to form the proper vesicular structures for encapsulating both hydrophilic and hydrophobic compounds. The methods of niosome preparation, the vesicle stability related aspects and many examples of pharmaceutical applications of NSVs will be presented. The routes of administration of these amphiphilic assemblies are also discussed.
This document discusses bioadhesion, providing an introduction, theories, fundamentals and models. It defines bioadhesion as adhesion between biological materials, with mucoadhesion being adhesion to mucosal membranes. Theories of bioadhesion include wetting, diffusion, electronic, fracture and adsorption. Fundamentals discussed are biological membranes, bioadhesive polymers and modulation of mucoadhesion. Models of measuring bioadhesion described include falling liquid film, USP apparatus 4 and ex vivo methods. The conclusion states bioadhesion can facilitate adhesion of cells and biomolecules to develop novel biomaterials and therapies.
This document provides an overview of nanogels for drug delivery applications. It defines nanogels as nanosized polymer networks that swell in solvent. Nanogels have properties like biocompatibility and drug loading capacity. They can be administered via various routes and classified based on responsive behavior or linkage type. The document discusses synthesis, characterization, and applications of nanogels in cancer treatment, ophthalmic use, and more. Nanogels are a promising drug delivery system due to abilities like controlled drug release and delivery of therapeutics to targeted sites.
Nanogels are innovative drug delivery system that can play an integral part in pointing out many issues related to old and modern courses of treatment such as nonspecific effects and poor stability.
This document discusses complex formation in pharmaceutical science. It defines complexes as molecules with some anomalous bonding structures that can be described by classical valence theories. There are several types of complexes discussed, including metal complexes where a metal ion interacts with ligands, organic molecular complexes held by weaker forces, and inclusion complexes where one component is trapped within another. Methods for analyzing complexes include determining stoichiometry and stability constants using techniques like continuous variation, spectroscopy, distribution methods, and protein binding studies. The document explores how complex formation can impact drug action.
This document discusses Aquasomes, which are nanoparticle carrier systems composed of a central solid nanocrystalline core coated with polyhydroxy oligomers onto which drug molecules can be adsorbed. Aquasomes are spherical particles 60-300nm in size that are used for targeted drug and antigen delivery. They are prepared through a self-assembly process involving the preparation of a ceramic core, coating the core with carbohydrates, and then immobilizing a drug molecule onto the coated core. Aquasomes have properties such as preserving the integrity of biomolecules and avoiding clearance from the body. They can be characterized through techniques like SEM, TEM, FT-IR, and XRD. Potential applications of Aquasomes
Hydrogels introduction and applications in biology and enAndrew Simoi
Hydrogels are water-swollen, crosslinked polymers that can absorb large amounts of water. They have a variety of applications including in soft contact lenses, drug delivery, wound healing, and tissue engineering. Hydrogels are advantageous for tissue engineering and cell culture as they can mimic extracellular matrix, provide structural support, and allow for nutrient transport. They are also useful for drug delivery as they allow controlled release of molecules. The document discusses the properties, types, advantages and uses of hydrogels.
Biocompatibility of Poly (L-Lactic Acid) Synthesized In Polymerization Unit B...IJERA Editor
The absorbable polyacid is one of the most used and studied materials in tissue engineering. This work
synthesized a poly (L-lactic acid) (PLLA) through ring-opening polymerization and produced nanofibers by the
electrospinning process. The PLLA was analyzed by FTIR and the cytotoxicity was evaluated by the MTT assay
and Live/Dead®. The hemocompatibility was tested by platelet adhesion and hemolytic activity assay. The tests
were performed in contact with human mesenchymal cells at varying times. The high rates of cell viability and
proliferation shown by MTT and Live/Dead® tests demonstrate that this PLLA is a non-toxic material and the
hemocompatibility assay revealed that the biomaterial was also biocompatible. It was achieved as well the
successful production of electrospinning nanofibers, which can be converted for specific biomedical applications
in the future
Hydrogels,
introduction,
historical background,
properties,
classification,
difference between chemical and physical hydrogels,
common uses,
pharmaceutical applications,
preparation methods,
list of monomers used,
analytical machines,
advantages,
disadvantages,
conclusion
Nanogels are nanosized hydrogels that can be synthesized through various polymerization techniques. They have potential applications in drug delivery, tissue engineering, and bionanotechnology due to their 3D structure, mechanical properties, and biocompatibility. Hybrid nanogels are smart materials that can swell or collapse in response to physical or chemical stimuli like pH, temperature, or electric fields. This makes them useful for applications like cancer treatment by releasing drugs only in acidic tumor environments, water purification by absorbing contaminants, and glucose biosensing through a volume change signal.
The document discusses various physicochemical properties that can affect bioequivalence studies, including crystal morphology, polymorphism, solvates, hydrates, complexation, surface activity, hygroscopicity, particle size, solubility and dissolution. It explains how these properties can influence parameters like raw material characteristics, reproducibility, performance of the dosage form, absorption rate and extent. Factors like ionization, partitioning, distribution coefficient, chemical structure and salt forms are also covered in relation to their effects on solubility, dissolution and absorption of drug substances and products.
This document discusses co-crystals, which are crystalline materials composed of two or more components in the same crystal lattice. It outlines several advantages of co-crystals such as increased stability and solubility compared to amorphous forms. Common preparation methods include solution methods, grinding, and antisolvent techniques. Key characterization techniques are X-ray powder diffraction, infrared spectroscopy, and solubility analysis. Several marketed drug formulations utilizing co-crystals are also mentioned.
The document discusses co-crystals, which are crystalline materials composed of an active pharmaceutical ingredient and a co-crystal former. Co-crystals can improve properties like dissolution rate and stability. They are formed through hydrogen bonding, pi-stacking, or van der Waals forces between components. Common preparation methods include solution crystallization, grinding, and antisolvent crystallization. Co-crystals are characterized using techniques like infrared spectroscopy, X-ray crystallography, and thermal analysis. Examples of co-crystallized drugs discussed include itraconazole, caffeine, and carbamazepine.
In recent years, robustness and surface engineering of dosage form made improvement in pharmacokinetics with decrease in dose of drug. Specificity with adherence of ligands has now become the reality as surface modifi cation can easily deceive phagocytic system. Lipid molecules ensures the
release of drug at lymphatic system, entrapment of polymeric nanoparticles in lipoidal core led to the
avoidance of disadvantage of low entrapment effi ciency if use of hydrophobic drug with hydrophobic polymer becomes essential. Various studies have been published and the best formulations with optimal In vitro and In vivo results are highlighted in this paper. In this review most advanced researches and accepted patents were discussed so to act as a medium for getting everything regarding lipid polymer hybrid particles under one umbrella.
This document discusses characterization methods for hydrogels. Hydrogels are crosslinked polymeric networks that can absorb large amounts of water due to hydrophilic functional groups. The document outlines various physical and chemical characterization techniques to determine a hydrogel's structure, mechanical properties, porosity, water content, and chemical composition. Physical techniques include stress-strain tests, microscopy, atomic force microscopy, and mercury intrusion. Chemical techniques involve Fourier transform infrared spectroscopy, nuclear magnetic resonance, and differential scanning calorimetry. These characterization methods provide insights into a hydrogel's properties and structure-property relationships.
This document discusses preformulation studies, which examine the physicochemical properties of drugs and excipients before formulation to optimize the dosage form design. It covers fundamental properties like spectroscopy, solubility, melting point and assay. Derived properties include microscopy, flow properties, drug-excipient compatibility and drug stability studies. Preformulation helps ensure quality, uniformity and minimize costs and errors in product development and regulatory filings.
This document discusses mucoadhesive drug delivery systems, which use bioadhesive polymers that adhere to mucosal membranes to increase drug residence time and bioavailability. It covers the basics of mucosal membranes and theories of mucoadhesion, as well as the mechanisms, types of polymers, formulations, and targets for bioadhesive drug delivery. The goal of these systems is to deliver drugs through mucosal routes and potentially bypass first-pass metabolism through prolonged adhesion to the site of administration.
The document presents a research project on preparing and evaluating co-crystals of atorvastatin calcium with saccharin and urea. The objectives are to prepare the co-crystals using solvent drop grinding and solvent evaporation methods, characterize them using various techniques, and evaluate their solubility. The document outlines the materials, methods, results and discussion sections of the project including pre-formulation studies of atorvastatin calcium and the co-formers, characterization of the prepared co-crystals using FTIR, DSC and solubility testing, and evaluation of drug-excipient compatibility. The project aims to develop co-crystal formulations to improve the solubility and dissolution rate of the poorly soluble at
In this slide, you will learn about what is polymorphism, types, and properties of polymorphism, the application of polymorphism in pharmaceutical industries, polymorphism of several drugs. Hope you will like it.
