hydrogel in controlled drug delivery system

Iranian Polymer Journal

18 (1), 2009, 63-88

hydrogels;

drug delivery;

swelling;

thermodynamics;

mathematical modelling.

(*) To whom correspondence to be addressed.

E-mail: [email protected]

A B S T R A C T

Key Words:

Hydrogels in Controlled Drug Delivery

Systems

Fariba Ganji and Ebrahim Vasheghani-Farahani*

Chemical Engineering Department, Faculty of Engineering

Tarbiat Modares University, P.O. Box: 14115-143, Tehran, Iran

Received 21 September 2008; accepted 7 December 2008

Hydrogels are a unique class of macromolecular networks that can hold a large

fraction of an aqueous solvent within their structures. They are particularly suit-

able for biomedical applications, including controlled drug delivery, because of

their ability to simulate biological tissues. Many hydrogel-based networks have been

designed and fabricated to meet the needs of pharmaceutical and medical fields. The

objective of this paper is to give a brief review on the fundamentals and recent

advances in the design of hydrogel-based drug delivery systems (DDS) as well as the

description of the release mechanism of bioactive molecules from these hydrogels.

The structure and classification of hydrogels, swelling behaviour of hydrogels, differ-

ent mechanisms of solvent diffusion into and drug release from hydrogels and mathe-

matical description of these phenomena are elucidated. The most important properties

of hydrogels relevant to their biomedical applications are also identified, especially for

use of hydrogels as drug delivery systems. Kinetics of drug release from hydrogels

and the relevant mathematical modelling are also reviewed in this manuscript.

CONTENTS

Available online at: http://journal.ippi.ac.ir

Introduction .................................................................................................................... 64Hydrogels ....................................................................................................................... 64Swelling Behaviour of Hydrogels .................................................................................. 65

Thermodynamics of Gel Swelling ............................................................................... 66Kinetics of Gel Swelling ............................................................................................. 67

Biomedical Application of Hydrogels ........................................................................... 69Intelligent Hydrogels in DDS ........................................................................................ 70

Temperature Responsive Hydrogels in DDS ............................................................... 70Negatively Thermosensitive Hydrogels .................................................................. 70Positively Thermosensitive Hydrogels ................................................................... 71Thermally Reversible Hydrogels ............................................................................ 72

pH Sensitive Hydrogels in DDS .................................................................................. 74Temperature/pH Sensitive Hydrogels in DDS ............................................................ 75Bioresponsive Hydrogels in DDS ................................................................................ 76

Kinetics of Drug Release from Hydrogels ................................ 77Diffusion-controlled Delivery Systems .................................. 77Swelling-controlled Delivery Systems ................................... 80Chemically-controlled Delivery Systems ............................... 81

Erodible Drug Delivery Systems ....................................... 81Pendant Chain Systems ..................................................... 82

Conclusion ................................................................................ 82References ................................................................................ 83

INTRODUCTION

In recent years, extensive efforts have been devoted tothe use of potential pharmaceutical devices such asnovel drug delivery systems (DDS), since it proposesa suitable means of site-specific and/or time-con-trolled delivery of therapeutic agents [1,2]. Amongvarious kinds of polymeric systems, which have beenused as drug containers or release rate controlling bar-riers, hydrogels have gained considerable interest [3-11]. Hydrogels are cross-linked, three-dimensionalhydrophilic networks that swell but not dissolve whenbrought into contact with water. Hydrogels can be formulated in a variety of physical forms, includingslabs, microparticles, nanoparticles, coatings, andfilms. As a result, they are commonly used in clinicalpractice and experimental medicine for a wide rangeof applications, including biosensors, tissue engineer-ing and regenerative medicine, separation of biomol-ecules or cells and barrier materials to regulate bio-logical adhesions [7,12,13]. Among these applica-tions, hydrogel-based drug delivery devices havebecome a major area of research interest. Hydrogelscan protect drugs from hostile environments, e.g. thepresence of enzymes and low pH in the stomach.Their porosity permits loading of drugs into the gelmatrix and subsequent drug release at a pre-designedrate. Hydrogels can also control drug release bychanging the gel structure in response to environmen-tal stimuli, such as pH [14], temperature [10], ionicstrength [15], and electric field [16].

This article provides an overview of currentresearch in the fields of synthesis and application ofhydrogels in the pharmaceutical field, hydrogels char-acterization and their use as intelligent carriers fornovel pharmaceutical formulations. Swelling behav-iour of hydrogels, different mechanisms of solventdiffusion into and drug release from hydrogels and

mathematical description of these phenomena are alsopresented. In spite of numerous published reviewpapers, books and encyclopedias which focus directlyor indirectly on biomedical application of hydrogels,this review aims to throw light on the specific appli-cations that hydrogels have in the drug delivery areas.

HYDROGELS

Hydrogels are water swollen polymer matrices, with ahuge tendency to absorb water. Their ability to swell,under physiological conditions, makes them an idealmaterial for biomedical applications [17]. Thehydrophilicity of the network is due to the presence ofchemical residues such as hydroxylic, carboxylic,amidic, primary amidic, sulphonic and others that canbe found within the polymer backbone or as lateralchains. It is also possible to produce hydrogels con-taining a significant portion of hydrophobic polymers,by blending or copolymerizing hydrophilic andhydrophobic polymers, or by producing interpenetrat-ing networks (IPN) or semi-interpenetrating polymernetworks (s-IPN) of hydrophobic and hydrophilicpolymers.

Hydrogels can be classified as neutral or ionic,based on the nature of the side groups. In neutralhydrogels, the driving force for swelling is due to thewater-polymer thermodynamic mixing contribution tothe overall free energy, along with elastic polymercontribution [6]. Hydrogels can be classified as affineor phantom, based on their mechanical and structuralcharacteristics. Hydrogels are also classified ashomopolymers or copolymers, based on the methodsof preparation. Additionally, they can be classifiedbased on the physical properties of the network asamorphous, semi-crystalline, hydrogen bonded struc-tures, super-molecular structures and hydrocolloidalaggregates [6]. An important class of hydrogels is thestimuli responsive gels. These gels show swellingbehaviour dependent on their physical environment,allow for usage in a number of applications [18].

Hydrogels can be prepared from natural or syn-thetic polymers (Table 1). Several techniques havebeen reported for the synthesis of biomedical hydro-gels [19,20]. Chemically cross-linked gels have ionicor covalent bonds between polymer chains.

Hydrogels in Controlled Drug Delivery Systems ... Ganji F et al.

Iranian Polymer Journal / Volume 18 Number 1 (2009)64

Copolymerization [21,22], suspension polymerization[23], polymerization by irradiation [24], chemicalreaction of complementary groups [25-27], and cross-linking using enzymes [28] are some common exam-ples. Chemically cross-linked gels imply the use of across-linking agent which is often toxic. This requiresthat the cross-linking agent be removed from the gel,which can affect the gel integrity. For these reasons,physically cross-linked gels are now coming intoprominence. Several cross-linking methods such asionic interactions [29-32], crystallization [33], hydro-gen bonds [34,35], protein interaction [36], and cross-linking by hydrophobic interactions [7,20] have beeninvestigated exploring preparation of physicallycross-linked gels [37].

SWELLING BEHAVIOUR OF HYDROGELS

When a hydrogel in its initial state is placed in anaqueous solution, water molecules will penetrate intothe polymer network. The entering molecules aregoing to occupy some space, and as a result somemeshes of the network will start expanding, allowingother water molecules to enter within the network.Evidently, swelling is not a continual process, theelasticity of the covalently or physically cross-linkednetwork will counter-balance the infinite stretching ofthe network to prevent its destruction. Thus, by bal-ancing these two opposite forces, a net force, known

as the swelling pressure (Psw) is produced, which isequal to zero at equilibrium obtained with pure water,and that can be expressed as [7]:

(1)

where, k and n are constants, and C is the polymerconcentration. At the equilibrium there is no addition-al swelling. Swelling can be described as the increasein weight, volume, or length. Thus, the amount ofwater up-taken by the hydrogel (mw) is given by [7]:

(2)

where, mHG,w and mHG,d are the wet and dry hydrogelweights, respectively. In addition, while the percent ofswelling does not exceed 100, the percent of hydra-tion does. Then, the degree of swelling (Dsw) is givenby [7]:

(3)

whereas, the swelling ratio (Rsw) is [7]:

(4)

where, 0 is the density of the hydrogel in the dry

65Iranian Polymer Journal / Volume 18 Number 1 (2009)

Hydrogels in Controlled Drug Delivery Systems ...Ganji F et al.

nsw CkP =

w,HG

d,HGw,HGw m

mmm

=

,

,

1HG wsw swHG d

mD D

m=

0 ssw sw

sw r

VR DV

= =

Table 1. Natural polymers and synthetic monomers used in hydrogel fabrication [25].

Natural polymers Synthetic monomers/polymers

Chitosan

Alginate

Fibrin

Collagen

Gelatin

Hyaluronic acid

Dextran

Hydroxyethylmethacryate (HEMA)

N-(2-Hydroxy propyl)methacrylate (HPMA)N-Vinyl-2-pyrrolidone (NVP)N-Isopropylacrylamide (NIPAMM)Vinyl acctate (VAc)

Acryolic acid (AA)

Methacrylic acid (MAA)

Polyethylene glycol acrylate/methacrylate

(IPEGA/PEGMA)

Polyethylene glycol diacrylate/dimethacrylate

(PEGDA/PEGDMA)

state, sw is the density of the swollen gel, whereas Vsand Vr are the volumes of the hydrogel in the wet anddry states, respectively.

