Independently Tunable Viscoelasticity in Hydrogels as a Mechanical Cue for Tissue Engineering

Abstract

The mechanical properties of the extracellular matrix (ECM) play a critical role in regulating cellular behavior and fate. In the design and application of tissue engineering materials, previous studies have primarily focused on the role of material stiffness (elastic modulus) in modulating cellular events. However, biological tissues and the ECM exhibit more complex mechanical behaviors, such as viscoelasticity, highlighting the importance of considering viscoelasticity as a design parameter for biomaterials. Current biomimetic strategies might place less emphasis on the dynamic mechanical microenvironment of viscoelastic ECMs. Emerging evidence suggests that independently tuning the viscoelasticity of matrices can influence cellular biological processes and enhance tissue regeneration outcomes. This review highlights the emerging focus on independently tunable viscoelastic hydrogels and their potential applications in tissue engineering. In this article, we review the design of hydrogels with adjustable viscoelasticity aimed at guiding cellular and tissue behavior, advancing the development of in vitro cell culture models and in vivo regenerative therapies. This review introduces the concept of viscoelasticity, elaborates on the viscoelastic properties of biological tissues, and summarizes commonly used evaluation metrics and characterization techniques for viscoelasticity. Next, it highlights the strategies for constructing hydrogels with tunable viscoelasticity and discusses the regulatory effects of viscoelasticity on cellular behaviors, along with the associated mechanobiological mechanisms and signaling pathways. Finally, the review provides an overview of the current applications of viscoelastic hydrogels in tissue engineering and offers perspectives on future research directions.

Impact Statement

Viscoelasticity is an essential but often overlooked mechanical property that governs cellular behaviors and tissue remodeling. Recent advances reveal that cells actively sense and respond to viscoelastic cues, influencing adhesion, migration, differentiation, and proliferation. By examining emerging hydrogel designs with independently tunable viscoelasticity, we highlight their potential to enhance cell-instructive biomaterials, improve organoid models, and enable personalized regenerative therapies. This review provides a comprehensive perspective on viscoelasticity-driven cell regulation and offers insights into future directions for designing biomaterials that better mimic native tissue mechanics.

Keywords

viscoelasticity hydrogels mechanotransduction tissue engineering regenerative medicine

Introduction

Mechanical properties fundamentally determine the suitability of scaffolds for biomedical applications. The elastic modulus is commonly used to characterize material stiffness.^1–4 However, biological tissues exhibit viscoelasticity rather than pure elasticity.^5–7 The extracellular matrix (ECM) exhibits viscoelastic behavior across multiple length scales, from molecular-level rearrangements to tissue-scale deformations.^8,9 Increasing evidence shows that cells sense and respond to ECM viscoelasticity. Controlling matrix viscoelasticity alone offers a method of pure mechanical regulation without the involvement of growth factors, which can serve as a reference for the differentiation of specific cell lineages in tissue engineering.^10,11 This challenges the traditional viewpoint of cell–matrix mechanotransduction that is centered on stiffness.^11–13 In addition, matrix viscoelasticity plays a crucial role in tissue morphogenesis, providing a potential strategy for guiding tissue development in regenerative medicine.¹⁴

Elasticity and stiffness both refer to the ability of materials to resist elastic deformation.¹⁵ Most materials exhibit approximate elastic behavior under specific conditions but may display viscoelasticity or other complex mechanical behavior under different conditions.¹⁶ Viscoelastic materials display both time-dependent elastic deformation and viscous flow, characterized by phenomena such as stress relaxation, creep, and hysteresis (Fig. 1A).^45,46

FIG. 1.

Mechanical behavior and characterization of materials and biological tissues. (A) Distinction between the mechanical behavior of elastic and viscoelastic materials. Elastic materials exhibit an instantaneous linear stress–strain relationship and recover fully upon removal of the external force, following Hooke’s law. Viscoelastic materials demonstrate time-dependent stress relaxation and creep behavior, resulting in a hysteresis loop in stress–strain response, indicative of energy dissipation during cyclic loading. (B) Viscoelastic properties of biological tissues and engineered hydrogels. The loss tangent versus storage modulus at 1 Hz is plotted for various biological tissues (pink and green symbols) and hydrogels (blue symbols). Biological tissues exhibit a wide range of viscoelastic properties. Hydrogels, such as fibrin and GelMA, mimic the viscoelastic microenvironment of most tissues, making them ideal candidates for tissue engineering. The values of storage modulus and loss tangent were extracted from published studies,^17–44 and for consistency, we used values measured at 1 Hz. The loss tangent was calculated as tan δ = G″/G′, where G′ and G″ are the storage and loss moduli, respectively.

From macroscopic tissues and organs to microscopic ECMs, viscoelasticity is a common property.^12,47,48 For instance, the brain,¹⁷ liver,¹⁸ muscle,¹⁹ and adipose tissue²⁰ exhibit higher viscoelasticity, while bone,²¹ ligament,²² tendon,²³ and skin²⁴ have lower viscoelasticity. The viscoelasticity of cartilage^25,26 and vocal cord²⁷ falls in between (Fig. 1B). At the microscale, ECM viscoelasticity arises from polymer entanglements, structural protein folding, and reversible noncovalent interactions.^45,49,50

Evaluation Indicators and Characterization Methods for Viscoelasticity

Viscoelasticity of biological tissues

The viscoelasticity of biological tissues plays a vital role in maintaining physiological activities. For example, the energy dissipation in viscoelastic connective tissue protects against continuous or periodic high stress or strain. Blood vessels endure millions of periodic mechanical loads, and viscoelasticity prolongs their fatigue life.^51,52 Similarly, the viscoelasticity of the periodontal ligament dissipates energy during mastication, protecting tooth roots and alveolar bone from high masticatory forces.^53,54 Bones are also viscoelastic, capable of withstanding long-term physiological loads. Furthermore, viscoelasticity changes often occur in specific pathological processes, such as lung and liver fibrosis⁵⁵ or tumor tissue formation.^9,56

At the molecular level, the viscoelastic behavior arises from the dynamic and hierarchical organization of ECM components.⁵⁷ Fibrillar collagens contribute to ECM viscoelasticity through their hierarchical architecture. Time-dependent behaviors, such as stress relaxation and creep, result from fiber sliding and reversible dissociation of intrafibrillar and enzymatic cross-links.^58,59 Glycosaminoglycans (GAGs), rich in anionic groups such as carboxylates and sulfates, attract and retain water, forming highly hydrated gel-like environments. This hydration not only provides compressive resistance but also affects ECM topology by influencing collagen spacing and network organization.⁶⁰ Proteoglycans, consisting of core proteins and GAG chains, form supramolecular assemblies that regulate ECM poroelasticity and viscoelasticity. Hydration-driven swelling, reversible GAG slippage, and core protein unfolding contribute to energy dissipation and mechanical adaptability.^59,61 Collectively, these components form a dynamic, multiscale network that enables the ECM to store and dissipate mechanical energy, remodel in response to force, and transmit mechanical cues to resident cells.

