Spatiotemporal Neocartilage Growth in Matrix-Metalloproteinase-Sensitive Poly(Ethylene Glycol) Hydrogels Under Dynamic Compressive Loading: An Experimental and Computational Approach

Abstract

Enzyme-sensitive hydrogels containing encapsulated chondrocytes are a promising platform for cartilage tissue engineering. However, the growth of neotissue is closely coupled to the degradation of the hydrogel and is further complicated due to the encapsulated cells serving as the enzyme source for hydrogel degradation. To better understand these coupled processes, this study combined experimental and computational methods to analyze the transition from hydrogel to neotissue in a biomimetic MMP-sensitive poly(ethylene glycol) (PEG) hydrogel with encapsulated chondrocytes. A physics-based computational model that describes spatial heterogeneities in cell distribution was used. Experimentally, cell-laden hydrogels were cultured for six weeks under free swelling or subjected daily to one-hour of dynamic compressive loading. Extracellular matrix (ECM) synthesis rates were used as model inputs, and the model was fit to the experimentally determined construct modulus over time for the free swelling condition. Experimentally, ECM accumulation comprising collagen II and aggrecan increased over time concomitant with hydrogel degradation observed by a loss in PEG. Simulations demonstrated rapid degradation in regions of high cell density (i.e., cell clusters) reaching complete degradation by day 13, which facilitated localized ECM growth. Regions of low cell density degraded more slowly, had limited ECM, and led to the decrease in construct modulus during the first two weeks. The primary difference between the two culture environments was greater ECM accumulation in the clusters under free swelling, which facilitated a faster recovery in construct modulus. By 6 weeks the compressive modulus increased 2.5-fold to 107 kPa under free swelling, but dropped 1.6-fold to 26 kPa under loading. In summary, this biomimetic MMP-sensitive hydrogel supports neocartilage growth by facilitating rapid ECM growth within cell clusters, which was followed by slower growth in the rest of the hydrogel. Subtle temporal differences in hydrogel degradation and ECM accumulation, however, had a significant impact on the evolving mechanical properties.

Introduction

Degradable hydrogels formed from crosslinked poly(ethylene glycol) (PEG) are promising for the encapsulation of chondrocytes (i.e., cartilage forming cells) and promoting cartilage-specific extracellular matrix (ECM) deposition.^1–5 The mechanism of hydrogel degradation is critical to achieving macroscopic tissue formation. Slow degrading hydrogels restrict newly deposited ECM to regions immediately surrounding the cell and prevent tissue growth^6,7 while complete degradation is required for ECM molecules to assemble and form a connected ECM.⁸ During the transition from hydrogel to neotissue, the hydrogel construct is susceptible to a loss in mechanical properties that if not carefully matched can lead to compete failure. Thus, the rate of hydrogel degradation must closely match the spatial and temporal elaboration of ECM deposition to prevent failure. One way to achieve this requirement is through spatial control over degradation. Hydrogels with crosslinks sensitive to cell-secreted enzymes, such as matrix metalloproteinases (MMPs), provide one such mechanism where embedded cells locally degrade the crosslinks.⁹ One complicating factor in designing such hydrogels is that cues from the environment can influence synthesis of MMPs as well as ECM molecules. Thus, a better understanding of the coupled processes of cell-mediated hydrogel degradation and ECM growth is needed.

One environmental cue that is important to the development and maintenance of articular cartilage is dynamic mechanical loading. Bioreactors have been employed to study the role of loading on chondrocyte activity in a controlled environment.¹⁰ These studies have revealed that chondrocytes respond in a manner that depends on the type and timing of loading.^11–13 For example, production of sulfated glycosaminoglycans (sGAGs) by chondrocytes encapsulated in PEG hydrogels and cultured under dynamic compressive loading increased over time, but this increase was greater under low strain rates.¹² In a separate study with similar PEG hydrogels, collagen II gene expression was higher under intermittent loading when compared to continuous loading, but the opposite was observed for aggrecan expression.¹³ When chondrocytes were encapsulated in a self-assembling peptide hydrogel, dynamic compressive loading led to higher expressions of matrix degrading enzymes (i.e., MMPs and aggrecanases).¹⁴ These and other studies point to load-induced changes in ECM production and matrix degrading enzyme activity, which for enzyme-sensitive hydrogels will influence hydrogel degradation and ultimately how neotissue develops.

Understanding the spatiotemporal degradation pattern of enzyme-sensitive hydrogels and its effect on neotissue growth is key to designing successful hydrogels for cartilage tissue engineering. However, it is difficult if not impossible to study hydrogel degradation when there is concurrent tissue growth. To address this shortcoming, we developed a physics-based computational model that describes the coupled processes of hydrogel degradation and tissue growth, but which can be independently examined to identify their respective contributions to the overall properties of the construct.^15–20 Moreover, the model incorporates non-idealities of real hydrogel systems, which include: a) a heterogenous distribution of cells that can occur due to cells aggregating prior to encapsulation and b) cell-mediated inhibition of the polymerization during encapsulation that leads to spatial variation in hydrogel crosslinking.^8,20 With inputs of cellular synthesis rates for ECM and enzyme, we have shown that the model captures the experimentally observed spatiotemporal changes in ECM growth and construct mechanical properties over time in culture for chondrocytes encapsulated in an aggrecanase-sensitive hydrogel.¹⁹ The model also provided insight into the profile of the hydrogel itself by mapping spatiotemporal changes in crosslink density, which is not possible through experiments alone. The model has enabled us to identify degradation patterns in enzyme-sensitive hydrogels that range from diffusion-dominated to reaction-dominated or a combination thereof.^17,18,21 For example, the model identified diffusion-dominated degradation behavior in aggrecanase-sensitive hydrogels, which occurs due to the low levels of aggrecanase secreted by encapsulated chondrocytes and also explained the slow degradation, where the hydrogel was still present even after 12 weeks.¹⁹ Overall, our computational model has been a valuable tool for gaining new insights into the closely coupled processes of hydrogel degradation and tissue growth.

The goal of the present study was to investigate the impact of dynamic compressive loading on hydrogel degradation and neocartilage growth by chondrocytes encapsulated in an MMP-sensitive biomimetic hydrogel (Fig. 1). We applied our computational model to gain insights into the spatiotemporal degradation behavior of the hydrogel and the local elaboration of ECM as a result of changes in cellular activity due to dynamic loading. Overall, this work shows that neocartilage tissue forms within MMP-sensitive hydrogels, but that loading delays ECM growth. The combined experimental and computational approach revealed insights into the transition from hydrogel to neotissue under two culture environments of free swelling and dynamic loading and the combined role of hydrogel degradation and ECM growth on evolution of mechanical properties over time.

Fig. 1.

Schematic of the MMP-sensitive biomimetic hydrogel formation and culture conditions. A) Hydrogel precursors consisting of 8-arm PEG-NB, CVPLS-LYSGC as the MMP-sensitive crosslinker, and thiolated chondroitin sulfate (ChS-SH) were mixed with freshly isolated bovine chondrocytes and then exposed to 365 nm light to form a 3D crosslinked network with encapsulated chondrocytes. B) Cell-laden hydrogel constructs were cultured in two environments: free swelling or loading. Under loading, the constructs were subjected to dynamic compressive loading applied in a sinusoidal wave at an amplitude of 5% strain on top of a 2% tare strain and 1 Hz for one hr per day.

