Hydrogels in controlled release formulations: Network design and mathematical modeling

Abstract

Over the past few decades, advances in hydrogel technologies have spurred development in many biomedical applications including controlled drug delivery. Many novel hydrogel-based delivery matrices have been designed and fabricated to fulfill the ever-increasing needs of the pharmaceutical and medical fields. Mathematical modeling plays an important role in facilitating hydrogel network design by identifying key parameters and molecule release mechanisms. The objective of this article is to review the fundamentals and recent advances in hydrogel network design as well as mathematical modeling approaches related to controlled molecule release from hydrogels. In the first section, the niche roles of hydrogels in controlled release, molecule release mechanisms, and hydrogel design criteria for controlled release applications are discussed. Novel hydrogel systems for drug delivery including biodegradable, smart, and biomimetic hydrogels are reviewed in the second section. Several mechanisms have been elucidated to describe molecule release from polymer hydrogel systems including diffusion, swelling, and chemically-controlled release. The focus of the final part of this article is discussion of emerging hydrogel delivery systems and challenges associated with modeling the performance of these devices.

Introduction

Since the establishment of the first synthetic hydrogels by Wichterle and Lim in 1954 [1], the growth of hydrogel technologies has advanced many fields ranging from food additives [2] to pharmaceuticals [3] to biomedical implants [4]. In addition, the development of an ever-increasing spectrum of functional monomers and macromers continue to broaden the versatility of hydrogel applications. Hydrogels now play a critical role in many tissue engineering scaffolds, biosensor and BioMEMS devices, and drug carriers. Among these applications, hydrogel-based drug delivery devices have become a major area of research interest with several commercial products already developed [5]. A successful drug delivery device relies not only on intelligent network design but also on accurate a priori mathematical modeling of drug release profiles. An ordered polymer network composed of macromers with well-understood chemistries yields hydrogels with well-defined physicochemical properties and reproducible drug-release profiles. In a complimentary fashion, a quantitative mathematical understanding of material properties, interaction parameters, kinetic events, and transport phenomena within complex hydrogel systems assists network design by identifying the key parameters and mechanisms that govern the rate and extent of drug release. In addition, mathematical modeling accelerates device design by limiting the number of experiments researchers must perform to understand the release mechanisms governing a particular delivery system.

Many excellent review articles have been published detailing the modeling of drug release from polymeric devices including hydrogels. This review builds on the established literature by not only tracking recent advances in the development of mathematical models for quantitatively predicting drug delivery from hydrogel systems, but also highlights how these models are playing a critical role in the design of novel hydrogel networks for future applications. In addition to describing the mechanisms governing drug release from conventional hydrogels, the fabrication and modeling of several emerging and intelligently designed hydrogel systems for drug delivery applications are discussed. Specifically, these novel systems aim to incorporate advanced drug delivery strategies into tissue engineering scaffolds and other biomedical implants and require rigorous methods for quantifying multiple phenomena influencing molecule release.

Hydrogels are polymeric networks that absorb large quantities of water while remaining insoluble in aqueous solutions due to chemical or physical crosslinking of individual polymer chains. Differing from hydrophobic polymeric networks such as poly(lactic acid) (PLA) or poly(lactide-co-glycolide) (PLGA) which have limited water-absorption capabilities (< 5–10 wt.%), hydrophilic hydrogels exhibit many unique physicochemical properties that make them advantageous for biomedical applications including drug delivery. For example, hydrogels are excellent candidates for encapsulating biomacromolecules including proteins and DNA due to their lack of hydrophobic interactions which can denature these fragile species [6]. In addition, compared to commonly used hydrophobic polymers such as PLGA, the conditions for fabricating hydrogels are relatively mild. Gel formation usually proceeds at ambient temperature and organic solvents are rarely required. In-situ gelation with cell and drug encapsulation capabilities further distinguishes hydrogels from the other hydrophobic polymers.

Hydrogels can be prepared from natural or synthetic polymers [7]. Although hydrogels made from natural polymers may not provide sufficient mechanical properties and may contain pathogens or evoke immune/inflammatory responses, they do offer several advantageous properties such as inherent biocompatibility, biodegradability, and biologically recognizable moieties that support cellular activities. Synthetic hydrogels, on the other hand, do not possess these inherent bioactive properties. Fortunately, synthetic polymers usually have well-defined structures that can be modified to yield tailorable degradability and functionality. Table 1 lists natural polymers as well as synthetic monomers that arecommonly used in hydrogel fabrication.