Evaluation indicators

The commonly used indicators for viscoelasticity can be divided into three categories, corresponding to stress relaxation,^62–64 creep,^65–67 and energy dissipation^68,69 of materials. First, the relaxation time τ_1/2 or τ_1/e represents the time required for stress to decay to 1/2 or 1/e under constant strain.⁷⁰ Similarly, the creep time (τ_3/2) is the time required for a material to reach 150% initial strain under constant stress.^65,71 The third category describes the stress–strain behavior under periodic stress. The storage modulus (G′) represents the energy stored in the material, while the loss modulus (G″) represents the energy dissipation related to its viscous behavior. The loss tangent (tanδ = G″/G′) expresses material viscoelasticity.^69,72 A higher loss tangent indicates greater viscous behavior. The loss tangent of biological tissues typically ranges between 10% and 30%.⁶⁸ The half-life of stress relaxation in biological tissues varies from 10 to 1000 s.⁷⁰

Characterization methods

At present, various techniques are available to characterize material viscoelasticity. These include static and dynamic tests at macro- and microscales.^73–75 Static mechanical tests are conducted by applying and measuring tensile, compressive, and shear stresses and strains, primarily through stress relaxation and creep tests.^76–81 Dynamic mechanical tests include frequency-dependent rheological tests and cyclic loading tests.^82–84 Recently, particle-based microrheological measurement methods have also emerged, enabling in situ detection of materials at micron or smaller length scales.^85–87 Thus, it is possible to measure viscoelasticity within a material rather than only on its surface.^85,88 In addition, elastography technologies,^89–92 such as magnetic resonance elastography,^90,93–95 shear-wave dispersion ultrasound vibrometry,⁹⁶ and shear-wave elastography,⁹⁷ have enabled completely noninvasive characterization of in vivo tissue viscoelasticity by detecting shear wave velocity in biological tissues (Fig. 2).⁹⁸

FIG. 2.

Multiscale mechanical characterization of biological tissues and materials. (A) Uniaxial testing.⁸⁰ (B) A rheometer can analyze characteristics such as viscosity, elasticity, viscoelasticity, as well as shear thinning and shear thickening.⁶⁸ (C) Magnetic resonance elastography (MRE) combines MRI with vibrations to assess viscoelasticity, often used for liver and brain imaging.⁹⁴ The right half shows details related to the application of MRE in a mouse model.⁹⁵ (D) Atomic force microscope (AFM) methods can quantify the elastic and viscoelastic properties of materials, ranging from molecules, subcellular organelles, and cells to entire tissues.⁶⁹ (E) Particle-based microrheology probes nanoscale viscoelastic properties by tracking the motion of embedded tracer particles in soft matter systems.⁸⁶

Preparation Strategy of Viscoelasticity Adjustable Hydrogel

Preparation strategy of viscoelastic hydrogels

Hydrogels are hydrophilic polymer networks capable of absorbing and retaining water.⁹⁹ Common cross-linking methods include chemical and physical cross-linking.¹⁰⁰ Chemically cross-linking hydrogels typically have stable and permanent binding points. In contrast, physically cross-linked hydrogels contain reversible noncovalent interactions, forming dynamic networks with notable viscoelasticity.^101–103 Reversible covalent bonds dynamically break and reform under certain conditions, imparting self-adaptability and viscoelastic properties.⁵⁰ Examples of reversible dynamic covalent bonds include borate ester bonds,⁸² disulfide bonds, imine bonds, and acylhydrazone bonds.^104,105

Meanwhile, viscoelasticity can also emerge from higher order structural features such as sliding cross-links, supramolecular assemblies, or interpenetrating networks, where energy dissipation results from topological rearrangements or multicomponent coupling rather than bond exchange alone. These strategies are orthogonal but often synergistic, and their integration provides versatile platforms for tailoring viscoelasticity in biomaterial design (Table 1).

Table 1.

Comparative Strategies for Introducing Viscoelasticity into Hydrogels

Strategy	Mechanism	Representative hydrogels	Advantages	Limitations
Reversible noncovalent cross-linking	Ionic interaction Hydrogen bonding Host–guest recognition Hydrophobic interaction	a) Ca²⁺–alginate^{63,64,106–109} b) DNA-based hydrogels^110,111 c) β-cyclodextrin–adamantane hydrogels¹⁰⁵ d) PEO-hydrophobic triblock copolymer hydrogels¹¹²	Highly reversible Self-healing Tunable by stimuli Biofriendly	◼ Mechanically weak ◼ Sensitive to environmental changes ◼ Limited long-term stability
Dynamic covalent cross-linking	Reversible covalent bond formation and cleavage (e.g., hydrazone, boronate ester, imine, disulfide)	a) PEG–aldehyde/hydrazide gels¹¹³ b) Boronate ester cross-linked hydrogels¹¹⁴	Stable under physiological conditions Tunable stress relaxation Enhanced mechanical properties compared with noncovalent systems	◼ Requires precise chemical control, some bonds sensitive to pH or redox environment ◼ May need catalyst or buffering to ensure reversibility
Sliding/topological cross-linking	Topologically interlocked cross-links enable reversible chain sliding without bond cleavage, allowing energy dissipation through molecular mobility	Succinylated polyrotaxane hydrogels¹¹⁵	Highly reversible without requiring bond breaking Decouples elasticity from viscosity	◼ Synthetic complexity ◼ Limited types of available topological components ◼ Requires precise molecular design
Supramolecular assembly	Network formed via noncovalent self-assembly such as host–guest interaction, hydrogen bonding, or π–π stacking	a) sGAG–peptide assembly systems¹¹⁶ b) UPy-based quadruple H-bonded gels¹¹⁷ c) CD–ADA hydrogels (host–guest)¹¹⁸	ECM-mimetic, highly reversible, bioactive, suitable for cell-instructive signaling Often self-healing	◼ Relatively weak mechanical strength ◼ Batch-to-batch variability ◼ Costly synthesis, difficult to precisely control kinetics of assembly/disassembly
Interpenetrating network (IPN)	Constructed from two interpenetrating networks with distinct mechanical or dynamic properties:	a) Elastic + dissipative: sGAG-IPN hydrogels¹¹⁶ b) Covalent + noncovalent: HA–collagen dual networks¹¹⁹	Allows independent tuning of G′ and G″; Combines mechanical robustness with tunable relaxation; Highly customizable	◼ Complex fabrication; ◼ Risk of phase separation; ◼ Requires careful balancing of components and cross-linking kinetics

sGAG, sulfated glycosaminoglycan; UPy, ureidopyrimidinone; CD–ADA, cyclodextrin–adamantane; G′, storage modulus; G″, loss modulus.