Biodegradable polymers based transdermal drug delivery systemDeepanjan Datta
Friends..me and my best buddy miss.pragya paramita pal prepared this presentation during the last semester of our graduation.I am just uploading this so that this can help you to prepare better presentations based on such topics.Thanks to my guide and my friend miss.pragya.Enjoy friends & best of luck..
This document discusses polymorphism as part of a preformulation study seminar. It defines polymorphism as the ability of a substance to exist in two or more crystalline forms that have different molecular arrangements. The key points covered include:
- The need to study polymorphism to select the most stable and soluble form for formulations. Metastable forms often have better bioavailability.
- Various methods to identify and characterize polymorphs such as X-ray diffraction, thermal analysis techniques like DSC and TGA, and microscopy.
- Factors that can influence polymorphic transitions like temperature, humidity, solvents, grinding, and compression during tableting.
- The importance of understanding polymorphism for properties like
Abstract
Niosomes, non-ionic surfactant vesicles (NSVs), are the hydrated lipids composed mainly of different classes of non-ionic surfactants, introduced in the seventies as a cosmetic vehicle. Nowadays, niosomes are used as important new drug delivery systems by many research groups and also they are effective immunoadjuvants which some commercial forms are available in the market. These vesicles recently used as gene transfer vectors as well. This review article presents a brief report about the achievements in the field of nanoscience related to NSVs. Different polar head groups from a vast list of various surfactants with one, two or three lipophilic alkyl, perfluoroalkyl and steroidal moieties may be utilized to form the proper vesicular structures for encapsulating both hydrophilic and hydrophobic compounds. The methods of niosome preparation, the vesicle stability related aspects and many examples of pharmaceutical applications of NSVs will be presented. The routes of administration of these amphiphilic assemblies are also discussed.
This document discusses bioadhesion, providing an introduction, theories, fundamentals and models. It defines bioadhesion as adhesion between biological materials, with mucoadhesion being adhesion to mucosal membranes. Theories of bioadhesion include wetting, diffusion, electronic, fracture and adsorption. Fundamentals discussed are biological membranes, bioadhesive polymers and modulation of mucoadhesion. Models of measuring bioadhesion described include falling liquid film, USP apparatus 4 and ex vivo methods. The conclusion states bioadhesion can facilitate adhesion of cells and biomolecules to develop novel biomaterials and therapies.
This document provides an overview of nanogels for drug delivery applications. It defines nanogels as nanosized polymer networks that swell in solvent. Nanogels have properties like biocompatibility and drug loading capacity. They can be administered via various routes and classified based on responsive behavior or linkage type. The document discusses synthesis, characterization, and applications of nanogels in cancer treatment, ophthalmic use, and more. Nanogels are a promising drug delivery system due to abilities like controlled drug release and delivery of therapeutics to targeted sites.
Nanogels are innovative drug delivery system that can play an integral part in pointing out many issues related to old and modern courses of treatment such as nonspecific effects and poor stability.
This document discusses complex formation in pharmaceutical science. It defines complexes as molecules with some anomalous bonding structures that can be described by classical valence theories. There are several types of complexes discussed, including metal complexes where a metal ion interacts with ligands, organic molecular complexes held by weaker forces, and inclusion complexes where one component is trapped within another. Methods for analyzing complexes include determining stoichiometry and stability constants using techniques like continuous variation, spectroscopy, distribution methods, and protein binding studies. The document explores how complex formation can impact drug action.
This document discusses Aquasomes, which are nanoparticle carrier systems composed of a central solid nanocrystalline core coated with polyhydroxy oligomers onto which drug molecules can be adsorbed. Aquasomes are spherical particles 60-300nm in size that are used for targeted drug and antigen delivery. They are prepared through a self-assembly process involving the preparation of a ceramic core, coating the core with carbohydrates, and then immobilizing a drug molecule onto the coated core. Aquasomes have properties such as preserving the integrity of biomolecules and avoiding clearance from the body. They can be characterized through techniques like SEM, TEM, FT-IR, and XRD. Potential applications of Aquasomes
Hydrogels introduction and applications in biology and enAndrew Simoi
Hydrogels are water-swollen, crosslinked polymers that can absorb large amounts of water. They have a variety of applications including in soft contact lenses, drug delivery, wound healing, and tissue engineering. Hydrogels are advantageous for tissue engineering and cell culture as they can mimic extracellular matrix, provide structural support, and allow for nutrient transport. They are also useful for drug delivery as they allow controlled release of molecules. The document discusses the properties, types, advantages and uses of hydrogels.
Biocompatibility of Poly (L-Lactic Acid) Synthesized In Polymerization Unit B...IJERA Editor
The absorbable polyacid is one of the most used and studied materials in tissue engineering. This work
synthesized a poly (L-lactic acid) (PLLA) through ring-opening polymerization and produced nanofibers by the
electrospinning process. The PLLA was analyzed by FTIR and the cytotoxicity was evaluated by the MTT assay
and Live/Dead®. The hemocompatibility was tested by platelet adhesion and hemolytic activity assay. The tests
were performed in contact with human mesenchymal cells at varying times. The high rates of cell viability and
proliferation shown by MTT and Live/Dead® tests demonstrate that this PLLA is a non-toxic material and the
hemocompatibility assay revealed that the biomaterial was also biocompatible. It was achieved as well the
successful production of electrospinning nanofibers, which can be converted for specific biomedical applications
in the future
Hydrogels,
introduction,
historical background,
properties,
classification,
difference between chemical and physical hydrogels,
common uses,
pharmaceutical applications,
preparation methods,
list of monomers used,
analytical machines,
advantages,
disadvantages,
conclusion
Mini review of polysaccharide nanoparticles and drug delivery process AANBTJournal
This document discusses polysaccharide nanoparticles and their use in drug delivery. It begins by explaining that polysaccharides like hyaluronic acid have attracted attention as drug carriers due to their biocompatibility, biodegradability, and ability to be chemically modified. It then focuses on hyaluronic acid specifically, describing its structure and properties, as well as its various applications in drug delivery like using it to create nanoparticles, hydrogels, and conjugates that can selectively target drugs to tumors. The document emphasizes that hyaluronic acid is a promising material for drug delivery due to its biocompatibility and ability to target cancer cells, but that more research is still needed to optimize its use and chemical modification
Pharmacophore Modeling and Docking Techniques.pptDrVivekChauhan1
Pharmacophore modeling and molecular docking techniques are important computational methods used in drug design and discovery. Pharmacophore models identify the essential molecular features responsible for biological activity. Molecular docking predicts how drug molecules bind to protein targets. The document discusses key concepts like pharmacophores, bioisosterism, and molecular docking workflows. It also covers common docking software and factors that influence docking results like intramolecular forces and target preparation. Overall, the document provides an overview of pharmacophore modeling and molecular docking techniques that are widely applied in rational drug design.
Factors influencing absorption of drugs can be categorized as pharmaceutical or patient related. Pharmaceutical factors include drug properties like solubility, particle size and polymorphism that impact dissolution rate, a key step for absorption. Patient factors involve aspects like age, disease state, gastrointestinal pH and transit time. Together, these factors determine the extent and rate of drug absorption after oral administration.
This document describes the development of an in vitro model to study the foreign body response by modulating biomaterial surface properties. The model uses polymeric rods with tailored surface topography, roughness, wettability and chemistry achieved through surface modification techniques. Results showed that surface microstructuring increased cell adhesion, proliferation, and balanced cytokine secretion to optimize collagen and elastin synthesis for tissue regeneration. By linking surface parameters to cell activity, the fate of regenerated tissue could be determined to create successful soft tissue replacements.
The document discusses bioadhesion and mucoadhesion. It defines bioadhesion as materials adhering to biological tissues for extended periods via interfacial forces. Mucoadhesion specifically refers to adhesion between materials and mucosal surfaces. Mucoadhesive drug delivery systems can prolong drug release at application sites, improving therapeutic outcomes. Ideal mucoadhesive polymers rapidly adhere to mucosal layers without interfering with drug release, are biodegradable and non-toxic, and enhance drug penetration at delivery sites. The mechanisms of bioadhesion involve wetting, swelling, interpenetration and entanglement of polymer chains followed by secondary bonding formations. Key factors influencing bioadhesion are discussed.
