Decoding Hydrogel Porosity: Advancing the Structural Analysis of Hydrogels for Biomedical Applications

Abstract

Hydrogels are essential biomaterials for biomedical applications, valued for their tunable properties and biocompatibility. A key feature influencing their function is porosity, which governs transport properties. Cryogenic scanning electron microscopy (cryo-SEM) is widely used to directly characterize porosity, but may introduce structural artifacts. Accurately characterizing the porosity of a hydrogel in its native state remains a challenge. Here, we characterized the hydrogel porosity in its native state using particle tracking assay and compared the results with cryo-SEM in polyethylene glycol (PEG) hydrogels. Both methods revealed the presence of micropores in PEG, likely arising from defects during polymerization. The equilibrium swelling assay showed nanoscale mesh sizes between polymer chains, distinct from the micron-scale pores. To overcome conventional limitations, we developed a novel three-dimensional (3D) pore reconstruction approach by leveraging the convex hull algorithm. The method enabled measurement of pore volume, surface area, sphericity, and size distribution. We found that cryo-SEM underestimates pore diameters due to the two-dimensional (2D) depiction, but after the 2D-to-3D conversion, remarkably similar pore dimensions are obtained. By advancing porosity analysis, this work provides insights for tailoring hydrogels to optimize interactions with cells, biomolecules, and therapeutic agents, opening avenues in drug delivery, tissue engineering, and other biomedical applications.

Keywords: convex hull algorithm; diffusion; hydrogel structure; packing algorithm; particle tracking; porosity characterization.

Figure 1

a) Schematic of the nanoscale and microscale molecular networks of PEG hydrogels in nanoscale and microscale. b) Mesh size of PEG hydrogels determined by a swelling assay based on Flory–Rehner equilibrium swelling theory. c) The pore diameter distribution of PEG hydrogels with median values of 9.67 and 11.36 µm for 0.7 and 1.5 kPa PEG, respectively. Pore data pooled from three samples for each hydrogel determined from the cryo‐SEM images of the PEG hydrogels: d) 0.7 kPa, and e) 1.5 kPa. The scale bar is 100 µm long. f) Mean‐squared displacement (MSD) curves showing the confined motion of the beads (n ≥ 1000) inside PEG hydrogels (n = 3) as compared to the linear behavior of simulated free diffusion. g) Diffusion length from the MSD curves in (f) as estimated pore sizes for 0.7 and 1.5 kPa PEG. T‐test: ^* indicates 0.01 < p ≤ 0.05, ns indicates not significant.

Figure 2

The convex hull algorithm enables geometric mapping of hydrogel geometry. The time stamp for each coordinate for a‐g is depicted in the color bar on the right of c. a) 2D tracks of particle diffusion. b) 2D tracks were simplified to position coordinates and the convex hull algorithm was applied. c) Visualized result of the convex hull algorithm applied to b. The position coordinates identified as vertices are highlighted in gray circles. The resulting 2D shape is shown in blue from which the pore dimensions can be extracted. d–g) The convex hull algorithm can also be applied to 3D position coordinates to generate a 3D shape. f) The gray lines show the edges of the faces of the 3D shape. (g) The side view perspective of f along the yz plane. h) Illustration of an identified vertex at position x, y which is the center of the yellow bead with radius r. The dashed gray lines are the better approximation of the boundary of the pore. i) Representative illustration of the 2D shape with correction (gray dashed line) and without correction (blue filled shape). Histogram of the cavity diameters determined using two different bead sizes j) without correction and k) with correction. The yellow and blue vertical lines show the median cavity diameter for the 2 and 0.5 µm bead diameters, respectively.

Figure 3

Micro‐structured models of confined volumes show reliable determination of pore diameters. a) Schematic for creating microcavity with defined dimensions. Hot liquid agarose was poured onto the polydimethylsiloxane (PDMS) molds to fabricate agarose microwells. b) Representative image of the resulting agarose 250 µm microwells (Scale bar = 250 µm). c) Representative result of particle tracking of fluorescent beads in 55 µm microwells with defined dimensions (Scale bar = 100 µm). d) Linear correlation of the measured diameters using convex hull particle diffusion analysis against the true fabricated diameter of the microwells (n = 4–52).

Figure 4

Measurement of pore dimensions of the PEG hydrogels using the convex hull algorithm: a) empirical cumulative distribution function of pore volume and b) pore surface area, histograms of c) sphericity, and d) pore diameter. Dashed lines of the same color legend represent the median values. Data was pooled from four samples of each PEG hydrogel. e) Schematic of a gel cross‐sectioned along the xy plane (blue dashed line) which may or may not overlap with the longest diameter of the 3D pores represented as red lines. f) Simulated SEM pore diameters derived from the empirical 3D pores which is comparable to the values obtained from the empirical SEM data in Figure 1c.

Figure 5

Reconstruction of pseudo‐2D pore images derived from the simulated 2D pore data. Reconstructed 2D pores from the flattened geometric models (a,b) as is, and (c,d) with a 10 µm gap between pores. e) Using the diameter of a subset of geometric models, circles were generated and fitted together using the circle packing algorithm. These circles serve as a placeholder for the flattened geometric models. f) The flattened geometric models were circumscribed to their corresponding circles. g) The model circles were removed. This packing method was scaled up to the data and used to reconstruct the pseudo‐2D pore images of h) 0.7 kPa and i) 1.5 kPa hydrogel.