Strategies for controlling viscoelasticity of hydrogels

Previously, researchers used various strategies to control the viscoelastic properties of hydrogels (Fig. 3).^120–124 It is important to note that some methods only affect the viscoelastic parameters, while others may alter additional mechanical properties (such as elastic modulus) or even the three-dimensional (3D) structure (e.g., pore size, porosity).^104,110,125 Therefore, it is crucial to select appropriate methods for specific applications.^126–129

FIG. 3.

Strategies for fabricating hydrogels with tunable viscoelasticity. (A) Modulating polymer architecture: Reducing alginate molecular weight cross-linked by calcium decreases network entanglement and connectivity, while introducing small spacers increases the distance between cross-links.⁶³ (B) Engineering cross-linking dynamics: Monoacryloyl cyclodextrin (ac-β-CD) was preassembled on hyaluronic acid (HA) to prepare two physically cross-linked hydrogels (HA–ADA and HA–CA) via CD–ADA or CD–CA host–guest interactions. By adjusting the weight ratio of HA–ADA to HA–CA, the viscoelasticity can be tuned.¹¹² (C) Applying supramolecular interactions: Coassembled ureidopyrimidinone (UPy)-based supramolecular hydrogels achieve tunable viscoelasticity and enhanced glomerulogenesis via modulation of hydrogen bonding density.¹¹⁷ (D) Using topological sliding networks: Sliding hydrogels formed from polyrotaxane structures introduce movable cross-linking sites that enhance stress relaxation independently of stiffness.¹¹⁵ (E) Interpenetrating polymer networks (IPNs): IPN hydrogels composed of dynamic peptide—sGAG and covalent polyethylene glycol (PEG) networks, enable tunable viscoelasticity and promote 3D cell spreading.¹¹⁶ (F) Controlling formation parameters: Modulating the self-assembly of collagen fibers by adjusting the low-temperature incubation time of the collagen solution regulates the viscoelastic properties, independent of the initial elastic modulus.⁶⁷

Controlling viscoelasticity by changing polymer structure

Viscoelastic properties of hydrogels can be modulated by tailoring the molecular structure of the polymer building blocks. Specifically, molecular weight, chain flexibility, and block architecture significantly influence stress relaxation behavior and energy dissipation capacity.¹³⁰ Chaudhuri et al. applied different molecular weight alginates with varying cross-linking densities of calcium to modulate the stress relaxation properties of the hydrogels by altering connectivity and chain mobility in the network. A decrease in the initial elastic modulus resulting from decreased polymer molecular weight could be compensated for by increased cross-linking. Also, the covalent coupling of short polyethylene glycol (PEG) spacers to the alginate provided a steric hindrance to cross-linking of alginate chains, enhancing stress relaxation in the gel (Fig. 3A).^63,131 In a related approach, Walker et al. produced PEG-maleimide (MAL) hydrogels with similar initial elastic moduli but different viscoelasticities by varying the molecular weight of PEG.⁶⁹ Furthermore, Jung et al. tuned the viscoelasticity of PEO-based ABA triblock copolymer hydrogels by varying hydrophobic end-block length, with longer blocks increasing relaxation time.¹¹² Notably, Hafeez et al. independently tuned hydrogel viscoelasticity by altering the hydrophobic length of end-groups (Fig. 3B).¹³² Using a distinct strategy, Peng et al. used programmable DNA sequences with varying lengths to adjust hydrogel stress relaxation by altering DNA chain overlap.¹¹¹ These studies demonstrate that polymer chain architecture and hydrophobic segment design can offer predictable and tunable control over hydrogel viscoelasticity.

Controlling viscoelasticity by adjusting cross-linking method or density

Beyond polymer architecture, the viscoelastic behavior of hydrogels can be finely tuned by altering the mode and density of cross-linking.^133,134 Chaudhuri et al. ionically cross-linked Arg-Gly-Asp peptide (RGD)-alginate with Ca²⁺ to obtain a soft viscoelastic hydrogel and, in parallel, covalently cross-linked RGD-alginate with acyl-hydrazide cross-linking to yield an elastic hydrogel. By adjusting cross-linker concentrations, both gels shared the same initial stiffness.¹³⁵ Similarly, Narita et al. found that polyvinyl alcohol hydrogels prepared using different cross-linking methods exhibited variations in viscoelasticity (Fig. 3C).¹³⁶ Regarding dynamic cross-linking, McKinnon et al. prepared multiarm PEG hydrogels based on reversible dynamic acylhydrazone bond cross-linking. Hydrogels with similar initial elastic moduli but different viscoelastic properties were developed by adjusting the proportion of two acylhydrazone bonds.¹¹³ Likewise, Yang et al. precisely controlled the viscoelasticity of hyaluronic acid (HA) hydrogels by adjusting the proportions of reversible supramolecular cross-links with different kinetic constants in the cross-linking bond (Fig. 3D).¹¹⁸ Meanwhile, Chrisnandy et al. developed a dynamically cross-linked hydrogel system with reversible cytosine–cytosine triple hydrogen bonding. By tuning the proportion of physical cross-links, they precisely controlled the percentage of stress relaxation.¹³⁷ Together, these findings highlight that both the chemistry and kinetics of cross-link formation can determine the viscoelastic response of hydrogels.

Controlling viscoelasticity via supramolecular interactions

Specific hydrogel systems harness noncovalent supramolecular motifs, such as self-complementary hydrogen bonding,¹¹⁷ host–guest interactions,¹¹⁸ π–π stacking, or metal coordination, to form physically cross-linked and dynamically reconfigurable networks. For instance, ureidopyrimidinone (UPy)-based supramolecular hydrogels self-assemble into nanofibrous networks through quadruple hydrogen bonding, and their viscoelastic behavior can be finely tuned by adjusting the ratio of mono- and bifunctional UPy monomers, as well as the density of RGD-functionalized UPy motifs. This approach offers a versatile platform for dynamically controlling matrix mechanics and mechanotransduction in bioengineered microenvironments.¹¹⁷

Controlling viscoelasticity by topological sliding networks

Sliding hydrogels leverage topologically interlocked architectures, such as polyrotaxanes composed of cyclic molecules (e.g., α-cyclodextrins) threaded onto linear polymer chains (e.g., PEG), to introduce locally mobile yet topologically fixed cross-linking points. These movable cross-links and ligands endow the hydrogel with dynamic mechanical adaptability while maintaining overall structural integrity. For example, Tong and Yang et al. developed a sliding hydrogel based on polyrotaxane structures in which α-cyclodextrins were threaded onto PEG chains and capped at both ends to prevent unthreading.¹¹⁵ The cross-linkers and RGD ligands attached to the α-cyclodextrins were thus free to move along the polymer backbone. Rheological characterization revealed that increased mobility of the sliding units significantly enhanced stress relaxation without altering the initial elastic modulus.