Thermodynamics of Gel Swelling

The structure of hydrogels that do not contain ionicmoieties can be analyzed by the Flory-Rehner theory[38]. The combination of thermodynamic and elastic-ity theories states that a cross-linked polymer gel thatis immersed in a fluid and allowed to reach equilibri-um with its surroundings is subject only to two oppos-ing forces: the thermodynamic force of mixing andthe retractive force of the polymer chains. The changeof chemical potential due to mixing can be expressedusing heat and the entropy of mixing. The change inchemical potential due to the elastic retractive forcesof the polymer chains can be determined from the theory of rubber elasticity. Upon equal contributionsof these two, the expression for determining themolecular weight between two adjacent cross-links ofa neutral hydrogel prepared in the absence of a solventcan be derived [1].

In the case of ionic polymers, the swelling equilib-rium of the polymeric matrix is more complicated asit heavily depends also on the ionic strength (Figure1). The free energy change of ionic hydrogel, corre-sponding to the volume change during swelling, G,is the sum of contributions due to mixing of pure sol-vent with an initially pure, amorphous, unstrained gelnetwork, G1, due to configurational changes of thegel structure, G2, and due to mixing of ions with sol-vent, G3. An ionic gel is subjected to a swellingpressure, , which is expressed as the sum of threecomponents corresponding to each contribution to G[39,40].

A molecular theory of swollen gels by includingfree volume as a third component in the binary mix-ture of solvent and polymer was developed byMarchetti et al. [41]. This theory could predict thephase behaviour such as near-critical lower consoluteboundaries, low-temperature upper consolute bound-aries and closed-loop miscibility gaps. The theory wasfurther applied to correlate the experimental data ofpoly(isopropylacrylamide) and poly(diethylacryl-amide) gels. The predicted values by the theory agreeclosely with those measured experimentally.

In 2001, a multi-component, one and two-dimen-

Figure 1. Schematic of an ionic polymeric hydrogel (a), and

the swelling phenomena of an ionic hydrogel in a buffered

pH solution (b).

sional model for the transient and equilibriumswelling of polyelectrolyte gels was developed byAchilleosa et al. [42]. The model accounts for theeffect of network stress, osmotic pressure, and electri-cal potential on the species diffusive flux. The osmot-ic pressure and the network stress were derived fromthe Helmholtz free energy of the system. They try tosimulate one and two dimensional swelling in uncon-strained and constrained geometries for a salt-solvent-polymer system. Through solving their mathematicalmodel numerically, one can obtain the transient andequilibrium fields of electrical potential, concentra-tions, deformation, and stress.

The swelling behaviour of cross-linked ionic



(a)

(b)

hydrogels has been studied by Oliveira et al., by usinga quasi-chemical thermodynamic model [43]. The cal-culated volume transition temperature of PNIPAm gelis 0.8C lower than the experimental value and thepredicted solvent volume fraction in the collapsed andswollen gel states are about 2% larger than the corre-sponding experimental data measured at the transitionpoint. Applying the same energy parameters obtainedfrom regressing PNIPAm gel swelling pressure data,their model has also been capable to correctly repre-sent the major features found in the swelling behav-iour of linear poly(N-tert-butylacrylamide) andpoly(N-tert-butylacrylamide) gels, after the modelparameters that characterize the molecular structurewere changed in accordance to each polymer repeti-tive unit.

Yang et al. [44] developed a lattice model for thebinary polymer solutions based on statistical associat-ing theory. In this work, a new molecular thermody-namic model for thermo-sensitive hydrogels was pro-posed through combining Yang et al.s lattice modeland an elastic term. When the energy parameter isexpressed as a quadratic of inverse temperature, thismodel can describe the swelling behaviour of neutralthermo-sensitive hydrogels. The experimentalswelling curves of two kinds of polyacrylamide basedgels were correlated.

The swelling equilibrium of IPAAm/NaMA hydro-gels in aqueous solutions of the single salts, NaCl andNa2HPO4, was investigated experimentally anddescribed mathematically by developing a new ther-modynamic model [45]. This new model combines anextension of Pitzers model for aqueous electrolytesolutions for the excess Gibbs energy of an aqueousphase with an extension of the phantom network theory. Orlov et al. indicated that such an extension isnecessary to account for the large volume changesobserved when ionic hydrogels are dissolved in waterand salt solutions at low salt concentrations.Wallmersperger et al. assumed that the swellingmechanism results from the equilibrium of differentforces and can be triggered by chemical, thermal orelectrical stimulations [46]. The chemical field coulddescribe by a convection-diffusion equation, while theelectric field was directly obtained by solving thePoisson equation in the gel and solution domain. Themechanical field was formulated by the momentum

equation. To model the global macroscopic behaviour,they just used the statistical theory which is capable todescribe the overall swelling ratio. By refining thescale, the mesoscopic coupled multi-field theory wasapplied. Their mesoscopic formulation is capable tocapture the whole gel and solution domain for chemi-cal, thermal and electrical stimulations without prescribing any jumps of concentration or electricpotential at the interface.

A new molecular thermodynamic model fordescribing the swelling behaviour of thermo-sensitivehydrogels was developed by Huang et al. [47]. Theyassumed that a neutral hydrogel system contains onlypolymer network and water. The Gibbs energy insidethe hydrogel is defined as: G = Gm + Ge, whereGm is the mixing term of hydrogel network andwater and Ge is the elastic term deriving from thenetwork elasticity. Their model consists of two terms:the contribution of the mixing of hydrogel networkand water, which is dependent on the local polymerconcentration and the interaction between polymersegment and solvent, and the elastic contributionderived from the network elasticity, which is depend-ent on the cross-linking degree of gel network. Theirimportant parameters are (energy parameter, reflect-ing the interaction between water and gel network)and V* (a size parameter which represents the cross-linking degree of the hydrogel). When the energyparameter is expressed as a quadratic of inverse tem-perature, this model can describe the swelling equilib-rium behaviour of neutral thermo-sensitive hydrogelsquite well.

Kinetics of Gel Swelling

It is well known that sorption processes for polymer-solvent systems frequently do not conform to thebehaviour expected from the classical theory of diffu-sion [48]. The slow reorientation of polymer mole-cules can lead to a wide variety of anomalous effectsfor both permeation and sorption experiments. Thefour basic categories of the sorption phenomena inpolymers may be described as follows.

Fickian or Case I transport is characterized by thesingle parameter D, the diffusion coefficient.

Penetrants in rubbery polymers and at low activi-ties in glassy polymers typically exhibit Fickianbehaviour. Molecular relaxation is either faster than


Iranian Polymer Journal / Volume 18 Number 1 (2009) 67

diffusion (well above glass transition temperature, Tg)or so slow that is not observed on the time scale of theexperiment (well below Tg). In slab samples, Case Idiffusion is characterized by a linear increase of poly-mer weight gain as a function of the square root ofsorption time. It asymptotically approaches a fixedequilibrium value.

Case II transport is characterized by the singleparameter V, the velocity of the advancing penetrantfront. Diffusion is very rapid compared to relaxation,with relaxation occurring at an observation rate. Here,the rate of mass uptake is directly proportional totime.

Diffusion behaviour which is intermediatebetween that of Case I and Case II is regarded as Non-Fickian behaviour. Therefore, non-Fickian or anom-alous transport is observed when the diffusion andrelaxation rates are comparable.

Super Case II diffusion is characterized by anacceleration of absorption rate towards the end of thefront penetration process. This change is attributed tothe expansion forces exerted by the swollen gel on theglassy core.

The role of Case II diffusion as another limitingcase of diffusion may be debated because of the con-troversy over the existence of Super Case II diffusion,and the fact that Case I diffusion generally precedesthe onset of Case II diffusion. In addition, Case Ibehaviour may reoccur in Case II diffusion when thesample dimension is large. Therefore, Case II diffu-sion may be more appropriately named as Case IItransport or Case II sorption. Case II sorption isuniquely characterized by a constant movement ofpenetration front after a glassy polymer is immersedin a non-dissolving liquid penetrant.

Numerous mathematical models have been pro-posed describing the kinetics of hydrogel swelling.The models may be divided into three categories [49].The Fickian diffusion models apply Fick's laws to thedistribution of solvent in a gel sample during swellingor collapse. These models predict that the fractionalapproach to equilibrium increases linearly with thesquare root of time up to roughly 0.4 and that theswelling curve, the fractional approach to equilibriumvs. square root of time, is not sigmoidal even if thediffusion coefficient is a function of composition. Thecollective diffusion models, developed by Tanaka et al.,

treat the swelling of a gel as the expansion of a net-work driven by a gradient of stress [50]. These mod-els describe small volume changes, but they fail topredict the sigmoidal swelling curves resulting fromlarge volume change. Sigmoidal experimentalswelling curves are often taken to indicate non-Fickian behaviour. Deviations from the fixed bound-ary Fickian behaviour are usually attributed to someof the following phenomena: (i) variable surface con-centration, (ii) a history dependent diffusion coeffi-cient, (iii) stresses between parts of the gel swollen todifferent extents and (iv) polymer relaxation. The firstthree have been discussed by Crank et al. [51], whilethe last has been modelled by Joshi et al. [52].However, it has been shown that the sigmoidalswelling behaviour can be well described by Fickiandiffusion when the movement of the gel surface istaken into account correctly [53]. Although thesemodels predict the swelling curves for large volumechanges reasonably well, they are subject to threeobjections: (i) they do not allow for the movement ofthe gel boundary, (ii) they require three or moreparameters to fit experimental data, and (iii) the diffu-sion coefficients may show unusual compositiondependence, e.g. a maximum at an intermediate com-position.

Singh and Fan developed a generalized mathemat-ical model for the simultaneous transport of a drugand a solvent in a planar glassy polymer matrix [54].The swelling behaviour of the polymer is character-ized by a stress-induced drift velocity term v. Thechange of volume due to the relaxation phenomenonis assumed instantaneous. The model incorporatesconvective transport of the two species induced byvolume expansion and by stress gradient.

