; accepted 4 September 2006

diffusion, swelling, and chemically-controlled release. The focus of the final part of this article is discussion of emerginghydrogel delivery systems and challenges associated with modeling the performance of these devices.

Advanced Drug Delivery Reviews 58 (2006) 13791408www.elsevier.com/locate/add

e issue on Computational Drug Delivery, Vol. 58/12-13, 2006. This review is part of the Advanced Drug Delivery Reviews them 2006 Elsevier B.V. All rights reserved.

Keywords: Hydrogel; Drug delivery; Modeling; Controlled release; Diffusion; Degradation

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13801.1. Overview of manuscript/scope of this review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13801.2. Hydrogel definition, classification, and network structure . . . . . . . . . . . . . . . . . . . . . . . . 13811.3. Niche roles of hydrogels in drug delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1383Available online 22 September 2006

Abstract

Over the past few decades, advances in hydrogel technologies have spurred development in many biomedical applicationsincluding controlled drug delivery. Many novel hydrogel-based delivery matrices have been designed and fabricated to fulfillthe ever-increasing needs of the pharmaceutical and medical fields. Mathematical modeling plays an important role infacilitating hydrogel network design by identifying key parameters and molecule release mechanisms. The objective of thisarticle is to review the fundamentals and recent advances in hydrogel network design as well as mathematical modelingapproaches related to controlled molecule release from hydrogels. In the first section, the niche roles of hydrogels in controlledrelease, molecule release mechanisms, and hydrogel design criteria for controlled release applications are discussed. Novelhydrogel systems for drug delivery including biodegradable, smart, and biomimetic hydrogels are reviewed in the secondsection. Several mechanisms have been elucidated to describe molecule release from polymer hydrogel systems includingReceived 15 August 2006Hydrogels in controlled release formulations: Networkdesign and mathematical modeling

Chien-Chi Lin a, Andrew T. Metters a,b,

a Department of Bioengineering, Clemson University, Clemson, SC 29634, USAb Department of Chemical and Biomolecular Engineering, Clemson University, Clemson, SC 29634, USA Corresponding author. Department of Chemical and Biomolecular Engineering, 127 Earle Hall, Clemson University, Clemson, SC 29634USA. Tel.: +1 864 656 0290; fax: +1 864 656 0784.

E-mail address: metters@clemson.edu (A.T. Metters).

0169-409X/$ - see front matter 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.addr.2006.09.004r,

es .formu. .. .. .. .ns .. .. .. .chainrodinbu

af. .. .. .. .. .. .

s . .deliv

ug De4.3. Micro/nanoscaled hydrogel delivery systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14004.4. In-situ forming hydrogels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1401

5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1403References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1403

1. Introduction

1.1. Overview of manuscript/scope of this review

Since the establishment of the first synthetic hy-drogels by Wichterle and Lim in 1954 [1], the growthof hydrogel technologies has advanced many fieldsranging from food additives [2] to pharmaceuticals[3] to biomedical implants [4]. In addition, the devel-opment of an ever-increasing spectrum of functionalmonomers and macromers continue to broaden theversatility of hydrogel applications. Hydrogels nowplay a critical role in many tissue engineering scaffolds,biosensor and BioMEMS devices, and drug carriers.Among these applications, hydrogel-based drug deliverydevices have become a major area of research interestwith several commercial products already developed [5].A successful drug delivery device relies not only onintelligent network design but also on accurate a priorimathematical modeling of drug release profiles. An

with well-defined physicochemical properties and re-producible drug-release profiles. In a complimentaryfashion, a quantitative mathematical understanding ofmaterial properties, interaction parameters, kineticevents, and transport phenomena within complex hy-drogel systems assists network design by identifyingthe key parameters and mechanisms that govern therate and extent of drug release. In addition, mathemat-ical modeling accelerates device design by limiting thenumber of experiments researchers must perform tounderstand the release mechanisms governing a par-ticular delivery system.

Many excellent review articles have been pub-lished detailing the modeling of drug release frompolymeric devices including hydrogels. This reviewbuilds on the established literature by not only track-ing recent advances in the development of mathe-matical models for quantitatively predicting drugdelivery from hydrogel systems, but also highlightshow these models are playing a critical role in the1.4. Drug release mechanisms from hydrogel devic1.5. Design criteria for hydrogels in drug delivery

2. Novel engineering of hydrogels for drug delivery . .2.1. Biodegradable hydrogels . . . . . . . . . . . .2.2. Smart hydrogels . . . . . . . . . . . . . . . .2.3. Biomimetic hydrogels . . . . . . . . . . . . .

3. Molecule release mechanisms for hydrogel formulatio3.1. Diffusion-controlled delivery systems . . . . .3.2. Swelling-controlled delivery systems . . . . .3.3. Chemically-controlled delivery systems . . . .

3.3.1. Kinetic-controlled release pendant3.3.2. Kinetic-controlled release surface-e3.3.3. Reaction-diffusion-controlled release 3.3.4. Reactiondiffusion-controlled release

4. Emerging systems and remaining challenges . . . . .4.1. Dynamic hydrogel delivery systems . . . . . .

4.1.1. Degradable hydrogels . . . . . . . . .4.1.2. Stimuli-sensitive hydrogels . . . . . .

4.2. Composite hydrogel delivery systems . . . . .4.2.1. Multi-layer hydrogel delivery systems4.2.2. Multi-phase hydrogel delivery system4.2.3. Challenges facing composite hydrogel

1380 C.-C. Lin, A.T. Metters / Advanced Drordered polymer network composed of macromerswith well-understood chemistries yields hydrogels. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1384lations . . . . . . . . . . . . . . . . . . . . . . . . 1384. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1385. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1385. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1386. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1386. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1387. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1387. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1389. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1391systems . . . . . . . . . . . . . . . . . . . . . . . 1391g systems . . . . . . . . . . . . . . . . . . . . . . 1392lk-degrading systems. . . . . . . . . . . . . . . . . 1393finity hydrogel systems . . . . . . . . . . . . . . . 1395. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1396. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1397. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1397. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1397. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1398. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1399. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1400ery systems . . . . . . . . . . . . . . . . . . . . . 1400

livery Reviews 58 (2006) 13791408design of novel hydrogel networks for future ap-plications. In addition to describing the mechanisms

chains together determine the mobility of encapsulatedmolecules and their rates of diffusion within a swollenhydrogel matrix.

The polymer volume fraction in the swollen state(2,s) describes the amount of liquid that can beimbibed in hydrogels and is described as a ratio ofthe polymer volume (Vp) to the swollen gel volume(Vg). It is also a reciprocal of the volumetric swollenratio (Q) which can be related to the densities of thesolvent (1) and polymer (2) and the mass swollenratio (Qm) as described by Eq. (1):

m2;s VpVg Q1 1=q2

Qm=q1 1=q21

ug Degoverning drug release from conventional hydrogels,the fabrication and modeling of several emerging andintelligently designed hydrogel systems for drug deli-very applications are discussed. Specifically, thesenovel systems aim to incorporate advanced drug de-livery strategies into tissue engineering scaffolds andother biomedical implants and require rigorous meth-ods for quantifying multiple phenomena influencingmolecule release.

1.2. Hydrogel definition, classification, and networkstructure

Hydrogels are polymeric networks that absorblarge quantities of water while remaining insoluble inaqueous solutions due to chemical or physical cross-linking of individual polymer chains. Differing fromhydrophobic polymeric networks such as poly(lacticacid) (PLA) or poly(lactide-co-glycolide) (PLGA)which have limited water-absorption capabilities(b510 wt.%), hydrophilic hydrogels exhibit manyunique physicochemical properties that make themadvantageous for biomedical applications includingdrug delivery. For example, hydrogels are excellentcandidates for encapsulating biomacromolecules in-cluding proteins and DNA due to their lack of hydro-phobic interactions which can denature these fragilespecies [6]. In addition, compared to commonly usedhydrophobic polymers such as PLGA, the conditionsfor fabricating hydrogels are relatively mild. Gel for-mation usually proceeds at ambient temperature andorganic solvents are rarely required. In-situ gelationwith cell and drug encapsulation capabilities furtherdistinguishes hydrogels from the other hydrophobicpolymers.

Hydrogels can be prepared from natural or syntheticpolymers [7]. Although hydrogels made from naturalpolymers may not provide sufficient mechanical prop-erties and may contain pathogens or evoke immune/inflammatory responses, they do offer several advan-tageous properties such as inherent biocompatibility,biodegradability, and biologically recognizable moie-ties that support cellular activities. Synthetic hydro-gels, on the other hand, do not possess these inherentbioactive properties. Fortunately, synthetic polymersusually have well-defined structures that can be

C.-C. Lin, A.T. Metters / Advanced Drmodified to yield tailorable degradability and func-tionality. Table 1 lists natural polymers as well as syn-

The average molecular weight between two ad-jacent crosslinks (Mc) represents the degree ofthetic monomers that are commonly used in hydrogelfabrication.

Since the favorable properties of hydrogels stemfrom their hydrophilicity, the characterization of theirwater-sorption capabilities is the first step towardsunderstanding the nanoscopic structure of hydrogelnetworks. Generally, three parameters are critical indescribing the nanostructure of crosslinked hydrogelnetworks: (1) polymer volume fraction in the swollenstate, 2,s, (2) number average molecular weightbetween crosslinks, Mc, and (3) network mesh size, [8]. For non-porous hydrogels, the amount of li-quid being retained in the hydrogel, the distance be-tween polymer chains, and the flexibility of those

Table 1Natural polymers and synthetic monomers used in hydrogelfabrication [6,7]

Natural polymer Synthetic monomer

Chitosan Hydroxyethyl methacrylate (HEMA)Alginate N-(2-hydroxypropyl) methacrylate (HPMA)Fibrin N-vinyl-2-pyrrolidone (NVP)Collagen N-isopropyl acrylamide (NIPAAm)Gelatin Vinyl acetate (VAc)Hyaluronic acid Acrylic acid (AA)Dextran Methacrylic acid (MAA)

Polyethylene glycol acrylate/methacrylate(PEGA/PEGMA)Polyethylene glycol diacrylate/dimethacrylate(PEGDA/PEGDMA)

1381livery Reviews 58 (2006) 13791408

swolle

ug Decrosslinking of the hydrogel networks. Mc in a neutral,divinyl crosslinked network can be expressed as thefollowing FloryRehner Equation [9].