Controlling viscoelasticity using interpenetrating polymer networks

Interpenetrating polymer networks (IPNs), formed by combining covalent and dynamic or degradable networks, offer a strategy to modulate hydrogel viscoelasticity. By adjusting the composition or cross-linking of each network, IPNs enable independent control of stress relaxation without altering initial stiffness. By constructing a semi-interpenetrating polymer network (sGAG-IPN) hydrogel composed of a covalently cross-linked PEG-MAL network and a noncovalently assembled matrix metalloproteinase (MMP)-degradable sGAG-like network, the overall viscoelastic properties of the hydrogel could be precisely tuned by adjusting the molar ratio between the covalent and noncovalent components.¹¹⁶ By combining covalent and supramolecular cross-links, Loebel et al. designed a double-network hydrogel comprising a covalent PEG-fibrinogen network and a β-cyclodextrin adamantane supramolecular network, which exhibited independent control of viscosity and elasticity.¹³⁸

Controlling viscoelasticity by changing the conditions of hydrogel formation

Environmental factors during hydrogel formation, such as temperature, pH, and reaction time, can also influence polymer assembly and network configuration, thereby affecting viscoelasticity. Huang et al. extended low-temperature incubation of the collagen solution, which resulted in more weak interactions within the collagen fiber network, and increased diameter of collagen fibers. Self-assembly changes of collagen fibers led to different stress relaxation behaviors (Fig. 3E).⁶⁷ In addition, Kaewprasit et al. found that the addition of monohydric alcohol enhanced the formation of self-assembled β-fold structures by increasing hydrophobic interactions with silk fibroin chains, significantly improving the mechanical properties and viscoelasticity of the hydrogels.¹³⁹ Under pH-responsive conditions, Jay et al. developed a reversible covalent hydrogel using dynamic cross-linking between boronic acid and diol groups for vaginal applications. The hydrogel rapidly reformed at vaginal pH (4.5–5), leading to a viscoelastic response but stabilized at pH >5.5 (Fig. 3F).¹¹⁴ Moheimani et al. regulated the viscoelasticity of alginate hydrogels through repeated high-pressure sterilization. With increasing sterilization cycles, the molecular weight of the alginate decreased significantly, thereby modulating the hydrogel’s mechanical properties.¹⁴⁰ These studies underscore that even without modifying polymer composition or cross-linking chemistry, process conditions alone can be leveraged to dynamically tune viscoelasticity.

Effect of Viscoelastic Matrix on Cell Behavior

The ECM is not only a structural network but also provides 3D biochemical and biophysical cues that regulate cellular behavior in development, physiology, and pathophysiology.^141–144 Increasing evidence has shown that biophysical cues significantly affect the behavior and fate of cells.^145,146 Previous studies have focused primarily on ECM stiffness.^11,147,148 Recent research has found that the mechanotransduction response of cells to their surrounding environment may play a key role in determining the fate of stem cells.¹²⁸ Controlling the viscoelasticity can guide the differentiation of specific cell pedigrees in tissue engineering,^149–152 as well as regulate other cell behaviors (Fig. 4).^153–155

FIG. 4.

Matrix viscoelasticity regulates a wide array of cellular functions.

Cell adhesion

Cell adhesion, encompassing both cell–matrix and cell–cell interactions, plays a vital role in regulating stem cell behavior, including spreading, migration, and differentiation.^156–158 Focal adhesions (FAs) act as hubs of mechanical and biological signals, essential for cell-ECM mechanical sensitivity, while cadherin-mediated adhesions regulate intercellular cohesion and tissue organization (Fig. 5A, B).^160,161 In type-I collagen hydrogels with fast stress relaxation, the FAs of mesenchymal stem cells (MSCs) displayed a more mature structure.¹⁵⁰ Similar results were observed in a 3D culture of human MSCs (hMSCs).¹¹⁹ In contrast, FA size and number differed significantly when hMSCs were cultured on polyacrylamide hydrogels. Specifically, FA maturation was reduced on substrates with higher tanδ, while cell aggregation was enhanced in 3D PEG-MAL hydrogels under the same conditions, promoting mesenchymal condensation and chondrogenic differentiation (Fig. 5C).⁶⁹ Cameron et al. reported similar findings.⁶⁵ Adebowale et al. also concluded that cell migration was associated with fewer and weaker paxillin adhesions on matrices with fast relaxation.⁷⁰

FIG. 5.

Impact of matrix viscoelasticity on cell–matrix adhesion, cell–cell adhesion, cytoskeletal organization, and cell spreading and morphology. (A) 3D renderings of mesenchymal stem cells (MSCs) cultured in hydrogels with different viscoelastic properties show distinct vinculin distribution, actin organization, and pseudopodia formation.⁶⁷ (B) NIH3T3 cells on elastic substrates form large focal adhesions (FAs) with prominent stress fibers, while those on viscoelastic hydrogels show smaller stress fibers, an actin cortex, and punctate FAs at the periphery. Despite smaller FA size, cells on viscoelastic substrates exhibit higher FA tension, indicating increased mechanical sensitivity and cytoskeletal tension.¹⁵⁹ (C) Human MSCs (hMSCs) cultured on 2D polyacrylamide (PAAm) hydrogels, showing increased N-cadherin and β-catenin expression with higher loss tangent, indicating enhanced cell–cell adhesion.⁶⁹ (D) Human bone marrow MSCs (hBMSCs), encapsulated in hydrogels with different viscoelasticity, showing changes in cell circularity and Yes-associated protein (YAP) nuclear/cytoplasmic ratio after 3 days of culture.¹¹²

Cell spreading and cell morphology

Most previous studies have shown that matrices with high stiffness can enhance cell traction forces and promote cell spreading to maintain tension balance.¹⁶² However, the effect of viscoelasticity on cell spreading and morphology remains uncertain. Cameron et al. found that a high loss modulus in the matrix increased the spreading area of hMSCs.⁶⁵ Chaudhuri et al. observed that U2OS cells and 3T3 mouse fibroblasts exhibited larger spreading areas and more stress fiber formation on substrates with stress relaxation.¹³⁵ A similar phenomenon was observed in mouse MSCs.⁶³ Lou et al. identified a linear relationship between matrix relaxation rate and cell roundness, with cells in viscoelastic hydrogels being less circular and developing longer protrusions.¹¹⁹ However, Mandal et al. reported smaller spreading areas in primary human hepatocytes (PHHs) and fibroblasts, but larger areas and faster spreading rates in hepatocellular carcinoma cells (Huh7) on viscoelastic substrates. The opposite responses of PHHs and Huh7 cells to viscoelasticity may be explained by differences in the characteristic lifetimes of substrate binding between liver cancer and normal cells, which could lead to altered cell spreading and motility within diseased tissue.¹⁶³ In addition, Gong et al. found that viscosity promoted cell spreading at low long-term stiffness—defined as the residual equilibrium modulus after stress relaxation—with maximum spreading achieved at medium viscosity (Fig. 5D).¹⁶⁴