Toxicology is the field that studies the adverse effects of chemicals on living organisms. Key figures in the history of toxicology include Paracelsus, Rachel Carson, and Orfila. Important chemicals include mercury, DDT, and alcohol. Risk assessment involves hazard identification, hazard characterization, exposure assessment, and risk characterization. Toxicokinetics describes what happens to a compound in the body, including absorption, distribution, metabolism and excretion, while toxicodynamics describes how the compound causes toxicity. Biotransformation can activate or deactivate compounds through phase I and phase II reactions.
This document discusses molecular docking and different models used to describe molecular recognition between biomolecules. It begins by defining molecular recognition and docking, and describes early models like the lock-and-key and induced-fit models. It then discusses computational docking methods, including representing molecules, scoring docked poses, and search algorithms to generate poses. Flexibility is an important consideration, and methods to incorporate flexibility of both small molecule ligands and protein receptors are described.
computational modeling of drug disposition Naveen Reddy
Computational Modelling of Drug disposition, modelling techniques, drug absorption, drug distribution, drug Excretion, quantitative approach, qualitative approach, in silico models, blood brain barrier, plasma protein binding, QSAR, QSPR, Volume of distribution
Introduction
Rheology and Viscosity
Rheology in Pharmaceuticals
• Pharmaceutical formulation
• Pharmaceutical manufacturing
• Dispensing pharmacy
• Pharmaceutical technology
• Physical pharmacy
• Pharmaceutical jurisprudence
Scope of rheology
Applications:
Examples
Conclusion
Rheology has applications in materials science engineering, geophysics, physiology, human biology and pharmaceutics. Materials science is utilized in the production of many industrially important substances, such as cement, paint, and chocolate, which have complex flow characteristics. In addition, plasticity theory has been similarly important for the design of metal forming processes. The science of rheology and the characterization of viscoelastic properties in the production and use of polymeric materials has been critical for the production of many products for use in both the industrial and military sectors. Study of flow properties of liquids is important for pharmacists working in the manufacture of several dosage forms, such as simple liquids, ointments, creams, pastes etc. The flow behavior of liquids under applied stress is of great relevance in the field of pharmacy. Flow properties are used as important quality control tools to maintain the superiority of the product and reduce batch to batch variations
This document discusses release kinetics and various drug release mechanisms and models. It begins by outlining the objectives of studying release kinetics, including predicting in vitro release and release profiles. It then covers key topics like modified Noyes-Whitney equation, drug release mechanisms, and theoretical models for diffusion, swelling, and erosion controlled systems. Specific models discussed in detail include zero order, first order, Hixson-Crowell, and various swelling and erosion models. The document provides information on interpreting release kinetics data using these mathematical models.
This document discusses preformulation in pharmaceutical research and development. It defines preformulation as characterizing the physical and chemical properties of a new drug substance to develop a stable, safe and effective dosage form. The goals are to establish the physicochemical parameters, physical characteristics, kinetic rate profile, and excipient compatibility of a new drug. The objectives are to develop elegant, stable, and safe dosage forms and have an understanding of the drug substance before dosage form development. The document outlines various physicochemical characteristics that are evaluated during preformulation including physical properties like solubility, partition coefficient, stability, and chemical properties like hydrolysis, oxidation, reduction, racemization, and polymerization.
Nanogels are particles composed of physically or chemically cross linked polymer networks that expand in an appropriate solvent. Nanogels are hydrophilic three dimensional networks. Due to their relatively high drug encapsulation ability, consistency, tunable size, effortless preparation, negligible toxicity, and stability in the presence of serum, including stimuli responsiveness, these studies integrate characteristics for topical drug delivery. These are soluble in water and permit immediate drug loading in aqueous media. These are created using a vast array of methods, including photolithographic technique, membrane emulsification, and polymerization methods. Due to the entrapment of nanoparticles in the gel matrix, nanogels used as dermatological preparations have prolonged exposure times on the skin, thereby extending the duration of therapeutic efficacy. B. Karthikeyan | G. Alagumanivasagam "A Review on Nanogels" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-7 | Issue-3 , June 2023, URL: https://www.ijtsrd.com.com/papers/ijtsrd57514.pdf Paper URL: https://www.ijtsrd.com.com/pharmacy/other/57514/a-review-on-nanogels/b-karthikeyan
This document discusses the use of nanotechnology in drug delivery systems. It begins by outlining areas where nanotechnology is being used, including improving drug solubility and bioavailability. It then discusses ideal characteristics of drug delivery carriers and challenges in developing effective systems. Various types of drug delivery carriers are described, including liposomes, niosomes, micelles, nanoparticles, and nanopowders. Controlled release systems, targeting ligands, and applications for cancer treatment are also summarized. The document concludes by stating that nanotechnology has significant potential to improve drug delivery but more research is still needed to understand biological interactions and ensure safety.
Computational chemistry is a branch of chemistry that uses computer simulation to assist in solving complex chemical problems. It exploits methods of theoretical chemistry, incorporated into efficient computer programs, to calculate the structures, the interactions, and the properties of molecules
This document discusses microspheres, which are defined as solid spherical particles containing dispersed drug. Microspheres can be used for controlled drug release applications to reduce side effects and eliminate repeated injections. They have various advantages including flexibility in design and improved safety. The document discusses the types of microspheres including fluorescent, glass, and paramagnetic microspheres. It also discusses the preparation methods, routes of administration including oral and parenteral, mechanisms of drug release, applications, and evaluation of microspheres.
This document discusses microspheres, which are defined as solid spherical particles containing dispersed drug. Microspheres can be used for controlled drug release applications to reduce side effects and eliminate repeated injections. They have various advantages including flexibility in design and improved safety. The document discusses the types of microspheres including fluorescent, glass, and paramagnetic microspheres. It also discusses the preparation methods, materials used, routes of administration including oral and parenteral, mechanisms of drug release, applications, and evaluation of microspheres.
1) The document describes a study on using mesoporous metal-organic frameworks (MOFs) as nanocarriers for controlled drug release in chemotherapy. Zirconium-based MOF nanoparticles were synthesized to carry and release doxorubicin and cisplatin.
2) The MOF nanoparticles were found to have high drug loading capacity and provided controlled release of the chemotherapeutic drugs through their porous structure. In vitro tests showed the drugs were effectively released and reduced cancer cell viability.
3) The results suggest mesoporous MOFs have potential as nanocarriers for chemotherapy by improving drug pharmacokinetics and maximizing effectiveness through controlled release at tumor sites.
This document outlines the syllabus for the course GE 6351 Environmental Science and Engineering. It is divided into 4 units that cover topics such as ecosystems, environmental pollution, natural resources, and social issues related to the environment. Each unit includes multiple choice and short answer questions in Part A as well as longer answer questions requiring explanations in Part B. The questions assess students' understanding of key concepts like the food chain, biodiversity, different types of pollution, natural resources like forests and water, and social issues including global warming, waste management, and environmental regulations.
This document describes research into developing a biodegradable polyurethane polymer suitable for melt electrospinning into tissue engineering scaffolds. The researchers synthesized various polyurethane formulations based on aliphatic diisocyanates, polycaprolactone, 1,4-butanediamine, and 1,4-butanediol. The final optimized polymer formulation consisted of a purified polyurethane based on 1,4-butane diisocyanate, polycaprolactone, and 1,4-butanediol in a 4/1/3 molar ratio with a weight-average molecular weight of around 40 kDa. This polymer could be readily melt electrospun into scaffolds exhibiting point
The document is from the Food and Drug Administration (FDA) and provides information about mammograms. It discusses how mammograms can help detect breast cancer early, when it is most treatable. It also explains that the FDA inspects and certifies all mammogram facilities in the US to ensure safety and quality standards are met. The document provides guidance on getting mammograms and what to do if a mammogram shows abnormalities.
1. The study examines the effects of supernatant from Serratia marcescens bacterial cultures on various cancer cell lines and non-malignant cells. They find the supernatant induces rapid apoptosis in cancer cell lines through DNA fragmentation and caspase activation, but with little toxicity to non-cancerous cells.
2. They identify the compound responsible as prodigiosin, a red pigment produced by S. marcescens. Mutant bacterial strains that do not produce prodigiosin do not induce apoptosis, and prodigiosin is isolated and identified from S. marcescens.
3. The results suggest prodigiosin induces apoptosis in hematopoietic cancer cells specifically, raising
1) Prodigiosin, a bacterial metabolite, induces apoptosis in human breast cancer cells. Gene expression profiling found that prodigiosin strongly increased expression of the NAG-1 gene.
2) Experiments showed that prodigiosin triggers accumulation of the tumor suppressor protein p53, but induction of NAG-1 was independent of p53.