1PM c

2PM n

m

V1

ln1m2;s m2;s v12m22;sh i

m1=32;s m2;s2

2

Here, Mn is the average molecular weight of thelinear polymer chains, is the specific volume of thepolymer, V1 is the molar volume of water, and 12 is thepolymerwater interaction parameter. More complexversions of the FloryRehner expression have beendeveloped by Peppas and others to describe the swellingbehavior of ionic gels or gels crosslinked duringpolymerization [8]. For neutral gels at highly swellingconditions (QN10), Eq. (2) can be simplified to illustratehow gel swelling scales with the average molecularweight between crosslinks (Mc) [10]:

Fig. 1. Schematic of mesh size in hydrogels at

1382 C.-C. Lin, A.T. Metters / Advanced DrQ m1=22v12PM c

V1

3=5 b PM c

3=5 3Another important parameter used to describe

hydrogel swelling is the network mesh size () whichcan be described as follows [11]:

n m1=32;sPr2o

1=2 Q1=3

Pr2o

1=24

Here,Pr2o

1=2is the root-mean-squared end-to-end

distance of network chains between two adjacent

(3) external stimuli such as temperature, pH and ionicstrength. Mesh size is important in determining thephysical properties of the hydrogels including me-chanical strength, degradability, and diffusivity of thereleasing molecule [10,13]. Typical mesh sizesreported for biomedical hydrogels range from 5 to100 nm in their swollen state [10,14]. These size scalesare much larger than most small-molecule drugs andtherefore diffusion of these drugs are not significantlyretarded in swollen hydrogel matrices. However, therelease of macromolecules such as peptides, proteinsand oligonucleotides can be sustained from swollenhydrogels due to their significant hydrodynamic radiiWhen designed appropriately, the structure and meshsize of swollen hydrogels can be tailored to obtain,

.crosslinks in the unperturbed state. It can be determinedusing the following relationship [11]:

Pr2o

1=2 lCnN1=2 l Cn 2Mc

P

Mr

1=25

where Cn is the Flory characteristic ratio, l is the bondlength along the polymer backbone, N is the number ofbonds between adjacent crosslinks, and Mr is themolecular weight of the repeating units of thecomposed polymer.

Combining Eqs. (4) and (5), one can easilycalculate the mesh size of a hydrogel network andfurther compare it with the hydrodynamic radii of themolecules to be delivered. Theoretically, no solutediffusion is possible within the hydrogel matrix whenmesh size approaches the size of the solute as shown inFig. 1 [12]. Mesh size is affected by several factorsincluding (1) degree of crosslinking of the gel; (2)chemical structure of the composing monomers; and

n or shrunken states. Adapted from Ref. [12].

livery Reviews 58 (2006) 13791408

ug Dedesired rates of macromolecule diffusion [15]. Alter-natively, the rate and degree of gel swelling ordegradation can also be tailored to control the releaseof molecules much smaller than the gel mesh size.

1.3. Niche roles of hydrogels in drug delivery

The advance in recombinant protein technology hasidentified numerous protein and peptide therapeuticsfor disease treatment. However, the effective deliveryof these biomolecules is challenging mainly becauseof their large molecular weights and unique three-dimensional structures. Intravenous or subcutaneousinjection is by far the most commonly used route fordrug administration. However, these biomolecules areprone to proteolytic degradation and therefore expe-rience extremely short plasma circulation times andrapid renal clearance, leading to multiple daily in-jections or increased dosage to maintain the drug con-centration in the therapeutic window. Multiple dailyinjections decrease patient compliance while high dosesmay induce local toxicity and serious systemic immuneresponses. Polymeric controlled release formulationssuch as PLGA offer a sustained release mechanism inwhich the drug release rates can be controlled bychanging polymer molecular weight and composition.However, it is well recognized that these hydrophobicpolymers induce detrimental effects to the encapsulatedproteins or peptides during network preparation anddelivery [16] as well as trigger the host immuneresponse [17]. Hydrophilic hydrogels, on the otherhand, provide relatively mild network fabrication anddrug encapsulation conditions that make them suitablefor protein delivery [6]. The common niche forhydrogels in controlled release is the encapsulation(and subsequent release) of bioactive materials. There-fore, the systems we will focus on in this review dealwith delivery from matrix devices rather than mem-brane devices. Through proper design, hydrogels can beused in a variety of applications including sustained,targeted, or stealth biomolecule delivery.

Several unique properties that hydrogels possessmake them useful in delivering biomolecules. Forexample, stimuli responsiveness can be easily tailoredinto hydrogel networks during fabrication [18]. Thisenables sustained or bolus drug delivery correspond-

C.-C. Lin, A.T. Metters / Advanced Dring to external stimuli such as pH or temperature. Forexample, pH-sensitive hydrogels are useful in oraldrug delivery as they can protect peptide/protein drugsin the digestive track [19]. The pH responsiveness ofhydrogels also facilitates lysosomal escape duringgene delivery [20,21]. Such responsiveness changesthe mode of drug administration from merely passiverelease to active delivery. These exclusive properties ofhydrogels can be attributed to the variety of availablenetwork precursors. Acrylic acid (AA) and methacry-lic acid (MAA) [19,22,23] are the most commonlyused monomers to fabricate anionic pH-sensitivehydrogels while 2-(dimethylamino)ethyl methacrylate(DMAEMA) [24,25] is used for cationic hydrogel fab-rication. N-isopropylacrylamide (NIPAAM) [2628]and polypropylene oxidepolyethylene oxidepolypro-pylene oxide (PPOPEOPPO) block copolymers [2830] are well-suited for the fabrication of temperature-sensitive hydrogels. The reversible swell-collapsetransition modulates drug release rates and largelyenhances the therapeutic efficacy of biomolecules.

Hydrogels can also be engineered to exhibit bio-adhesiveness to facilitate drug targeting, especiallythrough mucus membranes, for non-invasive drugadministration [3134]. Both natural polymers (e.g.chitosan) and synthetic monomers (e.g. AA) providethis advantageous property. Some bioadhesive poly-mers have been used to fabricate hydrogels for oral [6]and buccal drug delivery [35,36].

Hydrogels offer an important stealth characteris-tic in vivo owing to their hydrophilicity which in-creases the in vivo circulation time of the deliverydevice by evading the host immune response anddecreasing phagocytic activities [37,38]. For example,Hubbell and coworkers developed poly(ethyleneglycol)-based hydrogel nanoparticles as colloidaldrug carriers [39]. Several other stealth delivery sys-tems, such as PEGylated gold nanoparticles [37,40],have also been developed utilizing a PEG shell as ameans of steric hindrance. This strategy exploits thehydrophilicity of PEG in excluding enzymatic degra-dation of the drug to be delivered. When conjugatedwith other protein therapeutics such as tumor necrosisfactor (TNF), these PEGylated gold nanoparticles aregood carriers for tumor-targeted delivery [41].

Another prospect of hydrogels is their role asscaffolding materials in tissue engineering applications[4244]. Excellent examples are cartilage [45,46] and

1383livery Reviews 58 (2006) 13791408nerve [47] tissue engineering. The mild gelling con-ditions and in-situ polymerization capabilities of

ug Dehydrogels enable the simultaneous encapsulation ofcells and growth factors. Controlled release ofencapsulated growth factors and other agents fromthese tissue constructs is critical to providing thenecessary cues for cell migration, differentiation,angiogenesis, and upregulation of extracellular matrixproduction required for neotissue growth or regener-ation [48,49].

1.4. Drug release mechanisms from hydrogel devices

As discussed in the previous sections, hydrogelshave a unique combination of characteristics that makethem useful in drug delivery applications. Due to theirhydrophilicity, hydrogels can imbibe large amounts ofwater (N90 wt.%). Therefore, the molecule releasemechanisms from hydrogels are very different fromhydrophobic polymers. Both simple and sophisticatedmodels have been previously developed to predict therelease of an active agent from a hydrogel device as afunction of time. These models are based on the rate-limiting step for controlled release and are thereforecategorized as follows:

1. Diffusion-controlled2. Swelling-controlled3. Chemically-controlled.

Diffusion-controlled is the most widely applicablemechanism for describing drug release from hydro-gels. Fick's law of diffusion with either constant orvariable diffusion coefficients is commonly used inmodeling diffusion-controlled release [13]. Drugdiffusivities are generally determined empirically orestimated a priori using free volume, hydrodynamic, orobstruction-based theories [13].

Swelling-controlled release occurs when diffusionof drug is faster than hydrogel swelling. The modelingof this mechanism usually involves moving boundaryconditions where molecules are released at theinterface of rubbery and glassy phases of swollenhydrogels [50]. The release of many small moleculedrugs from hydroxypropyl methylcellulose (HPMC)hydrogel tablets is commonly modeled using thismechanism. For example, Methocel matrices, acombination of methylcellulose and HPMC, from

1384 C.-C. Lin, A.T. Metters / Advanced DrDow Chemical Company are commercially availablefor preparing swelling-controlled drug delivery for-mulations exhibiting a broad range of delivery time-scales [50,51].

