Tunable Stress Relaxation Behavior of an Alginate ... - ACS Publications

Mar 26, 2015 - Factors controlling the time-dependent mechanical properties of interpenetrating network (IPN) hydrogel materials are not well understo...
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Tunable Stress Relaxation Behavior of an Alginate-Polyacrylamide Hydrogel: Comparison with Muscle Tissue Martha M. Fitzgerald, Katherine Bootsma, Jason A. Berberich,* and Jessica L. Sparks* Department of Chemical, Paper and Biomedical Engineering, Miami University, Oxford, Ohio 45056, United States S Supporting Information *

ABSTRACT: Factors controlling the time-dependent mechanical properties of interpenetrating network (IPN) hydrogel materials are not well understood. In this study, alginate-polyacrylamide IPN were synthesized to mimic the stress relaxation behavior and elastic modulus of porcine muscle tissue. Hydrogel samples were created with single-parameter chemical concentration variations from a baseline formula to establish trends. The concentration of total monomer material had the largest effect on the elastic modulus, while concentration of the acrylamide cross-linker, N,N-methylenebis(acrylamide) (MBAA), changed the stress relaxation behavior most effectively. The IPN material was then tuned to mimic the mechanical response of muscle tissue using these trends. Swelling the hydrogel samples to equilibrium resulted in a dramatic decrease in both elastic modulus and stress relaxation behavior. Collectively, the results demonstrate that alginate-polyacrylamide IPN hydrogels can be tuned to closely mimic both the elastic and the viscoelastic behaviors of muscle tissue, although swelling detrimentally affects these desired properties.

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INTRODUCTION Hydrogels that mimic biomechanical properties of soft biological tissues have important applications in several fields, including ballistics testing, injury biomechanics,1,2 mechanosensitivity studies,3 drug delivery,4,5 and tissue engineering.6 Muscle tissue engineering has a particular need for scaffold materials that simulate extracellular matrix (ECM) mechanics3 and architecture. 7 In native muscle tissue, the ECM immediately surrounding muscle cells is termed the basal lamina and is critical for providing mechanical support, modulating cell metabolism, facilitating cell migration, and promoting cell survival, proliferation, and differentiation.7 In previous studies, successful skeletal muscle scaffold designs have been linked to specific tissue-like mechanical behaviors of the scaffold materials. For example, Singh et al. reported that cryogel scaffolds made of polyhydroxyethyl methacrylate (pHEMA) gelatin support the survival and proliferation of myoblast skeletal muscle cells. Success in this study was attributed in part to the fact that the viscoelastic properties of the cryogel scaffolds mimicked the native ECM.8 In another study, polyethylene glycol (PEG)-based hydrogel scaffolds were able to rejuvenate aged skeletal muscle derived pericytes by mimicking the 3D microenvironment of young ECM. The authors argued that, compared with its older counterpart, young ECM has a lower stiffness and generates mechanical cues that are more conducive to supporting angiogenesis and muscular tissue development.9 In the work by Ostrovidov et al., myotubes were formed on gelatin nanofibers, where multiwalled carbon nanotubes were used to © XXXX American Chemical Society

improve the mechanical properties, specifically the Young’s modulus, of the scaffolds. The methods in this study were determined to be successful because of their ability to mimic the viscoelastic and stiffness properties of the ECM that triggered mechanotransduction for the regulation of gene expression by the myoblast cells.10 Finally, McKinnon et al. have created a hydrazone cross-linked hydrogel material that is capable of mimicking both the viscoelastic and the elastic mechanical properties of native tissues so that it can be used as a more successful cell scaffold.11 The studies cited above noted the importance of mimicking both elastic (time-independent) and viscoelastic (time-dependent) mechanical properties of native biological tissue. While the elastic stiffness of various scaffold materials was quantified and reported in some of these studies, scaffold viscoelastic properties were quantified only by McKinnon et al.11 Viscoelastic properties of skeletal muscle tissue were evaluated by Van Loocke et al., among others.12−15 They conducted unconfined compression stress relaxation tests on passive porcine muscle at varying strains and strain rates. The authors concluded that the viscoelastic component plays a significant role in skeletal muscle mechanical properties.15,18 These results can be extended to human skeletal muscle as porcine models are commonly used to study soft tissue properties.15,16 Collectively, results from these studies suggest that both elastic Received: December 18, 2014 Revised: February 26, 2015