Materials and Methods

Materials

Eight-arm poly(ethylene glycol) (PEG) terminated with NH₂ (MW 20000 Da, HCl salt) and 8-arm PEG-hexaglycerol (MW 20000 Da) was from JenKem USA (Plano, TX). Dimethylformamide (DMF), 5-norbornene-2-carboxylic acid, dichloromethane (DCM), 4-(dimethyleamino)pyridine (DMAP), N,N’-diisopropylcarbodiimide (DIC), pyridine, chondroitin sulfate, hydrdazine hydrate, 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide (EDC), dithiothreitol (DTT), trypan blue, L-ascorbic acid, sodium pyruvate, L-proline, paraformaldehyde, hyaluronidase, chondroitinase-ABC, keratinase, and dimethylmethylene blue were from Sigma Aldrich (St. Louis, MO). Fungizone, gentamicin, LIVE/DEAD assay, 4’,6-diamidino-2-phenylindole (DAPI), Dulbecco’s Modified Eagle’s Medium-F12 Nutrient Mix (DMEM/F12), and Alexafluor 488 and 546 secondary antibodies were from Life Technologies (Grand Island, NY). Phosphate-buffered saline (PBS), 100x penicillin/streptomycin, DMEM, ITS+ Premix, HEPES buffer, and GlutaGro were from Corning (Corning, NY). Recombinant human MMP-2 was from Millipore Sigma (Burlington, MA). N,N’-diisopropylethylamine (DIPEA) and O-(7-azabenzotriazol-1-yl)-N,N,N’,N’-tetramethyluronium hexafluorophosphate (HATU) were from ChemImpex (Wood Dale, IL). Ethylenediaminetetraacetic acid (EDTA) and Tris were from BioRad Laboratories (Hercules, CA). Irgacure 2959 (I2959) was from BASF (Tarrytown, NY). Fetal bovine serum (FBS) was from Atlanta Biologicals (Lawrenceville, GA). Dithiobis(propanoic dihydrazide) (DTP) was from Alfa Chemistry (Ronkonkoma, NY). Retrievagen A was from BD Biosciences (San Diego, CA). Diethyl ether was from Fisher Scientific (Fair Lawn, NJ). Hoechst 33258 was from Polysciences, Inc. (Warrington, PA). Recombinant human transforming growth factor-β3 was from R&D Systems (Minneapolis, MN). Primary antibody for collagen type II (C7510-21C) was from US Biological (Salem, MA). Primary antibody for aggrecan (ab3778) was from Abcam (Cambridge, MA). Primary antibody for PEG (PEG 6.3-PABG-A) was from the Institute of Biomedical Sciences at Academia Sinica (Taipei, Taiwan). The MMP-sensitive crosslinker (CVPLS-LYSGC) was from GenScript (Piscataway, NJ). Collagenase type II and papain were from Worthington Biochemical (Lakewood, NJ). SensoLyte 520 MMP-2 assay kit was from Anaspec (Fremont, CA). Bovine joints were obtained from Research 87 (Marlborough, MA).

Macromer Synthesis

Macromers of PEG-amide-norbornene (PEG-amide-NB) were synthesized from 8-arm PEG-NH₂ (MW 20000 Da, HCl salt) and 5-norbornene-2-carboxylic acid.^22,23 Briefly, norbornene (4 molar excess per PEG arm) was pre-activated with 6 molar excess DIPEA and 3 molar excess HATU in DMF at room temperature for 5 minutes under argon. The activated norbornene was added to a solution of PEG in DMF and reacted overnight under argon at room temperature. The product was precipitated in diethyl ether, filtered through 11 μm filter paper, dialyzed for 4 days against deionized water, and lyophilized. The norbornene conjugation to PEG was determined to be 100% by ¹H NMR spectroscopy. The peak area of the norbornene vinyl protons (δ = 5.9-6.25 ppm) was compared to the peak area of the methylene protons (δ = 3.3-3.9 ppm) in the PEG molecule.

Macromers of PEG-ester-NB were synthesized from 8-arm PEG-hexaglycerol (MW 20000) and 5-norbornene-2-carboxylic acid PEG was dissolved in DCM, 1x excess DMAP, and 10x excess pyridine under argon. Norbornene was mixed with DCM and activated with 10x excess DIC for 15 minutes under argon at room temperature. The PEG solution was added to the activated norbornene and reacted overnight. The product was precipitated in diethyl ether, dissolved in diH₂O, briefly dialyzed against diH₂O, and lyophilized. The norbornene conjugation to PEG was determined to be 100% by ¹H NMR.

Thiolated chondroitin sulfate (ChS-SH) was prepared following methods adapted from Shu, et al.²⁴ Briefly, DTP was dissolved in methanol with trace concentrated H₂SO₄. The solution was refluxed under nitrogen at 60°C for 1 hour and concentrated under reduced pressure. The solution was transferred to a separatory funnel using diethyl ether. The organic layer of DTP ester was washed multiple times with water and concentrated under vacuum. Hydrazine hydrate (8 molar excess per ester group) was added dropwise to the DTP ester and reacted for 4 hours at 40°C. Thioacid hydrazide products were precipitated with hexane, filtered, and vacuumed. Chondroitin sulfate (25 mM) was added to the DTP product at a 1:2 molar ratio. The pH of the solution was adjusted to 4.75 using HCl. EDC was added to the solution at a 1:1 molar ratio with DTP product. After 4 hours, the reaction was stopped by adjusting the pH to 7 with NaOH. DTT was added at a molar ratio of 1:6.5 DTP to DTT and the pH was adjusted to 8.5 with NaOH to reduce disulfide bonds for 24 hours. The pH was adjusted to 3.5 with HCl prior to dialyzing the product against 0.3 mM HCl with 100 mM NaCl. The dialyzed product (ChS-SH) was centrifuged and the product was recovered from the supernatant and lyophilized. Thiol conjugation to ChS was determined to be 15% via ¹H NMR. The peak area for the two side chain methylenes of DTP (δ=2.5-2.6 and 2.6-2.8 ppm) was compared to the peak area of the methyl protons of the acetyl amine side chain (δ=1.8-2.0 ppm).

Chondrocyte Isolation

Bovine articular chondrocytes were isolated from the femoral condyles and femoral patellar groove of 1-3 week old calves. Cartilage tissue was washed in PBS containing antibiotics (1% Penicillin/streptomycin, 0.5 μg/mL fungizone, and 4 μg/mL gentamicin) and digested using 0.2% collagenase type II in DMEM with 5% FBS for 15-17 hours and then filtered through a 100 μm cell strainer. Isolated cells were recovered via centrifugation at 1200 rpm for 10 min. Cells were washed in PBS with 0.02% EDTA, centrifuged, and resuspended in PBS with antibiotics for two additional washes. The isolated cells were 95% viable as determined by the trypan blue exclusion assay.

Hydrogel Formation

Cell-laden hydrogels were formed from a precursor solution containing 9% (w/w) solution of PEG-amide-NB, 1% (w/w) ChS-SH, MMP-sensitive peptide (CVPLS-LYSGC) at a 1:1 thiol:norbornene ratio, 0.05% (w/w) Irgacure 2959 photoinitiator in PBS and 100 million cells/mL of precursor solution. The polymer solution (25 μL) was photopolymerized under UV light (352 nm, 5 mW/cm²) for 5 min into cylindrical constructs (3 mm diameter by 3 mm height).