Chemically-controlled release is used to describemolecule release determined by reactions occurringwithin a delivery matrix. The most common reactionsthat occur within hydrogel delivery systems arecleavage of polymer chains via hydrolytic or enzy-matic degradation or reversible or irreversible reac-tions occurring between the polymer network andreleasable drug. Under certain conditions the surfaceor bulk erosion of hydrogels will control the rate ofdrug release. Alternatively, if drug-binding moietiesare incorporated in the hydrogels, the bindingequilibrium may determine the drug release rate.Chemically-controlled release can be further catego-rized according to the type of chemical reactionoccurring during drug release. Generally, the liberationof encapsulated or tethered drugs can occur throughthe degradation of pendant chains or during surface-erosion or bulk-degradation of the polymer backbone.A more thorough discussion of these mechanisms canbe seen in a later section of this review as well as inseveral other excellent reviews [6,13,52].

1.5. Design criteria for hydrogels in drug deliveryformulations

Materials selection and network fabrication governsthe rate and mode of drug release from hydrogelmatrices. Several design criteria are crucial for drugdelivery formulations and have to be evaluated prior tohydrogel fabrication and drug loading. These criteriaare also important in mathematical modeling of drugrelease. Table 2 lists these important criteria andvariables for designing hydrogel-based drug carriers.Within the realm of transport properties, the mostnotable variable is the drug diffusion coefficient,which is affected by the molecular size of the drug andcharacteristics of the polymer network. Hydrogelcrosslinking density affects diffusivity to a large extentas shown in Fig. 1 and as discussed previously. Ifspecial functionalities, such as ionic groups, are intro-duced into the hydrogel networks, interactions betweenthese functionalities and encapsulated drugs certainlyaffect drug diffusivity. Physical properties of the hydro-gel also affect drug release. For example, polymer

livery Reviews 58 (2006) 13791408molecular weights, composition, and polymer/initiatorconcentrations influence hydrogel swelling and

ing the delivery device creates additional diffusionbarriers that may limit drug release rates while increasedproteolytic activity may increase rates of matrix anddrug degradation. Proper material selection, fabricationprocess, and surface texture of the device are thereforealways critical in designing biocompatible hydrogeformulations for controlled release.

2. Novel engineering of hydrogels for drug delivery

2.1. Biodegradable hydrogels

For most biomedical applications, biodegradablehydrogels are favored over non-degradable gels sincethey degrade in clinically relevant time-scales underrelatively mild conditions. Compared to non-degrad-able hydrogels, degradable carriers eliminate the needfor additional surgeries to recover the implanted gelsHowever, proper techniques for predicting hydrogedegradation rates are critical for successful application

ug Del

.degradation. Finally, the stimuli-responsiveness of ahydrogel network can also mediate the amount and rateof drug delivery. The understanding of transport andphysical properties is especially crucial in modelingmolecule release.

Even if a hydrogel delivery formulation is designedwith the appropriate physical and transport properties,it may still fail to perform its therapeutic role whenimplanted in vivo due to a localized inflammatoryresponse. The formation of a fibrous capsule surround-

Table 2Design criteria for hydrogels in drug delivery formulations

Design criteria Design variables

Transport properties Molecular weight and size of proteinMolecule diffusion Molecular weight of polymer

Crosslinking density Polymerprotein interactions Hydrogel degradation rate Additional functionalities

Physical properties Polymer/crosslinker/initiatorconcentrations

Gelling mechanisms /conditions

Temperature, pH, ionic strength

Structural properties Molecular weight of polymerBiodegradability Mechanical strengthStimuli-responsiveness Concentration of degradable groups

Concentration of responsive groupsBiological properties Cytotoxicity of the hydrogelBiocompatibility Capsule formation

C.-C. Lin, A.T. Metters / Advanced Drlof these degradable systems as they facilitate thedesign of implants with optimal degradation profilesthat result in proper rates of drug release or tissueregeneration and hence maximize therapeutic effects.

The fabrication and modeling of hydrolyticallydegradable hydrogels are well-developed. For exam-ple, West and Hubbell fabricated PLA-b-PEG-b-PLAhydrogels composed of poly(lactic acid) (PLA) andpoly(ethylene glycol) (PEG) block copolymers forprotein release applications [53]. Metters et al.developed scaling laws to predict the degradationrates of PLA-b-PEG-b-PLA hydrogels based onmacroscopic properties such as compressive modulusand volumetric swelling ratio [5456]. Mason et al.further applied these scaling laws to predicting proteindiffusion and release during bulk network degradation[10]. Using a more rigorous approach, Hennink andcoworkers recently utilized a Monte Carlo simulationtechnique to microscopically predict the degradationand protein delivery behaviors of hydroxyethylmethacrylated dextran (dex-HEMA) microspheres[57].

In addition to hydrolytically degradable hydrogels,synthetic gels incorporating biological moieties thatcan be degraded enzymatically are also under intensiveinvestigation. One way to fabricate this type ofhydrogel is to incorporate peptide substrates forenzymatic hydrogel formation [58] and degradation[59,60]. Alternatively, polymers that can be naturallydegraded by enzymes (e.g. polycaprolactone can bedegraded by lipase) can be copolymerized with PEG toform enzymatically degradable gels [61]. Althoughhydrogels derived from natural sources (such aschitosan, gelatin, dextran, etc.) can also be degradedenzymatically, in many cases synthetic hydrogelscontaining defined biological moieties are morefavorable because of their tunable physicochemicalproperties. For example, the degradation behavior canbe more accurately tailored to obtain better controlover gel degradation and drug release rates. Hubbelland colleagues have developed a hydrogel systemcontaining integrin-binding sites for cell attachmentand peptide substrates for matrix metalloproteinases(MMPs) or plasmin to mimic the natural bidirectionalcommunication between extracellular matrix andmigrating cells. Cells can only infiltrate the designer

1385livery Reviews 58 (2006) 13791408matrices once the gels are locally degraded in responseto secretion of MMPs by invading cells [59,60].

2.2. Smart hydrogels

Smart hydrogels, or stimuli-sensitive hydrogelsare very different from inert hydrogels in that they cansense changes in environmental properties such as pHand temperature and respond by increasing or decreas-ing their degree of swelling. These sensing capabili-ties are attractive in many biomedical applications andseveral review papers have been published in this field[18,28]. The volume-changing behavior of smarthydrogels is particularly useful in drug delivery appli-

1386 C.-C. Lin, A.T. Metters / Advanced D ug Decations as drug release can be triggered upon environ-mental changes [18,29,62]. For non-ionic hydrogels,the degree of swelling only depends on the chemicalcompositions of the polymers and does not respond toexternal pH change. When ionic moieties are incorpo-rated into hydrogels, the swelling depends not only onthe chemical composition of the gel but also on the pHofthe surrounding medium. Generally, anionic hydrogelsdeprotonate and swell more when external pH is higherthan pKa of the ionizable groups tethered on polymerchains while cationic hydrogels protonate and swellmore when external pH is lower than the pKb of theionizable groups. Depending on the ionic monomersused to fabricate the gel, the pH-dependent swellingcurves exhibit one or more inflection points near thepKa/pKb of the ionizable groups as shown in Fig. 2.Many modeling efforts have been devoted to predictingthe dynamic and equilibrium swelling of ionic hydrogels[23,6366]. Because the swelling/deswelling behaviorof the ionic hydrogels is closely related to ion move-ment, the swelling kinetics depends not only on the pHbut also on the compositions of the external solutions.Hydrogels with pH-responsiveness have been used in anumber of applications including oral peptide deliveryFig. 2. Schematic of relative ionic hydrogel swelling as a function of pH,

r.[6771], valves for microfluidic devices [72], andartificial muscles [7375].

Another important stimulus for causing hydrogelresponsiveness is temperature. The most commonlyused synthetic polymer for fabricating temperature-sensitive hydrogels is poly(N-isopropylacrylamide)(poly(NIPAAM)), which possesses a lower criticalsolution temperature (LCST) at around 32 C. Thevalue of the LCST can be increased or decreased bycopolymerizing hydrophilic or hydrophobic polymerswith poly(NIPAAM). When the bulk temperature ishigher than the LCST of the polymer, the polymerchains lose their bound-water. Hydrophobic interac-tions between the polymer chains lead to a rapidcollapse (deswelling) of the gel [76]. Readers aredirected to other more thorough reviews discussing themechanisms and applications of thermo-sensitivehydrogels [28,30]. Temperature-responsiveness isparticularly useful for in-situ formation of drug-delivery devices since it allows handling of theformulation in the sol-phase at room temperature andsolidification of the carrier upon injection [28].

More recently, studies have been conducted tofabricate and characterize hydrogels with dual-sensi-tivities. This was accomplished by copolymerizing atemperature-sensitive monomer, usually N-isopropy-lacrylamide, and a pH-sensitive monomer such asacrylic acid or methacrylic acid [21,7782]. Forexample, Stayton's group has investigated a series ofcopolymers containing propylacrylic acid (PAA) andN-isopropylacrylamide pendant chains as pH- andthermo-sensitive moieties, respectively [20]. This newclass of copolymers can sense environmental changesin the physiological range and has found usefulness inintracellular drug delivery in which subtle pHdifferences across the endosomal membrane triggersthe delivery of protein or DNA.

2.3. Biomimetic hydrogels

One drawback of using synthetic and some naturalhydrogels for in vivo applications is that they do notpossess biological recognition sites for supportingcellular activities. For this reason, relatively inertpolymer chains can be tailored with select biologicalmoieties to yield bioactive hydrogels for tissue engi-

livery Reviews 58 (2006) 13791408neering applications. The ArginineGlycineAsparticacid (RGD) tri-peptide derived from fibronectin is the

ug Demost commonly used biological moiety in this regard asit mediates the adhesion of many cell types throughintegrin-binding without the need for protein adsorptionon a hydrogel surface [8386]. Through the selectivepresentation of bioactive ligands on otherwise bioinerthydrogel background, researchers are able to bettercontrol cellhydrogel interactions to fulfill specificbiomedical applications.