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Scheme 1. Interpenetrating Network is Made of Tough, Elastic Chemical Cross-Links and Brittle, Self-Healing Physical CrossLinks That Are All Formed Together in Solution To Ensure Entanglement

that the gelling time and homogeneity could be controlled by utilizing a system of D-glucono-δ-lactone (GDL), and calcium carbonate (CaCO3).23 Calcium carbonate has a low solubility in water at neutral pH. As the GDL hydrolyzes, the acid that is formed liberates calcium ions which are then free to cross-link with the alginate. The present study used this approach to synthesize homogeneous alginateacrylamide IPN hydrogels. Alginate, sold as Manugel GMB, was donated by FMC Biopolymer and was used as received. Calcium carbonate (CaCO3) was always present in a 1:2 molar ratio with the D-glucono-δ-lactone (GDL; Sigma).23 The weight percent values, Table 1, refer to the total amount

and viscoelastic properties of a gel-based scaffold material are important considerations in skeletal muscle scaffold design. While hydrogel materials are capable of mimicking certain elastic and viscoelastic properties that are characteristic of soft biological tissues, such materials often suffer from low strength, low fracture toughness, and otherwise poor mechanical properties that may limit their utility. An interpenetrating network (IPN) is a combination of two polymer networks where at least one of the networks has been cross-linked and synthesized in the presence of the other.17 IPN hydrogel systems have been reported to possess remarkable fracture toughness and maximum compressive strain compared with traditional hydrogel materials due to the ability of one network to maintain its elasticity and the other to self-heal upon removal of the load (Scheme 1).17,19,20 Certain formulations of these hydrogels made with polyacrylamide and alginate have been shown to sustain a compressive strain of over 90% with a minimal decrease in the elastic modulus upon recovery.18 Fracture energies of approximately 9000 J·m−2 have also been reported for polyacrylamide-alginate IPN hydogels, and they have been stretched up to 20× their length.20 The strength, toughness, and biocompatibility of these hydrogels make them a good potential material for tissue engineering scaffold applications,19 such as cartilage tissue engineering.21 The fracture toughness and elastic properties of polyacrylamide-alginate IPN hydrogels were investigated in several previous studies;17,19,20 however, the factors controlling the stress relaxation behavior of this material are not well understood. Since stress relaxation behavior offers a means to quantify both elastic and viscoelastic properties of a material, the factors controlling stress relaxation behavior of IPN hydrogels are important for future development of muscle tissue engineering scaffolds based on these materials. In this study, we seek to investigate the effects of formula variations on the stress relaxation behavior of alginate-polyacrylamide IPN hydrogels. In addition, we will demonstrate the feasibility of “tuning” an alginate-polyacrylamide IPN hydrogel material to closely mimic the stress relaxation behavior of native muscle tissue.

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Table 1. Baseline Formulation Parameters and the Variable Ranges Considered in Subsequent Sectionsa variable

baseline (wt %)

range (wt %)

total monomer CaCO3 + GDLb APSc MBAAc

14.0 2.0 0.5 0.1

14.0−20.0 0−40.0 0.3−0.88 0.004−1.0

a

The ratio of alginate to acrylamide was held constant at 1:10, and the UV initiation was performed for 20 min at a wavelength of 254 nm. See Table S.1 for baseline formula details by total weight concentration. bWt % with respect to the amount of alginate. cWt % with respect to the amount of acrylamide.

of CaCO3 plus GDL that were present. Acrylamide monomer (Fisher) was used as received. Ammonium persulfate (APS) was used as the initiator and was held in a constant 25:17 weight ratio20 to the accelerator tetramethylethylenediamine (TEMED; Fisher). N,Nmethylenebis(acrylamide) (MBAA; Fisher) was used as the crosslinker. To prepare the monomer solution, a stock solution of 2−4 wt % alginate was mixed with a stock solution of 1 wt % MBAA in a conical tube for a final solution concentration of 1.27−2.73 wt % alginate and 0.004−1.0 wt % MBAA with respect to acrylamide. TEMED was then added as a liquid. The solution was vigorously mixed to ensure even distribution. The additional water required to bring the solution to its final concentration was used to dissolve the dry weight of acrylamide into solution. The acrylamide/water solution was then added and vigorously mixed into the monomer solution. The alginate to acrylamide ratio was 1:10. The final polymer concentration was 14− 30 wt % of the solution. The initiator solution was made by combining the required amount of 20 wt % APS stock solution with equal amounts of 200 mM GDL and 100 mM CaCO3 stock solutions in a conical tube. The initiator solution was then added into the monomer solution to induce cross-linking. The final IPN formulation was vigorously mixed for approximately 1 min before being poured into custom-made Delrin molds. The cylindrical molds were 12 mm in height and 17 mm in diameter resulting in a 0.70 aspect ratio. The

MATERIALS AND METHODS

Hydrogel Preparation. Polyacrylamide-alginate IPN gels have previously been synthesized using calcium sulfate (CaSO4) as the source of calcium ions for the alginate portion of the matrix.20 However, the kinetics of the gelling time proved difficult to control, and the resulting hydrogel structure was not homogeneous.22 A previous single-network alginate hydrogel study by Kuo and Ma found B