Determination of Hydrogel Degradation Kinetics

Acellular hydrogels were formed from a precursor solution containing 4% (w/w) solution of PEG-amide-NB, MMP-sensitive peptide at a 0.6:1 thiol:norbornene ratio, and 0.05% (w/w) I2959 in PBS. A low crosslink density formulation was used to allow for rapid enzyme diffusion and bulk hydrogel degradation. ChS-SH was not used in the formulation because it contributes crosslinks to the hydrogel. The polymer solution (30 µL) was photopolymerized under UV light (352 nm, 5 mW/cm2) for 5 min into cylindrical constructs (3 mm diameter by 3 mm height). Hydrogels were degraded with 10 nM exogenous MMP-2, replenished daily, for 50 h. Hydrogels were collected and analyzed by compressive modulus, wet weight, and dry weight until reverse gelation was reached. The crosslink density in the dry state of the hydrogels at each time point was determined using a self-learning algorithm (SLA).²⁵ Crosslink density in the swollen state was determined from the crosslink density in the dry state and the volumetric swelling ratio of the hydrogel. The degradation constant, k_cat, was determined to be 0.05 s⁻¹ and K_M was found to be 20 µM from a fit of the crosslink density in the swollen state with time.

Determination of Reverse Gelation Point

Acellular hydrogels were formed from the same formulation that was used in the cellular experiments with the exception that the 8-arm PEG macromer had an ester linkage. This enabled the hydrogel to be rapidly degraded by base-mediated hydrolysis. Hydrogels were formed from a precursor solution containing 9% (w/w) solution of PEG-ester-NB, 1% (w/w) ChS-SH, MMP-sensitive peptide (CVPLS-LYSGC) at a 1:1 thiol:norbornene ratio, and 0.05% (w/w) I2959 in PBS. The polymer solution (25 μL) was photopolymerized under UV light (352 nm, 5 mW/cm²) for 5 min into cylindrical constructs (3 mm diameter by 3 mm height). Hydrogels were degraded via ester hydrolysis in a pH 9 tris buffer (1 M Tris in diH₂O). At select time points, hydrogels were collected and analyzed by compressive modulus, wet weight, and dry weight until reverse gelation was reached. The crosslink density in the dry state of the hydrogels at each time point was determined using a self-learning algorithm (SLA).²⁵ Crosslink density as a function of time was fit with exponential decay. Crosslink density at the point of reverse gelation was determined by extrapolating the degradation curve to the time at which reverse gelation was experimentally observed. The ratio of crosslink density at reverse gelation to the initial crosslink density for crosslink density in the dry state was determined and is defined by β.

Culture of Cell-Laden Hydrogel Construct

Chondrocyte-laden hydrogels were cultured in defined chondrocyte medium (DMEM/F12 with 1% ITS+ Premix, 1% Pen/Strep, 0.5 μg/mL fungizone, 4 μg/mL gentimicin, 10 μM HEPES, 50 μg/mL L-ascorbic acid, 5 ng/mL TGF-β3, and supplemented with an additional 45 μg/mL sodium pyruvate, 0.25 mM L-proline, and 1.5 mM GlutaGro up to 6 weeks at 37°C in 5% CO₂. Cell-laden gels were placed in medium immediately after polymerization and allowed to reach equilibrium swelling. One-day post-encapsulation hydrogel constructs were placed in custom bioreactors and set to apply 5% compressive strain in a sinusoidal waveform at 1 Hz for 1 hour per day or cultured in free swelling conditions. Platens applied 2% tare strain. Medium was collected and replaced every 2-3 days. The spent medium was flash frozen in liquid nitrogen and stored at −70°C.

Characterization of Cell-Laden Hydrogel Construct

On days 1, 15, 29, and 43, hydrogels were collected and assessed by compressive modulus. Hydrogels were compressed with an MTS Synergie 100 (10N) to 15% at 0.5 mm/mm. The compressive modulus was estimated from the linear region of the stress strain curve between 10 and 15% strain. After compression testing gels were cut in half with one half processed for biochemical content and one half processed for histology.

Immunohistochemical Analysis

On days 1, 15, 29, and 43, half constructs were fixed in 4% paraformaldehyde overnight, dehydrated in ethanol and Neoclear gradients, and embedded in paraffin. Samples were sectioned to 10 μm and stained for collagen II (1:50), aggrecan (1:100), and PEG (1:50). All sections were treated with Retrievagen A for antigen retrieval. Sections for collagen II and aggrecan were pretreated with hyaluronidase (200 U) for 1 hr at 37°C. Sections for aggrecan were also pretreated with chondroitinase-ABC (10 mU) and 3.4 mU keratinase I for 1 hr at 37°C. The primary antibody was applied overnight at 4°C. Sections were treated with Alexfluor 488 or 546 secondary antibodies for 2 h at room temperature in the dark. Nuclei were counterstained with DAPI. Images were taken at 400x with a confocal laser scanning microscope using the same settings across all samples for each antibody.

Characterization of Cell Clusters

At the encapsulation density (100 million cells/mL) used in this study, we previous reported that chondrocytes naturally aggregate in solution prior to encapsulation leading to regions of high and low cell density in the hydrogel.⁸ The distribution of cells was determined at day 1 from histological images (6 images in total from 2 constructs) that were stained for cell nuclei. The effective cluster diameter (d’) was calculated by the following:

$$d^{\prime }=2{\int }_0^L\frac{2f_i\pi r}{n_{cells,L}}dr$$ (Eq. 1)

where L is the distance between the center of two clusters, f_i is the cell density around the cluster center, r is the radius of a cluster, n_cells,L is the total number of cells in the distance L. Images were also analyzed to determine cluster parameters for cluster size, cell density based on nuclei in the clusters, f_cl (defined as the number of cells per volume of clusters) and cell density in the background, f_bg (defined as the number of cells per volume of background). The cluster contrast parameter, c_f, which is ratio f_cl/f_bg was also determined. The volume fraction of clusters in the construct volume is noted by F.

MMP-2 Activity Analysis

On days 1, 15, 29, and 43, half constructs were collected, flash frozen, and stored at −70°C. Medium was collected every 2-3 days and grouped by week for analysis. Constructs were homogenized in Sensolyte kit assay buffer with 0.1% Triton-X for 10 min at 30 Hz. The lysate and conditioned media were analyzed for MMP-2 activity using the Sensolyte 520 assay kit for MMP-2. Human MMP-2 was used as an activity standard.

Biochemical Analysis

Half constructs were collected, flash frozen, and stored at −70°C on days 1, 15, 29, and 43. Constructs were lyophilized prior to homogenization in 0.125 mg/ml papain digest with a Qiagen TissueLyser II for 10 min at 30 Hz. Samples were digested for 18-24 hours at 60°C. DNA content was immediately assayed using Hoechst 33258 dye. Cell number was estimated using 7.7 pg DNA per chondrocyte.²⁶ Constructs were analyzed for sulfated glycosaminoglycans (sGAGs) and total collagen content using dimethylmethylene blue²⁷ and hydroxyproline,²⁸ respectively. Hydroxyproline was estimated as 10% of total collagen. The fraction of hydrogel digested relative to the whole construct was used to extrapolate the total biochemical content of the construct. Collagen and sGAG contents in the constructs were normalized to cell number. Conditioned media was collected every 2-3 days and flash frozen. Media samples were grouped by week and assessed for sGAGs and collagen content using the previously stated methods.

Mathematical and Numerical Modeling

A multiscale computational approach^16–20 was used to model the combined effects of cell-mediate hydrogel degradation and ECM growth. The model spans three characteristic length scales (Fig. 2A). The sub-microscale describes crosslink degradation and corresponding mechanical properties and diffusion of the ECM and enzyme. The microscale captures the interactions between the hydrogel and small numbers of cells. The macroscale represents the experimental constructs with a large population of cells.

Fig. 2.