Since the favorable properties of hydrogels stem from their hydrophilicity, the characterization of their water-sorption capabilities is the first step towards understanding the nanoscopic structure of hydrogel networks. Generally, three parameters are critical in describing the nanostructure of crosslinked hydrogel networks: (1) polymer volume fraction in the swollen state, ν_2,s, (2) number average molecular weight between crosslinks, M¯_c, and (3) network mesh size, ξ [8]. For non-porous hydrogels, the amount of liquid being retained in the hydrogel, the distance between polymer chains, and the flexibility of those chains together determine the mobility of encapsulated molecules and their rates of diffusion within a swollen hydrogel matrix.

The polymer volume fraction in the swollen state (ν_2,s) describes the amount of liquid that can be imbibed in hydrogels and is described as a ratio of the polymer volume (V_p) to the swollen gel volume (V_g). It is also a reciprocal of the volumetric swollen ratio (Q) which can be related to the densities of the solvent (ρ₁) and polymer (ρ₂) and the mass swollen ratio (Q_m) as described by Eq. (1):

$${\nu }_{2,s}=\frac{V_{\text{p}}}{V_{\text{g}}}=Q^{-1}=\frac{1/{\rho }_2}{Q_{\text{m}}/{\rho }_1+1/{\rho }_2}$$

The average molecular weight between two adjacent crosslinks (M¯_c) represents the degree of crosslinking of the hydrogel networks. M¯_c in a neutral, divinyl crosslinked network can be expressed as the following Flory–Rehner Equation [9].

$$\frac{1}{{\bar{M}}_{\text{c}}}=\frac{2}{{\bar{M}}_{\text{n}}}-\frac{\left(\frac{\overline{\nu }}{V_1}\right)[\ln (1-{\nu }_{2,s})+{\nu }_{2,s}+{\chi }_{12}{\nu }_{2,s}^2]}{{\nu }_{2,s}^{1/3}-\frac{{\nu }_{2,s}}{2}}$$

Here, M¯_n is the average molecular weight of the linear polymer chains, ν¯ is the specific volume of the polymer, V₁ is the molar volume of water, and χ₁₂ is the polymer–water interaction parameter. More complex versions of the Flory–Rehner expression have been developed by Peppas and others to describe the swelling behavior of ionic gels or gels crosslinked during polymerization [8]. For neutral gels at highly swelling conditions (Q > 10), Eq. (2) can be simplified to illustrate how gel swelling scales with the average molecular weight between crosslinks (M¯_c) [10]:

$$Q={\left[\frac{\overline{\nu }(1/2-2{\chi }_{12}){\bar{M}}_{\text{c}}}{V_1}\right]}^{3/5}=\beta {\left({\bar{M}}_{\text{c}}\right)}^{3/5}$$

Another important parameter used to describe hydrogel swelling is the network mesh size (ξ) which can be described as follows [11]:

$$\xi ={\nu }_{2,s}^{-1/3}{\left(\overline{r_{\text{o}}^2}\right)}^{1/2}=Q^{1/3}{\left(\overline{r_{\text{o}}^2}\right)}^{1/2}$$

Here, ${\left(\overline{r_{\text{o}}^2}\right)}^{1/2}$ is the root-mean-squared end-to-end distance of network chains between two adjacent crosslinks in the unperturbed state. It can be determined using the following relationship [11]:

$${\left(\overline{r_{\text{o}}^2}\right)}^{1/2}=l{\left(C_{\text{n}}N\right)}^{1/2}=l{\left(C_{\text{n}}\frac{2M_{\text{c}}}{M_{\text{r}}}\right)}^{1/2}$$

where C_n is the Flory characteristic ratio, l is the bond length along the polymer backbone, N is the number of bonds between adjacent crosslinks, and M_r is the molecular weight of the repeating units of the composed polymer.