The controlled incorporation and presentation ofbiological cues within hydrogel matrices has also playeda role in the development of novel controlled deliverydevices. For example, in vivo observations of thesequestering and protection of proteins by the extracel-lular matrix (ECM) have inspired the design of novelbiomimetic hydrogels with specific and reversibleprotein-binding capabilities [8789]. This approach isespecially useful in controlled release of growth factorsfor tissue regeneration as it mimics the mechanism andtemporal profiles of endogenously produced growthfactors. Through judicious selection of network-immobi-lized ligands with desired protein-binding affinities or byadjusting the molar ratio of protein to protein-bindingligand, researchers can readily manipulate protein releaserates form these bioactive matrices.

Another biomimetic hydrogel system used incontrolled release applications is the enzymatically-cleavable prodrug system. The main advantage of thisapproach is that the degradation rate of the prodruglinkage is directly proportional to the concentration ofspecific enzymes secreted by local cells. Therefore therate of drug release self-adjusts to the rate of cellularinfiltration and cell-mediated matrix remodeling. Ther-apeutic proteins such as vascular endothelial growthfactor (VEGF) have been covalently immobilizedwithinhydrogel networks by enzyme-sensitive oligopeptides[90]. VEGF release ismediated by proteases (e.g. matrixmetalloproteinases or MMPs) secreted by migratingfibroblast and endothelial cells and is therefore madeavailable only when specific cellular processes occur.This cell-demanded VEGF release has been shown tonot only preserve growth factor bioactivity but alsopromote localized angiogenesis.

3. Molecule release mechanisms for hydrogelformulations

C.-C. Lin, A.T. Metters / Advanced DrThe physicochemical properties of the hydrogelnetwork as well as the selection of drug-loadingmethod will determine the mechanism(s) by whichthe loaded drug is released from the crosslinked matrix.The incorporation of drugs into hydrogel deliverymatrices can be performed via one of the followingways: (1) Post-loading: absorption of drugs is achievedafter hydrogel networks are formed. If an inert hydrogelsystem is used, diffusion is the major driving force fordrug uptake and release will be determined by diffusionand/or gel swelling. In the presence of hydrogelscontaining drug-binding ligands, terms accounting fordrugpolymer interaction and drug diffusionmust bothbe included in any model description of release; (2) in-situ loading: drugs or drugpolymer conjugates aremixed with polymer precursor solution and hydro-gel network formation and drug encapsulation areaccomplished simultaneously. In these systems, therelease of drugs can be controlled by diffusion,hydrogel swelling, reversible drugpolymer interac-tions, or degradation of labile covalent bonds.

3.1. Diffusion-controlled delivery systems

Understanding the mechanisms and identifying thekey parameters that govern drug release from hydrogelsare the first step toward accurately predicting the entirerelease profile. For porous hydrogels, when pore sizesare much larger than the molecular dimensions of thedrug, the diffusion coefficient can be related to theporosity and the tortuosity of the hydrogels [91].However, for non-porous hydrogels and for porousgels with pore sizes comparable to the drug molecularsize, drug diffusion coefficients are decreased due tosteric hindrance provided by polymer chains within thecrosslinked networks [13,91,92]. In these cases, theaverage free volume per molecule available to the drugis decreased and the hydrodynamic drag experienced bythe drug is increased, leading to increased drug diffusionpath length compared to porous hydrogels with poresizes much larger than the encapsulated drug [9395].Due to the usually high permeabilities of hydrogelnetworks and the advantages of in-situ fabrication, mostresearch efforts are focused on understanding diffusion-controlled release of encapsulated drugs from three-dimensional hydrogel matrices.

Drug diffusion within highly swollen hydrogels isbest described by Fick's law of diffusion or Stefan

1387livery Reviews 58 (2006) 13791408Maxwell equations [8]. Diffusion-controlled hydrogeldelivery systems can be either reservoir or matrix

This equation can be used to predict the diffusion ofa broad range of molecules including small molecularweight drugs and biomacromolecules like proteins andDNA once an appropriate diffusion coefficient isobtained. Although this simple solution applies tomany diffusion-controlled drug release systems, modelcomplexity will increase as other mechanisms, poly-merdrug interactions, and when non-spherical drugs

ug Delivery Reviews 58 (2006) 13791408systems [96]. For a reservoir system where the drugdepot is surrounded by a polymeric hydrogel mem-brane, Fick's first law of diffusion can be used todescribe drug release through the membrane:

JA D dCAdx 6

Here, JA is the flux of the drug,D is the drug diffusioncoefficient, and CA is drug concentration. In many cases,the drug diffusion coefficient is assumed constant tosimplify themodeling. However, in the general case it is afunction of drug concentration and a special correlationincorporating the concentration-dependent drug diffusiv-ity must be utilized to accurately predict drug flux. An-other assumption of this expression is that JA is the drugflux corresponding to the mass average velocity of thesystem.

For a matrix system where the drug is uniformlydispersed throughout the matrix, unsteady-state drugdiffusion in a one-dimensional slap-shaped matrix canbe described using Fick's second law of diffusion:

dCAdt

D d2CAdx2

7

Here, the drug diffusion coefficient is again assumedas a constant. Other assumptions include sink conditionand a thin planar geometry where the release throughslab edges is neglected. When diffusivity is concentra-tion-dependent the following equation is used:

@CA@t

@@x

DCA @CA@x

8

Many previous attempts to model diffusion-con-trolled drug delivery from hydrogels rely largely onempirically determined diffusion coefficients. Once thediffusion coefficient is determined, Eqs. (6)(8) can besolved, together with proper initial and boundary con-ditions, to yield drug concentration profiles that dictatethe release kinetics. For example, an exact analyticalsolution to Eq. (7) can be obtained using separation ofvariable technique. The ratio of the amount of moleculereleased up to any time t (Mt) to the final amount ofmolecule release (M) can be expressed as:

MtMl

1Xln0

8

2n 12k2 d exp2n 12k2D

L2t

" #

1388 C.-C. Lin, A.T. Metters / Advanced Dr9are used [15].Another empirical equation developed by Peppas

et al. assumes a time-dependent power law function[6,50]:

MtMl

kd tn 10

Here, k is a structural/geometric constant for aparticular system and n is designated as release ex-ponent representing the release mechanism. Table 3 liststhe n values for delivery matrices with different geo-metries and release mechanisms [50]. It is noteworthythat in a purely swelling-controlled slab-based deliverysystem, the drug fractional release (Mt/M) appears to bezero-order as the release exponent equals unity. Thepower law is easy to use and can be applied to mostdiffusion-controlled release systems. However, it is toosimple to offer a robust prediction for complicated re-lease phenomena. For example, in diffusion-controlledsystemswhere n=0.5, the power law is only valid for thefirst 60% of the release profile. These empirical modelscan only predict the release profile after certain releaseexperiments are conducted and have limited capability topredict how the release profiles will change as thechemical or network properties of the system are varied.

Analytical solutions to Fick's law are not availablewhen more complex geometries or non-constant drugdiffusivities are incorporated into the model descrip-tions. Except in extremely dilute systems, drug diffusion

Table 3Release exponent values (n) in the empirical power law model

MatrixGeometry

Diffusion-controlleddelivery system (Case I)

Swelling-controlleddelivery system (Case II)

Slab n=0.5 n=1Cylinder n=0.45 n=0.89Sphere n=0.43 n=85Adapted from Ref. [50].

delivery systems, the time-scale of drug diffusion, t,(where t=(t)2 /D and (t) is the time-dependentthickness of the swollen phase) is the rate-limitingstep while in swelling-controlled delivery systems thetime-scale for polymer relaxation () is the rate-limiting step. The Deborah number (De) is used tocompare these two time-scales [99,100]:

k kD

ug Decoefficients will be a function of drug concentration.Additionally for hydrogel systems diffusivities ofencapsulated molecules will depend on the degree ofswelling and crosslinking density of the gels. Thereforethe diffusion coefficient used to describe drug releasewill be sensitive to environmental changes or degrada-tion of the polymer network andmay vary over the time-scale of release. Several theoretical models have beendeveloped to relate molecule diffusion coefficients tofundamental hydrogel characteristics and have beenreviewed elsewhere [6,13]. Generally, theoretical mod-els for predicting molecule diffusion coefficients havethe following general form:

DgDo

f rs; m2;s; n 11

Here,Dg andDo are the drug diffusion coefficients inthe swollen hydrogel network and in pure solvent,respectively. rs is the size of the drug to be delivered. Thisgeneral expression takes into account factors affectingdrug release such as the structure of the gel, the polymercomposition, the water content, and the size of themolecules. For a degradable hydrogel,Dg changes as thenetwork degrades due to an increase in gel mesh size anda decrease in polymer volume fraction over time.

Several theories have been developed to correlate therelationship between drug diffusivity in the gels and inthe solution [13]. For example, the following equationusing a free-volume approach proposed by Lustig andPeppas can be used to describe the relationship betweendrug diffusivity and network structure [15]:

DgDo

1 rsn

exp Y

m2;s1m2;s

12

Here, Y is defined as the ratio of the critical volumerequired for a translational movement of the encapsu-lated drug molecule and the average free volume permolecule of solvent. A good approximation for Y isunity. For highly swollen (QN10) hydrogels withdegradable crosslinks the diffusivity correlation shownin Eq. (12) can be simplified during the initial stages ofdegradation to [10,97]:

1DgDo

rsnfe7=5jkE Vt 13

C.-C. Lin, A.T. Metters / Advanced DrHere, the lumped parameter jkE is the pseudo-first-order reaction rate constant for the hydrolysis of alabile crosslink. From this expression one can realizethat mesh size is time-dependent due to networkdegradation. It is clear that Dg increases as degradationproceeds and approaches Do. The rate of increase indrug diffusivity depends on network structure andbond cleavage kinetics [10,98].