Multiscale computational approach. A) The submicro scale consists of the hydrogel properties. The microscale consists of a small region of cells, hydrogel, and ECM. The regions account for variations in cell distribution and spatial variation in hydrogel crosslink density based on distance from the cell. The macroscale represents a macroscopic hydrogel construct composed of the microscale regions. B) Schematic of boundary conditions for enzyme diffusion.

The sub-microscale describes crosslink degradation and diffusion of the ECM and enzyme. Degradation of the hydrogel was modeled using Michaelis-Menten kinetics with the crosslink density in the swollen state (${\rho }_x^s$) acting as the substrate described by the following:

$$\frac{D{\rho }_x^S}{Dt}=-k_{cat}{c}_e\left(\frac{{\rho }_x^S}{K_M+{\rho }_x^S}\right)$$ (Eq. 2)

where k_cat is the catalytic rate constant, c_e is the concentration of the enzyme, K_M is the Michaelis-Menten constant, and t is time. The value of K_M was found to have a negligible effect on the model prediction due to a relatively large magnitude of the crosslink density.

A characteristic of hydrogel degradation is the reverse gelation point, the critical point when a minimum number of crosslinks have been cleaved that the hydrogel transitions from a solid polymer to polymer chains that are soluble. The network connectivity (β) relates the number of crosslinks that must be cleaved to reach reverse gelation and is described by $\beta ={\rho }_c/{\rho }_x^0$, where ${\rho }_c$ is the critical crosslink density and ${\rho }_x^0$ is the initial crosslink density. The value of ${\rho }_x^0$ was determined from Flory-Rehner and rubber elasticity theories.²⁹ The crosslink density is defined as a function of space (coordinate x) and time such that:

$${\rho }_x={\rho }_x\left(x,t\right)\text{\hspace{0.17em} when \hspace{0.17em}}{\rho }_x>{\rho }_c{\rho }_x\left(x,t\right)=0\text{\hspace{0.17em} when \hspace{0.17em}}{\rho }_x\le {\rho }_c$$ (Eq. 3)

The concentration of the enzyme as a function of location and time is dependent on diffusion, which is modeled with Fick’s law³⁰ and deactivation of the enzyme. Enzyme concentration is determined in the volume surrounding the cell, denoted by Ω, (Fig. 2B) by solving the diffusion equation:

$$\frac{D{c}_e}{Dt}=\nabla \cdot \left[D_e\left({\rho }_x\right)\nabla c_e\right]-k_d{c}_e$$ (Eq. 4)

where D_e is the diffusivity of the enzyme in the hydrogel and k_d is the enzyme deactivation constant. The boundary conditions are prescribed on the surface of the cell denoted by Γ_cell in terms of a mass flux rate $Q_e=-D_e\nabla c_e$ released by the cell whose measured values are determined experimentally. The diffusivity of the enzyme as a function of the hydrogel crosslink density and enzyme size was determined following the approach described by Lustig and Peppas³¹:

$$\frac{D_e}{D_e^{\infty }}=\left(1-\frac{r_e}{\xi \left({\rho }_x\right)}\right)\exp \left(-Y\left(\frac{v_{2,s}}{1-v_{2,s}}\right)\right)\text{for}{r}_e<\xi$$ (Eq. 5)

where $D_e^{\infty }$ is the diffusivity of the enzyme in pure solvent estimated using the Stokes-Einstein relationship, r_e is the radius of the enzyme, ξ is the hydrogel mesh size, which is a function of ρ_x, Y is the ratio of the critical volume required for a translational movement of the diffusing species relative to the average free volume occupied by the solvent molecules and is assumed to be unity,³¹ v_2,s is the polymer volume fraction. Once the hydrogel reaches reverse gelation (ρ_x ≤ ρ_c) the diffusivity is assumed to be $D_e^{\infty }$.

ECM deposition was modeled considering only fibrillar collagen and aggrecan aggregates, the primary ECM molecules in cartilage. The ECM molecules are initially unlinked and can freely diffuse within the gel depending on the diffusion coefficient D_m. Extracellularly, these molecules assemble to form the large ECM molecules which then link together to form a solid-like neo-tissue. This process is modelled by the rate of conversion, γ_m, between unlinked (fluid) ECM macromolecules and linked (solid) ECM. The above two processes can, therefore, be described by a standard reaction-diffusion equation of the form:

$$\frac{\partial c_m}{\partial t}=D_m\left({\rho }_x\right){\nabla }^2{c}_m-{\gamma }_m$$ (Eq. 6)

where c_m is the unlinked ECM concentration and rate of linkage is assumed to linearly depend on this concentration through γ_m = k_ECMc_m. Collagen and aggrecan molecules are much larger than the mesh size of the hydrogel at any point during degradation. This allowed us to assume that ECM deposition was restricted to the fully degraded regions Ω_d in Fig. 2B where ρ_x ≤ ρ_c around the cell where diffusivity is fast. For simplicity, we assume that the linked ECM in the degraded region offers no hindrance to the diffusivity of free ECM macromolecules in that region. The rate of ECM synthesis from cell surface Γ_cell is finally represented in terms of its mass flux, Q_m, which is defined on the basis of homeostasis as $Q_m=Q_m^0\left(1-c_m/c_m^0\right)$ in moles per area per time. This definition accounts for a decreasing rate of ECM production with accumulation. This yields a boundary condition for Eq. 6 in the form:

$$Q_m=-D_m\nabla c_m$$ (Eq. 7)

The accumulation of solid ECM with concentration c_ECM at a given location x in the construct is finally captured by integrating the rate γ_m following the equation:

$$\frac{\partial c_{ECM}}{\partial t}={\gamma }_m$$ (Eq. 8)

The time scale for ECM diffusion is given by l²/D_m, where l is the radius of the degradation region around the cell. Assuming that this time scale and that of the linkage rate constant 1/k_ecm are much faster than the degradation time scale 1/k_cat, the deposited ECM was modelled to fill uniformly the entire degraded region as the molecules were produced by the cells. Additionally, the ECM production rates obtained from experiments were based only on ECM molecules retained in the hydrogels and did not account for the diffusion and assembly of ECM precursors.

The microscale accounts for the compressive modulus of the hydrogel, the ECM, and the cells. Now assuming that hydrogel and ECM are interpenetrating and do not strongly interact with one-another, the mechanical response of a material point within the construct follows an additive mixture rule,²⁰ i.e. the total stress σ_t arises from additive contribution of each component, as

$${\sigma }_t={\sigma }_1+{\sigma }_2+{\sigma }_3$$ (Eq. 9)

where the stress for each material namely the gel, ECM and cell are denoted by subscripts i = 1,2 and 3. The stress-strain relationship is assumed to be a linearized form of rubber elasticity applicable for small strains and is described by

$${\sigma }_i=\frac{E_i}{\left(1+v_i\right)}\left(\mathit{\in }+\frac{v_i}{\left(1-2v_i\right)}tr\left(\mathit{\in }\right)1\right)$$ (Eq. 10)

where E_i is the Young’s modulus, v_i is the Poisson’s ratio, ϵ is the strain tensor of the composite, and 1 is the identity tensor. For the hydrogel, the Poisson’s ratio was approximated as 0.5 because the gel is assumed quasi-incompressible during mechanical loading.³² E_gel was estimated from rubber elasticity theory,³³ assuming a linear elastic model described by

$$E_{gel}=2\left(1+v\right){\rho }_{x}RT{Q}^{-1/3}$$ (Eq. 11)

where R is the gas constant and T is temperature.