3) Prodigiosin causes inhibition of AKT and activation of glycogen synthase kinase-3B (GSK-3B). Induction of NAG-1 and apoptosis correlated with GSK-3B activation. Inhibiting GSK-3B reduced apoptosis, suggesting GSK-3B plays a key role in the proap
This document discusses the synthesis of poly(lactic acid) (PLA) biomaterials. There are two main synthetic methods - direct polycondensation and ring-opening polymerization of lactide monomers. Direct polycondensation includes solution and melt polycondensation, but yields PLA with low molecular weight. Ring-opening polymerization using metal catalysts is more common and can produce high molecular weight PLA, but the metal catalysts require removal. Recent research focuses on developing non-toxic catalysts and new polymerization conditions.
Advanced control scheme of doubly fed induction generator for wind turbine us...IJECEIAES
This paper describes a speed control device for generating electrical energy on an electricity network based on the doubly fed induction generator (DFIG) used for wind power conversion systems. At first, a double-fed induction generator model was constructed. A control law is formulated to govern the flow of energy between the stator of a DFIG and the energy network using three types of controllers: proportional integral (PI), sliding mode controller (SMC) and second order sliding mode controller (SOSMC). Their different results in terms of power reference tracking, reaction to unexpected speed fluctuations, sensitivity to perturbations, and resilience against machine parameter alterations are compared. MATLAB/Simulink was used to conduct the simulations for the preceding study. Multiple simulations have shown very satisfying results, and the investigations demonstrate the efficacy and power-enhancing capabilities of the suggested control system.
Low power architecture of logic gates using adiabatic techniquesnooriasukmaningtyas
The growing significance of portable systems to limit power consumption in ultra-large-scale-integration chips of very high density, has recently led to rapid and inventive progresses in low-power design. The most effective technique is adiabatic logic circuit design in energy-efficient hardware. This paper presents two adiabatic approaches for the design of low power circuits, modified positive feedback adiabatic logic (modified PFAL) and the other is direct current diode based positive feedback adiabatic logic (DC-DB PFAL). Logic gates are the preliminary components in any digital circuit design. By improving the performance of basic gates, one can improvise the whole system performance. In this paper proposed circuit design of the low power architecture of OR/NOR, AND/NAND, and XOR/XNOR gates are presented using the said approaches and their results are analyzed for powerdissipation, delay, power-delay-product and rise time and compared with the other adiabatic techniques along with the conventional complementary metal oxide semiconductor (CMOS) designs reported in the literature. It has been found that the designs with DC-DB PFAL technique outperform with the percentage improvement of 65% for NOR gate and 7% for NAND gate and 34% for XNOR gate over the modified PFAL techniques at 10 MHz respectively.
Harnessing WebAssembly for Real-time Stateless Streaming PipelinesChristina Lin
Traditionally, dealing with real-time data pipelines has involved significant overhead, even for straightforward tasks like data transformation or masking. However, in this talk, we’ll venture into the dynamic realm of WebAssembly (WASM) and discover how it can revolutionize the creation of stateless streaming pipelines within a Kafka (Redpanda) broker. These pipelines are adept at managing low-latency, high-data-volume scenarios.
Literature Review Basics and Understanding Reference Management.pptxDr Ramhari Poudyal
Three-day training on academic research focuses on analytical tools at United Technical College, supported by the University Grant Commission, Nepal. 24-26 May 2024
A review on techniques and modelling methodologies used for checking electrom...nooriasukmaningtyas
The proper function of the integrated circuit (IC) in an inhibiting electromagnetic environment has always been a serious concern throughout the decades of revolution in the world of electronics, from disjunct devices to today’s integrated circuit technology, where billions of transistors are combined on a single chip. The automotive industry and smart vehicles in particular, are confronting design issues such as being prone to electromagnetic interference (EMI). Electronic control devices calculate incorrect outputs because of EMI and sensors give misleading values which can prove fatal in case of automotives. In this paper, the authors have non exhaustively tried to review research work concerned with the investigation of EMI in ICs and prediction of this EMI using various modelling methodologies and measurement setups.
ACRP 4-09 Risk Assessment Method to Support Modification of Airfield Separat...
Theories on hydrogel structure
1. ECOLOGICAL CHEMISTRY AND ENGINEERING S
Vol. 17, No. 2 2010
Roman ZARZYCKI1
, Zofia MODRZEJEWSKA1
and Katarzyna NAWROTEK1*
DRUG RELEASE FROM HYDROGEL MATRICES
UWALNIANIE LEKÓW Z HYDROŻELI
Abstract: Description of the kinetics of drug release from hydrogels is a domain of steadily increasing academic
and industrial importance. The aim of this paper is to review mathematical approaches to drug release from
hydrogel matrix devices. In the first section the parameters of hydrogel structure are described. Than the
phenomena that influencing resulting drug release are discussed. Finally, mechanisms of physical release and
release with chemical reaction are studied. In this section mathematical expression that predicting drug release
profiles are described.
Keywords: hydrogel, mathematical modelling, controlled release, drug delivery, diffusion, swelling, erosion
Introduction
Hydrogel is a hydrophilic mixture which has the properties of both solid and liquid [1,
2]. Hydrogel structure consists of networks that are formed from randomly cross-linked
macromolecules [3]. It contains three phases:
1) polymeric-network matrix solid phase,
2) interstitial fluid phase,
3) ionic phase.
The solid phase includes a network of cross-linked polymeric chains. Polymeric chains
create a three-dimensional matrix with interstitial space filled up with water and often
biological fluids. The cross-linked polymeric network can be formed physico-chemically,
for example by van der Waals interactions, hydrogen bonding, electrostatic interactions and
physical entanglements as well as by covalent bonds. The fluid phase fills in the pores of the
polymeric matrix and makes that hydrogel has wet and elastic properties. Due to these
properties structure of hydrogel resembles to living tissue. The ionic phase consists of the
ionisable groups that are bounded to the polymer chains and the mobile ions (counter-ions
and co-ions). This phase exists due to the presence of electrolytic solvent.
Hydrogels can be formed from both natural and synthetic polymers [4-6]. Hydrogels
based on natural polymers can have insufficient mechanical properties, contain pathogens
1
Faculty of Process and Environmental Engineering, Lodz University of Technology, ul. Wólczańska 175,
90-924 Łódź
*
Corresponding author: katarzynanawrotek@onet.eu
2. Roman Zarzycki, Zofia Modrzejewska and Katarzyna Nawrotek118
and evoke immune responses. On the other hand, they have numerous advantageous
properties like inherent biocompatibility, biodegradability, bacteriostatic and wound-healing
properties. Synthetic hydrogels do not have these inherent bioactive properties.
Drugs can be incorporated into hydrogel matrices by two ways [4]:
1) post-loading,
2) in-situ loading.
In the post-loading method a hydrogel matrix is formed and than the drug is absorbed
to this matrix. For an inert hydrogel system diffusion is the major force for drug uptake.
Drug release will be determined by diffusion and/or gel swelling. For hydrogel containing
drug-binding ligands the release will be determined by a drug-polymer interaction and drug
diffusion. In the in-situ loading a polymer precursor solution is mixed with drugs
or drug-polymer conjugates. Hydrogel network formulation and drug encapsulation are
accomplished simultaneously. The drug release will be determined by diffusion, hydrogel
swelling, reversible drug-polymer interactions or degradation of labile covalent bonds.
The device geometry significantly influences the resulting drug release kinetics [1, 7].
The delivery device can be in the shape of:
1) thin film,
2) sphere,
3) cylinder,
4) irregular solid.
The nanostructure of hydrogel can be described by three parameters [4, 8]:
1) s2,ν - polymer volume fraction in the swollen state of hydrogel,
2) cM - average molecular weight between crosslinks,
3) ξ - network mesh size.
The mobility of molecules and their rates of diffusion in swollen non-porous hydrogels
are determined by the amount of liquid which is retained in the hydrogel, the distance
between polymer chains and flexibility of those chains.
The polymer volume fraction in the swollen state is the amount of fluid which can be
absorbed and retained in the hydrogel matrix. It is expressed as a ratio of the polymer
volume (Vp) to the swollen gel volume (Vg):
g
p
s2,
V
V
ν = (1)
The average molecular weight between two consecutive cross-links ( cM ) is a measure
of the degree of hydrogel cross-linking. The cross-links can be both chemical and physical
in nature. Due to the random nature of the polymerization process only an average value of
molecular weight is calculated. It can be described by the Flory-Rehner equation:
( )[ ]
2
ν
ν
νχνν1ln
V
ν
M
2
M
1
s2,3
1
s2,
2
s2,12s2,s2,
1
nc
−
++−
−== (2)
where:
nM - average molecular weight of the polymer chains,
3. Drug release from hydrogel matrices 119
v - specific volume of the polymer,
V1 - molar volume of water,
12χ - parameter of polymer-water interaction.
