Mechanics of 3D Cell-Hydrogel Interactions: Experiments, Models, and Mechanisms.

Hydrogels are highly water-swollen molecular networks that are ideal platforms to create tissue mimetics owing to their vast and tunable properties. As such, hydrogels are promising cell-delivery vehicles for applications in tissue engineering and have also emerged as an important base for ex vivo models to study healthy and pathophysiological events in a carefully controlled three-dimensional environment. Cells are readily encapsulated in hydrogels resulting in a plethora of biochemical and mechanical communication mechanisms, which recapitulates the natural cell and extracellular matrix interaction in tissues. These interactions are complex, with multiple events that are invariably coupled and spanning multiple length and time scales. To study and identify the underlying mechanisms involved, an integrated experimental and computational approach is ideally needed. This review discusses the state of our knowledge on cell-hydrogel interactions, with a focus on mechanics and transport, and in this context, highlights recent advancements in experiments, mathematical and computational modeling. The review begins with a background on the thermodynamics and physics fundamentals that govern hydrogel mechanics and transport. The review focuses on two main classes of hydrogels, described as semiflexible polymer networks that represent physically cross-linked fibrous hydrogels and flexible polymer networks representing the chemically cross-linked synthetic and natural hydrogels. In this review, we highlight five main cell-hydrogel interactions that involve key cellular functions related to communication, mechanosensing, migration, growth, and tissue deposition and elaboration. For each of these cellular functions, recent experiments and the most up to date modeling strategies are discussed and then followed by a summary of how to tune hydrogel properties to achieve a desired functional cellular outcome. We conclude with a summary linking these advancements and make the case for the need to integrate experiments and modeling to advance our fundamental understanding of cell-matrix interactions that will ultimately help identify new therapeutic approaches and enable successful tissue engineering.

Thermosensitive P(AAc-co-NIPAm) Hydrogels Display Enhanced Toughness and Self-Healing via Ion-Ligand Interactions.

Hydrogels containing thermosensitive polymers such as poly(N-isopropylacrylamide) (P(NIPAm)) may contract during heating and show great promise in fields ranging from soft robotics to thermosensitive biosensors. However, these gels often exhibit low stiffness, tensile strength, and mechanical toughness, limiting their applicability. Through copolymerization of P(NIPAm) with poly(Acrylic acid) (P(AAc)) and introduction of ferric ions (Fe3+ ) that coordinate with functional groups along the P(AAc) chains, here a thermoresponsive hydrogel with enhanced mechanical extensibility, strength, and toughness is introduced. Using both experimentation and constitutive modeling, it is found that increasing the ratio of m(AAc):m(NIPAm) in the prepolymer decreases strength and toughness but improves extensibility. In contrast, increasing Fe3+ concentration generally improves strength and toughness with little decrease in extensibility. Due to reversible coordination of the Fe3+ bonds, these gels display excellent recovery of mechanical strength during cyclic loading and self-healing ability. While thermosensitive contraction imbued by the underlying P(NIPAm) decreases slightly with increased Fe3+ concentration, the temperature transition range is widened and shifted upward toward that of human body temperature (between 30 and 40 °C), perhaps rendering these gels suitable as in vivo biosensors. Finally, these gels display excellent adsorptive properties with a variety of materials, rendering them possible candidates in adhesive applications.

Dynamic competition of inflation and delamination in the finite deformation of thin membranes.

The mechanics of blister delamination and growth plays a major role in a diversity of areas including medicine (skin pathology and mechanics of cell membranes), materials (adhesive and fracture) or soft robotics (actuation and morphing). The behavior of a blister in this context is typically difficult to grasp as it arises from the interplay of two highly nonlinear and time-dependent processes: membrane attachment and decohesion from a substrate. In the present work, we device a simplified approach, based on experimental systems, to predict the deformation path of a blister under various conditions. For this, we consider the problem of a growing blister made of a rubber-like membrane adhered on a rigid substrate, and develop a theoretical and experimental framework to study its stability and growth. We start by constructing a theoretical model of viscoelastic blister growth which we later validate with an experimental setup. We show that blister growth is controlled by the competition between two instabilities: one inherent to the rubber, and a second one pertaining to the adhesion with the substrate. Using these concepts, we show that a "targeted" stable blister shape can be achieved by controlling two parameters: the thickness of the film and the inflation rate.