The mechanical properties of the deposited ECM were assumed to represent a linear elastic isotropic material at small strains following the same stress-strain relationship given in Eq. 10.¹⁸ The modulus of the newly deposited ECM, E_ECM, was estimated as a function of ECM concentration, c_ECM, such that E_ECM =m·c_ECM, where m was determined with a model fit to the experimental modulus data and the experimentally determined concentration of deposited ECM. Poisson’s ratio for ECM was assumed to be 0.22.^34,35

The mechanical properties of the chondrocytes were assumed to follow linear elastic behavior at small strains for simplicity. At small strains, the stress-strain relationship can be linearized from rubber elasticity and follow Eq. 7, where E_cell is 0.6 kPa.³⁶

The representative volume elements (RVEs) at the microscale encompass localized hydrogel degradation and the production, transport, and deposition of ECM molecules. The modulus of the RVE depends on the hydrogel degradation governed by enzyme concentration, kinetics, and diffusion and the deposition of ECM defined by the ECM flux from the cell surface as determined by experimental ECM synthesis rates. The three components of the RVE (hydrogel, ECM, and cells) are assumed to be non-interpenetrating, or comprised of discrete regions of ECM, gel, and cells. This assumption is reasonable as the ECM molecules are much larger than the polymer mesh size and, therefore, cannot penetrate the gel. The average stress of the RVE can be derived from homogenization methods^37,38 and is described by

$$\overline{{\sigma }_{IJ}}=\frac{1}{\overline{V}}{\int }_{\overline{S}}{\sigma }_{ij}dV=\frac{1}{\overline{V}}{\int }_{\overline{S}}\frac{1}{2}\left({\tau }_i{x}_j+{\tau }_j{x}_i\right)dS$$ (Eq. 12)

Where $\overline{V}$ and $\overline{S}$ are the volume and boundary surface of the RVE, and i and j are indices that can take values 1, 2, and 3 representing directions in three dimensions. The position vector is represented by x and τ is the traction vector at the RVE boundary surface. The stress is calculated numerically using a finite element approach.²⁰ The modulus of the multicomponent RVE is described by

$$E=\frac{\overline{{\sigma }_{11}}}{\overline{{\in }_{11}}}$$ (Eq. 13)

Where $\overline{{\in }_{11}}$ and $\overline{{\sigma }_{11}}$ are the average uniaxial strain and stress on the RVE in the direction of loading.

The macroscale representing the experimental cell-laden construct considered the effect of heterogeneous distribution of cells based on the initial cluster analysis at day one. The cell distribution in the macroscale RVE was assigned by (a) distributing cluster seeds randomly using a Poisson distribution, and (b) random generation of cluster morphology from the seed point based on the previously defined cluster parameters.²⁰ The cluster distribution resulted in regions of both high and low cell density and corresponding regions of variable crosslink density and tissue deposition. Computational homogenization and a 3D finite element analysis as described at the microscale were used to assess the evolution of the averaged macroscopic properties resulting from these variable regions of cells, crosslinks, and tissue.

The constants and inputs to the model are shown in Table 1. The initial modulus, network connectivity, initial crosslink density, and catalytic rate constant were obtained experimentally. The cell radius, radius of ECM molecules, and radius of degradation were obtained from literature. The hydrodynamic radius of MMP-2 was calculated using online tools (nanocomposix.com) based on a 72 kDa protein. The diffusivity of MMP-2 was estimated by the Stokes-Einstein equation for diffusion. The kinetic constant, k_d was determined by fitting the computational model to the experimental modulus data for the free swelling condition. This value was then used in simulations for the dynamic loading condition, where good agreement between experimental modulus data and modeling modulus data was observed.

Table 1.

Model Constants

Parameter	Definition	Value	Unit	Reference
E0	Initial modulus of cell-laden hydrogel	42	kPa	This study
β	Network connectivity	0.044	--	This study
${\rho }_x^{s,0}$	Initial crosslink density in swollen state	400	µM	This study
rcell	Cell radius	5.75	μm	Ref 39
re	Hydrodynamic radius of enzyme	6.5	nm	Nanocomposix.com
De∞	Diffusivity of enzyme in pure solvent	5.7E-5	mm2/s	Stokes-Einstein
kcat	Enzyme catalytic rate constant	0.05	s−1	This study
KM	Michaelis-Menten constant	20	µM	This study
rm	Hydrodynamic radius of ECM molecules	>200	nm	Ref 40,41
Rd	Radius of degradation	1.5rcell	μm	Ref 42
kd	Enzyme deactivation constant	0.00029	s−1	Model fit
m	ECM stiffness correlation constant	5.0E5	kJ/mol	Model fit

Statistics

Experimental data are reported as mean with standard deviation shown parenthetically in the text or as error bars in plots. Real Statistics in Excel was used for statistical analysis. Data were confirmed to follow a normal distribution and have homogeneous variances with Levene’s test. Data sets had n=3 with the following exceptions. Day 1 was limited to n=2, but at this time point there is minimal ECM elaborated and the properties are largely dominated by the hydrogel which is highly reproducible. For the loaded samples, total collagen measurements at day 15 and modulus data at day 29 and 43 were limited to n=2. For total collagen measurements under dynamic loading at day 29, there two samples were lost during processing resulting in n=1. This time point was excluded from statistical analysis. Data were analyzed with a two-way ANOVA where appropriate with time and mechanical environment as the factors. If the two-way ANOVA established a significant interaction between the parameters, follow up analysis was performed. One-way ANOVA was conducted with time as the factor. An unpaired t-test assuming equal variances was performed to compare environments. Pairwise comparisons were conducted where appropriate using Tukey’s HSD (α=0.05) as a post-hoc analysis. P-values <0.05 are reported and considered significant. Correlation between ECM and modulus was analyzed with the Pearson coefficient.

Results

Cell Clusters in MMP-Sensitive Hydrogels

Primary bovine chondrocytes were encapsulated in the MMP-sensitive biomimetic hydrogel. The spatial distribution of encapsulated cells was analyzed one day post-encapsulation from histological images stained for cell nuclei (Fig. 3). Clusters of cell nuclei were evident throughout the hydrogel (Fig. 3A,B). At the same time, there were areas where cell nuclei were not in close contact with other cells (i.e., not associated with cell clusters) (Fig. 3B). These cells are referred herein as background cells. A histogram plot for effective cluster diameter (d’) indicates a range from 30 μm to 220 μm with a median cluster diameter of 76 μm (Fig. 3C). These cluster density maps were then used to determine the background cell densities, cluster cell densities, cluster contrast parameter, and cluster volume fraction (Fig. 3D), which were used in the computational model.

Fig. 3.

Spatial distribution of chondrocytes encapsulated in the MMP-sensitive biomimetic hydrogels. A-B) Representative confocal microscopy images of histological sections from three different hydrogel samples one day post-encapsulation. In A, cell clusters are denoted by red dotted outlines. In B, cell clusters are shown by the red box and a region of individual cells denoted as background are shown by the green box. The sections were stained for nuclei by DAPI. In A, scale bar is 100 µm. C-D) Analysis of the microscopy images were performed to determine a histogram for effective cluster diameter, d’ (C) and cluster parameters (D). Data were acquired from six images (100x) for two hydrogel samples.