Combining Eqs. (4), (5), one can easily calculate the mesh size of a hydrogel network and further compare it with the hydrodynamic radii of the molecules to be delivered. Theoretically, no solute diffusion is possible within the hydrogel matrix when mesh size approaches the size of the solute as shown in Fig. 1 [12]. Mesh size is affected by several factors including (1) degree of crosslinking of the gel; (2) chemical structure of the composing monomers; and (3) external stimuli such as temperature, pH and ionic strength. Mesh size is important in determining the physical properties of the hydrogels including mechanical strength, degradability, and diffusivity of the releasing molecule [10], [13]. Typical mesh sizes reported for biomedical hydrogels range from 5 to 100 nm in their swollen state [10], [14]. These size scales are much larger than most small-molecule drugs and therefore diffusion of these drugs are not significantly retarded in swollen hydrogel matrices. However, the release of macromolecules such as peptides, proteins, and oligonucleotides can be sustained from swollen hydrogels due to their significant hydrodynamic radii. When designed appropriately, the structure and mesh size of swollen hydrogels can be tailored to obtain desired rates of macromolecule diffusion [15]. Alternatively, the rate and degree of gel swelling or degradation can also be tailored to control the release of molecules much smaller than the gel mesh size.

The advance in recombinant protein technology has identified numerous protein and peptide therapeutics for disease treatment. However, the effective delivery of these biomolecules is challenging mainly because of their large molecular weights and unique three-dimensional structures. Intravenous or subcutaneous injection is by far the most commonly used route for drug administration. However, these biomolecules are prone to proteolytic degradation and therefore experience extremely short plasma circulation times and rapid renal clearance, leading to multiple daily injections or increased dosage to maintain the drug concentration in the therapeutic window. Multiple daily injections decrease patient compliance while high doses may induce local toxicity and serious systemic immune responses. Polymeric controlled release formulations such as PLGA offer a sustained release mechanism in which the drug release rates can be controlled by changing polymer molecular weight and composition. However, it is well recognized that these hydrophobic polymers induce detrimental effects to the encapsulated proteins or peptides during network preparation and delivery [16] as well as trigger the host immune response [17]. Hydrophilic hydrogels, on the other hand, provide relatively mild network fabrication and drug encapsulation conditions that make them suitable for protein delivery [6]. The common niche for hydrogels in controlled release is the encapsulation (and subsequent release) of bioactive materials. Therefore, the systems we will focus on in this review deal with delivery from matrix devices rather than membrane devices. Through proper design, hydrogels can be used in a variety of applications including sustained, targeted, or stealth biomolecule delivery.

Several unique properties that hydrogels possess make them useful in delivering biomolecules. For example, stimuli responsiveness can be easily tailored into hydrogel networks during fabrication [18]. This enables sustained or bolus drug delivery corresponding to external stimuli such as pH or temperature. For example, pH-sensitive hydrogels are useful in oral drug delivery as they can protect peptide/protein drugs in the digestive track [19]. The pH responsiveness of hydrogels also facilitates lysosomal escape during gene delivery [20], [21]. Such responsiveness changes the mode of drug administration from merely passive release to active delivery. These exclusive properties of hydrogels can be attributed to the variety of available network precursors. Acrylic acid (AA) and methacrylic acid (MAA) [19], [22], [23] are the most commonly used monomers to fabricate anionic pH-sensitive hydrogels while 2-(dimethylamino)ethyl methacrylate (DMAEMA) [24], [25] is used for cationic hydrogel fabrication. N-isopropylacrylamide (NIPAAM) [26], [27], [28] and polypropylene oxide–polyethylene oxide–polypropylene oxide (PPO–PEO–PPO) block copolymers [28], [29], [30] are well-suited for the fabrication of temperature-sensitive hydrogels. The reversible swell-collapse transition modulates drug release rates and largely enhances the therapeutic efficacy of biomolecules.

Hydrogels can also be engineered to exhibit bioadhesiveness to facilitate drug targeting, especially through mucus membranes, for non-invasive drug administration [31], [32], [33], [34]. Both natural polymers (e.g. chitosan) and synthetic monomers (e.g. AA) provide this advantageous property. Some bioadhesive polymers have been used to fabricate hydrogels for oral [6] and buccal drug delivery [35], [36].

Hydrogels offer an important “stealth” characteristic in vivo owing to their hydrophilicity which increases the in vivo circulation time of the delivery device by evading the host immune response and decreasing phagocytic activities [37], [38]. For example, Hubbell and coworkers developed poly(ethylene glycol)-based hydrogel nanoparticles as colloidal drug carriers [39]. Several other stealth delivery systems, such as PEGylated gold nanoparticles [37], [40], have also been developed utilizing a PEG shell as a means of steric hindrance. This strategy exploits the hydrophilicity of PEG in excluding enzymatic degradation of the drug to be delivered. When conjugated with other protein therapeutics such as tumor necrosis factor (TNF), these PEGylated gold nanoparticles are good carriers for tumor-targeted delivery [41].