The network mesh size is a measure of space accessible between the macromolecular
chains (eg for the drug diffusion). This space is considered as molecular mesh or pores.
Hydrogels can be classified as:
1) macroporous,
2) microporous,
3) nonporous.
The size of pores is described by correlation length ξ. This structural parameter is
defined as a linear distance between two neighbouring crosslinks. It can be expressed by the
following equation:
( )2
1
2
0
3
1
s2, rvξ
−
= (3)
In this expression ( )2
1
2
0r is the root-mean-squared end-to-end distance of network
chains between two neighbouring crosslinks in the swollen state.
A B
drug
cross-link
mesh size
polymer chain
Degree of crosslinking
Chemical structure
External stimuli
Fig. 1. Schematic illustration of mesh size in hydrogel at (A) swollen state and (B) deswollen state
(adapted from [4])
The mash size in the swollen and deswollen state is shown in Figure 1. This parameter
depends on several factors like the degree of gel cross-linking, chemical structure of the
composing monomers and external stimuli (temperature, pH and ionic strength).
These three parameters ξ)andM,(ν cs2, can be determined theoretically or through
experimental techniques.
The mechanism of release
Depending on the composition of hydrogel (type of polymer, type of drug and
additives), geometry (size and shape), preparation technique and environmental conditions
during drug release, one or more of the following physical and chemical phenomena affect
the drug release kinetics [7, 9]:
1) Wetting of the drug delivery device surface with release medium (water).
2) Release medium (water) penetration into the drug delivery device (eg via pores).
4. Roman Zarzycki, Zofia Modrzejewska and Katarzyna Nawrotek120
3) Creation of pores filled with water.
4) Degradation of drug and/or polymer.
5) Diffusion of drug and/or products of polymer degradation inside the hydrogel matrix.
6) Diffusion of drug and/or products of polymer degradation in the fluid.
7) Dissolution and/or precipitation of drug and/or degradation products.
8) Microenvironmental pH changes inside the hydrogel matrix caused by the degradation
of polymer.
9) Autocatalytic effects during hydrogel matrix degradation.
10) Swelling of polymer.
11) Closing of pores caused by polymer swelling.
12) Osmotic effects caused by creation of significant hydrostatic pressure in the drug
delivery device.
13) Creation of acidic or basic microenvironments in the dosage forms caused by
degradation products.
14) Physical drug-products of polymer degradation interactions (eg ion-ion
attraction/repulsion and van der Waals forces) which can significantly vary with time
and position caused by changes in microenvironmental conditions.
15) Chemical reactions between the drugs and products of polymer degradation and/or
water.
16) Convection processes caused by significant hydrostatic pressure created in drug
delivery device.
17) Adsorption and/or desorption processes.
18) Changes in the drug delivery device geometry and/or dimensions caused by shear
forces.
It is not reasonable to take all the mentioned phenomena into account. It is crucial for
a mathematical model to take into account only dominating physical and chemical
processes. Moreover, these phenomena concern only drug transport in the model system,
not in the living organism. To describe the mechanism of drug transport in the living body
various additional phenomena must be taken into account, eg enzymatic degradation,
protein binding, active and passive drug uptake into cells, interactions with compounds in
extra- and intracellular space [7].
From the process engineering point of view, the mechanism of release consists of the
following phenomena:
1) exterior diffusion,
2) interior diffusion,
3) desorption,
4) chemical reactions.
Moreover, the processes of shape change (eg heterogeneous and homogeneous erosion)
and processes of surface change (desorption, reconstruction and reaction) can overlap to
above phenomena. These processes (diffusion, desorption, chemical reactions and matrix
erosion) are studied below.
Exterior diffusion
The mechanism of release consists of exterior and interior processes of diffusion [10].
Exterior diffusion takes place when drug molecules diffuse from surface of the hydrogel
5. Drug release from hydrogel matrices 121
matrix to bulk of the liquid phase (Fig. 2). The rate of mass transfer can be described by the
following expressions:
( )δ
AL
*
ALLA CCkN −= (4)
or
( )δ
AL
*
ALLA CCAkG −= (5)
where:
NA - flux of the drug,
GA - mass transfer rate,
kL - mass transfer coefficient,
*
ALC - surface concentration of the drug,
δ
ALC - bulk concentration of the drug,
A - area of mass transfer.
The mass transfer coefficient (kL) is expressed as:
L
LAB
L
δ
)(D
k = (6)
where LAB )(D - drug diffusion coefficient.
Fig. 2. Exterior diffusion: model concentration profile of drug, real
concentration profile of drug
6. Roman Zarzycki, Zofia Modrzejewska and Katarzyna Nawrotek122
Drug concentration is the highest close to the surface of the hydrogel matrix and it
decreases with the length. When the bulk of liquid is well stirred the value of drug
concentration is constant. Exterior diffusion can control the rate of drug release only in
exceptional cases. In general, the rate of drug release depends on interior phenomena,
especially on interior diffusion.
Interior diffusion
In general, the rate of drug release is controlled by interior diffusion (Fig. 3).
Fig. 3. Interior diffusion of drug molecules
Theories which are based on Fick’s law of diffusion distinguish two types of systems
(1) reservoir and (2) monolithic devices (Fig. 4).
Fig. 4. Schematic illustration of two types of diffusion-controlled spherical drug delivery devices
7. Drug release from hydrogel matrices 123
In the reservoir system a polymer membrane surrounds inner bulk of dissolved,
suspended or neat drug [11, 12]. Diffusion of an encapsulated drug through the membrane is
the rate-limiting step in this delivery system. A constant concentration gradient across the
polymer membrane is achieved by saturated concentration of the drug core. Drug is
absorbed from inner bulk by the membrane. Then it diffuses through the membrane and is
desorbed from the membrane to the fluid which surrounds the reservoir device.
The drug release in a reservoir system where a polymeric hydrogel membrane
surrounds the drug bulk can be described by Fick’s first law of diffusion [1, 4]:
dx
dC
DN A
A −= (7)
where:
NA - flux of the drug,
D - drug diffusion coefficient,
CA - drug concentration.
For the reservoir device with initial drug concentration smaller than drug solubility, the
drug concentration at inner surface of the membrane decreases with time. The process runs
at the unsteady state conditions and the exact solution can be obtained by solving the
equations of mass balance for the membrane and bulk of the liquid. For a short time in the
case of non-swelling or dissolving membrane and perfect sink conditions of release, the
drug release can be described by the first order kinetics. The drug release kinetics is not
dependent on the device geometry [7]:
−
==
V
MM
l
ADK
l
ADKC
dt
dM t0tt
(8)
where:
Mt - absolute cumulative amount of drug released at time t,
Ct - concentration of drug in the release medium at time t,
M0 - initial amount of drug in the device,
V - volume of drug reservoir,
A - total surface area of the device,
l - thickness of the membrane,
K - partition coefficient of the drug between the membrane and the reservoir,
D - diffusion coefficient of the drug within the membrane.
In the case of a system with initial drug concentration much bigger than the drug
solubility in the reservoir device, the released molecules are replaced by the dissolution
molecules of drug crystals/amorphous aggregates. The inner membrane surface
concentration of drug is constant. If the membrane thickness and drug permeability are
constant and perfect sink conditions are maintained during the release, the drug release may
be described by zero order release kinetics. It is independent on the drug delivery device
geometry [7]:
l
ADKC
l
AJ
dt
dM slimt
== (9)
where:
dt
dMt
- steady state release rate at time t,
8. Roman Zarzycki, Zofia Modrzejewska and Katarzyna Nawrotek124
Jlim - membrane-limiting flux,
Cs - solubility of the drug in the reservoir.
In the matrix system the drug is equally dissolved or dispersed in the polymer matrix
[11, 12]. A disadvantage of this system is the release with a continuously decreasing release
rate. This is caused by an increase of diffusion way length and decrease of drug area in the
polymer matrix as the drug release proceeds.