Vasheghani-Farahani has already indicated that theNIPAm gels exhibit Fickian behaviour upon swelling,but their shirking at 35C is non-Fickian [55]. Also,the rate of swell is slower than the rate of collapse. Hehas developed a Fickian mathematical model, whichdescribes the kinetics of swelling and collapse ofionic hydrogels, through the use of a material coordi-nate and a chemical potential driving force. In thisway, explicit relationships between diffusion coeffi-cients in polymer material coordinate and in laborato-ry coordinate for cylindrical and spherical geometrieshave been obtained.


68 Iranian Polymer Journal / Volume 18 Number 1 (2009)

Swelling of superabsorbent acrylamide/sodiumacrylate hydrogels prepared using multifunctionalcross-linkers have been studied by Karadag et al. [56].The research involved the study of the influence ofcross-linkers and the relative content of sodium acry-late on swelling, initial swelling rate, swelling rateconstant, swelling coefficient and diffusional behav-iour of water in the hydrogel. Results indicate thatacrylamide-sodium acrylate hydrogels showed greaterswelling in water compared to acrylamide hydrogelsand the water intake of hydrogels followed non-Fickian type diffusion.

Swelling behaviour and drug release kinetics ofionic and non-ionic IPNs of PNIPAm and calciumalginate were studied by Khorram et al. [57]. Theyused calcium alginate as a mould to obtain uniform,large size, macroporous spherical beads of NIPPAmhydrogels. Their swelling observations indicated thatthe equilibrium swelling degree of homopolymer gelincreased after calcium alginate extraction, while ithad no effect on lower critical solution temperature(LCST). In addition, equilibrium swelling degree ofcopolymer composite hydrogels containing Na+ andCa2+ cations were greater than that of the extractedhydrogel containing only monovalent cations. It wasalso observed that, swelling kinetics of hydrogels aswell as their drug release followed Fickian behaviour.Bouquerand et al. developed a model of flavourrelease from encapsulated flavour particles immersedin water by considering a pseudo-steady state condi-tion in the swollen region of the particles [58]. Theirmodel predicts a very different release with time fromthe encapsulated flavour if the particle develops ahydrogel at the surface (swelling) compared to grad-ual erosion. But, the proposed model contains someerrors which are corrected by Vasheghani-Farahani[59].

Osmotic swelling and de-swelling studies havebeen performed on gelatin suspended in water-ethanolmarginal solvent at room temperature, where the alco-hol concentration was changed from 0 to 100% (v/v)[60]. Boral et al. reported that the osmotic pressure ofpolymer-solvent mixing (m) is much smaller than theosmotic pressure due to network elasticity (e). Inaddition, the osmotic pressure arising from ionic con-tributions, ion was found to play a significant role incontrolling volume phase transitions. For gelatin

hydrogels, total swelling pressure of gel, tot could berelated to gelatin volume fraction (2), relaxed vol-ume of network (V0), and cross-link density (ve)while it is independent of gel pH and swelling time.

BIOMEDICAL APPLICATIONS OF HYDRO-

GELS

Hydrogels have been successfully used in biomedicalfields due to their high water content and the conse-quent biocompatibility. Potential applications ofhydrogels in tissue engineering, synthetic extracellu-lar matrix (ECM) and three dimensional scaffolds arewell highlighted in a recent work. The proliferationand differentiation of mesenchymal stem cells (MSC)in a three dimensional (3-D) network of nanofibresformed by self-assembly of peptide-amphiphile (PA)molecules was investigated by Hosseinkhani et al.[61]. A 3-D network of nanofibres was formed bymixing cell suspensions in media with dilute aqueoussolution of PA. In another work, a hybrid scaffoldconsists of two biopolymers, a hydrogel formedthrough self-assembly of peptide-amphiphile with cellsuspensions in media and a collagen sponge rein-forced with poly(glycolic acid) fibre incorporation,were used successfully to enhance bone formation[62]. A novel injectable 3-D scaffolds with encapsu-lated growth factor was formed by mixing of PA aque-ous solution with basic fibroblast growth factor(bFGF) suspension [63]. Hosseinkhani et al. showedthat when aqueous solution of PA was subcutaneous-ly injected together with bFGF suspension into theback of mice, a transparent 3-D hydrogel was formedat the injected site and induced significant angiogene-sis around the injected site, in marked contrast tobFGF injection alone or PA injection alone.

Materials controlling the activity of enzymes,phospholipids bilayer destabilizing agents, materialscontrolling reversible cell attachment, nanoreactorswith precisely placed reactive groups in three-dimen-sional space, smart microfluidics with responsivehydrogels, and energy-conversion systems are thepromising applications of hydrogels in biomedicaland pharmaceutical areas [64-67]. The soft andhydrophilic nature of hydrogels makes them particu-larly suitable as novel drug delivery systems [68].



Control of hydrogel swelling properties can be usedas a method to trigger drug release. Through properdesign, hydrogels can be used in a variety of applica-tions including sustained, targeted, or stealth biomol-ecule delivery. Hydrogels can be engineered to exhib-it bioadhesiveness to facilitate drug targeting, espe-cially through mucus membranes, for non-invasivedrug administration [69]. Hydrogels offer an impor-tant stealth characteristic in vivo owing to theirhydrophilicity which increases the in vivo circulationtime of the delivery device by evading the hostimmune response and decreasing phagocytic activi-ties [70]. Dinarvand's group developed poly(lactide-co-glycolide)-based hydrogel nanoparticles withmodified surface properties to increase the blood cir-culating half life of drug carriers [71].

INTELLIGENT HYDROGELS IN DDS

The intelligent response of environmentally respon-sive hydrogels allows for release that is controlled bythe conditions of the environment. Temperature-responsive and pH-responsive hydrogels have beenwidely used to create drug delivery systems thatexhibit a pulsatile release in response to temperatureor pH changes [72]. By incorporating enzymes withinenvironmentally responsive hydrogels, researchershave created drug delivery systems that are respon-sive to biological analytes [73]. Another area of drugdelivery where hydrogels have proven beneficial is insystems where molecular recognition is utilized forenhanced residence times, sustained delivery, and/ortargeted drug delivery [74].

Temperature Responsive Hydrogels in DDS

Temperature sensitive hydrogels can be classified asnegatively thermosensitive, positively thermosensi-tive, and thermally reversible hydrogels. Negativelythermosensitive hydrogels are those showing lowercritical solution temperature (LCST) behaviour, whilepositively thermosensitive gels are known to have anupper critical solution temperature (UCST) [75]. TheLCST polymers exhibit a hydrophilic-to-hydrophobictransition with increasing temperature, whereas theUCST systems undergo the opposite transition.Thermally reversible hydrogels are those that can

experience cyclic phase transitions (sol-gel transi-tion), such as poloxamers, gelatin and other naturalpolymers. Negatively Thermosensitive HydrogelsThe LCSTs of several typical negatively thermosensi-tive polymers are listed in Table 2 [9]. Negativelythermosensitive hydrogels tend to shrink or collapseas the temperature is increased above the LCST, andswell upon lowering the temperature below the LCST.The change in the hydration state, which causes thevolume phase transition, reflects competing hydrogenbonding properties, where intra- and inter-molecularhydrogen bonding of the polymer molecules arefavoured compared to a solubilization by water [10].Thermodynamics can explain this with a balancebetween entropic effects due to the dissolutionprocess itself and due to the ordered state of watermolecules in the vicinity of the polymer. Enthalpiceffects are due to the balance between intra- and inter-molecular forces and due to solvation, e.g. hydrogenbonding and hydrophobic interaction. The transitionis then accompanied by coil-to-globule transition. Bycontrolling the polymer composition and topology,the coil-to-globule transition could be kinetically andthermodynamically controlled [76]. Control ofdeswelling kinetics was achieved by using graftcopolymer structure. The comb-type grafted hydro-gels of cross-linked P(NIPAAm) grafted with oligo-NIPAAm and poly(NIPAAm-g-PEG) exhibited fastresponse to temperature changes [77]. Grafted shortchains of oligo-NIPAAm in the former case con-tributed to fast dehydration, whereas in the latter casethe hydrophilic PEG chains provided a water channel

Table 2. Lower critical solution temperatures (LCST)s of

several typical thermosensitive polymers [9].



Polymer LCSTs (C)

Poly(N-isopropylacrylamide) (PNIPAM)Poly(N,N-diethylacrylamide) (PDEAM)Poly(N-ethylmethacrylamide) (PNEMAM)Poly(methyl vinyl ether) (PMVE)

Poly(2-ethoxyethyl vinyl ether) (PEOVE)

Ploy(N-vinylcaprolactam (PNVCa)Poly(N-vinylisobutyramide) (PNVIBAM)Poly(N-vinyl-n-butyramide) (PNVIBAM)

32

25

58

34

20

30-35

39

32

for a fast deswelling mechanism. Copolymerizationof NIPAAm with hydrophobic butylmethacrylatedecreases the LCST of aqueous copolymer solutionand copolymerization with hydrophilic comonomers,such as acrylic acid or hydroxy ethyl methacrylate,results in an increase in LCST.

Bulmus et al. used the PNIPAAm polymers foron/off control of avidin-biotin binding [78]. Belowthe transition temperature of 32C, NIPAAm copoly-mers are in a fully extended conformation in waterbecause of favourable polymer-water interactions.The PNIPAAm with fully extended conformationinterferes with the biotin-binding site on the avidin,whereas above the transition temperature, the poly-mers are collapsed and cannot interfere with the bind-ing sites.