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The Prony series parameters gi and τi were optimized to fit the average experimental data for the stress relaxation of each material using a trust-region algorithm in Matlab (MathWorks, Inc., Natick, MA). The weighting constant g1 was unconstrained. Weighting constants g2 and g3 were fixed at g2 = 0.075 and g3 = 0.05 for consistency, and time constants τ2 and τ3 were unconstrained, while τ1 was fixed at τ1 = 2 × 10−5. Therefore, the optimized parameters were g1, τ2, and τ3. This optimization protocol was designed to isolate the variation seen between native tissue and the different hydrogel formulations in the smallest number of variables while still being able to use an identical fitting protocol across all the data sets being considered (see Supporting Information, section 5 for more details). Optimized Prony series constants were used to compare the mechanical behavior of the various materials tested. In addition, differences between material formulations were quantified by determining the total percent relaxation that occurred during the hold period. This was calculated from the maximum stress at the peak of the ramp phase to the long-term (equilibrium) stress value averaged over the last 10 seconds of testing. A metric pertaining to the relative rate of relaxation was also considered. This metric was quantified by calculating how much of the total amount of relaxation occurred within the first 100 s of the hold period. For example, two gels that had the same total percent relaxation may have reached their equilibrium stress values at different times during the hold phase. Thus, total percent relaxation and relative rate of relaxation were used as additional measures to evaluate and compare the materials’ timedependent behavior. Mechanical data (Eramp) was used to calculate the apparent molecular weight of the polymer chains between cross-links (Mc) using rubber elasticity theory:33,34

molds were put into a UV initiator box (Fisher Scientific, model 13− 245−221, 115 VAC, 175 W, 1.6 A) under a wavelength of 254 nm for 20 min (∼10−11 mW/cm2).24 Gel samples were allowed to remain in the molds at room temperature conditions for at least an additional 2 h before removal to ensure that the reaction had completed (Scheme 1). To verify adequate mixing throughout the sample height, homogeneity tests were conducted (see Supporting Information, section 1, for details). Baseline Formulation Established to Isolate Effects of Variable Variation. A baseline polyacrylamide-alginate IPN hydrogel formula was determined from preliminary testing and literature review of previous groups using a similar polyacrylamide-alginate system (Table 1).19,20,22,25−27 This formula is considered a “baseline” because to establish the effect of each variable on the mechanical properties of the IPN gels, only one variable was changed at a time. The four variables identified for consideration in the IPN gel formulations include the concentration of total monomer, CaCO3 and GDL, APS, and MBAA. The variable ranges were determined by reaching limits at which the gels either formed too quickly, gelled nonhomogeneously, could not gel, or could not support their shape. Each range was established as a variation from the baseline. Swelling. The initial weights of the IPN hydrogel samples were recorded when they were first polymerized. The samples were then stored in deionized water, PBS, and CaCl2 baths for varying amounts of time. The first group was kept in the bath for 72 h before being mechanically tested using the procedure outlined in Supporting Information, section 4. The second group of samples was weighed each day until their equilibrium weight was reached. Equilibrium was defined as the point at which the swollen weight of the gel was no longer changing (within 5% over 72 h). When the gels reached equilibrium, compression tests were run using the same protocol. No gels were compressed more than once. Swelling ratios were calculated by dividing the swollen weight at each time point by the initial weight of the gel. Homogeneity Testing. Homogeneity tests were performed and the results are reported in Supporting Information, section 1. Weight ratios were calculated by dividing the initial weight by the dry weight. The dry weight was determined by allowing sliced samples to sit out open to the air for 72 h, then measuring their weight after all the water had evaporated. Characterization of Stress Relaxation Behavior. Unconfined compression stress relaxation experiments were conducted on porcine muscle samples and polyacrylamide-alginate IPN hydrogel samples. Mechanical testing details are provided in the Supporting Information, section 4. To characterize each material’s stress relaxation behavior, muscle tissue and all hydrogel material formulations were modeled as linear viscoelastic materials.28 The time-independent elastic response for each material was defined by specifying the long-term elastic modulus, Einf, and Poisson’s ratio, ν. Einf was determined from the average fully relaxed force data collected during the last ten seconds of the hold period. Poisson’s ratio was defined as ν = 0.499 to reflect the near incompressibility of hydrogels and biological tissues, consistent with previous studies.29,30 These material constants were used in subsequent viscoelastic material model optimization as described below. An elastic “ramp” modulus, Eramp, was also determined for each material by calculating the slope of the averaged engineering stress versus engineering strain response during the ramp phase of the stress relaxation test. A Prony series was used to model the linear viscoelastic relaxation data in order to allow quantifiable comparisons to be made between different materials. The time-dependent relaxation function, E(t), was defined by eq 1:

E(t ) =

E inf i=1

1 − ∑n gi

Mc =

∑ gi(1 − e−t / τi)] n

(2)

where Eramp is the elastic ramp modulus, R is the universal gas constant, T is the temperature, and c is the polymer concentration. It was assumed that the interpenetrating network deforms in an affine manner. Resulting values of Mc were then used to examine the effect of changes in MBAA concentration on the apparent molecular weight between cross-links within the IPN structure.