For a matrix system in which the drug is equally dispersed throughout the polymeric
matrix, unsteady-state drug diffusion in a one-dimensional slap-shaped matrix can be
described by Fick’s second law of diffusion [4, 13]:
2
A
2
A
dx
Cd
D
dx
dC
= (10)
In this equation the drug diffusion coefficient is assumed to be constant. In the case in
which diffusivity is concentration-dependent the following equation can be used:
( )
∂
∂
∂
∂
=
∂
∂
x
C
CD
xt
C A
A
A
(11)
For monolithic devices the system geometry strongly affects the resulting drug release
profile. In the case of the device with the initial drug concentration below drug solubility,
the drug molecules are dissolved in the hydrogel (monolithic solution). Otherwise, the drug
molecules coexist with amorphous aggregates and/or drug crystals (monolithic dispersion).
For monolithic solution with the following release conditions:
1) the absence of significant changes in the hydrogel matrix during the release,
2) perfect sink conditions during the release,
3) the release of drug is mostly controlled by diffusion through the hydrogel matrix,
different equations are used to calculate a resulting release profile, depending on the system
geometry.
For example, an analytical solution of Eq. (10) can be obtained using separation
of variable technique [1]:
1) thin film with negligible edge effects:
( )
( )
∑
∞
=
+−
+
−=
0n
2
22
22
0
t
L
tπ12nD
exp
12n
1
π
8
1
M
M
(12)
where:
n - dummy variable,
L - thickness of the film.
2) spherical delivery device:
∑
∞
=
−
−=
0n
2
22
22
0
t
R
tπDn
exp
n
1
π
6
1
M
M
(13)
where R - sphere radius.
3) cylinders delivery device:
( )
( )
∑∑
∞
=
∞
=
+−
+
×
−
−=
0p
2
22
2
1n
2
2
n
2
n
2
0
t
H
tπ12pD
exp
12p
1
R
Dtq
exp
q
1
π
32
1
M
M
(14)
9. Drug release from hydrogel matrices 125
where:
p - dummy variable,
qn - the roots of the Bessel function of the first kind of zero order,
R - cylinder radius,
H - cylinder height.
For monolithic dispersion the mathematical model is more complicated. Higuchi
developed a mathematical equation to predict drug release from a monolithic matrix system
with the simplest geometry of thin films with negligible edge effects [1, 7, 14, 15]:
( ) s0ss0
t
CCfortCC2CD
A
M
>>−= (15)
where:
Mt - cumulative absolute amount of drug released at time t,
A - surface area of the controlled release device exposed to the release medium,
D - drug diffusivity in the polymer,
C0 - initial drug concentration,
Cs - drug solubility in the polymer.
Equation (15) can be simplified to the following equation:
tK
M
Mt
=
∞
(16)
where:
∞M - absolute cumulative amount of drug released at time t that should be equal to the
initial amount of drug in the system at time t = 0,
K - system constant.
Higuchi developed this model using the pseudo-steady state assumptions. A controlled
drug delivery system must fulfil the following conditions:
1) The initial drug concentration must be much higher than the solubility of the drug
(C0>>Cs).
2) The release is one-dimensional and thus the edge effects can be neglected.
3) The drug particles are much smaller than the thickness of drug delivery device.
4) The polymer matrix does not swell or dissolve.
5) The drug diffusivity is constant with the time and position.
6) Perfect sink conditions are maintained in the system.
The simplicity of Higuchi’s model is its important advantage.
Peppas and co-workers developed another empirical equation which assumes
a time-dependent power low function [8]:
nt
tk
M
M
⋅=
∞
(17)
where:
∞M
Mt
- fractional release,
k - structural/geometric constant for a particular system,
n - release exponent representing the release mechanism.
Table 1 gives values of n for delivery matrices with different geometries and release
mechanisms.
10. Roman Zarzycki, Zofia Modrzejewska and Katarzyna Nawrotek126
Table 1
Release exponent values (n) in the Peppas equation [7]
Exponent, n
Slab Cylinder Sphere
Drug release mechanism
0.5 0.45 0.43 Controlled diffusion
0.5 < n < 1.0 0.45 < n < 0.89 0.43 < n < 0.85 Anomalous transport
1.0 0.89 0.85 Controlled swelling
Fick’s law equations cannot be solved analytically when more complex geometries or
non-constant drug diffusivities are incorporated into the model. Moreover, in the case of
swelling polymers diffusivities of encapsulated molecules will be strongly affected by the
degree of swelling and cross-linking density of the gel. Thus D will be sensitive to
environmental changes or degradation polymer matrix and might vary over the time-scale of
release. Theoretical models for calculation of molecule diffusion coefficients can be
described by the following general form [4]:
( )ξ,ν,rf
D
D
s2,s
0
g
= (18)
where:
Dg - drug diffusion coefficient in the swollen hydrogel network,
D0 - drug diffusion coefficient in pure solvent,
rs - size of the drug to be delivered.
This expression takes into account factors which affect drug release, like the gel
structure, the polymer composition, water content, and the size of molecules. In the case of
degradable polymer Dg changes with the degradation of polymer network due to an increase
in hydrogel mesh size and decrease in polymer volume fraction over time.
Several expressions have been developed to describe the relationship between drug
diffusivity in the hydrogels and in the solution. For example, Lusting and Peppas proposed
the following equation to correlate the relationship between drug diffusivity and network
structure [4]:
−
−=
s2,
s2,s
0
g
ν1
ν
Yexp
ξ
r
1
D
D
-
(19)
where Y - ratio of the critical volume required for translation movement of the encapsulated
drug molecule and the average free volume per solvent molecule.
Finally [10], the influence of pore size on diffusion coefficients should be mentioned.
If:
1) pore diameter is much bigger than average free length of molecules - effective diffusion
coefficient (De) can be calculated from the formula:
l
ν
DD s2,
e = (20)
dx
dC
DN A
eA −= (21)
2) pore diameter is lower than average free length of molecules - Knudsen’s diffusion
coefficient (Dk) govern the law:
11. Drug release from hydrogel matrices 127
A
3
k
M
T
r109.7D ⋅= (22)
dx
dC
DN A
kA −= (23)
Simultaneous diffusion and desorption of drug
Drug molecules can be adsorbed either chemically or physically on the pore surface
[16]. In chemisorptions, the electronic structure (electronic density) of adsorbate molecule
is strongly modified. In physical adsorption the adorbate is weakly adherent by secondary
interactions (eg van der Waals forces).
Fig. 5. Desorption and diffusion
The rate of mass transfer can be controlled by physical adsorption if the rate of
desorption is finite (or is comparable to the rate of diffusion). In literature, a description of
such processes is lacking. A simple model of drug release with desorption is described in
the work [17]. The drug is desorbed from the hydrogel pore surface and then diffuses within
the pore (Fig. 5). In the system with following conditions:
1) distribution of pores in the hydrogel is homogeneous,
2) movement of molecules is described by first Fick’s law of diffusion,
3) diffusion coefficient is constant,
4) the release medium is ideally mixed - without exterior resistance,
12. Roman Zarzycki, Zofia Modrzejewska and Katarzyna Nawrotek128
the drug release can be described (Fig. 5) by the following equation:
( )[ ] dVrlaNdNN
dt
dC
dV AAAA −−+= (24)
This equation describes the differential volume of the medium that is in the pore
between x and x+dx. The final results of the model can be found in the paper [17].
Chemical reactions
In the case of release with a chemical reaction drugs and/or products of polymer
degradation can react with the released medium inside its pores. The released medium
molecules diffuse to hydrogel medium pores. During the contact with drugs or products of
polymer degradation they undergo a chemical reaction. This reaction can be reversible or
irreversible, simple or complex and slow or fast. Then, the products of chemical reactions
undergo interior and exterior processes of diffusion.
Change of shape
Hydrogel matrix can change of its shape during the release. Change of shape can be
caused by following phenomena:
1) chain cleavage,
2) matrix swelling,
3) matrix erosion.
These processes are discussed below.
Chain cleavage
In the case of systems with pendant chain (prodrugs), the drug is covalently linked to
the polymer network and its release depends on the rate of bond splitting [4]. The drug
release is not mediated by diffusion in this system.
The prodrugs system is used to improve the therapeutic efficiency of the drug. In
general, the release of covalently bound drugs depends by the degradation rate of the
polymer-drug link. Most of these links are hydrolytically degradable. This causes that the
rate of drug release is absolutely characterized by simple first-order kinetics.
Göpferich formulated [18-20] a theory of polymer degradation and erosion. He
assumed that the rate of polymer degradation is identical in the whole polymer matrix.
When the polymer is initially insoluble in water and hydrolysis is the only mechanism of
polymer erosion, then erosion is controlled by:
1) rate of water diffusion into the bulk of polymer (tdiff),
2) rate of the polymer backbone degradation by water (tc).