Cellulose nitrate and cellulose acetate monolayermembranes containing n-heptyl-cyanobiphenyl weredeveloped as thermoresponsive barriers for drug per-meation [79]. Methimazole and paracetamol ashydrophilic and hydrophobic drug models were used,respectively. Atyabi's group found that upon changingthe temperature of the system around 41.5C, bothcellulose membranes without cyanobiphenyl showedno temperature sensitivity to drug permeation, where-as the results for cyanobiphenyl entrapped mem-branes exhibited a distinct jump in permeability whentemperature was raised to above the 41.5C for bothdrug models. Drug permeation through the mem-branes was reversible, reproducible and followed zeroorder kinetics. The pattern of on/off permeationthrough these membranes was more distinguished formethimazole compared to that of paracetamol, seem-ingly due to its lower molecular weight.Positively Thermosensitive HydrogelsCertain hydrogels formed by IPNs show positive ther-mosensitivity, i.e. swelling at high temperature andshrinking at low temperature. IPNs of poly(acrylicacid) and polyacrylamide (PAAm) or P(AAm-co-BMA) perform as positively thermosensitive hydro-gels [80]. Increasing the BMA content shifted thetransition temperature to higher temperature. Theswelling of those hydrogels was reversible, respond-ing to stepwise temperature changes. This resulted inreversible changes in the release rate of a model drug,ketoprofen, from a monolithic device.

Another UCST system was fabricated by Aoki et

al., based on a combination of acrylamide (AAm) andacrylic acid (AAc) [81]. The obtained IPNs were verystable at 70C in an aqueous solution. Dissociationtemperatures of the hydrogels shifted to higher valueswith increasing AAm content. These IPNs showedlimited swelling ratios between their swelling transi-tion temperatures and lower swelling ratios abovethese transition temperatures. Transition temperaturesshift to higher values with increasing AAm content.Reversible and pulsatile solute release, reflecting the"on" state at higher temperatures and the "off" state atlower temperatures, was recorded by Aoki et al.

A positively thermosensitive drug-release micro-capsule was fabricated by Ichikawa et al. [82]. Themicrocapsule had a core layered with carbazochromesodium sulphonate (a water-soluble model drug) par-ticles and a thermosensitive coat composed of an eth-ylcellulose matrix containing nano-sized thermosensi-tive hydrogels (Figure 2). The hydrogel particles con-sisted of newly synthesized composite latex with aPNIPAAm shell that could reversibly change the shellthickness in water with response to an environmentaltemperature change. This microcapsule demonstrateda positively thermosensitive on-off pulsatile drugrelease around 32C, suggesting that the shrinkage ofPNIPAAm shells most likely created many voids inthe coat and thereby imparted the higher water-perme-ability to the coat.

Figure 2. Ideal structure of microcapsules with positively

thermosensitive drug release. (a) Calcium carbonate core;

(b) drug; (c) thermosensitive coat; (d) Aquacoat; (e) & (f)

swollen and shrunken hydrogel particles; (g) void. Adopted

from ref [80].



A novel family of monodisperse thermosensitivecore-shell microspheres has been developed by Xiaoet al. [83]. The microspheres were fabricated in athree-step process. First, monodisperse poly(acry-lamid-co-styrene) seeds were prepared by emulsifierfree emulsion polymerization. Then, poly(acryl-amide) or poly[acrylamid-co(butylate)] shells werefabricated on the microsphere seeds by free radicalpolymerization. Finally, the core-shell microsphereswith poly(acrylamide)/poly(acrylic acid) based IPNshells were finished by a method of sequential IPNsynthesis. The swelling ratio of the microspherescould be tuned by controlling the hydrophobicmonomer (BMA) or cross-linker (MBA) dosage inthe PAAM shell fabrication and IPN synthesis. Thermally Reversible HydrogelsAqueous solutions of some polymers undergo sol togel transition in response to a certain stimulus (Figure3) [84]. Among them, thermally reversible hydrogelsare of most interest and will be discussed in this sec-tion.

Polymers with hydrophobic domains can cross-link in aqueous environments via reverse thermalgelation. Hydrophobicity-driven gelation often occursvia the mechanism shown in Figure 4. The hydropho-bic segment is coupled to a hydrophilic polymer seg-ment by post-polymerization grafting or by directlysynthesizing a block copolymer to create a polymeramphiphile. Such amphiphiles are water soluble at

Figure 3. Schematic representation of sol-to-gel transition

in stimuli-sensitive polymers.

Figure 4. Mechanism of in situ physical gelation driven by

hydrophobic interactions. Adopted from ref [4].

low temperature. As the temperature is increased,hydrophobic domains aggregate to minimize thehydrophobic surface area contacting the bulk water,reducing the amount of structured water surroundingthe hydrophobic domains and maximizing the solvententropy. The temperature at which gelation occursdepends on the concentration of the polymer, thelength of the hydrophobic block, and the chemicalstructure of the polymer [4].

The chemical structures of some commonhydrophobic blocks which can undergo reverse ther-mal gelation at or near physiological temperature areshown in Figure 5.

Triblock copolymers of poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) (PEO-PPO-PEO, the Poloxamers/Pluronics) are the mostwidely used thermally reversible hydrogels [85].Aqueous solution of poloxamers demonstrates phasetransitions from sol to gel at 5-30C and gel to sol at35-50C with the temperature increasing monotoni-cally over the polymer concentration range of 20 to 30wt% [76]. The transition mechanism from gel-to-solis related to the shrinkage of PEO corona of themicelles because of temperature effects on PEO solu-bility and interaction of PEO chains with the PPOhard core. A recent small angle neutron scatteringstudy proposed the transition of micelle structurefrom spherical to cylindrical, thus releasing micelle-packing constraints, as the cause of the high tempera-ture gel-sol transition [76]. A sol-gel transition behav-iour was also observed for an altered triblock struc-ture in which poly(butylenes oxide) (PBO) was usedin place of PPO in the middle block or with PEO-PBOdiblock copolymers.

Poloxamers can also be modified by adding anadditional polymer block at each chain terminus,



forming multi-block copolymer with improved prop-erties for drug delivery [86,87]. PL(G)A-based gela-tors typically exhibit better biodegradability, highergelation temperatures, and longer periods of sustaineddrug release compared to poloxamer systems. Releaseof hydrophilic compounds from PLGA-PEG-PLGAcopolymers was found to be diffusion controlled,while release of hydrophobic compounds showed aninitial diffusion-controlled stage followed by a pro-longed polymer degradation-controlled stage [88].

Some natural polymers also undergo reverse ther-mal gelation. Chitosan-glycerol phosphate-water system is an interesting example, which has beinginvestigated for protein delivery, gene delivery andtissue engineering applications [89]. Recently, noveldi-block copolymers of chitosan and PEG were syn-thesized were synthesized by block copolymerizationof monomethoxy-PEG onto chitosan backbone, usingpotassium persulphonate as a free radical initiator

[90]. The obtained hydrogels undergo a thermosensi-tive transition from a free flowing solution at roomtemperature to a gel around body temperature. Theirgelation time varied from 6 to 11 min. Figure 6 illus-trates viscosity of a 2% w/v of chitosan-b-PEGcopolymer in an aqueous solution versus temperature.A sharp increase in viscosity around 35C indicatesthe beginning of the gelation process. It is also foundthat solutions with high polymer concentrations andlow PEG content gel faster than those with low poly-mer concentrations or high PEG content. Similartrends were observed by Bhattarai et al. for their thermosensitive PEG-grafted chitosan copolymers[91]. Their hydrogel is synthesized by grafting anappropriate amount of PEG onto the chitosan back-bone and used for drug release of bovine serum albu-min (BSA) as a model protein. Chitosan was firstmodified with a PEG-aldehyde to yield an imine(Schiff base) that was subsequently converted into



O

CH3

n

O

m

O

CH3

O

O

n

O

O

O

n

O

O

n

O

NH

NH

O

O

O O

n

P

HN

HNN

R O

C2H5

R

O

C2H5

n

HNO

H3C CH3

n

Poly(propylene oxide) Poly(lactide-co-glycolide) Poly(N-isopropylacrylamide)

PPO PLGA PNIPAM

Poly(propylene fumarate) Poly(caprolactone)

PPF PCL

Poly(uretane) Poly(organophosphazene)

PU POP

Figure 5. Chemical structures and abbreviations of common thermogelling hydrophobic blocks; R = any

thermogelling polymer. Adopted from ref [4].

Figure 6. Viscosity of chitosan-b-PEG copolymer versustemperature for 2% w/v polymer solution.

PEG-g-chitosan through reduction with sodiumcyanoborohydride (NaCNBH3). The required time forgelation of their PEG-g-chitosan copolymers variedfrom 10 min to 1 h, depending on polymer concentra-tion. They have found that the required amount ofgrafted PEG for an injectable thermosensitive copoly-mer is approximately 36-55 wt%. Below the 36 wt%of grafted PEG, the obtained copolymers were foundto be hardly soluble in water [92].

Grafting PNIPAM linear chains onto natural poly-mers can also convert those polymers into physicallycross-linkable hydrogels. For example, PNIPAM-grafted hyaluronic acid formed a gel in vivo whichshowed a burst release of riboflavin for 12 h and sus-tained release thereafter [91]; NIPAM-grafted chi-tosan has also been used to control the release of 5-fluorouracil [94].

pH Sensitive Hydrogels in DDS

Since the pH change occurs at many specific or patho-logical body sites, it is one of the important environ-mental parameter for drug delivery systems. For non-ionic hydrogels, the degree of swelling only dependson the chemical compositions of the polymers.However, for ionic hydrogels the swelling dependsnot only on the chemical composition but also on thepH of the surrounding medium. Therefore, the pH-sensitive polymers show dramatic changes on the pH

Figure 7. Schematic of relative ionic hydrogel swelling as a

function of pH. Adopted from ref [24].

and on the compositions of the external solutions. The pH-sensitive polymers can be classified as

acidic weak polyelectrolytes and basic weak polyelec-trolytes according to the method of ionization i.e.,donating or accepting protons. Anionic hydrogelsdeprotonate and swell more when external pH is high-er than pKa of the ionizable groups bonded on poly-mer chains, while cationic hydrogels protonate andswell more when external pH is lower than the pKb ofthe ionizable groups [18]. Depending on the ionicmonomers used to fabricate the hydrogel, the pH-dependent swelling curves exhibit one or more inflec-tion points near the pKa/pKb of the ionizable groupsas shown in Figure 7.