Based on the motor-clutch model combined with a standard linear viscoelastic substrate, the differential cellular responses to substrate viscoelasticity are primarily determined by whether the cell possesses clutch reinforcement mechanisms, as well as its traction force generation, clutch density and binding kinetics, sensitivity to mechanical feedback, and FA lifetime. Cells with strong traction forces, stable FAs, and reinforcement capacity, such as fibroblasts, exhibit saturated spreading on stiff substrates and show limited sensitivity to viscosity. In contrast, cells lacking reinforcement mechanisms, with weaker traction forces or short-lived FAs—such as neurons—rely more heavily on substrate viscoelastic matching to sustain effective spreading.^11,164,165

Cell proliferation

Cell proliferation is influenced by microenvironmental physical properties.^166,167 Alginate hydrogels with fast stress relaxation promote proliferation of C2C12 myoblasts and fibroblasts.^62,63 Liu et al. found that the proliferation and migration of human bone marrow MSCs (hBMSCs) were enhanced as the loss modulus increased.⁶⁸ Lee et al. found that fast stress-relaxing hydrogels promoted chondrocyte proliferation while inhibiting cell death.¹⁰⁶ Similarly, viscoelastic scaffolds supported 1.67-fold higher chondrocyte proliferation compared with unmodified scaffolds after 3 days.¹⁶⁸ Indana et al. revealed that a higher RGD density and faster stress relaxation promoted human induced pluripotent stem cell (hiPSC) activity, proliferation, and lumen formation (Fig. 6C).¹⁰⁷

FIG. 6.

Impact of matrix viscoelasticity on cell migration, proliferation, stemness maintenance, and differentiation. (A) Mesenchymal stem cells (MSCs) migrate within confining viscoelastic matrices but not in more elastic environments. Representative 3D track reconstructions, along with quantification of mean speeds and migration track lengths.¹⁶⁹ (B) Film loss tangent influences migration modes.¹⁷⁰ (C) Representative maximum intensity projection images and quantification of live cells reveal increased viability in human induced pluripotent stem cells (hiPSCs) cultured in faster relaxing matrices.¹⁰⁷ (D) Representative images and quantification of CD105 intensity in MSCs cultured in hydrogels with varying stress relaxation rates. MSCs in slower relaxing hydrogels maintain higher CD105 expression, indicating better stemness retention.¹⁷¹ (E) MSCs show reduced adipogenesis and promoted osteogenesis, with increased mineralization and collagen deposition, in hydrogels with faster stress relaxation and varying stiffness.⁶³

Cell migration

The cell–matrix connection and the formation of cell movement-related structures are two major factors determining cell migration.¹⁷² ECM stress relaxation regulates cell migration speed and mode (Fig. 6A).^173,174 Darnell et al. observed nearly doubled migration distance over a week on fast-relaxing alginate hydrogels compared with slow-relaxing gels.⁶⁴ Adebowale et al. showed minimal cell migration on 2 kPa substrates with slow relaxation but significantly increased migration on substrates with faster relaxation.⁷⁰ Matrix mechanical properties also influence migration modes. On soft viscoelastic substrates with fast stress relaxation, cells adopted a rounded morphology and migrated using filopodia-like protrusions, forming only nascent peripheral adhesions. In contrast, on purely elastic substrates of similar stiffness, cells spread more extensively, exhibited lamellipodia-driven migration, and developed larger, more stable FAs.⁷⁰ Chester et al. demonstrated that viscoelasticity influences migration mode: a high loss tangent promotes amoeboid migration, while a low loss tangent supports mesenchymal migration. Signaling molecules such as Rho-associated kinase (ROCK) and Ras-related C3 botulinum toxin substrate (Rac) play central roles in this process—ROCK enhances actomyosin contractility and cortical tension, supporting rounded, weakly adherent amoeboid migration, whereas Rac facilitates lamellipodia formation, FA maturation, and polarization, enabling mesenchymal migration with elongated morphology and directional motility (Fig. 6B).¹⁷⁰

Stemness maintenance

Stemness maintenance is also a critical feature of stem cells in regenerative medicine applications.^175–177 Appropriate mechanical signals can promote stem cell self-renewal, while excessive mechanical stress may induce differentiation.^178–180 Madl et al. found that inhibiting physical remodeling by adding covalent cross-linking to alginate materials reduced neural progenitor cell stemness.¹⁷⁸ However, Lee et al. found that MSCs exhibited a higher expression level of CD105 in hydrogels with slow relaxation rates (Fig. 6D).¹⁷¹ Lin et al. found that slow stress relaxation in the hydrogel could induce MSCs to enter a reversible resting G0 state, suggesting that MSC quiescence may help preserve stemness when exposed to low-deformation matrices.¹⁸¹

Cell differentiation and ECM deposition

The process of cell differentiation and ECM deposition is closely dependent on the microenvironment (Fig. 6E).^182–186 Increasing matrix loss modulus has been shown to enhance osteogenic and chondrogenic differentiation while suppressing adipogenesis.⁶⁸^,106,171 In contrast, hydrogels exhibiting slower stress relaxation fail to sustain early chondrogenic advantages over time, whereas those with faster relaxation kinetics promote long-term cartilage matrix deposition by MSCs.⁶⁷ In addition, the effectiveness of chondrogenic induction media appears contingent upon the mechanical context: while high-elasticity environments boost cartilage matrix deposition, this effect diminishes in high tanδ hydrogels, suggesting a saturable cellular response governed by mechanical cues alone.⁶⁹

Multicellular aggregates and collective morphogenesis

In addition to studies focused on single-cell behaviors, an emerging body of work investigates how viscoelasticity regulates cell behavior at the level of multicellular aggregates, bridging the gap between single-cell mechanobiology and complex organoid systems. These models exhibit collective behaviors such as aggregation, lumen formation, and tissue-like organization, and they undergo coordinated morphogenetic processes that often mimic early developmental events.