MMP-Mediated Hydrogel Degradation

The levels of active MMP-2 in the constructs and the media were analyzed as a representative MMP that contributes to hydrogel degradation (Fig. 4). Since the pro-form of MMPs do not participate in hydrogel degradation, we limited the quantification of MMP to its active form. Since MMPs have a relatively short half-life, the active MMP-2 measured was assumed to represent the MMP-2 produced within the previous 24 h. In the constructs, the amount of MMP-2 was determined at biweekly intervals (Fig. 4A). The MMP-2 levels in the constructs were dependent (p<0.001) on time, resulting in an increase over time, but was not dependent on loading. MMP-2 was collected at each media exchange and combined to estimate an amount of MMP-2 released each week and then normalized to determine an average release per day (Fig. 4B). MMP-2 in the media was dependent on loading (p=0.017), but not on time. Pairwise comparisons revealed that loading led to higher (p<0.05) MMP-2 levels at week 4 (i.e., corresponding to the time period between days 21 and 28) and week 6 (i.e., corresponding to the time period between days 35 and 43). MMP-2 levels in the construct and in the medium were combined to estimate an average flux of MMP-2 production at the cell surface and as a function of time (Fig. 4C). The flux was approximated as a step-wise function, which assumed average production rates per cell and were constant between biweekly experimental measurements. The flux was then used as an input in the computational model.

Fig. 4.

MMP-2 production and spatiotemporal changes in MMP concentration and hydrogel crosslink density for cell-laden hydrogel constructs cultured in free swelling and loading environments. A-B) Active MMP-2 levels measured in the construct (A) and in the media (B) in free swelling (white bars) and loading (gray bars). Data are presented as mean (n=2-3) with standard deviation as error bars. P-values above a column indicate difference from day 1 (*p<0.001). C) MMP-2 flux at the cell surface estimated for the free swelling (short-long dashed line) and loading (dotted line). D-E) Simulation results for MMP-2 concentration and normalized crosslink density as a function of distance from the surface of the cell with culture time for free swelling (D) and loading (E). The point at which the crosslink density reaches reverse gelation (ρ_c/ρ_o) is shown as red dotted line. The distance from the cell is normalized to a length of L_c, which is defined as the distance between two cells for a homogeneous cell distribution. F-G) Normalized crosslink density between two cells in the background that are separated by a distance of 1.2L_c (F) and between two cells in clusters that are separated by a distance of 0.6L_c (G). The contribution to crosslink degradation from one cell located at (0,0) is shown with a solid line on the plots in F-G. The contribution from a second cell at (1.2,0) for the background and (0.6,0) for the cluster is shown with a dotted line on the plots in F-G. The reverse gelation point is shown in red.

Spatiotemporal Changes in MMP and Crosslink Density

Using the experimentally determined MMP production rate and the model parameters reported in Table 1, simulations were run to determine MMP concentration and hydrogel crosslink density as a function of distance from the cell boundary and of time for both culture conditions. These simulations were run based on a single cell encapsulated in a hydrogel. Free swelling is shown in Fig. 4D and dynamic loading is shown in Fig. 4E. The distance from the cell is normalized to L_c, which is defined as the distance between two cells based on a homogeneous cell distribution. The results from the simulations for a single cell system show several key findings. MMP concentration is initially highest at the cell boundary and decreases as the enzyme diffuses from the cell surface into the hydrogel. The MMP profile is similar between free swelling and loading up to day 15. At day 19, the higher MMP production rates under loading lead to an overall higher enzyme concentration both at the cell surface and throughout the hydrogel when compared to free swelling.

Results from simulations of crosslink density normalized to the initial crosslink density for a single cell system show several key findings. At day 1, the lower crosslink density near the cell surface arises from the reduction in crosslink density that occurs during cell encapsulation. Over time, a region form near the cell surface that is devoid of hydrogel and is obvious at day 9. In this region, the hydrogel has undergone reverse gelation. Over time, this region grows. For example under free swelling conditions, the normalized distance is 0.11 at day 9 and increases to 0.58 by day 19. At the same time and farther away from the cell surface, the crosslink density also decreases over time. For example, at a normalized distance of one, the normalized crosslink density decreased from one at day 1 to 0.37 at day 19 under free swelling. After day 15, MMP levels increase under loading and differences in the spatiotemporal pattern of crosslink density begin to emerge. For example at day 21, the distance from the cell surface that is devoid of hydrogel is 0.74 under free swelling and 0.84 under loading. Moreover, at day 21 and at a normalized distance of one, the normalized crosslink density is 0.23 under free swelling and 0.13 under loading. By day 29, the hydrogel has reached reverse gelation across the entire normalized distance.

To illustrate the differences in crosslink density between two cells in the background and two cells in a cluster, the simulation results from above were re-plotted but as a function of the true average distance between two cells in the background and in the clusters for the free swelling constructs. For the background, cells are estimated to be separated on average by a distance of 1.2L_c (Fig. 4F). On the contrary, cells in clusters are estimated to be on average separated by a distance of 0.6L_c (Fig. 4G). Plots are shown for days 1, 7, 15, and day 19. The crosslinks in the clusters reached reverse gelation by day 15, while the crosslinks in the background reached reverse gelation by day 19.

Spatial Distribution of the Hydrogel

Hydrogel degradation was spatially characterized in experiments by immunohistochemistry using an antibody against PEG (Fig. 5A) and in 3D by simulations (Fig. 5B,C). PEG staining was initially prominent throughout the entire section at day 1 and still present throughout the construct at day 15. Regions from an image taken at day 15 highlight differences in the distribution of PEG in the background and in clusters, where PEG was less prominent in the clusters. At days 29 and 43, only punctate staining for PEG was observed indicating there was no longer a connected hydrogel matrix. Simulations were run for a multiple cell system. Results for crosslink density are shown by RVEs for regions of background (Fig. 5B) and clusters (Fig. 5C) up to the hydrogel reaching reverse gelation. The RVEs demonstrate overall similar degradation patterns between free swelling and dynamic loading in the clusters due to the similarities in MMP activity between the two environments up to day 15. Cluster regions were fully degraded by day 15. Background regions were fully degraded by day 19 under both environments, which is consistent with the experimental observations.

Fig. 5.

Degradation of cell-laden hydrogel constructs cultured in free swelling and dynamic loading environments. A) Representative confocal microscopy images of sections stained for PEG (green) by immunohistochemistry after days 1, 15, 29, and 43 for the free swelling and loading. Nuclei are stained with DAPI (blue). Scale bar = 100 µm. Representative images at day 15 demonstrate the different distributions of PEG in a cluster and background. Scale bar = 20 µm. B-C) Microscale RVEs show the spatial distribution of crosslinks for background regions (B) and cluster regions (C) for free swelling and loading up to the reverse gelation point.

Extracellular Matrix Production

The constructs were analyzed for biochemical content retained in the hydrogel and released to the media under free swelling and loading (Fig. 6). Cell number based on the DNA content per construct was not dependent on time or loading (Fig. 6A). The sGAG content retained in the construct and normalized to cell number increased (p=0.007) with time and was lower (p=0.010) under loading (Fig. 6B). However, the total amount of sGAGs produced by the cells was not affected by loading, but increased with time (p<0.001) (Fig. 6C). The percent of sGAGs released to the media increased (p<0.001) with time under loading, but was not affected by time in the free swelling constructs (Fig. 6D). Over 43 days, the constructs had more (p=0.008) sGAGs released to the media under loading than in free swelling.

Fig. 6.

Analysis of chondrocyte-laden degradable hydrogels cultured in free swelling (white bars) or loading (gray bars) environments by cell number (A), sGAG content normalized to cell number retained per construct (B), total sGAGs produced (C), percent of GAGs released to media (D), total collagen content normalized to cell number retained per construct (E), total collagen produced (F), percent of collagen released to media (G), ECM production rates per cell surface area for the free swelling condition (short-long dashed line) and the loading condition (dotted line) (H). Data are presented as mean with standard deviation (n=2-3) as error bars. P-values shown vertically above a column indicate difference from day 1. An * above a column indicates a difference of p<0.001 from day 1. The # in E-G indicates reduced sample size for this condition and time.