3.2. Swelling-controlled delivery systems

Another mechanism for drug delivery is swelling-controlled delivery. As shown in Fig. 3, hydrogels mayundergo a swelling-driven phase transition from a glassystate where entrapped molecules remain immobile to arubbery state where molecules rapidly diffuse. In thesesystems, the rate of molecule release depends on therate of gel swelling. One example of swelling-controlleddrug delivery systems is hydroxypropyl methylcellulose(HPMC). Drug loaded HPMC tablets are three-dimen-sional, hydrophilic matrices that are usually stored in adry, glassy state. After oral administration, HPMC poly-mer absorbs liquid and a rapid glassy-to-rubbery phase-transition occurs once the glass transition temperature(Tg) is reached, causing the systematic release of loadeddrugs. The drug release rates are modulated by the rateof water transport and the thickness of the gel layer.

Drug diffusion time and polymer chain relaxationtime are two key parameters determining drug deliveryfrom polymeric matrices. In diffusion-controlled

Fig. 3. Schematic of HPMC hydrogel tablet in the glassy (left) andrubbery (right) state.

1389livery Reviews 58 (2006) 13791408De tdt2 14

ug DeIn diffusion-controlled delivery systems (De1),Fickian diffusion dominates the molecule releaseprocess and diffusion equations described in theprevious section can be used to predict moleculerelease. In swelling-controlled delivery systems(De1), the rate of molecule release depends onthe swelling rate of polymer networks.

The empirical power law (Eq. (9)) used to describediffusion-controlled drug release from hydrogel matri-ces can also be used comprehensively in swelling-controlled delivery systems. A modification of Eq. (9)takes into account both the drug diffusion and polymerrelaxation [101]:

MtMl

k1tm k2t2m 15

where k1, k2, and m are constants. The two terms on theright side represent the diffusion and polymer relaxationcontribution to the release profile, respectively.

The above empirical relationship does not accountfor moving-boundary conditions in which the gelexpands heterogeneously as water penetrates andswells the gels. For this more rigorous description,Korsmeyer and Peppas introduced a dimensionlessswelling interface number, Sw, to correlate the movingboundary phenomena to hydrogel swelling [102104]:

Sw VdtD

16

Here, V is the velocity of the hydrogel swellingfront and D the drug diffusion coefficient in theswollen phase. For a slab system when Sw1, drugdiffusion is much faster than the movement of glassy-rubbery interface and thus a zero-order release profileis expected.

Building on several modeling iterations [11,15,105107], a more rigorous method for predictingmolecule release from swelling-controlled systems isprovided by a sequential layer model developed bySiepmann and Peppas [50,108112]. In this model,drug diffusion, polymer relaxation and dissolution areall taken into account. Drug transport in both radial and

1390 C.-C. Lin, A.T. Metters / Advanced Draxial directions is accounted for using Fick's sec-ond law of diffusion in a cylindrical geometry withconcentration-dependent diffusion coefficients asshown below [110,111]:

@Ck@t

@@r

Dk@Ck@r

Dk

r@Ck@r

@@z

Dk@Ck@z

17

Here, Ck and Dk are the concentration and diffu-sivity of the diffusible species (1: water; 2: drug),respectively. Concentration-dependent diffusivitiesderived by a Fujita-like free-volume model can beexpressed as [113]:

D1 D1eq exp b1 1C1C1eq

18

D2 D2eq exp b2 1C1C1eq

19

where 1 and 2 are dimensionless constants and eqrepresents the equilibrium drug concentration at thewater/matrix interface where polymer disentanglementoccurs.

Due to the concentration-dependent diffusioncoefficients, Eqs. (17)(19) can only be solved nu-merically. Siepmann et al. demonstrated that thesenumerical solutions agreed well with experimentalresults [50,108]. This model is therefore useful inpredicting the shape and dimensions of HPMC tabletsneeded to acquire desired release profiles [109].

Stemming from the work of Siepmann and Peppas,Wu and coworkers [114] recently developed a math-ematical model to describe swelling-controlled release.They introduced additional boundary conditions de-rived from a volume balance and accounted for two-dimensional movement of the swelling front in theradial or axial directions. This model assumes a homo-geneous mixture of drug and polymer at t=0, perfectsink conditions, and geometrical symmetry of the tab-let. Model predictions were verified using compressedpoly(ethylene oxide) (PEO) hydrogel tablets withdifferent molecular weights. The results of water up-take, swelling and dissolution of PEO matrices as

livery Reviews 58 (2006) 13791408well as drug release are shown to agree well with themathematical model [114].

degradable hydrogel matrices, the kinetics of gel de-gradation may also play a significant role in determiningoverall drug release profiles [118123].

Ehrbar et al. recently developed fibrin matricestethered with pendant vascular endothelial growth factor(VEGF) variants linked by plasmin-sensitive peptidysubstrates [122]. These covalently bound VEGF

1391ug Delivery Reviews 58 (2006) 137914083.3. Chemically-controlled delivery systems

In addition to diffusion and swelling-controlleddelivery systems discussed previously, a third type ofmolecule release mechanism is chemically-controlleddelivery. The latter can be further classified as (1)purely kinetic-controlled release where polymer deg-radation (bond-cleavage) is the rate-determining stepand diffusion term is assumed to be negligible; and (2)reaction-diffusion-controlled release in which bothreaction (e.g. polymer degradation, proteindruginteraction) and diffusion terms must be included inthe model to accurately predict drug release. Thereaction-diffusion-controlled release is particularlyintriguing as more synthetic hydrogel systemsdesigned with drug-binding capacity are utilized indrug delivery [87,88,115] and tissue engineering [89].

3.3.1. Kinetic-controlled release pendant chainsystems

There are two types of kinetic-controlled-releasesystems: pendant chain (prodrugs) and surface-erodingsystems. In pendant chain systems, drugs are covalent-ly linked to the hydrogel network via cleavable spacersand drug release is controlled by the rate of spacer-bondcleavage. In surface-eroding systems, drug release ismediated by the rate of surface erosion. Drug diffusiondoes not determine the rate of drug release in eithersystem.

Prodrugs or polymerdrug conjugates are designedto enhance the therapeutic efficacy of the drug. Thisstrategy is especially useful when growth factors are tobe delivered as most of them are susceptible to rapidproteolytic degradation. The design of prodrugs hasattracted much attention and extensive reviews on thedesign and therapeutic application of these systemscan be found elsewhere [116,117].

Generally, the release of covalently tethered prodrugsis determined by the degradation rate of the polymerdrug linkage [118121]. Most of these linkages havebeen designed to be hydrolytically degradable allowingdegradation and release rates to be characterized by fairlysimple first-order kinetic relationships [59]. However, inparticular applications, for example where a more tar-geted delivery profile is desired, it is advantageous todesign enzymatically cleavable spacer bonds [122].

C.-C. Lin, A.T. Metters / Advanced DrThese chemistries lead tomore complex release kinetics.Furthermore, in cases where the prodrugs are tethered toFig. 4. Mathematical modeling predicts experimental observations ofproteolysis-mediated release of fibrin-bound VEGF121 variants from

low- or high-density fibrin gel networks. Reproduced from Ref[122], Copyright (2005), with permission from Elsevier.l.

erosion occurs when the rate of water transport into thepolymer is much slower than the rate of bond hydro-lysis. However, due to the inherently high water contenof hydrogels, surface erosion only occurs in enzymatic-degrading systems where the transport of enzyme intothe gel is slower than the rate of enzymatic degradationWhile no hydrogels have been specifically designed todegrade in this fashion, surface erosion of enzymaticallydegradable poly(ethylene glycol)-polycaprolactone(PCL-b-PEG-b-PCL) block copolymer hydrogels hasbeen observed in vitro by Rice et al. when exposed torelatively high concentrations of lipase [61].

Most of the models focusing on surface-eroding

Fig. 5. Fractional probe release from degradable PEG-acrylatedithiol gels formed via step-growth polymerization (A) gelsfabricated from 30 wt.% eight-armed PEG-acrylate/DTT precursosolutions and degraded at varying temperatures: 37 C (), 46 C(), and 57 C (n). (B) Gels fabricated with either four-arm/10-kDa(n) or eight-arm/20-kDa () PEG were measured and comparedwith model predictions ( ). Reproduced with permission from[123]. Copyright 2005, John Wiley and Sons.

ug Devariants can only be liberated from the insoluble matrixthrough plasmin-mediated cleavage of the engineeredpeptide substrates. First-order cleavage kinetics wereused to model the time-dependent VEGF release. Ac-curate prediction of VEGF release profiles also requireda description of VEGF-release via matrix-mediated de-gradation. Two adjustable parameters were thereforeused to accurately predict complete VEGF release pro-files. The first parameter was the pseudo first-orderdegradation rate constant, k. The degradation of bondswithin the fibrin network and the plasmin-sensitivesubstrates used to link VEGF to the fibrin were assumedto follow the same first-order kinetics. The second ad-justable parameter, N, represented the number of fibrinrepeat units between two crosslinks and was an in-dication of fibrin network structure. As shown in Fig. 4,the developed model accurately predicted release ofcleavable and non-cleavable VEGF variants from bothlow and high-density fibrin matrices by accounting forboth network structure and kinetics of individual bondcleavage.

Unique release profiles unattainable with diffusion-controlled release mechanisms have also been dem-onstrated from hydrolytically degradable hydrogelswith tethered agents. Dubose et al. covalently incor-porated fluorescently labeled probe molecules withinthe three-dimensional network structure of PEG-basedhydrogels formed via step-growth polymerizations[123]. As shown in Fig. 5, they demonstrated thathydrolytic degradation of covalent bonds within thestep-crosslinked PEG network 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 geldissolution. The authors demonstrated that the slopeof the approximate zero-order delivery regime as wellas the extent of the latent burst could be controlled bycrosslinker functionality (tetra-functional versus octa-functional PEG, Fig. 5A) and degradation kinetics(varying temperature, pH, or chemistry of the de-gradable bond, Fig. 5B).