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RESULTS Homogeneity Can Be Controlled Using a CaCO3/GDL System. Homogeneity test results indicated that the CaCO3/ GDL method produced gels with a homogeneous structure (see Supporting Information, section 1). By introducing GDL to slow down the reaction and using CaCO3 instead of CaSO4, it was observed that IPN gel solutions could be mixed enough to sufficiently distribute the calcium ions before gelling occurred. In addition, the results support the expected trend that increasing the weight percent of total monomer decreased the Wwet/Wdry ratio.23 Time-Independent Parameters Are Tunable. As the concentration of APS in the IPN gels was increased from 0.3 to 0.88 wt %, the ramp modulus decreased from 16.1 to 8.2 kPa (Figure 1A). Poor gelation occurred at APS concentrations less than 0.17 wt %. The elastic modulus is thought to decrease with increased APS concentration because the chain length is shorter when there are more radical initiation sites. More radical initiation sites means there is a higher probability of early termination, and shorter chains provide less stiffness. Longer chains more easily entangle with each other in the network and are believed to assist in resisting an applied load.28 The ramp modulus increased from 12.2 to 62.8 kPa as the concentration of monomer increased from 14 to 30 wt % (Figure 1B). The larger error bars on the 30 wt % monomer concentration formula reflect the difficulty of making

i=1

[1 −

cRT Eramp

(1)

where Einf is the long-term elastic modulus and the Prony series parameters n, gi, and τi are material constants.28,31 A three-term Prony series (n = 3) was used, which corresponds to the three decades of relaxation time that were recorded.32 C

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wt % were necessary for the structural integrity of the gels (see Supporting Information, section 2 for qualitative details on gel tactile properties). The increase in elastic modulus was more significant for changes in concentration of the cross-linker MBAA than for CaCO3/GDL (Figure 1C). However, monomer concentration still maintained the largest effect on the modulus. This trend was also observed in studies on acrylamide-only gels, which showed that increasing the concentration of acrylamide monomer increased the elastic modulus, Eramp, much more than increasing the concentration of cross-linker material, MBAA.33 Only a small concentration of MBAA (0.005 wt % with respect to acrylamide) was necessary for these IPN gels to hold their shape. MBAA controls the number of covalent crosslinks that are formed between the polyacrylamide chains, which make up a larger portion of the material than the alginate. Introducing more covalent cross-links increases the ability of the gel to withstand a load. In all cases, Einf followed the same trends as Eramp. Time-Dependent Parameters Are Tunable. There was little difference in the time-dependent properties of the material for variable APS and CaCO3/GDL concentrations (data not shown). The effects of total monomer concentration were also examined and were found to have a small but consistent effect on the relaxation behavior (see Supporting Information, section 3). However, by decreasing the concentration of MBAA in the IPN gels, the total percent relaxation was increased dramatically. At the lowest levels of MBAA concentration, the IPN gel relaxation approached the 87% relaxation measured in muscle tissue (Figure 2A). The apparent molecular weight between cross-links, Mc, was also found to increase as the MBAA concentration decreased (Figure 2B). Lee et al. reported similar trends in their study.4 Collectively, the results shown in Figure 2 suggest that the apparent molecular weight between cross-links increases as the stress relaxation increases. Smaller concentrations of acrylamide cross-linking molecules (MBAA) result in longer lengths of uncross-linked polymer chains. This may allow the chains to move more freely to dissipate the energy of an applied load by relaxing. IPN gels made with very low concentrations of MBAA, especially the formulas that also had low CaCO3/GDL concentrations, had trouble holding their shape because there were not enough cross-links to maintain the cylindrical geometry. For this reason, as well as the consideration of the gels’ tactile properties (discussed in Supporting Information, section 2), the concentration of CaCO3/GDL was not decreased below 2.0 wt %. IPN gel formulations at these low cross-linker values could not be swollen in DI water because they easily dissociate, possibly due to the low degree of crosslinking. In the interest of understanding more about the physical properties of these hydrogel materials, information about the internal structure of the baseline formula was acquired using SEM. The pore structure is shown in Supporting Information, section 7. Hydrogel Formulations Tailored to Mimic Muscle Mechanical Properties. Four representative hydrogel formulations (Table 2) were selected for their ability to approximate the stress relaxation behavior of native porcine muscle tissue. Stress relaxation test results for these materials are given in Figure 3. Eramp and percent relaxation were mimicked most closely by formula 2, which used only 0.004 wt

Figure 1. Effects of formula variation on the time-independent parameters, ramp elastic modulus (Eramp) and long-term elastic modulus (Einf), are reported. (A) Eramp and Einf as the concentration of APS is increased and decreased from the baseline formula. (B) Eramp and Einf as the concentration of total monomer material is increased from the baseline. (C) Elastic modulus for three different concentrations of MBAA as the concentration of CaCO3/GDL is decreased from the baseline formula. The baseline formula is given in Table 1.

homogeneous hydrogels with high amounts of monomer material due to the increasingly high viscosity of the solutions (Figure 1B). Changes to the concentration of monomer had a larger effect on the elastic modulus parameters than changes to the APS concentration. As the concentration of CaCO3/GDL increased, there was only a slight increase in the elastic moduli of the IPN samples (Figure 1C). Since the ratio of alginate to acrylamide was held constant at 1:10, the amount of alginate in the gels was relatively small. Calcium ions cross-link the alginate portion of the IPN network, so changes to this concentration had a small overall effect. Amounts of CaCO3/GDL in the range of 2−40 D