Typical acidic pH-sensitive polymers for drugdelivery are based on the polymers containing car-boxylic groups, such as poly(acrylic acid) [95],poly(methacrylic acid) [96], poly(L-glutamic acid)[97], and polymers containing sulphonamide groups[98]. Typical examples of the basic polyelectrolytesinclude poly(tertiary amine methacrylate) such aspoly(2-(dimethylamino) ethyl methacrylate) andpoly(2-(diethylamino)ethyl methacrylate) [99],poly(2-vinylpyridine) [100] and biodegradablepoly(-amino ester) [101].

Kamada et al. synthesized a pH-sensitive polymer-ic carrier, in which a poly(vinylpyrrolidone-co-dimethyl maleic anhydride) (PVD) was conjugated todoxorubicin (DOX), that could gradually release freedrug in response to changes in pH, from near neutralto slightly acidic pH [102]. The superior anticanceractivity of PVD-DOX conjugate is mainly due to con-trolled release and enhanced tumor accumulation of



the drug. Alginate-N,O carboxymethyl chitosan (NOCC)

gel beads coated by chitosan were prepared for colon-specific drug delivery system and their swellingbehaviour was investigated by Dolatabadi-Farahani etal. [103]. Their studies showed that swelling degree atpH 7.4 was considerably higher than that at pH 1.2,which indicates the pH sensitivity of these networks.Swelling degree of beads also decreased by chitosancoating and presence of NOCC due to the hydrogenbond formation and ionic interaction of functionalgroups of the polymer chains.

The synthesis and swelling behaviour of a superabsorbent hydrogel based on starch (St) andpolyacrylonitrile (PAN) are investigated [104]. Theabsorbency of the hydrogels indicated that theswelling ratios decreased with increasing ionicstrength. The hydrogels exhibited a pH-responsiveswelling-deswelling behaviour at pHs 2 and 8. Thison/off switching behaviour provides the hydrogelwith the potential to control delivery of bioactiveagents. Release profiles of ibuprofen from the hydro-gels were studied under both simulated gastric andintestinal pH conditions. The release was much quick-er at pH 7.4 than at pH 1.2. The swelling rates of thehydrogels with various particle sizes were investigat-ed as well.

A biodegradable pH-sensitive hydrogel for poten-tial colon-specific drug delivery was synthesized byCasadei et al. [14]. Their composite hydrogel, basedon a methacrylated and succinic derivative of dextran,and a methacrylated and succinic derivative ofpoly(N-2-hydroxyethyl)-DL-aspartamide was pro-duced by photo cross-linking polymerization. In vitrodrug release studies, performed using 2-methoxyestradiol as a model drug, show that obtainedhydrogel is able to release the drug in simulated intes-tinal fluid, due to its pH-sensitive swelling and enzy-matic degradability.

Temperature/pH Sensitive Hydrogels in DDS

More recently, studies have been conducted to fabri-cate and characterize hydrogels with dual-sensitivi-ties. This was accomplished by copolymerizing a temperature-sensitive monomer, usually N-isopropy-lacrylamide, and a pH-sensitive monomer such asacrylic acid or methacrylic acid [105].

Stayton's group has investigated a series of copoly-mers containing propylacrylic acid (PAA) andNIPAAm pendant chains as pH- and thermosensitivemoieties, respectively [71]. This new class of copoly-mers can sense environmental changes in the physio-logical range and has found usefulness in intracellulardrug delivery in which subtle pH differences acrossthe endosomal membrane triggers the delivery of protein or DNA.

Hollow beads of IPN of PNIPAAm were synthe-sized using Ca-alginate as the polymerization mould[106]. Drug loading was carried out using injection ofdrug solution into the cores of hollow beads.Acetaminophen and diltiazem hydrochloride wereused as low-water-soluble and water-soluble modeldrugs. Drug loading into this hydrogel based reservoircontrolled release system indicated its advantage forloading of sparingly soluble drug in aqueous solu-tions.

Swelling behaviour of poly((2-dimethyl amino)ethyl methacrylate-co-BMA) was investigated byEmileh et al. [107]. These hydrogels demonstrateddual sensitivity to both pH and temperature. It wasshown that the pH-sensitive or temperature-sensitivephase transition behaviour of the gels can be changedby changing the temperature or pH of the swellingmedium at constant hydrogel composition. Increasingthe temperature decreased the transition pH, whileincreasing the pH of the surrounding mediumdecreased the transition temperature of the tempera-ture-sensitive phase transition. Increasing the BMAcontent reduced the transition pH and temperature ofthe pH and temperature-sensitive phase transition,respectively. The results of equilibrium swelling andcompression-strain measurements were used to calcu-late the polymer-solvent interaction parameters ofthese hydrogels using the Flory-Rehner equation ofequilibrium swelling.

The pH and temperature double responsivepoly(N-isopropylacrylamide-co-IA) hydrogels wereprepared by copolymerization in mixed solvents ofwater and dimethylsulphoxide (DMSO) [108]. Theresults indicated that only hydrogels prepared in thehighest DMSO/water ratio media exhibited improvedproperties such as higher swelling ratios, fasterdeswelling and reswelling kinetics compared with tra-ditional P(NIPAAm-co-IA) hydrogels. They have



proposed that there maybe an energy barrier existedfor conformation transitions in the process of removalof DMSO by water. Only the gels which could over-come the energy barrier exhibited expanded networkstructures and improved properties while, the othergels maintained their contracted network structuresand poor properties.

Bioresponsive Hydrogels in DDS

Bioresponsive hydrogels, which undergo structuraland/or morphological changes in response to a biolog-ical stimulus, have been investigated for numerousapplications in drug delivery, tissue regeneration,bioassays/biosensors, and biomimetic systems [109]. Much work on bioresponsive hydrogels for drugdelivery relates to the release of insulin in response toraised blood sugar levels as a potential autonomoustreatment of insulin-dependant diabetes [109,110].Glucose oxidase molecules are immobilized onto abasic polymeric carrier. Following the enzyme reac-tion glucose is converted to gluconic acid and there-fore the pH of the hydrogel is temporarily lowered. Inthis situation the basic groups on the polymer are pro-tonated and induced swelling of the gel whichenhancing the release profile of insulin (Figure 8).This system works as a feedback loop: upon release ofinsulin the sugar levels drop, resulting in a pHincrease that stops the release of further insulin [110].

Bioresponsive hydrogels can be designed in adegradable form in response to external stimuli suchas enzymes. Such systems deliver physicallyentrapped guest molecules, held freely within the car-rier, and do not require chemical modification for tar-geted delivery. Plunkett et al. have developed a proce-dure to synthesize hydrogels with cross-links com-posed of different enzyme-cleavable peptides [111].Law et al. described self-assembled peptide sequencesthat release therapeutic payloads upon specific inter-action with disease-associated proteases [112]. Thecore peptide sequence consists of a protease cleavableregion flanked by two self-assembly motifs.Successful enzyme cleavage results in drug release;however, the extent of cleavage is limited by thedegree of cross-linker required to form a suitable gel.

A biochemically and stimulus responsive triblockcopolymer is developed by Li et al. [113]. The poly-mer forms a micellar, dithiol cross-linked NIPAAm

Figure 8. Schematic representation of the glucose-sensitive

hydrogel membrane consisting of a poly(amine) and glu-

cose-oxidase-loaded membrane. Adopted from ref [108].

gel at 37C that can be degraded by glutathione viacleavage of a central disulphoide bond. Thus, the sys-tem offers the possibility of payload release from aloaded gel following glutathione-stimulated degrada-tion.

Kumashiro et al. have synthesized a temperature-responsive hydrogel that only allow enzyme-triggeredpolymer degradation above a lower critical solutiontemperature and below a higher critical solution tem-perature [114]. They anticipate that this technique willallow the release of drug molecules depending onboth enzyme selectivity and changes in body temper-ature.

Kim et al. have prepared the PNIPAm-co-AAchydrogels by photo-polymerization with the peptidecross-linker, which provides enzyme degradablecapability of the hydrogels [115]. In the presence ofcollagenase the peptide cross-linked hydrogels weresuccessfully degraded in dependence on the concen-tration of the enzyme and the initial cross-linking density.



By conjugating a bio-affinity pair to the hydrogelsa new group of bioresponsive hydrogels were pre-pared, which have been used as a convenient con-struct for post-functionalization. One interestingexample is in targeting cell as a potential drug carrier,where PNIPAm core-shell hydrogel nanoparticles areconjugated with the folic acid that is a ligand for tar-geting cancer cells. When the folic acid labelledhydrogel particles are incubated with cancer cells thatover express the folate receptors, the hydrogel parti-cles are incorporated into the cancer cells via recep-tor-mediated endocytosis [116].

KINETICS OF DRUG RELEASE FROM

HYDROGELS

Hydrogels can be used in many different types of con-trolled release systems, as diffusion-controlled sys-tems, swelling-controlled systems and chemically-controlled systems. In this section, the mechanism ofdrug release in each type of system is described.

Diffusion-controlled Delivery Systems

Diffusion-controlled is the most widely applicablemechanism for describing drug release from hydro-gels, dividing in two major types: reservoir devicesand matrix devices (Figure 9). Reservoir systemsconsist of a polymeric membrane surrounding a corecontaining the drug. In matrix devices, the drug isdispersed throughout the three-dimensional structureof the hydrogel. Drug release from each type of sys-tem occurs by diffusion through the macromolecularmesh or through the water filled pores. Fick's law ofdiffusion is commonly used in modelling diffusion-controlled release systems [18,37]. For a reservoirsystem where the drug depot is surrounded by a poly-meric hydrogel membrane, Fick's first law of diffu-sion can be used to describe drug release through themembrane:

(5)

where, Ji is the molar flux of the drug (mol/cm2s), Ciis the concentration of drug, and Dip is the diffusioncoefficient of the drug in the polymer. For the case ofa steady-state diffusion process, i.e. constant molar

Figure 9. Schematic representation of diffusional controlled

reservoir and matrix devices.

flux, and constant diffusion coefficient, eqn (5) can beintegrated to give the following expression:

(6)

where, is the thickness of the hydrogel and K is thepartition coefficient, defined as the ratio of drug con-centration in the gel per drug concentration in solu-tion. To maintain a constant release rate or flux ofdrug from the reservoir, the concentration differencemust remain constant. This can be achieved bydesigning a device with excess solid drug in the core.Under these conditions, the internal solution in thecore will remain saturated. This type of device is anextremely useful device, allows for time-independentor zero-order release.