3.3.2. Kinetic-controlled release surface-erodingsystems

Other kinetic-controlled systems occur when drug

1392 C.-C. Lin, A.T. Metters / Advanced Drrelease is mediated by surface erosion of the polymermatrix. For hydrophobic polymer networks, surface

polymers are based on hydrolytic-degrading polymersThese relationships, however, can also be applied tot

.

/

rlivery Reviews 58 (2006) 13791408.

ug Deenzymatically degradable, surface-eroding hydrogelsystems. Surface-eroding matrices are advantageous fordrug delivery applications as the structural integrity of thecarrier device is maintained during delivery and zero-order release of the encapsulatedmolecules can be readilyobtained by appropriate choice of device geometry [7].

Hopfenberg initially developed a drug deliverymodel where the release only depends onmatrix erosionrates. Eq. (22) describes the release from surface-eroding devices with an initial dimension a0 (radius for aspherical or cylindrical geometry and half-thickness forslab geometry) and drug concentration C0 [124]:

MtMl

1 1 katC0a0

n20

In this equation, n is a geometrical factor and anumber of 1, 2, or 3 is used for a slab, cylinder, orsphere, respectively. It is clear that when a slab-shapeddevice is used (n=1), drug release appears to be a zero-order profile.

Following Hopfenberg's work, Katzhendler, Hoff-man, and coworkers further developed a generalmathematical model for heterogeneous eroding net-works accounting for different radial and verticalerosion rate constants for a flat tablet (ka and kb forradial and vertical degradation constant, respectively)[125]:

MtMl

1 1 katC0a0

21

2KbtC0b0

21

Here, a0 is the initial radius of the tablet and b0 is thethickness of the tablet. By changing the radius tothickness ratio of the device, one can easily obtainvarious drug release rates. It is noteworthy that in thesemodels, swelling of the matrices is either not consideredor is assumed to occur prior to erosion and drug release.Stemming from these initial efforts, several additionalmodels have been developed to predict molecule releasevia surface-erosion [108,126,127].

3.3.3. Reaction-diffusion-controlled release bulk-degrading systems

Many of the approaches for modeling drug releasefrom hydrogel networks assume only one mechanism,

C.-C. Lin, A.T. Metters / Advanced Dreither diffusion, swelling, or degradation, dominatesthe release process. Although not realistic for manycases, this is one way to simplify the model and, inmany cases, obtain a reasonable fit to experimentalresults. As more complicated drug delivery systemsare designed to fulfill the ever-increasing needs foradvanced drug delivery and tissue engineering, theassumption of a single dominant release mechanismwill no longer be suitable. Overlooking the coupledeffects of diffusion and matrix degradation withinhydrogel matrices will result in significant deviationswhen comparing modeling and experimental results.

The coupling of reaction and diffusion phenomenais already notable in bulk degrading networks wheredrug release profiles are governed by both networkdegradation and molecule diffusion. Macroscopically,this degradationdiffusion coupling phenomena canbe observed through the swelling characteristics andmechanical properties. The degradation behavior ofchain-polymerized hydrogels with hydrolytically orenzymatically labile bonds can be tailored through avariety of parameters. Sawhney's pioneering workincorporated degradable PLA moieties within hydro-philic PEG macromers [128]. The resulting PLAPEGPLA block copolymers can be polymerized toform hydrolytically degradable hydrogels. Metterset al. further described the release of encapsulatedmacromolecules from bulk-degrading, covalentlycrosslinked PLAPEGPLA hydrogels consideringnetwork structure as well as degradation kinetics[55,56]. Generally, molecule diffusivity decreases ascrosslinking density increases (Mc decreases), as themolecular size (rs) increases, and as the polymer vol-ume fraction of the gel (2,s) increases [91,129,130]. InPLAPEGPLA hydrogel systems, molecule diffu-sivity can be correlated to gel degradation kinetics andcan be used to predict drug release corresponding togel degradation as shown in Fig. 6 [10,97]. Thediffusion coefficient of a solute from the degradingnetwork with time-dependent mesh size can then beobtained using Eq. (13) described in the previoussection. As shown in Fig. 6, the scaling model agreedwell with the volumetric swelling ratio of the de-grading gels while for solute release only a qualitativeagreement was obtained.

The degradation behaviors described above are onlyvalid for hydrogels made from di-vinyl macromers. Forhydrogels formed via chain-polymerization of multi-

1393livery Reviews 58 (2006) 13791408functional macromers such as acrylated poly(vinyl al-cohol) (PVA), Martens et al. developed a generalized

statistical-co-kinetic model to predict their degradationbehaviors [131133]. In this model, a statistical ap-proach was used to predict the different configurationsof the crosslinking molecules and kinetic chains. It alsoaccounts for the probability of an intact degradablelinkage. The model was verified by experimental obser-vation of gel swelling, mass loss and compressivemodulus [133]. Combining the degradation kineticsprovided by this model and the diffusivity estimated byEq. (13), the release of a model protein, bovine serumalbumin (BSA), was verified [97].

For hydrogels formed via step-growth polymeriza-tion, Metters and Hubbell have shown that thedegradation rates of networks depend on molecular

Fig. 6. (A) Volumetric swelling ratio and (B) fractional release oBSA as a function of degradation time from a series of PLA-b-PEGb-PLA hydrogels polymerized from increasing concentrations omacromer: () 25 wt.%, (n) 35 wt.%, and () 50 wt.%. Linesrepresent exponential fits to the swelling data (A) and solute releasepredictions based on scaling equations (B). D0=1.010

5 mm2/sfor all curves. Reproduced with permission from Ref. [10]Copyright 2001 American Chemical Society.

ug Def-f

.1394 C.-C. Lin, A.T. Metters / Advanced Drweight, hydrophilicity, and degree of functionality ofthe starting monomers [134].

In addition to the statistical modeling approachesassuming homogeneous changes in gel properties,Monte Carlo simulations have also been used to predictprotein release from degradable polymer networks at themicroscopic level. Gopferich and Langer developedMonte Carlo simulations to predict polymer erosion andmonomer release. Although this work was not forhydrogel systems, it allowed the calculation of porositydistributions within the polymer and was useful inpredicting drug and degraded monomer release [135138]. Monte Carlo simulation is good for describingnetwork morphological changes, however it does notprovide any information regarding molecule release.Diffusion equations (Fick's law)must be incorporated inorder to link the network degradation to moleculediffusion [138]. The following modified diffusionequation can be used to describe one-dimensionaldiffusion in porous polymers:

@

@tCx; tex; t @

@xDeff Cex; t @Cx; t

@x22

Here, C(x,t) is the concentration of diffusingmonomer, (x,t) is the porosity along the diffusionpath, and Deff(C) is the effective concentration-dependent diffusion coefficient.

Recently, Vlugt-Wensink et al. developed kineticMonte Carlo simulations to predict protein releasefrom crosslinked dextran microspheres [57]. Althoughthis approach, reasonably predicts protein release fromdegrading networks and incorporates spatial variationsin the network microstructure that are not accountedfor in the previously described macroscopic models ofnetwork degradation, some predictive limitations stillexist. Most importantly, swelling of the hydrophilicmicrospheres and changes in swelling with matrixdegradation were not accounted for in the describedmodel.

The macroscopic models used to correlate soluterelease (diffusion) with gel degradation (reaction)provide a powerful tool for predicting protein releasewith changing network structure. However, macro-scopic observations in gel swelling and mass erosionare not sufficient to obtain precise predictions due

livery Reviews 58 (2006) 13791408to the averaging of microscopic events. On theother hand, models describing network changes at a

ug Demicroscopic level may provide more accurate releasepredictions. However, gel swelling, a very importantcharacteristic of hydrogel drug carriers, must beincluded during the simulation since solute diffusivityis tightly coupled to water content.

3.3.4. Reactiondiffusion-controlled release affinityhydrogel systems

Inspired by the reversible sequestering of proteinsto the extracellular matrix (ECM), researchers havedeveloped biomimetic hydrogel carriers bearing re-versible binding capacities to decrease release rates oftarget protein therapeutics. These so-called affinityhydrogels can also be classified as reactiondiffusion-controlled hydrogel delivery systems. The releasekinetics of a molecule from affinity gels can bedepicted by a model developed by Crank [139] whereproteinligand (PL) binding equilibrium is describedusing simple binding kinetics:

P L ()kr

kfPd L 23

Here, kf and kr are association and dissociation rateconstants, respectively. In this model, binding ofproteins to immobilized elements is consideredreversible and a time-independent equilibrium con-stant Kb=CPL/CP is used to represent the concentrationequilibrium between bound (PL) and free (P) proteins.Kb can be therefore also described as a ratio of free-receptor concentration to dissociation constant (Kb=[L] /Kd). Assuming that the reaction is fast comparedto protein diffusion, the following equation can beobtained for the transport of reversibly bound proteinwithin an affinity hydrogel [140]:

DKb 1j

2Cp @Cp@t

24

Compared to the standard form of Fick's law ofdiffusion (Eq. (7)) the above equation illustrates thatthe presence of rapid and reversible proteinligandbinding retards the release of free protein bydecreasing the apparent protein diffusivity by a factorof (Kb+1).

From this simple reactiondiffusion model de-scribed above, one can easily obtain the concentrationprofile of free proteins in the affinity gels available for

C.-C. Lin, A.T. Metters / Advanced Drdiffusion. However, due to the fact that this modelassumes a time-independent equilibrium constant (Kb)and a rapid binding equilibrium, the model is limited todescribing systems with simple yet rapid bindingmechanisms with high ratios of ligand to protein.These assumptions may not be valid in the hydrogelmatrix where the mobility of therapeutic macromole-cules and therefore the intrinsic reaction constants areretarded by their size and limited free volume.