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Figure 3. “Best” hydrogel formulations for mimicking porcine muscle tissue. The stress relaxation behavior of the best formulas is compared to native porcine muscle.

in proportion to the amount of acrylamide, had a much larger effect on the peak stress than on the percent of relaxation (i.e., formulas 3 and 4). Acknowledging the small effect of MBAA concentration on modulus (Figure 1C)27 and monomer concentration on relaxation (Figure S.2), the effects of raising the modulus value by increasing the concentration of monomer could be largely separated from those of tuning the relaxation behavior by adjusting the amount of MBAA in the system. The stress relaxation behavior of formula 2 was further characterized at different amounts of total strain, for a constant strain rate of 1% s−1. The larger the initial strain, the higher the peak stress,36 and the more formula 2 was able to relax (Figure S.3). Muscle myofibrils have been shown to demonstrate similar stress relaxation behavior under ramp-hold experiments for varying strain levels.18 Viscoelastic Parameters of IPN Gels Compared with Porcine Muscle. The viscoelastic stress relaxation behavior of all IPN hydrogel formulations was modeled with a Prony series (eq 1) to allow for a quantitative comparison with muscle tissue. Best-fit values of g1, τ2, and τ3 are shown in Figure 4 for all materials tested. Best-fit values for the weighting constant g1 showed an exponential relationship with the total percent of relaxation achieved by each material (Figure 4A). Since g1 was the weighting factor associated with the smallest time constant, τ1 = 2e−5 s, the larger values of g1 indicate faster rates of relaxation. Native tissue had the highest g1 values. The four “best hydrogel” formulations (defined in Table 2) approached the native tissue values for g1, suggesting that the mechanical behavior of the IPN gels could be tuned toward that of muscle tissue (Figure 4A). The other two optimized parameters, τ2 and τ3, were also shown to be tunable toward muscle tissue (Figure 4B), with the “best” hydrogels approaching muscle tissue values for both τ2 and τ3

Figure 2. (A) Total percent relaxation at 10% strain after a hold phase of 500 s. As the concentration of MBAA was decreased from the baseline (Table 1), percent relaxation approached that of porcine muscle tissue. The two dashed reference lines represent the range of relaxation that was achieved by the porcine muscle samples. (B) The apparent molecular weight between cross-links was found to decrease as the ratio of MBAA to acrylamide was increased. Increasing the concentration of CaCO3/GDL also reduced the apparent distance between cross-links. This calculation was performed on the average modulus values using eq 2.

% MBAA with respect to acrylamide, and had a slightly higher concentration of calcium ions compared to the other three formulations (Figure 3). Formulas 1−3 all had a water content of 80% and formula 4 had a water content of 78%, which are comparable to striated muscle that is reported to have a water content of 79.52%.35 All four of the formulas had desirable tactile properties. The low MBAA concentrations in all four formulas resulted in a larger percent of relaxation, which is approaching the average value of 87.06% for porcine muscle (Figures 2 and 3). The concentration of total monomer was identified as the most controlling parameter for large adjustments of Eramp (Figure 1). Slightly increasing the concentration of total monomer, but keeping the concentration of MBAA the same

Table 2. Values Indicate the Nominal Formula Concentrations for the Four “Best” IPN Hydrogels and Their Resulting Relaxation Behavior, As Well As Their Maximum Stress formula formula formula formula formula muscle

1 2 3 4

wt % monomer

CaCO3/GDL (wt %)

wt % APS

wt % MBAA

20 20 20 18

2 7 2 2

0.33 0.33 0.5 0.5

0.004 0.004 0.005 0.005

E

% relaxation (std dev) 67.37 70.75 59.67 58.14 87.06

± ± ± ± ±

1.05 2.21 8.85 3.56 2.40

peak stress (Pa ± std dev) 2471 2264 1796 1425 2069

± ± ± ± ±

66.0 173 6.00 −52.0 −468

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(data not shown), however the linear regression was not statistically significant (p > 0.05). Plotting the relative rate of relaxation as a function of the best-fit time constant τ3 also illustrates that the native tissue values collapse into a shared trend with the rest of the data points for the IPN gel samples (Figure 4C). Swelling Experiments Indicate Decreased Viscoelastic Behavior at Equilibrium. Polyacrylamide-alginate IPN hydrogels lost most of their viscoelastic relaxation behavior as they swelled in DI water or PBS. These trends were demonstrated by performing ramp-hold compression tests at three time points in the swelling process (day 0, 72 h, and swelling equilibrium) for different gel formulations. Figure 5

Figure 5. Swelling ratio was calculated at various time points of storage in DI water. At three of these points, mechanical data was collected via ramp-hold compression tests for a formula representative of the baseline (Table 1) with an increased monomer concentration of 25 wt %. The largest amount of stress relaxation, and the highest ramp modulus, occurred at day zero. At swelling equilibrium, the peak stress was lower and the percent of relaxation also decreased considerably (see also, Supporting Information, section 8).

shows compression results for a formulation that contains 25 wt % monomer, which is an increase from the baseline (Table 1). This formula illustrates the decreased percent relaxation and peak stress values as swelling increased to equilibrium. Swelling experiments in PBS and 100 mM CaCl2 were also conducted and results are given in Figure S.6. Swelling characterization is commonly performed on hydrogels because of their high affinity for water and ability to uptake water at many times their weight.37 However, native muscle tissue has been found to only have approximately 80% water in its makeup,35 so IPN gels close to this water concentration may be more desirable from a muscle mimetic standpoint.