In a viscoelastic and degradable IPN hydrogel system, high viscoelasticity combined with proteolytic degradability most effectively promoted lumen formation, growth expansion, and maintenance of pluripotency in hiPSC-derived cysts, accompanied by increased YAP nuclear localization and enhanced secretion of ECM proteins.¹¹⁶ In a two-phase system combining hypoxic preconditioning and viscoelastic hydrogel encapsulation, hypoxia first induced endothelial progenitor cell (EPC) aggregation into clusters, and the subsequent exposure to high-viscoelasticity matrices specifically promoted vasculogenesis by enhancing sprouting, branching, and network formation.¹⁸⁷ In 3D alginate hydrogels with independently tunable viscoelasticity and RGD ligand density, fast stress relaxation combined with high RGD density promoted hiPSC viability, proliferation, apicobasal polarization, and lumen formation, whereas slow relaxation at low RGD density led to apoptosis and impaired morphogenesis, highlighting matrix viscoelasticity as a key regulator of collective morphogenesis.¹⁰⁷

Mechanism of Viscoelastic Mechanotransduction

Mechanobiology involves (1) mechanical sensing, the ability of cells to perceive biomechanical cues from the surrounding microenvironment, and (2) mechanotransduction, the ability of cells to convert external forces into biochemical signals that trigger specific cellular functions.^188–190 Current research on viscoelastic mechanical signal sensing focuses on two main categories of membrane proteins: (1) Integrin pathway: integrin is a transmembrane protein that interacts with various proteins, including FA kinase (FAK), within the FA complex. The FA complex connects with the actin cytoskeleton to form a mechanical link and transmits external physical signals into the cell; (2) Mechanosensitive ion channel-mediated pathways: mechanosensitive ion channels^{108,191–194} respond to external mechanical forces by opening or closing, thereby regulating the flow of ions inside and outside the cell, which subsequently triggers a series of downstream signaling pathways (Fig. 7A).^195–198

FIG. 7.

Schematic of viscoelastic mechanotransduction: Cellular structures and signaling pathways. (A) Cellular components involved in viscoelastic mechanotransduction. Extracellular viscoelastic cues are transmitted through integrins and ion channels on the cell membrane, modulating cytoskeletal tension and intracellular signaling. The cytoskeleton connects to the nucleus via mechanical linkages and transmembrane complexes, transferring external forces to the nucleus. This mechanotransmission maintains nuclear morphology and stability while modulating chromatin architecture and gene expression, thereby influencing cell differentiation, migration, and mechanical stress responses. (B) Overview of viscoelastic mechanotransduction pathways. (1) Cytoplasmic pathway: Mechanical signals mediated by integrin–extracellular matrix (ECM) interactions form focal adhesions and activate focal adhesion kinase (FAK), Src, and small GTPases (e.g., RhoA, Rac, Cdc42), leading to cytoskeletal remodeling and tension regulation without nuclear translocation. (2) Nuclear pathway: In contrast, mechanical signals transmitted via integrins or ion channels can activate transcription factors, which translocate to the nucleus to regulate gene expression, driving processes such as cell differentiation and proliferation.

Integrin-mediated mechanotransduction

During mechanotransduction, mechanical stimulation can alter the function of mechanosensitive proteins within the cell adhesion structure, triggering biochemical signals that regulate both the rapid mechanical response of cells and long-term changes in gene expression.^199,200 These pathways can be broadly divided into two categories: (1) Cytoskeletal regulators, including the FAK-Src complex and Rho-family small GTPases such as RhoA/ROCK, Rac1, and CDC42, control actin polymerization, contractility, and FA dynamics, thereby modulating cell tension, shape, and migration; and (2) transcriptional regulators, including YAP/TAZ, β-catenin, Smad2/3, ERK, and CyclinB/CDK1, are activated downstream of mechanosensitive signaling networks such as integrin–FAK–Src, Ras–MAPK, or PI3K–Akt pathways. These molecules translocate into the nucleus where they regulate gene expression governing cell fate.^{133,172,201–207}

Integrin signaling facilitates YAP nuclear translocation, along with Smad2/3 and β-catenin, thereby promoting chondrogenesis and osteogenesis.⁶⁸ Furthermore, integrin–FAK-mediated PI3K–Akt–CDK1 signaling in fast-relaxing hydrogels upregulates MSC proliferation.¹⁸¹ Meanwhile, small GTPases play an important role in integrin-mediated mechanotransduction. Integrin β1 activates FAK–RhoA–ROCK–MLCK signaling, enhancing actomyosin contractility and promoting MSC spreading on stress-relaxing substrates.¹³⁵ High-creep hydrogels increase Rac1 activity in hMSCs and upregulate N-cadherin expression, thereby promoting smooth muscle cell differentiation.⁷¹ In contrast, in mouse MSCs, high matrix viscosity suppresses ROCK and Rac signaling, reduces β1 integrin and β-catenin activation, while enhancing N-cadherin-mediated adhesion, suggesting cell-type-dependent and context-specific roles of viscoelasticity.⁶⁹

Ion channel protein-mediated mechanotransduction

Mechanosensitive ion channels are directly activated by stress exerted on lipid bilayers, converting physical stimuli into electrical signals and responding to mechanical stress.¹⁹⁷ Cell volume expansion can occur in biodegradable hydrogels or hydrogels with fast stress relaxation, but it is limited in more restrictive elastic hydrogels.¹⁷¹ Therefore, cell volume regulation may mediate viscoelastic mechanotransduction of the ECM.^172,208,209 Among mechanosensitive ion channels, TRPV4 channels have emerged as key sensors of cell volume changes.^208,209 Feedback between TRPV4 activation and volume expansion has been shown to regulate the nuclear localization of RUNX2, thereby promoting osteogenic differentiation.¹⁷¹ In pathological conditions such as osteoarthritis, dysfunction of the TRPV4–GSK3β signaling axis impairs the cell’s ability to sense and respond to viscoelastic cues from the surrounding matrix, resulting in persistently elevated intracellular calcium levels (Fig. 7B).¹⁹¹

Computational Biology Research on Viscoelasticity-Mediated Cell Behavior

Computational biology research can complement, analyze, and interpret experimental data in the field of cell mechanics. In addition, it can provide valuable insights for designing mechanical parameters of viscoelastic materials. Researchers have proposed numerous models, including the power-law model,^210,211 fractional model,²¹² and the viscoelastic and active viscoelastic model (Fig. 8A).^214,215 To study cell adhesion and migration, mechanical models^{70,135,164,216,217} were developed to understand molecular-level cellular responses to viscoelastic microenvironments. Furthermore, finite element analysis (FEA) can study the complex cell-ECM mechanical systems.^150,181

FIG. 8.