Heterogeneity is key to hydrogel-based cartilage tissue regeneration.

Degradable hydrogels have been developed to provide initial mechanical support to encapsulated cells while facilitating the growth of neo-tissues. When cells are encapsulated within degradable hydrogels, the process of neo-tissue growth is complicated by the coupled phenomena of transport of large extracellular matrix macromolecules and the rate of hydrogel degradation. If hydrogel degradation is too slow, neo-tissue growth is hindered, whereas if it is too fast, complete loss of mechanical integrity can occur. Therefore, there is a need for effective modelling techniques to predict hydrogel designs based on the growth parameters of the neo-tissue. In this article, hydrolytically degradable hydrogels are investigated due to their promise in tissue engineering. A key output of the model focuses on the ability of the construct to maintain overall structural integrity as the construct transitions from a pure hydrogel to engineered neo-tissue. We show that heterogeneity in cross-link density and cell distribution is the key to this successful transition and ultimately to achieve tissue growth. Specifically, we find that optimally large regions of weak cross-linking around cells in the hydrogel and well-connected and dense cell clusters create the optimum conditions needed for neo-tissue growth while maintaining structural integrity. Experimental observations using cartilage cells encapsulated in a hydrolytically degradable hydrogel are compared with model predictions to show the potential of the proposed model.

Locomotion of an untethered, worm-inspired soft robot driven by a shape-memory alloy skeleton.

Soft, worm-like robots show promise in complex and constrained environments due to their robust, yet simple movement patterns. Although many such robots have been developed, they either rely on tethered power supplies and complex designs or cannot move external loads. To address these issues, we here introduce a novel, maggot-inspired, magnetically driven "mag-bot" that utilizes shape memory alloy-induced, thermoresponsive actuation and surface pattern-induced anisotropic friction to achieve locomotion inspired by fly larvae. This simple, untethered design can carry cargo that weighs up to three times its own weight with only a 17% reduction in speed over unloaded conditions thereby demonstrating, for the first time, how soft, untethered robots may be used to carry loads in controlled environments. Given their small scale and low cost, we expect that these mag-bots may be used in remote, confined spaces for small objects handling or as components in more complex designs.

Spatiotemporal neocartilage growth in matrix-metalloproteinase-sensitive poly(ethylene glycol) hydrogels under dynamic compressive loading: an experimental and computational approach.

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.

Interplay of elastic instabilities and viscoelasticity in the finite deformation of thin membranes.

Pneumatic structures and actuators are found in a variety of natural and engineered systems such as dielectric actuators, soft robots, plants and fungi cells, or even the vocal sac of frogs. These structures are often subjected to mechanical instabilities arising from the thinning of their cross section and that may be harvested to perform mechanical work at a low energetic cost. While most of our understanding of this unstable behavior is for purely elastic membranes, real materials including lipid bilayers, elastomers, and connective tissues typically display a time-dependent viscoelastic response. This paper thus explores the role of viscous effects on the nature of this elastic instability when such membranes are dynamically inflated. For this, we first introduce an extension of the transient network theory to describe the finite strain viscoelastic response of membranes, enabling an elegant formulation while keeping a close connection with the dynamics of the underlying polymer network. We then combine experiments and simulations to analyze the viscoelastic behavior of an inflated blister made of a commercial adhesive tape (VHB 4905). Our results show that the viscous component induces a rich spectrum of behaviors bounded by two well-known elastic solutions corresponding to very high and very low inflation rates. We also show that membrane relaxation may induce unwanted buckling when it is subjected to cyclic inflations at certain frequencies. These results have clear implications for the inflation and mechanical work performed by time-dependent pneumatic structures and instability-based actuators.

* Understanding the Spatiotemporal Degradation Behavior of Aggrecanase-Sensitive Poly(ethylene glycol) Hydrogels for Use in Cartilage Tissue Engineering.