Figure 4. Matlab Prony series parameter optimization results, highlighting the four closest formulations to the mechanical behavior of muscle tissue, termed “best” hydrogels. (A) Exponential relationship between g1 weighting parameter for τ1 = 2e−5. (B) “Best” hydrogel formulas approach the τ2 and τ3 values to represent the total percent relaxation. (C) τ3 was observed to have a statistically significant (p < 0.05) linear relationship with the rate of relaxation during the first decade of data.

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DISCUSSION We have demonstrated that both the elastic and viscoelastic mechanical properties of alginate-polyacrylamide IPN hydrogels can be tuned to closely mimic porcine muscle tissue. The tunability of these properties makes the material a strong candidate for tissue scaffolding and other muscle mimetic applications. Previous studies indicate that tissue-like mechanical behavior can be linked to the success of skeletal muscle scaffold designs.9−12 Native muscle tissue has been shown to display rate-dependent viscoelasticity.16 The time-independent

The time constant τ3 had a statistically linear (p < 0.05) relationship to the relative rate of relaxation. This was quantified as the percent of the total amount of relaxation that occurred within the first 100 s of the hold period (Figure 4C). The linear trend line had a negative slope, relating a decreasing τ3 value to an increasing rate of relaxation, as expected. A similar trend was observed for the τ2 parameters F

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gels and the observed viscoelastic relaxation ability, rubber elasticity theory was applied (eq 2). Decreasing the amount of cross-linking molecules for both the alginate and acrylamide portions of the network resulted in increased relaxation and an increase in the apparent molecular weight between cross-links. Our results additionally indicated that submersion of the IPN hydrogel material in deionized water, or PBS, not only decreases the stiffness over time, but largely eliminates the gel’s stress relaxation behavior. Even 72 h of swelling (only about half way to the equilibrium point) prevented the hydrogel from achieving significant amounts of stress relaxation and dramatically decreased the elastic modulus from day zero. It is thought that viscoelasticity may decrease in swollen gels because of the decreased mobility of the polymer chains in a stretched, swollen network.27 For example, Zhao et al. report that the swelling of a hydrogel network in water will “prestretch” the polymer chains.52 In other studies considering a range of hydrogel materials, swelling has been shown to consistently weaken the elastic mechanical properties.53−55 For example, in a report by Jeon et al., the swelling of photo-crosslinked alginate-only hydrogels resulted in a statistically significant decrease in elastic modulus when the hydrogels were tested in compression.43 Another study considering polyacrylamide hydrogels cross-linked with MBAA found that the elastic modulus again decreases as the degree of swelling increases.56 This decrease was attributed to the water, which plasticizes the polymer and reduces mechanical strength. Sun et al. report mechanical data for the toughness of alginateacrylamide IPN gels in nonswollen gels only.20 A mathematical model reported by Anseth et al. additionally supports these experimental results,42 as the authors noted that most methods considered for improving the mechanical properties of hydrogels are designed to decrease the amount of water the material can hold. The consequences of eliminating the stress relaxation in swollen hydrogel materials may affect the microenvironment, and ultimately the health, of muscle cells seeded upon swollen hydrogel scaffold materials. However, we found that nonswollen polyacrylamide-alginate IPN hydrogels showed a strong correlation between the cross-linker concentration and the time-dependent response of the material. Control of the water uptake of this hydrogel material may lead to the long-term maintenance of desirable time-dependent properties in the future. The tunability of the stress-relaxation behavior in our IPN material makes it an attractive candidate for further development as a skeletal muscle scaffold. The optimized viscoelastic material property values (g1, τ2, and τ3) were used as a quantitative means to examine the hydrogels’ mechanical similarity to native tissue relaxation behavior. The resulting trends show that the four “best” hydrogel formulas are in fact approaching the Prony series constants representing the native tissue model. It also shows that the optimization procedure was able to capture the viscoelastic stress relaxation behavior of both the hydrogels and the native tissue using identical constraints. Finally, finite element (FE) models of the four “best” hydrogel formulas and muscle tissue (see Supporting Information, section 9) showed that the optimized material properties, which were fit to relaxation data only, could accurately simulate both ramp loading and the relaxation response. Collectively, these findings provide confidence that our modeling techniques capture the range of relaxation behaviors exhibited by the hydrogel materials developed in this work (Figure S.7).