For a matrix system where the drug is uniformlydispersed throughout the matrix, unsteady-state drugdiffusion in a one-dimensional slap-shaped matrixcan be described by the Ficks second law:

(7)

This form of the equation is for one-dimensionaltransport with non-moving boundaries and can beevaluated for the case of constant diffusion coeffi-cients and concentration-dependent diffusion coeffi-cients. For the case of concentration independent dif-fusion coefficients, eqn (6) can be analyzed by appli-cation of the appropriate boundary conditions. Upon



=

XCD

XtC i

ipi

dXdCDJ iipi =

iipi

CDKJ =

application of perfect-sink condition, the solution canbe written in terms of the amount of drug released ata given time, Mt, normalized to the amount released atinfinite times, M [37]:

(8)And at short times, this solution can be approximatedas [37]:

(9)

Fu et al. obtained an analytical solution of Ficks lawfor cylindrical geometry considering mass transfer inthree dimensions [117]:

(10)

where M3 and M are the amounts of drug released attime t and infinite, time respectively; and h denotesthe half length, and r the radius of the cylinder; D isthe constant diffusivity; n = (2n+1)/2h and J0(r) =0, such that J0 a zero order Bessel function and m andn are integers. This model is applicable to tablets thatrange from the shape of a flat disk (radius > thickness)to that of a cylindrical rod (radius < thickness).

The exact solution for the release kinetics of asolute from an infinite spherical and rectangular reser-voir with the burst effect initial condition into a finiteexternal volume was developed by Abdekhodaie[118,119]. The governing diffusional equation fortransport in the membrane is solved by the timeLaplace transform method. Abdekhodaie concludedthat the approximate solution is very accurate at latetime but at early time deviations from the exact solu-tion increase. His release kinetics results indicate thatas the external fluid volume increases the cumulativerelease at any time and the releasable amount of thesolute at infinite time increase. Based on the obtainedmodels, the fractional release of model drugs decreas-

es when the polymeric coating thickness increasesExperimentally, cumulative release profiles of theo-phylline microspheres coated with ethylene vinylacetate copolymer into different external volumesagreed with the mathematical predictions.

In most systems, the drug diffusion coefficient isdependent on the drug concentration as well as theconcentration of the swelling agent. In order to ana-lyze the diffusive behaviour of drug delivery systemsin this case, one must choose an appropriate relation-ship between the diffusion coefficient and the drugconcentration. Based on theories that account for thevoid space in the gel structure, known as free-volume,researchers have proposed relationships between thediffusion coefficient and to the gel property. One ofthe most widely used equations, proposed by Fujita in1961, relates the drug diffusion coefficient in the gelto the drug concentration in the following manner[120]:

(11)

where, Diw is the diffusion coefficient in the puresolution, is a constant dependent on the system, andCo is the concentration of drug in solution.Additionally, a similar equation was written to relatethe diffusion coefficient to the concentration of theswelling agent (Cs) and the drug in the gel [120]:

(12)

The structure and morphology of a polymer networkwill also significantly affect the ability of a drug todiffuse through a hydrogel. For porous hydrogels,when pore sizes are much larger than the moleculardimensions of the drug, the diffusion coefficient canbe related to the porosity and the tortuosity of thehydrogels [121]:

(13)

where Deff is the effective diffusion coefficient, Diw isthe diffusion coefficient of the solute in the pure sol-vent, Kp is the partition coefficient, is networkporosity and is its tortuosity.

In 1961, Higuchi developed a mathematical modelaimed to describe drug release from a matrix system



[ ])CC(expDD isiwip =

piweff

KDD =

=+

=

0n2/1

ip

n2/1

2/1ipt

)tD(2nierfc)1(21

tD4

MM

2/1

2ipt tD4

MM

=

=

=

)tDexp(rh

81MM 2

m1m

2m22

t

=

1m

2n

2n )tDexp(

[ ])CC(expDD oiiwip =

[122]. This model is based on the several hypotheses,as: (1) initial drug concentration in the matrix is muchhigher than drug solubility, (2) drug diffusion takesplace only in one dimension, (3) drug particles aremuch smaller than system thickness, (4) matrixswelling and dissolution is negligible, (5) drug diffu-sivity is constant and (6) perfect sink conditions arealways attained in the release environment.Accordingly, model expression is given by [122]:

(14)

where Mt is the amount of drug released until time t,A is the release area, D is the drug diffusion coeffi-cient, C0 is the initial drug concentration in the matrixwhile Cs is drug solubility. Interestingly, this modelshows an Mt square root dependence on time as exactFicks solution predicts when the amount released isless than the 60 percent. Another simple and usefulempirical equation is the so-called power law equa-tion:

(15)

The constants, k and n, are characteristics of the drug-polymer system. Peppas et al. were the first to give anintroduction to the use and the limitations of theseequations [123]. The diffusional exponent, n, isdependent on the geometry of the device as well as thephysical mechanism for release (Table 3). Based onthe diffusional exponent, the drug transport in slabgeometry is classified as Fickian diffusion, Case IItransport, non-Fickian or anomalous transport andSuper Case II transport. For systems exhibiting CaseII transport, the dominant mechanism for drug trans-port is due to polymer relaxation as the gels swells.These types of devices, known as swelling-controlledrelease systems, will be described in more detail later.

Anomalous transport occurs due to a coupling ofFickian diffusion and polymer relaxation.

For the case of anomalous transport, Peppas andSahlin developed the following model to describe therelease behaviour of dynamically swelling hydrogels[124]:

(16)

This expression describes the release rates in terms ofrelaxation-controlled transport process, k1t, and thediffusion-controlled process, k2t1/2.

Shang et al. have shown that the partition coeffi-cient can be controlled by immobilizing a certainamount of drug molecules in the membrane whilemaintaining diffusivity of the free drug of the sametype [125]. One of the potential applications of thiscontrol scheme is for hydrogel-based pulsatile DDS,which requires sharp change in the drug permeationrate when the device is elicited on and off to bettermimic the physiological release profile of certain hor-mones. Based on their hypothesis, the amount ofimmobilization needed for a required permeation ratecan be calculated from [125]:

(17)

where Keff is the partition coefficient of free drugs;D,0 and M,0 are the reference chemical potentials inthe donor and membrane, respectively; D,free andM,free are the activity coefficients of free drugs in thedonor and membrane, respectively; CD,free is the freedrug concentration in the donor and CM,immob is theconcentration of immobilized drug in the membrane;



Type of transport Diffusional exponent (n) Time dependence

Fickian diffusion

Anomalous transport

Case II transport

Super case II transport

0.5

0.5 < n < 1

1

n > 1

t1/2

tn-1

Time independent

tn-1

Table 3. Drug transport mechanisms and diffusional exponents for hydrogel slabs [68].

s0ss0t CCtC)CC2(DAM >=

2/121

t tktkMM

+=

/1

immob,Mfree,M1free,D

free,D0,M0,Deff

)bC(C

)RT/)exp((K

=

nt ktMM

=

0Cfor immob,M >

R is the gas constant and T is the temperature; , and b are fitting parameters. This partition controlscheme offers an opportunity to modify the drugrelease profile of reservoir drug delivery systems withgreater flexibility, i.e. the difference in drug perme-ation rates between the off-state and the on-statecan be increased and drug release profile can be mod-ified after its membrane is synthesized.

Swelling-controlled Delivery Systems

Swelling-controlled release occurs when diffusion ofdrug is faster than hydrogel swelling. The modellingof this mechanism usually involves moving boundaryconditions where molecules are released at the inter-face of rubbery and glassy phases of swollen hydro-gels. The rate of drug release is controlled by thevelocity and position of the front dividing the glassy(dry) and rubbery (swelled) portions of the polymer[126].

Drug diffusion time and polymer chain relaxationtime are two key parameters determining drug deliv-ery from polymeric matrices. In diffusion-controlleddelivery systems, the time-scale of drug diffusion, t,(where t = (t)2/D and (t) is the time-dependent thick-ness of the swollen phase) is the rate-limiting stepwhile in swelling-controlled delivery systems thetime-scale for polymer relaxation () is the rate limit-ing step. The Deborah number (De) is used to com-pare these two time-scales [18]:

(18)

In diffusion-controlled delivery systems (De1),Fickian diffusion dominates the molecule releaseprocess and diffusion equations described in the pre-vious section can be used to predict molecule release.In swelling-controlled delivery systems (De1), therate of molecule release depends on the swelling rateof polymer networks. This type of transport is knownas Case II transport and results in zero-order releasekinetics. A dimensionless swelling interface number,Sw, correlates the moving boundary phenomena tohydrogel swelling [127]:

(19)

where, V is the velocity of the hydrogel swelling front

and D is the drug diffusion coefficient in the swollenphase. For a slab system when Sw1, drug diffusion ismuch faster than the movement of glassy rubberyinterface and thus a zero-order release profile isexpected.

Among the first models aimed to describe drugrelease from a swellable matrix are those presented byPeppas et al. [128]. The considerable volume extension due to matrix swelling is accounted byintroducing a moving boundary diffusion problemand chemical potential for swelling of ionizable net-works. Good agreement between experimental resultsand model calculations was obtained for drug concen-tration profiles within the polymer in a system of KCldistributed in HPMC matrix tablets.