Heparin, a highly sulfated glycosaminoglycan(GAG), is known to serve as a growth factor depot invivo owing to its electrostatic affinity to various basicgrowth factors including NGF, bFGF, VEGF, etc.Matrices containing heparin have been used as deliverydepots to modulate the release rates of these growthfactors through affinity binding [141,142]. For exam-ple, Sakiyama-Elbert and Hubbell have developedaffinity hydrogels composed of fibrin gels copolymer-ized with peptides that bind to heparin [87,88,115].This system has been applied to deliver several growthfactors including NGF [87], basic fibroblast growthfactor (bFGF) [88], and neurotrophin-3 (NT-3) [89]. Inorder to incorporate heparin into the fibrin network andmodulate growth factor release, a group of shortpeptide sequences with different affinities for heparinhave been identified and copolymerized into the fibringel networks. To model growth factor release from thistri-component delivery system, six partial differentialequations based on diffusionreaction kinetics weresolved simultaneously [88]:

@CG@t

DG @2CG@x2

kFCGCH kRCGHkFCGCHP kRCGHP 25

@CH@t

DH @2CH@x2

kFCGCH kRCGHjFCHCP jRCHP 26

@CP@t

jFCHCP jRCHPjFCGHCP jRCGHP 27

@CGH@t

DGH @2CGH@x2

kFCGCHkRCGHjFCGHCP

1395livery Reviews 58 (2006) 13791408 jRCGHP 28

@CHP@t

jFCHCPjRCHPkFCGCHP kRCGHP 29

@CGHP@t

kFCGCHPkRCGHP jFCGHCPjRCGHP 30

In these equations CG, CH, and CP represent theconcentrations of growth factor (G), heparin (H ), andheparin-binding peptide (P), respectively. SimilarlyCGH, CHP, and CGHP represent the concentrations ofthe possible biomolecule complexes.

Assuming the system is in equilibrium between thespecies initially, these equations, in conjunction withproper initial and boundary conditions, can be solvednumerically and used to predict the fraction of growthfactor present in its freely diffusible and bound state(Fig. 7, [89]) and the ratio of heparin to growth factorneeded to obtain sustained growth factor release

mental results and model predictions agree qualita-tively, these results were never directly compared tothe theoretical predictions obtained from this model[8789].

4. Emerging systems and remaining challenges

Although mathematical simulations have beenperformed extensively to predict and design betterhydrogel systems, there are still many challengesassociated with the modeling of drug deliveryphenomena and accurate prediction of release profilesfrom complex hydrogel systems. Creating a funda-mental understanding of drug transport processes is thefirst step towards developing a suitable mathematicamodel. Mass transport governs the translocation ofdrug from the interior of hydrogels to the surroundingenvironments. Multiple factors affect the mass trans-port of encapsulated molecules including the networkcrosslinking density, extent of swelling, gel degrada-tion, the size and charge of the encapsulated

500. The decreasing concentration profile propagates inward ovetime, as one would expect. Reproduced from Ref. [88], Copyrigh(2000), with permission from Elsevier.

1396 C.-C. Lin, A.T. Metters / Advanced Drug De(Fig. 8, [88]). As can be seen from the above equa-tions, there are four kinetic constants (kF, kR, F, R)and three diffusion coefficients (DG, DH, DGH) re-quired to solve the equations which largely complicatethis modeling approach. Furthermore, while experi-

Fig. 7. Predicted initial equilibrium fractions of NT-3-containing

species versus initial heparin to NT-3 ratio. Reproduced from Ref[89], Copyright (2004), with permission from Elsevier.molecules, and the physical interactions these mole-cules exhibit for themselves and for the polymer

.l

rtFig. 8. Theoretical concentration of matrix-bound bFGF as afunction of distance from the midline of a model tubular nervegrowth guide, 6 mm long and open at both ends. Concentration isshown as percentage of the initial bound concentration, which was5.7108 M. The ratio of heparin to growth factor modeled was

livery Reviews 58 (2006) 13791408

ug Dematrix. If specific drug-binding motifs are presentwithin the hydrogels, the kinetics and/or thermody-namics of drugligand binding must also be under-stood and quantified to predict the controlled release ofthe encapsulated molecules. In this final section, thenetwork design and mathematical modeling of severalemerging hydrogel-based delivery systems as well asthe challenges associated with these systems arediscussed.

4.1. Dynamic hydrogel delivery systems

4.1.1. Degradable hydrogelsPrevious sections have detailed the fabrication,

degradation, and molecule release from degradablehydrogels. Understanding degradation mechanisms iscritical in designing hydrogels for drug deliveryapplications since the rates of matrix swelling anddegradation govern the diffusion of encapsulated ortethered molecules. Via appropriate design of polymerchemistries and network structure, degradable hydro-gel matrices can be engineered with proper degrada-tion profiles for achieving previously unattainablemolecule release regimes.

Mathematical modeling of molecule release hasprovided much information to facilitate the design ofdegradable hydrogels and identify key parametersdictating molecule release profiles. However, to accu-rately predict the unique molecule release profiles thatoccur with many degradable hydrogels, additionalparameters not commonly found in previous releasemodels must be included. For example, as discussed inthe previous section, enzymatically degradable hydrogelsare becoming more important in controlled releaseapplications. One challenge for this novel class ofhydrogel is how to model the rate of enzyme (e.g.MMPs) production by invading cells. As discussedbefore, enzyme concentration determines whether geldegradation occurs via surface-erosion (rate of enzyme/substrate reaction greater than rate of enzyme transport) orbulk-degradation (rate of enzyme transport greater thanrate of enzyme/substrate reaction). Therefore, the accu-racy of predicting gel degradation and molecule releasefrom enzymatically degradable hydrogels largelydepends on correctly understanding cellular physiologyand cellmaterial interactions and properly incorporating

C.-C. Lin, A.T. Metters / Advanced Drthese phenomena in a quantitative model along withmolecule transport and enzyme-substrate kinetics.4.1.2. Stimuli-sensitive hydrogelsStimuli-sensitive hydrogels represent another ad-

vanced hydrogel system that, under intelligent design,can sense changes in complex in vivo environments andutilize these triggers to modify drug release rates. Sincethe swelling or deswelling of these hydrogels is controlledby external stimuli, it is critical to model the dynamicswelling response in order to predict solute release.Several review articles have been published detailing thefabrication and application of stimuli-sensitive hydrogels[18,62,143]. Ionic or pH-sensitive hydrogels are probablythe most studied stimuli-sensitive gels. At a fixed pH andsalt concentration, the swelling of ionic hydrogels isbalanced by the osmotic pressure and the relaxation of thepolymer chains. Thermodynamically, the total free energycan be expressed as:

DGT DGe DGm DGo 31

Here,GT is the total Gibbs free energy,Ge is thefree energy contributed by elastic force of the polymerchains, Gm is the free energy of mixing, and Go isthe free energy due to osmotic pressure. When theswelling of an ionic hydrogel is in equilibrium(GT=0), the decreased elastic free energy is balancedby the free energy of mixing and osmotic pressure.Based on this concept, the simulations of ionichydrogel swelling have been derived in many reports[66,144146]. Grimshaw et al. developed a continuummodel to describe the macroscopic behaviors of pH-responsive poly(methacrylic acid) (PMAA) hydrogelmembranes accounting for charge density, ionicstrength, stress, strain, and electric field [144]. Thesimulation results were used to compare experimen-tally determined PMAA swelling and shrinking. It wasfound that the membrane swelling was slower thanshrinking. Following Grimshaw's work, De et al.derived an equilibrium model to predict the degree ofhydrogel swelling at given pH and ionic strength and akinetic model to predict the rate of swelling underchanging pH. Their simulation results agreed well withexperimental observations. The equilibrium swellingof anionic pH-responsive hydrogels appears to beproportional to the pH with a sharp increase around thepKa of the charge group.

For molecule release from pH-sensitive hydrogels,

1397livery Reviews 58 (2006) 13791408Peppas and coworkers developed a series of modelsfocusing on ionic hydrogel swelling, water transport,

their material and molecule transport properties changedramaticallywith spatial locationwithin the device. Twoprimary types of composite hydrogel delivery systemshave been investigated, multi-layer and multi-phasesystems. These composite systems have great potentialin delivering multiple protein therapeutics for tissueengineering applications where temporal and spatialcontrol over drug delivery is desirable. The simulta-neous delivery of multiple proteins is known to occur invivo during angiogenesis, bone remodeling, and nerveregeneration. For example, several angiogenic proteinsincluding vascular endothelial growth factor (VEGF),basic fibroblast growth factor (bFGF), transforminggrowth factor beta (TGF-), platelet-derived growthfactor (PDGF), and matrix metalloproteinases (MMPs)are involved in the angiogenesis process. Marui et al.

ug Deand molecule release [106,107,147,148]. For example,a concentration-dependent solute diffusion coefficientDi was used to predict cationic hydrogel swelling andsolute release upon pH changes induced by theproduction of gluconic acids [148]:

Di Di;0 exp adm1 32

where Di,0 is the solute diffusion coefficient in the drystate. From this expression, it is clear that the diffusioncoefficient changes exponentially with the watervolume fraction 1 and experimentally determinedwaterpolymer interaction parameter d. The model-ing of cationic hydrogel swelling agreed well withexperimental data. For insulin release, however, noexperimental results were compared to model predic-tions [148] indicating that verification of this modelingapproach is still required.