(elastic) response of tissue engineered scaffolds is known to direct stem cell differentiation, so control of this property is also important to successful scaffold design.4,38−40 We found that the time-independent elastic modulus can be tuned by changing the concentrations of monomer, APS, CaCO3, and MBAA. The most notable changes occurred with varying amounts of total monomer. As the concentration of monomer increased, long-term modulus and ramp-modulus also increased. LeRoux et al. reported that increasing the amount of alginate in a single-network hydrogel increases the solid volume fraction and the cross-link density leading to greater stiffness values.41 Entanglement of additional polymer chains by an increase in cross-link density also contributes to the stiffness of the gel.33,42 In a study done on methacrylated alginate gels that were photo-cross-linked, the elastic modulus could be increased by increasing the amount of methacrylation.43 Our findings are also in agreement with the trends seen by Sun et al.20 When tensile tests were performed on a polyacrylamide-alginate hydrogel material, changing the concentrations of both MBAA and the calcium ion source controlled the elastic modulus.20,44 The viscoelastic stress relaxation of the hydrogel material developed in this study can also be tuned to mimic muscle tissue. The two polymer systems, alginate and polyacrylamide, work together to give these hydrogels their unique properties. Single network hydrogels that use covalent bonds, such as acrylamide, are able to recover after deformation as long as their bonds are not broken, while hydrogels with only ionic cross-links, like alginate, undergo permanent deformation.45 When these two networks are combined into an IPN hydrogel, each is thought to provide a different mechanism for the dissipation of energy from an applied load. The first mechanism occurs with the stretching of the covalent portion of the network.44 The second mechanism occurs when the physical bonds of the alginate polymers break and reform under deformation.45 The interpenetration of the long-chained acrylamide network can then maintain the elasticity of the system and allow the gel to recover its shape.46 We report that decreasing the concentration of MBAA increases the apparent molecular weight between covalent cross-links and increases its viscoelastic stress relaxation response. The acrylamide polymer chains are thought to move more freely in relation to each other when a load is applied to a hydrogel with a lower degree of covalent cross-linking.47 This finding is in agreement with the studies done by Zhao et al. and Strange et al., which indicate a relationship between polymer chain rearrangement and rate-dependent viscoelasticity in reversibly cross-linked networks.45,48 The increased stress relaxation response can be tuned to approach that of muscle tissue while still maintaining the desired elastic modulus. The relative length between cross-links is important for hydrogel swelling and mechanical properties.33 For a single network hydrogel, the length between cross-links and the mesh size can be determined from equilibrium swelling data using the Peppas-Merrill equation for hydrogels with ionic moieties49 or from the theory of rubber elasticity.33,34 Traditional applications of the Peppas-Merrill model include single-network hydrogel structures50 and some extension to copolymer51 or semi-interpenetrating network applications.26 However, IPN hydrogels have a more complex chemical structure; the presence of two distinct networks makes the application of this theory difficult. Therefore, in order to approximate a relationship between the apparent cross-link length of our IPN G

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Biomacromolecules

porcine testing data. Funding for this research was provided by a Research Incentive Award granted to J.L.S. from Miami University.

Important considerations for future work include examining the role of muscle fiber anisotropy,10 conducting longer-term fatigue experiments, and making the un-cross-linked solution more conducive to cell growth. The current swelling behavior of this material means that the attractive viscoelastic mechanical properties cannot yet be preserved in a hydrated environment, but improvements to this property would make fatigue testing possible. The anisotropic nature of muscle tissue is an important structural feature that could be used to optimize the IPN material presented here, and may serve to give even more control over its mechanical behavior. And finally, while it has been shown to be biocompatible in the fully cross-linked form,18 the raw materials used for polyacrylamide/alginate hydrogel synthesis are harmful for cells. More inert source materials, such as PEGs, may make cell-seeding less of a risk.