The amount of collagen produced and retained in the constructs was also measured (Fig. 6E–G). There was minimal detectable collagen at days 1 and 15. The total collagen content per cell in the constructs increased (p<0.007) and was higher (p=0.014) under free swelling (Fig. 6E). However, the total amount of collagen produced by the cells increased (p<0.001) with time (Fig. 6F). The percent of total collagen released into the medium was greater (p<0.026) under loading, but was not affected by time (Fig. 6G). The sGAGs and collagen retained in each construct was combined to estimate an ECM production flux per day at the cell surface (Fig. 6H). Since only the ECM retained in the hydrogel contributes to the deposited ECM, this flux was used and approximated as a step-wise function for input in the computational model.

Spatial Distribution of ECM

Spatial organization of the deposited ECM was visualized by immunohistochemical staining for collagen II and aggrecan, the primary cartilage ECM molecules, and for total ECM in simulations (Fig. 7). Collagen II (Fig. 7A) and aggrecan (Fig. 7B) were detected as early as day 1 and were present regardless of loading throughout the culture period. The ECM molecules were largely located in the pericellular space initially and at day 15. By day 29, the ECM was present throughout the hydrogels in both conditions and was maintained at day 43. Simulations were run for a multiple cell system. Results for ECM deposition in RVEs are shown for background (Fig. 7C) and clusters (Fig. 7D) and correlates to the same cell distributions presented in Fig. 5B–C. Several key findings emerge. In both background and clusters, the ECM is localized around the cells regardless of loading, which is consistent with experimental observations. By day 15, ECM developed throughout the clusters, but was remained restricted to the pericellular regions in the background. By day 29 in the experimental results and simulations, greater ECM growth is observed in the clusters under free swelling when compared to loading, whereas ECM growth in the background appears similar under both environments.

Fig. 7.

ECM Distribution and growth in cell-laden hydrogel construct cultured in free swelling or loading environments. A-B) Representative confocal microscopy images for collagen II (green) (A) and aggrecan (red) (B) by immunohistochemistry after days 1, 15, 29, and 43 for the free swelling and loading. Nuclei are stained with DAPI (blue). Scale bar = 100 µm. C-D) Microscale RVEs showing the spatial distribution of ECM for background regions (C) and cluster regions (D) for free swelling and loading at days 1, 4, 9, 15, 21, and 29.

Evolution of Construct Mechanical Properties

The construct mechanical properties describes the combined extent of hydrogel degradation and deposited ECM (Fig. 8). The compressive modulus is shown for free swelling (Fig. 8A) and loading (Fig. 8B) from experimental measurements and simulations, which initially was 42.5(1.6) kPa. Experimental measurements are from discrete time points, while results from the simulation capture the continuous change in modulus over the course of the 43 days. Under free swelling, the modulus reached a minimum at day 12, which then was followed by an increase in modulus due to the contribution of the ECM. Experimental measurements determined a modulus of 10.9(10.8) kPa at day 15, which recovered to 107(41.9) kPa by day 43. Under loading, the modulus reached a minimum at day 14, which then recovered to a value that was similar to the starting modulus. Experimental measurements determined a modulus of 2.5(0.3) kPa at day 15, which recovered to 26.3(34.1) kPa at day 43. Results from simulations revealed several key findings. While the modulus started at the same point for both environments, the drop in modulus was steeper under loading, but took longer to reach its minimum. By day 43, the modulus recovered to half the modulus under free swelling. A two-way ANOVA revealed that the modulus of the constructs was not significantly affected by time or the loading environment. It is worth noting that the modulus is highly variable at day 29 under free swelling. This variability is attributed to the variability as to when individual hydrogel constructs undergo reverse gelation, which will depend on the relative rates of MMP synthesis and ECM production. If this time point is removed, a two-way ANOVA indicates a significant interaction between time and loading and follow-up analyses indicated that time was a factor for free swelling (p=0.020), but not for loading.

Fig. 8.

Temporal evolution of hydrogel construct mechanical properties. A-B) Compressive modulus in free swelling (A) and loading (B) environments. Experimental data are shown as square markers with the mean shown as a red line. Simulation data of the evolution of construct modulus with time is presented as the dotted line. Two-way ANOVA results shown in 8B correspond to the data for both free swelling and loading conditions. C-E) Scatter plots of compressive modulus plotted against sGAGs per construct (C), total collagen per construct (D), and total ECM per construct (E) for free swelling (circles) and loading (squares). Linear correlation of all data points is shown with a dashed line. Extent of correlation is indicated by the Pearson coefficient.

To investigate the contribution of the different ECM components (sGAG, total collagen or both) to the construct modulus, correlation plots were generated that included each individual construct from this study (Fig. 8D-F). Time points were limited to day 15 and thereafter, when cells had deposited measurable ECM and substantial hydrogel degradation had occurred. The Pearson coefficients ranged from 0.81-0.86 for sGAGs, collagen and when combined. These results further demonstrate that the increase in modulus observed under the free swelling is directly correlated to increased ECM deposition.

Discussion

In this study, we demonstrate macroscopic neocartilage formation by chondrocytes encapsulated in a MMP-sensitive hydrogel and cultured with or without intermittent dynamic compressive loading. A combined experimental and computational approach was taken to investigate the spatiotemporal behavior of hydrogel degradation concomitant with neocartilage growth. Simulations identified that cell clusters facilitated rapid hydrogel degradation and led to regions of ECM growth. While loading had modest effects on the accumulation and/or release of MMPs and ECM, loading slowed ECM accumulation within the hydrogel which ultimately influenced the mechanical properties. Overall, the combined experimental and computational approach provided novel insights into how differential changes in cellular activity resulting from the culture environment contribute to the evolution of neocartilage formation in MMP-sensitive hydrogels.

The MMP-sensitive hydrogels underwent complete degradation regardless of the culture environment over six weeks. Active MMPs were confirmed in the hydrogels and in the culture medium, indicating that MMPs were not only produced by the cells, but also diffused through the hydrogels. During the first two weeks, the hydrogels were largely intact evident by positive staining for PEG. The drop in construct modulus during the early stages of culture, regardless of culture environment, indicates that while still present, the bulk of the hydrogel (i.e., background) had substantially degraded. The spatiotemporal patterns of crosslink density illustrate that the hydrogel had reached reverse gelation in the region immediately around the cell by day 15. At the same time, the crosslink density farther away from the cell had decreased by ~50% of the initial bulk crosslink density. This degradation behavior is indicative of a combination of diffusion-dominated and reaction-dominated mechanisms.¹⁷ Between weeks two and four, the bulk hydrogel underwent reverse gelation, which was evident by the loss of connected PEG staining and which was also captured in the simulations. By day 29, the constructs were primarily neocartilage, which was maintained and/or continued to develop through day 43.

The experimental and computational results showed that the transition from hydrogel to neotissue caused the compressive modulus to drop around days 12 to 14, which was recovered as the deposited ECM grew over time. The drop in modulus is attributed to degradation of the bulk hydrogel while the inflection point at which the modulus begins to increase is attributed to ECM deposition within the clusters. ECM deposition is limited to the regions where the hydrogel has reached reverse gelation due to the much small mesh size of the hydrogel that prevents ECM assembly and deposition.^40,41 The magnitude of the drop can provide insights into the ability of ECM to develop within the clusters. Simulations indicated that crosslinks within clusters reached reverse gelation within the clusters by day 15 regardless of environment. The modulus drop, however, was more severe under loading. Since MMP levels were similar in both environments during the first two weeks, this result is attributed to lower ECM accumulation within the clusters under loading. Although the clusters comprise less than 5% by volume of the hydrogel construct, the modulus of the ECM is estimated to be greater than that of the hydrogel.¹⁹ These results indicate that a faster rate of ECM growth within clusters can minimize loss in mechanical properties during the hydrogel to neotissue transition.