While the benefits of using thermo-sensitivehydrogels are widely acknowledged, mathematicalsimulation of molecular release from these smarthydrogels is still very limited. A strategy correlatinggel swelling and diffusion-controlled molecule releasecan be readily constructed using equations for esti-mating molecule diffusivity. Amsden [13] reviewed avariety of hydrogel diffusivity models related to fun-damental characteristics such as hydrogel water con-tent and molecule free volume. Andersson et al.applied one such expression for assessing glucose andinsulin diffusivities in n-isopropylacrylamide gels[26]:

DeD0

1U3

1 U2 33

where De and D0 are the effective molecule diffusiv-ities in the gel and in pure solvent, respectively. isthe polymer volume fraction of the gel. Since theswelling of thermo-sensitive hydrogels depends ontemperature changes, one can readily obtain thepolymer volume fraction at the tested temperature.Using this equation, the effective diffusivities ofmolecules encapsulated within thermo-sensitivehydrogels can be estimated as a function of temper-ature. Once the molecule diffusivity is determined, arelease profile can then be predicted using Fick's law

1398 C.-C. Lin, A.T. Metters / Advanced Drof diffusion [26]. Fig. 9 shows one comparison ofsimulated and experimental results [26].Finally, several groups have devoted significantefforts to the fabrication and characterization of dual-stimuli responsive hydrogels that respond to changesin pH and temperature [7982]. Although the uniquedrug release profiles observed from these novelcarriers have revealed the usefulness of this excitingnew strategy of hydrogel design, mathematicalmodeling of drug release from these dual-responsivenetworks has yet to be developed.

4.2. Composite hydrogel delivery systems

Modeling drug release from composite hydrogelsystems has proven to be challenging due to the fact that

Fig. 9. Experimental and simulated concentration profiles for one ofthe glucose diffusion experiments at 10 C. Reproduced from Ref.[26], Copyright (1997), with permission from Elsevier.

livery Reviews 58 (2006) 13791408discovered that the dual delivery of bFGF andhepatocyte growth factor (HGF) from collagen

ug Demicrospheres greatly increased blood vessel formationin an animal model [149]. Peattie et al. utilized cross-linked hyaluronan (HA) hydrogels to simultaneousdeliver VEGF and keratinocyte growth factor (KGF)to enhance angiogenesis [150]. Simmons et al. usedalginate hydrogels to deliver bone morphogeneticprotein-2 (BMP2) and transforming growth factor-(TGF-3) and showed enhanced bone formationcompared to delivery of either single protein [49].Although in vivo tissue growth was improved in animalmodels using these dual-protein delivery systems, it isnot clear whether tissue growth would be furtherenhanced if the proteins were delivered at optimizedrates since no independent control over the releaseprofiles has been shown in these studies. Therefore, thedevelopment ofmodels that can relate drug transport andrelease in these composite systems to their fundamentalproperties would prove valuable and possibly lead to theengineering of devices capable of independently tunabledelivery of multiple proteins for modulating cellbehavior and tissue growth.

4.2.1. Multi-layer hydrogel delivery systemsIn multi-layer systems, a basal polymer layer is

fabricated, followed by lamination of subsequentlayers. Different proteins can be encapsulated intoeach layer during fabrication and tunable multiple-protein release or unique single-protein release profilesare made possible by independently adjusting thecrosslinking density of each layer. Many models havebeen developed for predicting drug release from multi-layer hydrogel composites. For example, Streubel et al.developed a multi-layer system to achieve bimodaldrug release [151]. Fick's second law of diffusion wasused to predict drug release profiles. They deriveddiffusion equations accounting for constant or non-constant diffusivities, as well as stationary or movingboundary conditions. Grassi et al. fit their experimentaldata into a semi-empirical model accounting for theresistance the drug experienced when diffusingthrough the multi-layer system [152]. They startedthe modeling with an equation governing the dissolu-tion of solid drug and accounted for the gel layerresistance (R) and drug dissolution resistance (1/K):

dC udA CSC

C.-C. Lin, A.T. Metters / Advanced Drdt

V 1=K R 34where C is the drug concentration, t is the dissolutiontime, CS is the solubility of the drug in the dissolutionmedium, d is the drug volume fraction, A is thesurface area at the solid/liquid interface, and V is thevolume of the medium. The release of some smallmolecular weight drugs from partially coated matricescontaining different drug to polymer fraction can be fitinto the analytical solution of this model.

Sohier and colleagues developed a porous scaffoldcontaining three hydrogel layers with different poros-ities to simultaneously deliver lysozyme and myoglo-bin [153]. The governing equations used to model thissystem were again based on Fick's second law with atime-dependent diffusion coefficient related to the rateof polymer degradation. Although this model success-fully predicted the release of lysozyme from a multi-layer polymer construct, it did not provide an accuratedescription of dual-protein delivery.

In addition to multiple-protein delivery, multi-layermatrices can also be used to decrease the problematicburst release, a common challenge facing drug deli-very. For example, Lu and Anseth developed a multi-laminated hydrogel system prepared by photopoly-merization. A desirable, zero-order release profile wasobtained through non-uniform initial drug loading inmulti-laminated hydrogels and the results were veri-fied by a diffusion model [154156]. Their model wasbased on the well-known diffusion model first de-veloped by Crank [139]. Assuming a constant diffu-sion coefficient and one-dimensional release undersink conditions, the fractional passive release of drug(Mt /M) from these composite hydrogels can beanalytically derived from Fick's second law of dif-fusion and expressed as the following equation:

MtMl

1

Xln0

1n1kn

ek2nDt

Z L0

f xsinknxdx

Pln0

1knek

2nDt

R L0 f xsinknxdx

;where kn n 0:5pL 35

In this expression, f (x) is the initial concentrationprofile, D is the molecule diffusion coefficient, and L isthe thickness of the gel. As shown in Fig. 10, experi-

1399livery Reviews 58 (2006) 13791408mental results verified the accuracy of this model andindicate that the initial burst was nearly eliminated.

ug De4.2.2. Multi-phase hydrogel delivery systemsAnother strategy for multiple-protein delivery is

multi-phase systems. In this approach, prefabricatedmicrospheres containing one or more proteins areuniformly embedded within a hydrogel containing asecond protein [157159]. The release of the micro-

Fig. 10. Comparison of theoretical and experimental solute release.The initial concentration profile used, from center outward, was:1.2 wt.%, 0.55 wt.%, 0.2 wt.%, and 0 wt.%, respectively. Modelresults (), experimental results (). Reproduced from Ref.[154], Copyright (1999), with permission from Elsevier.

1400 C.-C. Lin, A.T. Metters / Advanced Drsphere-encapsulated protein is delayed due to thecombined diffusional resistances of the microspherepolymer and surrounding gel. Richardson and collea-gues prepared a composite polymeric scaffold contain-ing PLGA microspheres embedded in porous PLGAmatrices with different intrinsic viscosities to simulta-neous deliver VEGF and PDGF. The in vitro and invivo results using this approach have shown promisingresults in an animal model to enhance the maturationof vasculatures [48]. Although this multi-phaseformulation is not considered to be a hydrogel system,it was the first heterogeneous polymeric system fordelivering two proteins with distinct release profiles.Holland et al. also fabricated degradable oligo(poly(ethylene glycol) fumarate) hydrogels containinggelatin microspheres to independently control thedelivery of insulin-like growth factor-1 (IGF-1) andtransforming growth factor-1 (TGF-1). Releaseprofiles can be adjusted by varying the protein loadingin each polymer phase [157]. These multi-phase dualdelivery systems have achieved substantial success,however, to date no rigorous mathematical models forpredicting molecule release from these compositenetworks have been developed.

4.2.3. Challenges facing composite hydrogel deliverysystems

The design and application of composite hydrogeldelivery systems have attracted much attention due totheir multi-faceted roles in advanced drug delivery andtissue engineering. However, many challenges facingthe design and modeling of these novel systems remainlargely unattended and need to be addressed to opti-mize their application as drug carriers. First, thesesystems have complex network geometries and phasemorphologies that must be properly parameterized toquantify diffusion length scales in each phase. Theindividually tailored physicochemical properties ofeach layer, which results in heterogeneous transportproperties within a single matrix, must also be eval-uated in the context of the overall device. For example,as shown by Sohier et al. the swelling, and thereforepermeability, of a highly hydrophilic layer can belimited by its attachment to layers exhibiting a lowerdegree of swelling [153]. Once identified, the po-sitional dependence of drug diffusion coefficients aswell as drugpolymer interaction parameters must betaken into account during the development of anyrigorous mathematical model describing these com-posite systems.

4.3. Micro/nanoscaled hydrogel delivery systems

Over the past few decades, polymeric microspheresand, more recently, nanoparticles have been widelyused for sustained or targeted drug delivery [160] aswell as cell encapsulation [161163]. Numerousstudies have been conducted using PLGA as a matrixfor encapsulating proteins, peptides, DNA, and smallmolecular weight drugs. However, the hydrophobicity,acidic degradation products, and harsh fabrication/encapsulation processes of PLGA micro/nanoparticlesmake them unfavorable as carriers for biomacromole-cules such as protein and DNA [164]. Alternatively,micro/nanoparticles made from hydrophilic hydrogelsare more suitable for encapsulating these fragilebiomacromolecules. These miniaturized drug-contain-ing vehicles can be fabricated in vitro and then

livery Reviews 58 (2006) 13791408administered via oral [165,166] or nasal route[167,168] or injected into the patients in a minimally

ug Deinvasive manner to increase patient compliance.Protein-containing microparticles can also be fabricat-ed and loaded into a bulk gel containing a secondprotein for dual-protein delivery as discussed in theprevious section. It is beyond the scope of this reviewto thoroughly discuss the fabrication and application ofmicro/nanoparticles and readers are advised to look tothe cited references for more information [169,170].

Two types of mathematical approaches have beenused to predict molecule release from hydrogelmicrospheres: macroscopic diffusion models andmicroscopic Monte Carlo simulations. For macroscop-ic modeling,