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(1) Crandall, J.; Bose, D.; Forman, J.; Untaroiu, C.; ArreguiDalmases, C.; Shaw, C.; Kerrigan, J. Clin. Anatomy 2011, 24, 362−371. (2) Shergold, O.; Fleck, N.; Radford, D. Int. J. Impact Eng. 2006, 32, 1384−1402. (3) Engler, A.; Sen, S.; Sweeney, H.; Discher, D. Cell 2006, 126, 677−689. (4) Lee, K.; Peters, M.; Anderson, K.; Mooney, D. Nature 2000, 408, 998−1000. (5) Lee, K.; Rowley, J.; Eiselt, P.; Moy, E.; Bouhadir, K.; Mooney, D. Macromolecules 2000, 33, 4291−4294. (6) Langer, R.; Tirrell, D. Nature 2004, 428, 487−492. (7) Alberts, B.; Johnson, A.; Lewis, J.; Raff, M.; Roberts, K.; Walter, P. Molecular Biology of the Cell, 5th ed.; Taylor and Francis, Garland Science Group LLC: New York, NY, 2008. (8) Singh, D.; Nayak, V.; Kumar, A. Int. J. Biol. Sci. 2010, 6 (4), 371− 381. (9) Fuoco, C.; Sangalli, E.; Vono, R.; Testa, S.; Sacchetti, B.; Latronico, M. V. G.; Bernardini, S.; Madeddu, P.; Cesareni, G.; Seliktar, D.; Rizzi, R.; Bearzi, C.; Cannata, S. M.; Spinetti, G.; Gargioli, C. Front. Physiol. 2014, 5, 203. (10) Ostrovidov, S.; Shi, X.; Zhang, L.; Liang, X.; Kim, S.; Fujie, T.; Ramalingam, M.; Chen, M.; Nakajima, K.; Al-Hazmi, F.; Bae, H.; Memic, A.; Khademhosseini, A. Biomaterials 2014, 35, 6268−6277. (11) McKinnon, D. D.; Domaille, D. W.; Cha, J. N.; Anseth, K. S. Adv. Mater. 2013, DOI: 10.1002/adma.201303680.. (12) Bosboom, E.; Hesselink, M.; Oomens, C.; Bouten, C.; Drost, M.; Baaijens, F. J. Biomech. 2001, 34, 1365−1368. (13) Minajeva, A.; Kulke, M.; Fernandez, J.; Linke, W. Biophys. J. 2001, 80, 1442−1451. (14) Best, T.; Mcelhaney, J.; Garrett, W.; Myers, B. J. Biomech. 1994, 27 (4), 413−419. (15) Van Loocke, M.; Lyons, C.; Simms, C. J. Biomech. 2008, 41, 1555−1566. (16) Palevski, A.; Glaich, I.; Portnoy, S.; Linder-Ganz, E.; Gefen, A. J. Biomech. Eng. 2006, 128, 782−782. (17) Sperling, L. J. Polym. Sci., Part D: Macromol. Rev. 1977, 12 (1), 141−180. (18) Lv, S.; Dudek, D.; Cao, Y.; Balamurali, M.; Gosline, J.; Li, H. Nature 2010, 465, 69−73. (19) Darnell, M.; Sun, J.; Mehta, M.; Johnson, C.; Arany, P.; Suo, Z.; Mooney, D. Biomaterials 2013, 34, 8042−8048. (20) Sun, J.; Zhao, X.; Illeperuma, W.; Chaudhuri, O.; Oh, K. H.; Mooney, D.; Vlassak, J. J.; Suo, Z. Nature 2012, 489, 133−136. (21) Guo, P.; Yuan, Y.; Chi, F. Mater. Sci. Eng., C 2014, 42, 622−628. (22) Widusha, J.; Illeperuma, R.; Suo, Z.; Vlassak, J. ACS Macro Lett. 2014, 3, 520−523. (23) Kuo, C.; Ma, P. Biomaterials 2001, 22, 511−521. (24) Moad, G.; Solomon, D. The Chemistry of Free Radical Polymerization; Pergamon: Oxford, U.K., 1995. (25) Omidian, H.; Rocca, J.; Park, K. Macromol. Biosci. 2006, 6, 703− 710. (26) Samanta, H.; Ray, S. Carbohydr. Polym. 2014, 99, 666−678. (27) Naficy, S.; Kawakami, S.; Sadegholvaad, S.; Wakisaka, M.; Spinks, G. J. Appl. Polym. Sci. 2013, 2504−2513. (28) ABAQUS. ABAQUS User’s Manual, Version 6.8; Dassault Systemes Simulia Corp.: Providence, RI, 2008. (29) Johnson, B.; Beebe, D.; Crone, W. Mater. Sci. Eng., C 2004, 24, 575−581. (30) Gefen, A.; Gefen, N.; Linder-Ganz, E.; Margulies, S. J. Biomech. Eng. 2005, 127, 512−512. (31) Evans, D.; Moran, E.; Baptista, P.; Soker, S.; Sparks, J. Biomech. Model. Mechanobiol. 2013, 12, 569−580. (32) Cheng, S.; Bilston, L. E. J. Biomech. 2005, 40, 117−124.

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CONCLUSIONS This study demonstrates that the mechanical properties of alginate-polyacrylamide IPN hydrogels can be tuned toward mimicking the behavior of porcine muscle tissue, which serves as a model for other skeletal muscle species, such as human. Mechanical trends established through parametric studies aided in the tuning process and may be of use in other applications where different mechanical properties are desired. The method of viscoelastic material property optimization provides a quantitative method to explore the similarity between one material’s relaxation behavior and another’s. Hydrogel materials with tunable elastic modulus and stress relaxation behavior, such as those reported here, are desirable for tissue engineering and numerous other applications. However, it should be considered that the swelling of this material to its equilibrium point resulted in poor mechanical integrity and loss of its viscoelastic behavior. Methods to reduce the swelling may be considered for future applications of this material in tissue engineering studies involving time-dependent relations.

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ASSOCIATED CONTENT

S Supporting Information *

Additional information, including homogeneity test results, details for baseline formulation synthesis, and stress-relaxation data for varying concentrations of total monomer. Stressrelaxation responses at various strain rates (linear viscoelasticity), and more examples of the swelling effect trend on mechanical properties of the hydrogels are also included. More details for replicating this study, and more information on the finite element model and its parameters, are provided as well. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to acknowledge Zach Hathaway for his assistance with data collection and the Instrumentation Laboratory at Miami University for their assistance with fabrication of Delrin molds. Dr. Justin Saul, Krysten Kasting, Jason Ina, Brian McGowan, and Ben Rachman also contributed H

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