Computational biology insights into motor-clutch models and finite element analysis of matrix viscoelasticity in cell behavior. (A) Viscoelastic models applied to various hydrogels.²¹³ (B) Depiction of the molecular clutch model used for viscoelastic materials. Maximum cell spreading occurs when the stress relaxation timescale closely matches the clutch binding timescale.⁵⁶ (C) Finite element simulations of cellular stress and deformation in elastic and viscoelastic substrates.¹⁵⁰ (D) Finite element simulations modeled MSC division in hydrogels. Faster stress relaxation allows for greater matrix deformation under constant stress, promoting mesenchymal stem cell (MSC) entry into a rapid cell cycle via activation of the PI3K/Akt-CDK1 pathway.¹⁸¹

Mechanical model of cell adhesion

Chan and Odde introduced the motor-clutch model of cell adhesion. Cells can detect and respond to the biophysical properties of the extracellular environment through integrin-based adhesion points (Fig. 8B). These adhesion points connect the ECM to the F-actin cytoskeleton, transmitting the mechanical forces generated by actin retrograde flow and myosin II to the ECM.^45,218–220 Adebowale et al. conducted two simulations using the motor-clutch model. The results of both were consistent with experimental data, demonstrating how stress relaxation and matrix stiffness affect cell behaviors.⁷⁰ Using the motor-clutch and linear viscoelastic models, Gong et al. found that medium viscosity maximized proliferation on soft matrices but had minimal effect on stiff ones.¹⁶⁴

3D finite element model analysis

FEA can simulate and analyze the behavior of complex physical systems.^221–223 It can be used in cell adhesion research, cell migration simulation, and tissue engineering design and optimization.^224,225 Huang et al. used FEA to predict the response of cells to external stress. In the viscoelastic matrix, stress distribution and cell deformation evolve to adapt to matrix deformation, promoting the dynamic expansion of cells (Fig. 8C).¹⁵⁰ Lin et al. showed that fast matrix relaxation induced significant deformation around MSCs, activating PI3K/Akt-CDK1 pathways to accelerate cell cycle progression (Fig. 8D).¹⁸¹

Application of Viscoelastic Hydrogels in Regenerative Medicine

Viscoelastic biomaterials have long been used in regenerative medicine.^226–230 These materials have been shown to promote the regeneration of various tissues, including cartilage and bone.^231–235 The most commonly used recombinant basement membrane materials for organoid culture are also viscoelastic.²³⁶ However, only a few studies have been conducted on hydrogels with adjustable viscoelasticity that control viscoelasticity as an independent variable (Table 2).

Table 2.

Independent Tuning of Viscoelasticity in Various Hydrogel Systems and Its Effects on Cell Behavior

Author (year)	Hydrogel system	Methods for tuning viscoelasticity	Characterization of viscoelasticity*	Cell type	Effects on cell behavior when dissipative properties increased
Cameron et al. (2011)⁶⁵	Polyacrylamide (PAM) gel system	Varying the initial combination of acrylamide (Acryl) monomer and bis-acrylamide (Bis) cross-linker	G′ ≈ 4 kPa G″ = 1, 10, 130 Pa	hMSCs	Cell spread area↑ Cell proliferation↑ FAs smaller, less mature, more transient Smooth muscle cell differentiation↑
McKinnon et al. (2014)¹¹³	PEG-based hydrogel cross-linked by reversible hydrazone bonds	Hydrazine- and aldehyde-terminated PEG macromers in combination with a benzaldehyde-terminated KGRGDS peptide. Different ratio of aliphatic and aryl aldehyde cross-links.	Young’s modulus = 1.8∼27 kPa 8-H:8-AA (λ = 91.0 s) 8-H:8-BA (λ ≈ 2370 s) (λ: the time constant of relaxation)	C2C12 myoblasts	Mean cell projected areas↑ Long-term cell viability↑ Filopodia and lamellipodia↑ Myoblast fusion↑
Chaudhuri et al. (2016)⁶³; Lee et al. (2017)¹⁰⁶; Nam et al. (2019)¹⁰⁸	Alginate gels	①Diﬀerent molecular-weight polymers with diﬀerent cross-linking densities of calcium；②Short PEG spacers to the alginate provide a steric hindrance to cross-linking of alginate chains	Initial elastic modulus: 9 kPa or 17 kPa τ_1/2: 2300 s, 300 s, 140 s, 60 s (data from Chaudhuri et al.)	3T3 fibroblasts; MSCs；chondrocytes；	Spreading and proliferation of 3T3↑ Osteogenic differentiation of MSCs↑ Enhanced chondrocyte proliferation and inhibited cell death Cartilage matrix by chondrocytes↑
Darnell et al. (2017)⁶⁴	Alginate gels	Alginate-type LF20/40 (280 kDa) was used for the slow-relaxing hydrogels and was irradiated with an 8 mRad cobalt source to form the fast-relaxing hydrogels (35 kDa)	Young’s modulus: 15-20 kPa τ_{1/2 fast} = 0∼100 s τ_{1/2 slow} = 700∼800 s	hMSCs	Migration speed↑ Osteogenic differentiation↑ Matrix mineralization↑
Lou et al. (2018)¹¹⁹	Hyaluronic acid (HA)–collagen type I interpenetrating network (IPN) hydrogel	Vary the hydrazone exchange groups (ALD vs. BLD), HA molecular weight (20 kDa vs. 120 kDa), or HA concentration (1%, 1.5%, and 2%)	Modulus: 10∼500Pa τ_1/2: 200∼18000 s	hMSCs	Cell protrusions↑ Cell roundness↓ Cell spreading↑ Collagen fiber network remodeling↑ Formation of FAs↑
Yang et al. (2021)¹¹⁸	Hyaluronic acid (HA)-based supramolecular hydrogels	Tuning the dissociation rate constants of dynamic cross-links (short vs. long lifetime) by varying CD-ADA and CD-CA guest polymers. Mixing HA–ADA and HA–CA at the different weight ratio.	G′ = 1kPa G″ = 0-400Pa	hBMSCs	Rapid stellate spreading↑ Mechanosensing of cells↑ Osteogenic differentiation↑
Huang et al. (2023)⁶⁷	Type I collagen hydrogels	Modulating the self-assembly degree of collagen fibers by controlling incubation times at low temperature (0.5 to 9 h)	Initial elastic modulus = 0.3 kPa τ_1/e = 0.4∼1 s	MSCs	Pseudopodia size and number↑ Cellular sphericity↓ Actin polymerization and intracellular mechanical transmission↑
Liu et al. (2023)⁶⁸	Gelatin methacryloyl (GelMA) hydrogels with dynamic bonds	The dynamic reversible covalent bond between the small molecule DB (3,4-dihydroxybenzaldehyde, DB) and GelMA/phenylboronic acid-modified gelatin (GP) offered the dissipative properties	G′ ≈4 kPa tanδ = 0.02, 0.21, 0.32	BMSCs	Cell and nuclear area↑ Cell migration and infiltration↑ Cell proliferation↑ Osteogenic and chondrogenic differentiation↑ Adipogenic differentiation↓
Walker et al. (2024)⁶⁹	Polyacrylamide (PAAm) and polyethylene glycol–maleimide (PEG-MAL) hydrogels	PAAm hydrogels: Adjusting the cross-linking ratio 8-arm PEG-MAL: Tuning viscoelasticity by controlling polymer molecular weight	Young’s modulus ≈12 kPa； tanδ = 0.1∼0.25	hMSCs	Cell spreading↓ Cell circularity↑ p-FAK intensity, average FA length↓ Cytoskeletal organization↓ Cell traction forces↓ Cell–cell junctions↑ Chondrogenesis ↑
Bernero et al. (2024)¹⁵⁵	Alginate–collagen interpenetrating network (IPN) hydrogels	Tuning stress relaxation by adjusting alginate molecular weight and calcium cross-linker concentration	Stiffnesses (4.4–4.7 kPa), fast-relaxing (τ_1/2 = 1.5s) slow-relaxing (τ_1/2 = 14.4 s)	IDG-SW3 cells	Early cell spreading↑ Osteogenic differentiation↓ Typical osteocyte morphology↓ Cell–cell connections↓
Liu et al. (2024)²³⁸	Alginate gels	Tuning stress relaxation time by varying molecular weight of alginate and calcium cross-linking	Shear storage modulus: ∼1 kPa Stress relaxation time: low-MW: ∼95 s mixed-MW: ∼345 s high-MW: ∼1061 s	hASCs	Cell viability↑ Metabolic activity↑ Cellular sphericity↓ Cell protrusions↑ Differentiation toward NP-like cells↑