Enzyme-sensitive hydrogels are promising cell delivery vehicles for cartilage tissue engineering. However, a better understanding of their spatiotemporal degradation behavior and its impact on tissue growth is needed. The goal of this study was to combine experimental and computational approaches to provide new insights into spatiotemporal changes in hydrogel crosslink density and extracellular matrix (ECM) growth and how these changes influence the evolving macroscopic properties as a function of time. Hydrogels were designed from aggrecanase-sensitive peptide crosslinks using a simple and robust thiol-norbornene photoclick reaction. To study the influence of variations in cellular activity of different donors, chondrocytes were isolated from either juvenile or adult bovine donors. Initial studies were performed to validate and calibrate the model against experiments. Through this process, two key features were identified. These included spatial variations in the hydrogel crosslink density in the immediate vicinity of the cell and the presence of cell clustering within the construct. When these spatial heterogeneities were incorporated into the computational model along with model inputs of initial hydrogel properties and cellular activity (i.e., enzyme and ECM production rates), the model was able to capture the spatial and temporal evolution of ECM growth that was observed experimentally for both donors. In this study, the juvenile chondrocytes produced an interconnected matrix within the cell clusters leading to overall improved ECM growth, while the adult chondrocytes resulted in poor ECM growth. Overall, the computational model was able to capture the spatiotemporal ECM growth of two different donors and provided new insights into the importance of spatial heterogeneities in facilitating ECM growth. Our long-term goal is to use this model to predict optimal hydrogel designs for a wide range of donors and improve cartilage tissue engineering.

A mixture approach to investigate interstitial growth in engineering scaffolds.

Controlling biological growth within a cell-laden polymeric scaffold is a critical challenge in the tissue engineering community. Indeed, construct growth must often be balanced with scaffold degradation and is often coupled to varying degrees of deformation that originate from swelling, external forces and the effects of confinement. These factors have been shown to affect growth in many ways, but to date, our understanding is mostly qualitative. While cell sensing, molecular transport and scaffold/tissue interactions are believed to be important players, it will be critical to quantify, predict and control these effects in order to eventually optimize tissue growth in the laboratory. The aim of this paper was thus to provide a theoretical framework to better understand how the scaffold-mediated mechanisms of transport, deposition (and possibly degradation) and elasticity affect the overall growth of a tissue subjected to finite deformations. We propose a formulation in which the macroscopic evolutions in tissue size, density as well as the appearance of residual stresses can be directly related to changes in internal composition by considering three fundamental principles: mechanical equilibrium, chemical equilibrium and molecular incompressibility. The resulting model allows us to pay particular attention to features that are critical to the interaction between growth and deformation: osmotic pressure and swelling, the strain mismatch between old and newly deposited material as well as the mechano-sensitive cell-mediated production. We show that all of these phenomena may indeed strongly affect the overall growth of a construct under finite deformations.

Tuning Reaction and Diffusion Mediated Degradation of Enzyme-Sensitive Hydrogels.

Enzyme-sensitive hydrogels are promising for cell encapsulation and tissue engineering, but result in complex spatiotemporal degradation behavior that is characteristic of reaction-diffusion mechanisms. An experimental and theoretical approach is presented to identify dimensionless quantities that serve as a design tool for engineering enzyme-sensitive hydrogels with controlled degradation patterns by tuning the initial hydrogel properties and enzyme kinetics.

Triphasic mixture model of cell-mediated enzymatic degradation of hydrogels.

One critical component of engineering living tissue equivalents is the design scaffolds (often made of hydrogels) whose degradation kinetics can match that of matrix production by cells. However, cell-mediated enzymatic degradation of a hydrogel is a highly complex and nonlinear process that is challenging to comprehend based solely on experimental observations. To address this issue, this study presents a triphasic mixture model of the enzyme-hydrogel system, which consists of a solid polymer network, water and enzyme. On the basis mixture theory, the rubber elasticity theory and the Michaelis-Menton kinetics for degradation, the model naturally incorporates a strong coupling between gel mechanical properties, the kinetics of degradation and the transport of enzyme through the gel. The model is then used to investigate the particular problem of a single spherical enzyme-producing cell, embedded in a spherical hydrogel domain, for which the governing equations can be cast within the cento-symmetric assumptions. The governing equations are subsequently solved using an implicit nonlinear finite element procedure to obtain the evolution of enzyme concentration and gel degradation through time and space. The model shows that two regimes of degradation behaviour exist, whereby degradation is dominated either by diffusion or dominated by reaction kinetics. Depending on the enzyme properties and the initial hydrogel design, the temporal and spatial changes in gel cross-linking are dramatically impacted, a feature that is likely to strongly affect new tissue development.