Wu et al. [129] developed a mathematical model todescribe swelling-controlled release. They introducedadditional boundary conditions derived from a volume balance and accounted for two dimensionalmovement of the swelling front in the radial or axialdirections. This model assumes a homogeneous mix-ture of drug and polymer at t = 0, perfect sink condi-tions, and geometrical symmetry of the tablet. Modelpredictions were verified using compressed poly(eth-ylene oxide) (PEO) hydrogel tablets with differentmolecular weights. The results of water uptake,swelling and dissolution of PEO matrices as well asdrug release are shown to agree well with the mathe-matical model.

Vasheghani et al. developed mathematical modelsfor drug release from swelling controlled systems[130]. Swelling process from rubbery state wasdescribed by taking into account the movement ofinterface position R(t) (Figure 10) as [131]:

(20)

where, Dm is diffusion coefficient of solvent in rub-bery polymer, r is distance and p is volume fractionof polymer at interface. It was shown that developedmodel is relatively accurate for describing simultane-ous drug release and hydrogel dimensional change.Also, modelling of swelling controlled drug releasefrom glassy polymers was developed by using Fick'slaw and considering movement of the interface ofhydrogel surrounding solution and the moving front



2)t(

eD

tD

==

)t(Rrp

p

m

rD

dt)t(dR

=

=

D)t(VSw

=

Figure 10. Schematic diagram representing the swelling of

the hydrogels with the inward movement of diffusing front of

the solvent.

of glassy gel interface, R1(t), as [131]:

(21)

where, the volume fraction of polymeric gel at diffu-sion front p*, is defined by:

(22)

where, C* is the concentration of solvent in terms ofg/g polymer at diffusion front and p and s are thedensity of polymer and solvent, respectively. The pro-posed model described accurately the dimensionalchanges of polymeric network (polymer-solvent andglassy-gel interfaces) and dichlofenac release fromHPMC discs.

Chemically-controlled Delivery Systems

There are two major types of chemically-controlledrelease systems; erodible drug delivery systems andpendant chain systems. In erodible systems, drugrelease occurs due to degradation or dissolution of thehydrogel. In pendant chain systems, the drug isaffixed to the polymer backbone through degradablelinkages. As these linkages degrade, the drug isreleased.Erodible Drug Delivery SystemsIn erodible drug delivery systems (either matrix orreservoir), also known as degradable or absorbablerelease systems, drug release is mediated by the rate

of surface erosion. In reservoir devices, an erodiblemembrane surrounds the drug core. In matrix devices,the drug is dispersed within the three-dimensionalstructure of the hydrogel. Drug release is controlledby drug diffusion through the gel or erosion of thepolymer. In true erosion controlled devices, the rate ofdrug diffusion will be significantly slower than therate of polymer erosion and the drug is released as thepolymer erodes [37]. One of the earliest mathematicalmodels, where the release mechanism only dependson matrix erosion rates, was developed byHopfenberg [132]:

(23)

where a0 is the radius of a spherical or cylindricalgeometry or half-thickness for slab geometry and C0is the drug concentration in the surface erodingdevice. In this equation, n is 1, 2, or 3 for slab, cylin-der, or sphere, respectively. It is clear that only for aslab-shaped device the drug release must be a zeroorder profile.

Later, a general mathematical model for hetero-geneous eroding networks developed by Katzhendleret al., accounting for different radial and vertical ero-sion rate constants for a flat tablet [133]:

(24)

where ka and kb are radial and vertical degradationconstant. Here, a0 is the initial radius of the tablet andb0 is the thickness of the tablet. By changing theradius to thickness ratio of the device, one can easilyobtain various drug release rates. It is important tonote that swelling of the matrices is either not consid-ered or is assumed to occur prior to erosion and drugrelease in two above models. Also, these models justfocused on the surface erosion of the hydrophobicpolymers.

Martens et al. developed a generalized statistical-co-kinetic model to predict the degradation behav-iours of acrylated poly(vinyl alcohol) (PVA) hydro-gels [134]. In this model, a statistical approach wasused to predict the different configurations of thecross-linking molecules and kinetic chains. It also



)t(Rrp

*p

m11r)1(

Ddt

)t(dR=

=

1)/(C1

sp*

*p

+=

0 0

1 1

n

t aM k tM C a

=

2

0 0 0 0

21 1 1t a b

M k t K tM C a C b

=

accounts for the probability of an intact degradablelinkage. The model was verified by experimentalobservation of gel swelling, mass loss and compres-sive modulus.

Monte Carlo simulation is used to predict proteinrelease from cross-linked dextran microspheres [135].Monte Carlo simulation is good for describing net-work morphological changes; however it does notprovide any information regarding molecule release.Diffusion equations (Fick's law) must be incorporatedin order to link the network degradation to moleculediffusion. Based on Vlugt-Wensink et al. studies akinetic Monte Carlo scheme for the degradation of asmall domain inside the dextran microsphere wasdeveloped. The only processes included in theirmodel are diffusion and degradation. The generaleffects of diffusion, cross-link density, protein load-ing, and clustering of proteins on the release were alsostudied in their report. However, swelling of thehydrophilic microspheres and changes in swellingwith matrix degradation were not accounted for in thedescribed model.Pendant Chain SystemsIn pendent chain system the drug molecule is chemi-cally linked to the backbone of a polymer. In the pres-ence of enzymes or fluids, chemical or enzymatichydrolysis occurs with concomitant release of thedrug as a controlled rate. The drug may be linkeddirectly to the polymer or can be linked via a spacergroup. In the biodegradable system, polymers gradu-ally decompose and bring about a controlled releaseof drug. The drug is dispersed uniformly throughoutthe polymer and is slowly released as the polymer dis-integrates. The release of covalently attached drugs isdetermined by the degradation rate of the polymer-drug linkage. Generally, these linkages degrade byhydrolysis allowing degradation and also release ratesto be illustrated by simple first-order kinetic relation-ships [18]. However, in specific applications, the drugpolymer linkages may design to be enzymaticallydegraded which lead to more complex release kinetics[136].

A statistical-co-kinetic model has been developedto predict the effects of hydrolytic or enzymaticdegradation on the macroscopic properties of hydro-gels [137]. Dubose et al. covalently incorporated fluorescently labelled probe molecules within the

three-dimensional network structure of PEG-basedhydrogels. Bond cleavage kinetics, microstructuralnetwork characteristics and detailed analysis of degra-dation products are the important parameters account-ed in this study. They demonstrated that hydrolyticdegradation of covalent bonds as well as the cleavageof immobilized probe molecules resulted in a biphasicrelease profile in which a constant molecular releaseprofile is obtained prior to gel dissolution and analmost instantaneous burst release following gel dis-solution.

CONCLUSION

During past decades, hydrogels have played a veryessential role in biomedical applications. New syn-thetic methods have been used to prepare homo- andcopolymeric hydrogels for a wide range of drugs, pep-tides, and protein delivery applications. Recentenhancements in the field of polymer science andtechnology have led to the development of variousstimuli sensitive hydrogels. Either pH-sensitiveand/or temperature-sensitive hydrogels can be usedfor site-specific controlled drug delivery. Hydrogelsthat are responsive to specific molecules, such as glu-cose or antigens, can be used as biosensors as well asdrug delivery systems. Polymer solutions in water (solphase) that transform into a gel phase on changing thetemperature (thermo-gelation) offer a very excitingfield of research.

Recent advances in the development of novelhydrogels for drug delivery applications have focusedon several aspects of their synthesis, characterizationand behaviour. Obviously, drug release from hydrogelnetworks is controlled by a complex combination ofdifferent mechanisms, such as matrix swelling, drugdissolution/diffusion and hydrogel erosion.Successful design of drug delivery systems relies notonly on proper network design but also on precisedescription of hydrogel behaviour as well as mathe-matical modelling of drug release profiles. As moreadvanced release devices, such as in-situ forminghydrogels are developed more rigorous mathematicalmodelling approaches are needed to describe the com-plete mechanisms governing drug release from thesesystems.



REFERENCES

1. Peppas NA, Zach Hilt J, Khademhosseini A,Langer R, Hydrogels in biology and medicine:from molecular principles to bionanotechnology,Adv Mater, 18, 1345-1360, 2006.

2. Huang X, Brazel CS, On the importance andmechanisms of burst release in matrix-controlleddrug delivery systems, J Control Rel, 73, 121-136,2001.

3. Hoffman AS, Hydrogels for biomedical applica-tions, Adv Drug Deliv Rev, 43, 3-12, 2002.

4. Hoare TR, Kohane DS, Hydrogels in drug deliv-ery: progress and challenges, Polymer, 49, 1993-2007, 2008

5. Brannon-Peppas L, Polymers in controlled drugdelivery, medical plastic and biomaterials maga-zine, November 1997, Medical device link,http://www.devicelink.com/mpb/archive/97/11/003.html, 10 August 2008.

6. Peppas NA, Bures P, Leobandung W, Ichikawa H,Hydrogels in pharmaceutical formulations, Eur JPharm Biopharm, 50, 27-46, 2000.

7. Baroli B, Hydrogels for tissue engineering anddelivery of tissue-inducing substances, J PharmSci, 96, 2197-2223, 2007.

8. Ganta S, Devalapally H, Shahiwala A, Amiji M, Areview of stimuli-responsive nanocarriers for drugand gene delivery, J Control Rel, 126, 187-204,2008.

9. He Ch, Kim SW, Lee DS, In situ gelling stimuli-sensitive block copolymer hydrogels for drugdelivery, J Control Rel, 127, 189-207, 2008.

10. Schmaljohann D, Thermo- and pH-responsivepolymers in drug delivery, Adv Drug DeliveryRev, 58, 1655-1670, 2006.

11. Peppas NA, Khare AR, Preparation, structure anddiffusional behavior of hydrogels in controlledrelease, Adv Drug Delivery Rev, 11, 1-35, 1993.

12. Entezami AA, Massoumi B, Artificial muscles,biosensors and drug delivery systems based onconducting polymers: a review, Iran Polym J, 15,13-30, 2006.

