Viscoelastic Properties of Bioprinted Alginate Microbeads Compared to Their Bulk Hydrogel Analogs

Abstract

Hydrogel microbeads are engineered spherical microgels widely used for biomedical applications in cell cultures, tissue engineering, and drug delivery. Their mechanical and physical properties (i.e., modulus, porosity, diffusion) heavily influence their utility by affecting encapsulated cellular behavior, biopayload elution kinetics, and stability for longer term cultures. There is a need to quantify these properties to guide microbead design for effective application. However, there are few techniques with the μN-level resolution required to evaluate these relatively small, compliant constructs. To circumvent mechanically testing individual microbeads, researchers often approximate microbead properties by characterizing larger bulk gel analogs of the same material formulation. This approach provides some insight into the hydrogel properties. However, bulk gels possess key structural and mechanical differences compared to their microbead equivalents, which may limit their accuracy and utility as analogs for estimating microbead properties. Herein, we explore how microbead properties are influenced by hydrogel formulation (i.e., alginate concentration, divalent cation crosslinker, and crosslinker concentration), and whether these trends are accurately reflected in bulk gel analogs. To accomplish this, we utilize laser direct-write bioprinting to create 12 × 12 arrays of alginate microbeads and characterize all 144 microbeads in parallel using a commercially available microcompression system. In this way, the compressive load is distributed across a large number of beads, thus amplifying sample signal. Comparing microbead properties to those of their bulk gel analogs, we found that their trends in modulus, porosity, and diffusion with hydrogel formulation are consistent, yet bulk gels exhibit significant discrepancies in their measured values.

Keywords: bulk gel; hydrogel; laser direct-write bioprinting; microbead; microcompression.

Fig. 1

Schematic of bulk gels compression setup (a), and representative force–% strain curve for alginate compression data to 10% strain (b). Two linear regions are shown, 1–4% strain and 8–10% strain. Region 2 was used to calculate Young's modulus within these studies to provide a stronger signal with less influence from noise.

Fig. 2

Elastic moduli of 2% alginate bulk hydrogels determined by compression testing. (a) Crosslinking gels for 1 h with increasing concentrations of BaCl₂ or CaCl₂. Bulk gel characterization revealed increasing moduli with increased crosslinker concentration. Ba-crosslinked alginate gels were stiffer than Ca-crosslinked gel analogs for all concentrations tested, with 2% BaCl₂ gels exhibiting similar moduli to 10% CaCl₂ gels. (b) Comparison of gels crosslinked with 2% BaCl₂ (cross-hatched bars) or CaCl₂ (solid bars) and cultured in medium for 1 h and 24 h to assess effects of aging on gel properties. Ba-crosslinked gels (cross-hatched bars) exhibited greater mechanical stability in culture than those crosslinked with Ca, as evidenced by the significantly smaller decrease in moduli from 1 h to 24 h (p = 0.25 and 0.009 for Ba- and Ca-crosslinked gels, respectively) (n = 6, all groups) (* = p < 0.05, ** = p < 0.01, *** = p < 0.001).

Fig. 3

Representative stress relaxation curve for an alginate bulk gel. The sample was compressed 20% of its original height over a 1 s period, then held at this displacement for 300 s. The black dashed lines indicate the half-relaxation point for the sample, while the red lines show the peak and equilibrium stress values between which total relaxation was calculated. The first 10 s of data, shown in blue shading, was truncated to avoid transient artifacts associated with a noninstantaneous stepped loading.

Fig. 4

(a) Representative image showing a section of an alginate microbead array. (b) Schematic displaying compression of an alginate microbead array. (c) Representative force–fractional deformation curve for a 12 × 12 array of alginate microbeads, where fractional deformation is defined as change in sample height due to deformation divided by undeformed sample height. (d) Fitting compression data to Hertz Theory.

Fig. 5

Elastic moduli of 2% alginate microbeads determined by compression testing. (a) Crosslinking beads for 1 h with increasing concentrations of BaCl₂ or CaCl₂. Microbead characterization revealed increasing moduli with increased crosslinker concentration, similar to results seen for bulk gels. Ba-crosslinked alginate bead arrays were stiffer than Ca-crosslinked analog arrays for all concentrations tested, with 2% BaCl₂ microbeads again exhibiting similar moduli to 10% CaCl₂ microbeads. (b) Comparison of microbead arrays at 1 h and 24 h in culture, for alginate microbeads crosslinked with 2% BaCl₂ (cross-hatched bars) or CaCl₂ (solid bars), to assess effects of aging on microbead properties. Ca-crosslinked bead arrays exhibited greater mechanical stability in culture (p = 0.17) than those crosslinked with Ba²⁺ (p = 0.005), an opposite finding of what was seen in the bulk alginate gels (12 × 12 microbead arrays, n = 4, all groups) (* = p < 0.05, ** = p < 0.01, *** = p < 0.001).

Fig. 6

Representative stress relaxation curve for an alginate microbead array. The array was compressed 20% of the original average bead height over a 1 s period, then held at this displacement for 300 s.

Fig. 7

Swelling data, represented as % change in volume over time for alginate gels cultured in either (a) saline, or (b) DMEM. 2% CaCl₂–2% alginate gels and 10% CaCl₂ 1.5% alginate gels swelled in saline and DMEM, while other conditions saw little change in percent volume. 2% alginate gels crosslinked with 10% CaCl₂ also exhibited swelling in DMEM (n = 3, all groups).

Fig. 8

Swelling data, represented as % change in volume over time for LDW-fabricated alginate microbeads, cultured in either (a) saline or (b) DMEM. Microbeads crosslinked with 10% CaCl₂ exhibited swelling, whereas all other formulations caused microbeads to shrink. Only 2% CaCl₂ beads swelled in DMEM, while all other conditions displayed overall shrinking trends (n = 3–6, all groups).

Fig. 9

Plot of (a) tracer concentration in media versus the square root of time for alginate gels, and (b) the corresponding diffusion coefficients. The diffusivity of 2% alginate gels crosslinked with 2% Ca²⁺ was significantly greater than that of all other gels tested (p values between 0.006 and 0.009). Remaining conditions exhibited similar diffusion behavior to one another (n = 3/group) (** = p < 0.01).

Fig. 10

Plot of (a) tracer in media versus time for alginate microbeads, and (b) the corresponding diffusion coefficients. The diffusivity of 2% alginate microbead arrays crosslinked with 2% Ca²⁺ was significantly greater than that of the other formulations (p values between 1.33 × 10⁻⁶ and 1.57 × 10⁻⁶). Remaining conditions exhibited similar diffusion behavior to one another (n = 3 arrays/condition) (*** = p < 0.001).