Water velocity inside hydrogel matrix pores can be described by diffusion. The rate of
water diffusion into the polymer matrix can be expressed by the following equation:
eff
2
diff
4D
Πx
t = (25)
where:
x - mean distance,
Deff - effective diffusion coefficient of water inside the polymer matrix.
13. Drug release from hydrogel matrices 129
The rate of chain cleavage by water can be expressed by the following equation:
( )
( )
−
−= s
A
A
c
ρ1NN
M
lnxln
λ
1
nt (26)
where:
n - number of polymer bonds,
λ - rate constant that takes into account differences in the reactivity of hydrogel
functional groups,
AM - average molecular weight number,
NA - Avogadro’s number,
N - average degree of polymerization (the number of monomers per polymer chain),
ρ - polymer density.
Erosion number is used to predict the erosion mechanism. It is a dimensionless number
expressed by the ratio of the rate of water diffusion to the rate of chain cleavage by water:
(n)t
t
ε
c
diff
= (27)
The values of erosion number can be divided into three ranges. For ε>>1 water reacts
with a polymer faster than the water diffuses. This system is controlled by surface erosion.
For ε~1 the erosion mechanism is changed. For ε<<1 water diffuses faster than it can react
with the polymer. This system is controlled by bulk erosion.
Matrix swelling
The mechanism of hydrogel swelling is one of the most important factors in drug
release phenomena. This mechanism of drug release occurs when diffusion of an active
agent is faster than hydrogel swelling [4, 15 and 21]. In swelling-controlled system
hydrogels may undergo a swelling-driven phase transition from a glassy state to rubbery
state (Fig. 6). This transition occurs when the characteristic glass-rubber polymer transition
temperature is lower than temperature of fluid which surrounds the drug delivery matrix. In
the glassy state, entrapped molecules remain immobile. In the rubbery state dissolved drug
molecules rapidly diffuse to the fluid through the swollen layer of polymer. Released fluid
molecules contact the external layer of hydrogel. This forms a moving front that divides
hydrogel matrix into a glassy and swollen region. In these systems the rate of molecule
release depends on the rate of gel swelling.
In the swelling-controlled delivery system following phenomena take places [7]:
1) The length of drug diffusion way increases. This causes a decrease of drug
concentration gradient (driving force of diffusion) and a decrease of drug release rates.
2) The mobility of drug molecules increases. This causes an increase of drug release rates.
Drug diffusion time and polymer chain relaxation time are two main parameters that
determine drug delivery from swelling polymeric matrices. In this system the time-scale for
polymer relaxation (λ) is the rate-limiting step. In the diffusion-controlled delivery system,
the time-scale of drug diffusion (t) is the rate limiting step. The Deborah number (De) is
applied to compare these two time-scales:
14. Roman Zarzycki, Zofia Modrzejewska and Katarzyna Nawrotek130
2
δ(t)
λD
t
λ
De == (28)
where δ(t) - time-dependent thickness of the swollen phase.
Fig. 6. Schematic illustration of drug delivery device in glassy and rubbery state matrix (adapted from
[4])
In the case of diffusion-controlled systems (De<<1) Fickian diffusion dominates the
molecule release process. In the case of swelling-controlled systems (De>>1) the rate of
molecule release depends on the swelling rate of polymer networks.
In the swelling-controlled delivery systems to describe molecule release a modified
empirical power law can be used. Peppas and Sahlin developed such a model taking into
account the drug diffusion and polymer relaxation [22]:
2m
2
m
1
t
tktk
M
M
+=
∞
(29)
where:
k1 - constant that corresponds to the release rate of diffusion,
k2 - constant that corresponds to the release rate of polymer relaxation,
m - constant.
The first term on the right-hand side represents the diffusion and the second term
represents polymer relaxation.
This empirical expression does not take into account „moving-boundary” conditions in
which the gel expands heterogeneously as water penetrates and swells the gels. For this case
Krosmeyer and Peppas introduced an equation to correlate the moving boundary
phenomena with hydrogel swelling:
D
δ(t)V
Sw = (30)
where:
Sw - swelling interface number,
V - velocity of the hydrogel swelling front,
D - drug diffusion coefficient in the swollen state.
In a slab system with Sw<<1 drug diffusion is much faster than the movement of
glassy-rubbery interface and a drug release has a zero-order release profile.
Siepmann and Peppas [23-25] developed a more rigorous method to predict molecule
release from SCDS, the so-called sequential layer model. This model takes into account
15. Drug release from hydrogel matrices 131
drug diffusion, polymer relaxation and dilution. For example, in the system with cylindrical
geometry and concentration-dependent diffusion coefficients the following equation should
be solved:
∂
∂
∂
∂
+
∂
∂
+
∂
∂
∂
∂
=
∂
∂
z
C
D
zr
C
r
D
r
C
D
rt
C k
k
kkk
k
k
(31)
where Ck and Dk are the concentration and diffusivity of the diffusible species, respectively.
Matrix erosion
Surface erosion
In systems with surface erosion (heterogeneous erosion) drug release is caused by
degradation of the polymer surface (Fig. 7).
Fig. 7. Schematic illustration of surface and bulk erosion (adapted from [9])
The rate of bond hydrolysis of hydrophobic polymer networks is much faster than the
rate of water transport into the polymer bulk. Erosion occurs mostly in the external layers of
the polymer matrix. The degradation takes place only on the surface (heterogeneous
process). This system of drug release occurs only in enzymatic-degrading systems in which
the rate of enzymatic degradation is much faster than the transport of enzyme into the
hydrogel [9, 15].
16. Roman Zarzycki, Zofia Modrzejewska and Katarzyna Nawrotek132
Most of the models with surface-erosion are based on hydrolytic- and
enzymatic-degrading polymers.
Hopfenberg proposed a model for theoretical prediction of the molecule release from
surface-eroding matrix in which the release depends only on matrix erosion rates [1, 13]:
n
00
at
aC
tk
11
M
M
−−=
∞
(32)
In this equation ka is the erosion-rate constant, a0 is the initial dimension of drug
delivery device (radius for a spherical or cylindrical geometry and half-thickness for slab
geometry) and C0 is the initial concentration of drug in the polymer matrix. n is the
geometric shape factor (1 for a slab, 2 for a cylinder and 3 for a sphere). In the case of slab
(n = 1) drug release has a zero-order profile.
Katzhendler, Hoffman and co-workers described a general mathematical model for
heterogeneous eroding networks [26]. In this model it is assumed that swelling of the
polymer matrix is slower than its erosion. It can be applied for the hydrogel tablets with
different rates of erosion in the radial and axial directions. The kinetics of drug release from
erodible polymer matrix with two coordinates a in radial and b in axial directions can be
described by the following equation:
−
−−=
∞ 00
b
2
00
at
bC
t2k
1
aC
tk
11
M
M
(33)
In this equation:
ka - radial erosion-rate constant,
kb - axial erosion-rate constant,
a0 - initial radius of the tablet,
b0 - initial thickness of the tablet.
Lee proposed another mathematical theory for surface-eroding hydrogel systems [7].
This model can be applied to film geometry devices with different “drug loading/drug
solubility” ratios. Lee considered movements of the diffusion front and erosion front (Fig.
8). This model assumes that the front of erosion moves at constant velocity, edge effects can
be neglected and there are perfect sink conditions throughout the test. The drug release can
be expressed by the following equation:
+−+=
∞ 6
a
2
1
A
C
δτ
D
Ba
δ
M
M 3st
(34)
h2δ1δh
C
A
δh
C
A
a
2
ss
3 −−
+−+= (35)
−=
sC
A
1
D
Ba
2
1
h (36)
In the above equations:
δ - relative separation between the diffusion and erosion fronts,
B - constant of surface erosion front,
a - half-thickness of the film,
17. Drug release from hydrogel matrices 133
D - drug diffusivity in the system,
τ - dimensionless time,
D
Ba
- measure of relative contribution of erosion and diffusion to drug release.
Fig. 8. Scheme of the drug concentration in the surface-eroding system (adapted from [7])
Bulk erosion
In bulk degrading systems the drug release is governed by degradation of the network
and molecule diffusion (Fig. 7). Bulk eroding polymers degrade slowly and water infusion
into the system is much faster than the degradation of polymer [4, 9, 15]. Thus, the whole
drug delivery device is rapidly hydrated and polymer chains break off throughout the
system. Erosion takes place in the entire system (homogeneous process).
Heller and Baker developed a mathematical theory predicting drug release from
waterinsoluble polymers that can be hydrolytically converted in water-soluble molecules
[9]. This model assumes that the degradation of bulk eroding polymers can be described by
first-order kinetics. Heller and Baker modified the classical Higuchi equation (Eq. (15)).