13. Ghazizadeh Y, Mirzadeh H, Amanpour S, AhmadiH, Rabbani Sh, Investigation of effectiveness ofchitosan hydrogel to stop bleeding and air leakagefrom lung fistula: an in vivo study, Iran Polym J,

15, 821-828, 2006.14. Casadei MA, Pitarresi G, Calabrese R, Paolicelli

P, Giammona G, Biodegradable and pH-sensitivehydrogels for potential colon-specific drug deliv-ery: characterization and in vitro release studies,Biomacromolecules, 9, 43-49, 2008.

15. Chiu HC, Wu AT, Lin YF, Synthesis and charac-terization of acrylic acid-containing dextranhydrogels, Polymer, 42, 1471-1479, 2001.

16. Tavakoli J, Jabbari E, Etrati Khosroshahi M,Boroujerdi M, Swelling characterization ofanionic acrylic acid hydrogel in an external elec-tric field, Iran Polym J, 15, 891-900, 2006.

17. Gao D, Xu H, Philbert MA, Kopelman R,Ultrafine hydrogel nanoparticles: syntheticapproach and therapeutic application in livingcells, Angew Chem Int Ed, 46, 2224-2227, 2007.

18. Lin CC, Metters AT, Hydrogels in controlledrelease formulations: network design and mathe-matical modeling, Adv Drug Delivery Rev, 58,1379-1408, 2006.

19. Satish CS, Satish KP, Shivakumar HG, Hydrogelsas controlled drug delivery systems: synthesis,cross-linking, water and drug transport mecha-nism, Ind J Pharm Sci, 68, 133-40, 2006.

20. Hennink WE, Van Nostrum CF, Novel cross-link-ing methods to design hydrogels, Adv DrugDelivery Rev, 54, 13-16, 2002

21. Wang Zh, Hou X, Mao Zh, Ye R, Mo Y, FinlowDE, Synthesis and characterization of biodegrad-able poly(lactic acid-co-glycine) via direct meltcopolymerization, Iran Polym J, 17, 791-798,2008.

22. Bagheri Sh, Mohammadi-Rovshandeh J, HassanA, Synthesis and characterization of biodegrad-able random copolymers of L-lactide, glycolideand trimethylene carbonate, Iran Polym J, 16,489-494, 2007.

23. Zhang Y, Zhu W, Ding J, Preparation of ther-mosensitive microgels via suspension polymer-ization using different temperature protocols, JBiomed Mater Res Part A, 75, 342-349, 2005.

24. Baroli B Photopolymerization in drug delivery,tissue engineering and cell encapsulation: issuesand potentialities, J Chem Tech Biotech, 81, 491-499, 2006.

25. Lopes MA, Felisberti MI, Mechanical behavior



and biocompatibility of poly(1-vinyl-2-pyrrolidi-none)-gelatin IPN hydrogels, Biomaterials, 24,1279-1284, 2003.

26. Oh EJ, Kang SW, Kim BS, Jiang G, Cho IH, HahnSK, Control of the molecular degradation ofhyaluronic acid hydrogels for tissue augmenta-tion, J Biomed Mater Res Part A, 86, 685-693,2008.

27. Coviello T, Grassi M, Rambone G, Alhaique F, Acrosslinked system from Scleroglucan derivative:preparation and characterization, Biomaterials,22, 1899-1909, 2001.

28. Garcia Y, Collighan R, Griffin M, Pandit A,Assessment of cell viability in a three-dimension-al enzymatically cross-linked collagen scaffold, JMater Sci Mater Med, 18, 1991-2001, 2007.

29. Ganji F, Abdekhodaie MJ, Ramazany-SadtabadiA, Gelation time and degradation rate of chitosanas a thermosensitive injectable hydrogel, J Sol-Gel Sci Technol, 42, 47-53, 2007.

30. Mohamadnia Z, Jamshidi A, Mobedi H, AhmadiE, Zohuriaan-Mehr MJ, Full natural hydrogelbeads for controlled release of acetate and disodi-um phosphate derivatives of betamethasone, IranPolym J, 16, 711-718, 2007.

31. Aalaie J, Vasheghani-Farahani E, Rahmatpour A,Semsarzadeh MA, Effect of montmorillonite ongelation and swelling behavior of sulfonatedpolyacrylamide nanocomposite hydrogels in elec-trolyte solutions, Eur Polym J, 44, 2024-2031,2008.

32. Aalaie J, Vasheghani-Farahani E, SemsarzadehMA, Rahmatpour A, Gelation and swellingbehavior of semi-interpenetrating polymer net-work hydrogels based on polyacrylamide andpoly(vinyl alcohol), J Macromol Sci, Part B, 47,1017-1027, 2008.

33. Stenekes RJ, Talsma H, Hennink WE, Formationof dextran hydrogels by crystallization,Biomaterials, 22, 1891-1898, 2001.

34. Kimura M, Fukumoto K, Watanabe J, Ishihara K,Hydrogen-bonding-driven spontaneous gelationof water-soluble phospholipid polymers in aque-ous medium, J Biomater Sci Polym Ed, 15, 631-644, 2004.

35. Oh KS, Han SK, Choi YW, Lee JH, Lee JY, YukSH, Hydrogen-bonded polymer gel and its appli-

cation as a temperature-sensitive drug deliverysystem, Biomaterials, 25, 2393-2398, 2004.

36. Cappello J, Crissman JW, Crissman M, FerrariFA, Textor G, Wallis O, Whitledge JR, Xia Zhou,Burman D, Aukerman L, Stedronsky ER, In-situself-assembling protein polymer gel systems foradministration, delivery, and release of drugs, JControl Rel, 53, 105-117, 1998.

37. Lowman AM, Smart Pharmaceuticals, www.gate-waycoalition.org/files/NewEH/htmls/lowman.doc, 7 September 2008.

38. Flory PJ, Rehner J, Statistical mechanics of cross-linked polymer networks. II. Swelling, J ChemPhys, 11, 521-526, 1943.

39. Vasheghani-Farahani E, Vera JH, Cooper DG,Weber ME, Swelling of ionic gels in electrolytesolutions, Ind Eng Chem Res, 29, 554-560, 1990.

40. Grassi M, Grassi G, Mathematical modeling andcontrolled drug delivery: matrix systems, CurrDrug Deliv, 2, 97-116, 2005.

41. Marchetti M, Prager S, Cussler EL,Thermodynamic predictions of volume changesin temperature-sensitive gels. 1. Theory,Macromolecules, 23, 1760-1765, 1990.

42. Achilleosa EC, Christodouloub KN, KevrekidisIG, A transport model for swelling of polyelec-trolyte gels in simple and complex geometries,Comput Theor Polym Sci, 11, 63-80, 2001.

43. Oliveira D, Silva AFS, Freitas RFS,Contributions to the thermodynamics of polymerhydrogel systems, Polymer, 45, 1287-1293, 2004.

44. Yang JY, Yan QL, Liu HL, Hu Y, A molecularthermodynamic model for compressible latticepolymers, Polymer, 47, 5187-5195, 2006.

45. Orlov Y, Xu X, Maurer G, An experimental andtheoretical investigation on the swelling of N-iso-propyl acrylamide based ionic hydrogels in aque-ous solutions of (sodium chloride or di-sodiumhydrogen phosphate), Fluid Phase Equilib, 254,1-10, 2007.

46. Wallmersperger T, Ballhause D, Kroplin B, Onthe modeling of polyelectrolyte gels, MacromolSymp, 254, 306-313, 2007

47. Huang y, Jin X, Liu H, Hu Y, A molecular thermo-dynamic model for the swelling of thermo-sensi-tive hydrogels, Fluid Phase Equilib, 263, 96-101,2008.



48. Park GS, The glassy state and slow processanomalies, In: Diffusion Polymers, Crank J, ParkGS, (Eds) Academic, London, 1968

49. Singh J, Weber ME, Kinetics of one-dimensionalgel swelling and collapse for large volumechange, Chem Eng Sci, 51, 4499-4508, 1996.

50. Li Y, Tanaka T, Kinetics of swelling and shrink-ing of gels, J Chem Phys, 92, 1365-1371, 1990.

51. Crank J, Park GS, Diffusion in high polymers,Trans Faraday Soc, 47, 1072-1084, 1951.

52. Joshi S, Astarita G, Diffusion-relaxation couplingin polymers which show two-stage sorption phe-nomena, Polymer, 20, 455-458, 1979.

53. Mazich KA, Rossi G, Smith CA, Kinetics of sol-vent diffusion and swelling in a model electro-metric system, Macromolecules, 25, 6929-6933,1992.

54. Singh SK, Fan LT, A generalized model forswelling controlled release systems, BiotechnolProg, 2, 45-156, 1986.

55. Vasheghani-Farahani E, Swelling and exclusionbehavior of hydrogels, PhD Thesis, McGillUniversity, June 1990.

56. Karadag E, Saraydin D, Swelling of superab-sorbent acrylamide/sodium acrylate hydrogelsprepared using multifunctional crosslinkers, TurkJ Chem, 26, 863-875, 2002.

57. Khorram M, Vasheghani-Farahani E, Golshan-Ebrahimi N, Fast responsive thermosensitivehydrogels as drug delivery systems, Iran Polym J,12, 315-322, 2003.

58. Bouquerand PE, Maio S, Normand V, SingletonS, Atkins D, Swelling and erosion affecting flavorrelease from glassy particles in water, AIChE, 50,3257-3270, 2004.

59. Vasheghani-Farahani E, Letter to the Editor,AIChE, 52, 1970, 2006.

60. Boral S, Gupta AN, Bohidar HB, Swelling andde-swelling kinetics of gelatin hydrogels inethanol-water marginal solvent, Int J BiolMacromol, 39, 240-249, 2006.

61. Hosseinkhani H, Hosseink

hydrogel in controlled drug delivery system

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