Another prospect of hydrogels is their role as scaffolding materials in tissue engineering applications [42], [43], [44]. Excellent examples are cartilage [45], [46] and nerve [47] tissue engineering. The mild gelling conditions and in-situ polymerization capabilities of hydrogels enable the simultaneous encapsulation of cells and growth factors. Controlled release of encapsulated growth factors and other agents from these tissue constructs is critical to providing the necessary cues for cell migration, differentiation, angiogenesis, and upregulation of extracellular matrix production required for neotissue growth or regeneration [48], [49].

As discussed in the previous sections, hydrogels have a unique combination of characteristics that make them useful in drug delivery applications. Due to their hydrophilicity, hydrogels can imbibe large amounts of water (> 90 wt.%). Therefore, the molecule release mechanisms from hydrogels are very different from hydrophobic polymers. Both simple and sophisticated models have been previously developed to predict the release of an active agent from a hydrogel device as a function of time. These models are based on the rate-limiting step for controlled release and are therefore categorized as follows:

• Diffusion-controlled

• Swelling-controlled

• Chemically-controlled.

Diffusion-controlled is the most widely applicable mechanism for describing drug release from hydrogels. Fick's law of diffusion with either constant or variable diffusion coefficients is commonly used in modeling diffusion-controlled release [13]. Drug diffusivities are generally determined empirically or estimated a priori using free volume, hydrodynamic, or obstruction-based theories [13].

Swelling-controlled release occurs when diffusion of drug is faster than hydrogel swelling. The modeling of this mechanism usually involves moving boundary conditions where molecules are released at the interface of rubbery and glassy phases of swollen hydrogels [50]. The release of many small molecule drugs from hydroxypropyl methylcellulose (HPMC) hydrogel tablets is commonly modeled using this mechanism. For example, Methocel® matrices, a combination of methylcellulose and HPMC, from Dow Chemical Company are commercially available for preparing swelling-controlled drug delivery formulations exhibiting a broad range of delivery time-scales [50], [51].

Chemically-controlled release is used to describe molecule release determined by reactions occurring within a delivery matrix. The most common reactions that occur within hydrogel delivery systems are cleavage of polymer chains via hydrolytic or enzymatic degradation or reversible or irreversible reactions occurring between the polymer network and releasable drug. Under certain conditions the surface or bulk erosion of hydrogels will control the rate of drug release. Alternatively, if drug-binding moieties are incorporated in the hydrogels, the binding equilibrium may determine the drug release rate. Chemically-controlled release can be further categorized according to the type of chemical reaction occurring during drug release. Generally, the liberation of encapsulated or tethered drugs can occur through the degradation of pendant chains or during surface-erosion or bulk-degradation of the polymer backbone. A more thorough discussion of these mechanisms can be seen in a later section of this review as well as in several other excellent reviews [6], [13], [52].

Materials selection and network fabrication governs the rate and mode of drug release from hydrogel matrices. Several design criteria are crucial for drug delivery formulations and have to be evaluated prior to hydrogel fabrication and drug loading. These criteria are also important in mathematical modeling of drug release. Table 2 lists these important criteria and variables for designing hydrogel-based drug carriers. Within the realm of transport properties, the most notable variable is the drug diffusion coefficient, which is affected by the molecular size of the drug and characteristics of the polymer network. Hydrogel crosslinking density affects diffusivity to a large extent as shown in Fig. 1 and as discussed previously. If special functionalities, such as ionic groups, are introduced into the hydrogel networks, interactions between these functionalities and encapsulated drugs certainly affect drug diffusivity. Physical properties of the hydrogel also affect drug release. For example, polymer molecular weights, composition, and polymer/initiator concentrations influence hydrogel swelling and degradation. Finally, the stimuli-responsiveness of a hydrogel network can also mediate the amount and rate of drug delivery. The understanding of transport and physical properties is especially crucial in modeling molecule release.

Even if a hydrogel delivery formulation is designed with the appropriate physical and transport properties, it may still fail to perform its therapeutic role when implanted in vivo due to a localized inflammatory response. The formation of a fibrous capsule surrounding the delivery device creates additional diffusion barriers that may limit drug release rates while increased proteolytic activity may increase rates of matrix and drug degradation. Proper material selection, fabrication process, and surface texture of the device are therefore always critical in designing biocompatible hydrogel formulations for controlled release.