With continued culturing, differences emerged in the MMP levels and ECM production rates under loading, which contributed to faster hydrogel degradation, slower ECM growth, and low mechanical properties. Load-induced increases in chondrocyte MMP production have been previously reported.^13,14 Interestingly, this study identified differences in MMP only after ECM had deposited. Thus, it is possible that this loading regime used did not have a direct effect on MMPs, but rather an indirect effect due to differences in ECM accumulation. Studies have reported that loading can either increase or decrease chondrocyte ECM synthesis depending on the specific loading regime and the 3D construct material.^12,14,43 Although loading reduced ECM accumulation, the neocartilage that formed was comprised of collagen II and aggrecan, the primary cartilage ECM molecules. This indicates that loading affected the magnitude of accumulated ECM, but not its biochemical quality. This observation could be due to load-induced effects on cellular activity or to load-induced transport of ECM precursors. The later could affect the ability of ECM precursors to assemble and form the large ECM macromolecules.

Dynamic compressive loading will induce fluid flow during each loading cycle, which can produce fluid-induced shear stresses on encapsulated cells and enhance transport of cell-secreted molecules by advection. However, the loading regime used in this study applies relatively low strains at 5%, which is under unconfined compression and limited to one hour per day with the remaining 23 hours each day under static culture. In a recent study, Aziz et al.⁴⁴ estimated fluid flows in similar PEG hydrogels under unconfined dynamic compressive strains using finite element modeling and reported fluid velocities ranging from 1-10 nm/s during compression. The low fluid velocities are attributed to the low permeability of PEG hydrogels.⁴⁵ It therefore seems unlikely that load-induced fluid velocities would have impacted transport of MMP molecules or ECM precursors. In further support, the Peclet number (P_e) was estimated, which describes the relative contribution of advective to diffusive transport and is defined by ratio of the product of fluid velocity and characteristic length to diffusivity. Assuming the most restrictive conditions, which include initial properties of the hydrogel (i.e., mesh size estimated⁴⁶ at 60 nm), the upper limit of the previously reported fluid velocities, and characteristic length of the gel at half its height) and the size of the diffusing species (e.g., 6.5 nm for enzyme, 10 nm diameter of procollagen molecules,⁴⁷ and 9 nm for a aggrecan monomer⁴⁸), the P_e number is less than one suggesting that diffusion plays a greater role during dynamic loading. Moreover, the computational model does not account for fluid flow and was able to predict ECM growth and modulus of the experimental data under dynamic loading. We therefore surmise that load-induced effects are due to changes in cellular activity rather than on transport effects.

Because load-induced ECM transport is likely negligible, an alternative hypothesis is load-induced changes in ECM accumulation. While differences in total ECM synthesis rates were similar between the two environments, the amount of ECM retained in the hydrogels was higher under free swelling, suggesting that loading negatively impacted ECM assembly. ECM assembly requires a critical concentration of precursors where for example, aggrecan monomers must assemble with hyaluronic acid to form aggrecan aggregates, while procollagen molecules must assemble to form collagen fibers. Thus, a concentration below the threshold for assembly could result in a greater release of ECM precursors. It is possible that loading impacted synthesis rates of the molecules required for assembly, such as hyaluronic acid, collagen XI, decorin, etc., but which were not investigated. It is also possible that load-induced matrix degrading enzymes, such as MMPs and/or aggrecanases, led to greater degradation of the newly deposited neotissue under loading; the release of ECM measured in the culture medium could be degraded ECM or ECM precursors. Further study is needed to identify load-induced effects on chondrocytes and on ECM assembly.

It is important to highlight several limitations of the model and the assumptions made and experimental limitations. First, the temporal profile of active MMPs used in the model was estimated from biweekly measurements in the hydrogel and weekly measurements in the culture medium. Thus, the temporal profiles represent assumed averages of MMP synthesis rates. Second, the model used experimental measurements of MMP, which were limited to MMP-2. This MMP was chosen because the peptide sequence was identified for its susceptibility to MMP-2.^49,50 However, this peptide crosslinker has been shown to be degraded by other MMPs (e.g., MMPs-1, −3, −7, −9),^49,51 which were not measured. Third, the interpretation of the experimentally measured MMPs is further complicated by the fact that MMPs have a short half-life on the order of hours.^52,53 The presence of matrix molecules, such as collagen I, fibronectin, and gelatin, can extend the active period of MMPs.⁵³ Thus for the purposes of this study, the active MMP-2 measured in the media and the hydrogels was assumed to capture the MMP-2 produced in the previous 24 h. However, additional studies are needed to confirm the half-life of MMP-2 in our system. Fourth, the model does not account for diffusion of enzyme through newly deposited ECM. Studies have estimated diffusivity of different solutes in cartilage and reported an inverse correlation with the Young’s modulus of the cartilage.⁵⁴ The nascent ECM formed in this study was estimated to have a modulus of 200 kPa at day 29. At this modulus, the difference in diffusivity between water and tissue is approximated to be 60%.⁵⁴ To overcome these above highlighted limitations and account for true levels of active MMPs, the model was fit to the experimental data by varying the deactivation constant, k_d for MMP. The value of k_d affects the active MMP concentration after it is produced by the cell and affects its diffusion through the hydrogel. Thus, the value of k_d used in the model does not necessarily represent the true deactivation constant of MMP-2, but rather is used as a parameter that can account for subtle differences in the true MMP concentration in time and space that is difficult to measure experimentally and to capture in the model. One limitation is that k_d was assumed to be constant. Despite this limitation, the model was able to match the mechanical properties of the construct and the spatial elaboration of ECM as a function of time with reasonable fidelity. There also several experimental limitations which are important to note. Our study is limited by a single donor and a relative small sample number, which reduces the statistical power of the study. The transition from hydrogel to ECM depends on the characteristics of the donor (i.e., enzyme and ECM synthesis) for a given hydrogel. Our previous study showed that model captured differences between donors from two different age groups¹⁹ and we show here that the model captures differences between two different culture environments for the same donor. Our growing body of work demonstrates that the model is able to describe experimentally observed tissue growth concomitant with hydrogel degradation under different conditions. This study was limited to cartilage-specific proteins and thus other ECM proteins, such as collagen I, might differ between clusters and the background and should be explored in future studies.

Conclusions

The experimental findings from this study demonstrate that this MMP-sensitive biomimetic hydrogel supports neocartilage growth under free swelling and dynamic loading. Dynamic loading had small, but significant effects on ECM accumulation and MMP synthesis rates that contributed to differences in the final construct properties after six weeks. The computational model provided new insights into the coupled behavior of hydrogel degradation and ECM deposition in MMP-sensitive PEG hydrogels and captured differences observed experimentally between the two environments. Importantly, the model identified that cell clusters supported ECM growth at a faster rate due to the accelerated hydrogel degradation in these regions under both environments. When coupled with faster rates of ECM accumulation, the mechanical properties recovered faster and then continued to improve, as was the case for free swelling. Overall, the model allowed us to decouple hydrogel degradation from ECM growth in time and space and observe their differential rates in clusters and in the background regions. The model points to the importance of clusters in form regions of connected ECM prior to the complete degradation of the hydrogel in the background.