They assumed that permeability of the drug in the biodegradable polymeric matrix is not
constant and increases with time. In their model they applied the following ratio of the drug
permeability at time t (Pt) to the initial permeability (P0):
ZN
N
boundsofnumberremaining
boundsofnumberinitial
P
P
0
t
−
== (37)
where:
N - initial number of bonds,
Z - number of cleavage during time interval [0,t].
Polymer bonds are split with the first-order kinetics:
( )ZNK
dt
dZ
−= (38)
where K - the first order rate constant.
18. Roman Zarzycki, Zofia Modrzejewska and Katarzyna Nawrotek134
After integration and rearrangement one can get the following equation which describes
the drug release from thin slab with initial drug concentration above the drug solubility in
hydrogel:
( )
t
CKtexp2P
2
A
dt
dM 00t
= (39)
Charlier and his co-workers described another mathematical model predicting drug
release from bulk eroding polymer films [27]. They assumed that the polymer degradation
and the drug diffusion are simultaneous. Experimental results of mifepristone release from
poly(lactic-co-glycolic) (PLGA) matrices were compared with model predictions. They
developed this model by the pseudo-steady state assumptions, similar to classical Higuchi
equation (Eq. 15). Moreover, the model assumes that polymer chains split with first-order
kinetics and drug diffusion coefficients are exponential functions of time:
( )ktexpDD 0= (40)
In this equation:
D0 - drug diffusion coefficient at time t = 0,
k - polymer degradation rate.
They got the following expression for the cumulative amount of drug release as
a function of time:
( )[ ]
k
1ktexpDC2C
SQ 0s0 −
= (41)
where:
S - surface area of film contacted with the release fluid,
C0 - initial drug concentration,
Cs - solubility of drug in the polymer.
Surface phenomena
The rate of drug delivery can be affected by surface phenomena. Different surface
phenomena can be distinguished:
1) desorption of species from surface,
2) surface reconstruction,
3) surface reactions.
The above phenomena significantly influence the resulting drug release kinetics. The
species can be desorbed from the hydrogel surface. It is related to surface erosion and has
been discussed above.
In surface reconstruction atomic or molecular rearrangement occurs on the surface
of the device, thus the surface/interfacial tension is reduced. Surface reactions take place
when drug molecules react with the release medium and new substances are formed.
Conclusions
Mathematical modeling of drug release from the polymeric matrix has big academic
and industrial importance. It is very difficult to accurately predict the mechanism of drug
release from the hydrogel device in living organisms. The drug transport in various organs
and in different cells should be described by different models. In the future mathematical
19. Drug release from hydrogel matrices 135
theories will attempt to take into account differences between in vitro and in vivo
conditions.
References
[1] Li H., Luo R. and Lam K.Y.: Modeling of environmentally sensitive hydrogels for drug delivery:
An overview and recent developments. Front. Drug Des. Discov., 2006, 2, 295-331.
[2] Van Tomme S.R., Storm G. and Hennink W.E.: In situ gelling hydrogels for pharmaceutical and
biomedical applications. Int. J. Pharm., 2008, 355, 1-18.
[3] Barbucci R.: Hydrogels: Biological properties and applications. Springer, Milan 2009.
[4] Lin C.C. and Metters A.T.: Hydrogels in controlled release formulations: Network design and
mathematical modeling. Adv. Drug Deliv. Rev., 2006, 58, 1379-1408.
[5] Klouda L. and Mikos A.G.: Thermoresponsive hydrogels in biomedical applications. Eur. J. Pharm.
Biopharm., 2008, 68, 34-45.
[6] Schuetz Y.B., Gurny R. and Jordan O.: Novel thermoresponsive hydrogel based on chitosan. Eur. J. Pharm.
Biopharm., 2000, 49, 177-182.
[7] Siepmann J. and Siepmann F.: Mathematical mdeling of drug delivery. Int. J. Pharm., 2008, 364, 328-343.
[8] Peppas N.A. et al: Hydrogels in pharmaceutical formulations. Eur. J. Pharm. Biopharm., 2000, 50, 27-46.
[9] Siepmann J. and Gopferich A.: Mathematical modeling of bioerodible, polymeric drug delivery systems.
Adv. Drug Del. Rev., 2001, 48, 229-247.
[10] Zarzycki R.: Wymiana ciepła i ruch masy w inżynierii środowiska. WNT, Warszawa 2005.
[11] Arifin D.Y., Lee L.Y. and Wang C.H.: Mathematical modeling and simulation of drug release from
microspheres: Implications to drug delivery systems. Adv. Drug Deliv. Rev., 2006, 58, 1247-1325.
[12] Bajpai A.K. et al: Responsive polymers in cogntrolled drug delivery. Progr. Polym. Sci., 2008, 33,
1088-1118.
[13] Costa P. and Sousa Lobo J.M.: Modeling and comparison of dissolution profiles. Eur. J. Pharm. Sci., 2001,
13, 123-133.
[14] Cooke N.E. and Chen C.: A contribution to a mathematical theory for polymer-based controlled release
devices. Int. J. Pharm., 1995, 115, 17-27.
[15] Grassi M. and Grassi G.: Mathematical modelling and controlled drug delivery: Matrix systems. Curr. Drug
Deliv., 2005, 2, 97-116.
[16] Berger J. et al: Structure and interactions in covalently and ionically crosslinked chitosan hydrogels for
biomedical applications. Eur. J. Pharm. Biopharm., 2004, 57, 19-34.
[17] Zarzycki R., Rogacki G. and Modrzejewska Z.: Modeling of drug release from thermosensitive chitosan
hydrogels. J. Control Release, in press.
[18] Gopferich A.: Polymer degradation and erosion: Mechanisms and applications. Eur. J. Pharm. Biopharm.,
1996, 42, 1-11.
[19] Gopferich A.: Mechanism of polymer degradation and erosion. Biomaterials, 1996, 17, 103-114.
[20] von Burkersroda F., Schedl L. and Gopferich A.: Why degradable polymers undergo surface erosion or
bulk erosion. Biomaterials, 2002, 23, 4221-4231.
[21] Colombo P., et al: Analysis of the swelling and release mechanisms from drug delivery systems with
emphasis on drug solubility and water transport. J. Control. Release., 1996, 39, 231-237.
[22] Peppas N.A. and Sahlin J.J.: A simple equation for the description of solute release. 3. Coupling of
diffusion and relaxation. Int. J. Pharm., 1989, 57, 169-172.
[23] Siepmann J., et al: HPMC - Matrices for controlled drug delivery: A new model combining diffusion,
swelling, and dissolution mechanism and predicting the release kinetics. Pharm. Res., 1999, 16,
1748-1756.
[24] Siepmann J. and Peppas N.A.: Hydrophilic matrices for controlled drug delivery: an improved
mathematical model to predict the resulting drug release kinetics (the “sequential layer” model). Pharm.
Res., 2000, 17, 1290-1298.
[25] Streubel A. et al: Bimodal drug release achieved with multi-layer matrix tablets: transport mechanisms and
device design. J. Control Release, 2000, 69, 455-468.
[26] Katzhendler I. et al: Modeling of drug release from erodible tablets. J. Pharm. Sci., 1997, 86, 110-115.
[27] Charlier A., Leclerc B. and Couarraze G.: Release of mifepristone from biodegradable matrices:
Experimental and theoretical evaluations. J. Pharm. Sci., 1997, 86, 110-115.
20. Roman Zarzycki, Zofia Modrzejewska and Katarzyna Nawrotek136
UWALNIANIE LEKÓW Z HYDROŻELI
Wydział Inżynierii Procesowej i Ochrony Środowiska, Politechnika Łódzka
Abstrakt: Zarówno z naukowego, jak i praktycznego punktu widzenia bardzo ważny jest opis kinetyki uwalniania
leków z hydrożeli. Celem tego artykułu jest przegląd opisanych w literaturze modeli matematycznych uwalniania
leków z matryc hydrożelowych. W pierwszej części omówiono parametry opisujące strukturę hydrożelu.
Następnie opisano zjawiska wpływające na mechanizm uwalniania leków. W ostatniej części przeglądu literatury
zostały przedstawione mechanizmy uwalniania. W tej części zebrano wyrażenia matematyczne stosowane do
opisu profili uwalniania leków.
Słowa kluczowe: hydrożel, modelowanie matematyczne, kontrolowane uwalnianie, podawanie leków, dyfuzja,
pęcznienie, erozja