G′, storage modulus; G″, loss modulus; tan δ, loss tangent, ratio of G″ to G′; τ_1/2, relaxation time, the time for stress to decay by half; τ_1/e, the time for the stress to decay to 1/e of its original value; hMSCs, human mesenchymal stem cells; hBMSCs, human bone marrow mesenchymal stem cells; C2C12, murine myoblast cell line; 3T3, mouse fibroblasts; IDG-SW3, osteocyte-like cell line; hASCs, human adipose-derived stem cells; BMSCs, bone marrow stem cells; NP-like cells, nucleus pulposus-like cells.

Application on tissue engineering scaffolds

Currently, research on the effect of viscoelastic matrices on cell behavior mainly focuses on 2D or 3D in vitro cell cultures or organoid models.^14,107,109 Few studies have explored the application of hydrogel materials with adjustable viscoelasticity for drug delivery, cell delivery and transplantation, or tissue engineering.^{46,150,167,237} Hydrogels with independently adjustable viscoelasticity have been used to regulate adipose-derived MSCs (ASCs) for nucleus pulposus regeneration, showing that fast stress-relaxing hydrogels significantly increased the long-term survival rate of ASCs, as well as the secretion of nucleus pulposus (NP)-like ECM proteoglycan and type II collagen. However, this study was limited to 3D cell culture in vitro.²³⁸ In vivo studies have demonstrated that fast stress-relaxing alginate hydrogels loaded with hMSCs can significantly enhance new bone formation in calvarial defect models.⁶⁴ Similarly, GelMA-based hydrogels with tunable viscoelasticity have been applied to femoral trochlear defects, where higher viscous dissipation correlated with improved cartilage and bone regeneration.⁶⁸ Lin et al. found that a hydrogel with the fastest stress relaxation delivered the largest area and volume of new periodontal ligament.²³⁹ Zhang et al. demonstrated that the viscoelasticity of Alg-PBA/Spd hydrogels could cooperate with biochemical factors to achieve optimal periodontal ligament repair (Fig. 9).²⁴⁰

FIG. 9.

Chronological representation of key studies illustrating the application of independently tunable viscoelastic hydrogels in regenerative medicine. These studies highlight the evolution of viscoelastic materials in both tissue engineering and organoid culture. These findings emphasize the role of tuning viscoelastic properties to regulate cell behavior, tissue formation, and matrix remodeling, driving innovation in regenerative medicine across various applications.^{14,64,68,109,238–241}

Application on organoid culture system

Recent research about organoids has expanded rapidly.^242,243 Elosegui-Artola et al. found that matrix viscoelasticity could induce morphological instability in cell spheroids, leading to symmetry disruption, the formation of finger-like protrusions, and epithelial–mesenchymal transition.²⁴⁴ In addition, the incorporation of carbon nanotubes promoted the proliferation and differentiation of intestinal organoids by modulating the viscoelasticity of the ECM and activating the Piezo-p38-YAP signaling pathway.¹⁰⁹ Studies also indicate that the viscoelasticity of HA hydrogel played a key role in the patterning and differentiation of stem cell-derived organoids. Viscoelasticity regulated cell–matrix mechanical signal transduction more effectively and promoted the expression of dorsal and interneuron markers more efficiently than traditional elastic properties. It also exhibited significant advantages in the vascularization of organoids, particularly in promoting the formation of the blood–spinal cord barrier.²⁴¹

Chrisnandy et al. demonstrated that their stress-relaxing synthetic hydrogel supports degradation-independent growth and morphogenesis of intestinal organoids. Compared with nondegradable elastic gels, this matrix significantly enhanced symmetry breaking and crypt-like structure formation, promoting spatial differentiation of stem/progenitor cells and Paneth cells.¹³⁷ van Sprang et al. developed an injectable UPy-based supramolecular hydrogel to encapsulate hiPSC-derived kidney organoids. The hydrogel’s tunable viscoelasticity and cell-adhesive properties contributed to modulating nephron patterning during the S-shaped body stage, leading to an increased proportion of WT1⁺ glomerular lineage cells and upregulated vascular endothelial growth factor (VEGF) expression.¹¹⁷

Current Challenges and Future Directions

Currently, the importance of viscoelasticity as a design parameter in tissue engineering biomaterials has been increasingly recognized. Despite these advances, several challenges remain that may hinder clinical translation: (1)

Trade-offs between viscoelastic tunability and biocompatibility: Covalent cross-linking often requires initiators or cross-linkers with potential cytotoxicity; degradation products of synthetic polymers may elicit adverse cellular responses.^65,68 In addition, commonly used inert materials lack cell-adhesive motifs, necessitating further biochemical functionalization.^{107,113,115,117}

(2)

Mechanical limitations: Although physically cross-linked systems exhibit favorable viscoelastic profiles, their inherently weak mechanical strength restricts their use in mechanically demanding scenarios.^110,111,117

(3)

Environmental constraints: Viscoelasticity tuning via dynamic covalent bonds is often highly dependent on specific physicochemical conditions.^113,114 For example, hydrazone bonds exhibit dynamic behavior predominantly under mildly acidic environments (pH 4.0–6.0), whereas under physiological pH, bond exchange is retarded.^114,130

(4)

Complexity and scalability of advanced network designs: Cutting-edge strategies such as topological sliding networks¹¹⁵ or supramolecular assemblies^116–118 offer exquisite control over stress relaxation behavior, yet they often require complex molecular design, multistep synthesis, and sophisticated fabrication processes.

Future research may focus on the following directions (Fig. 10):

FIG. 10.

Schematic representation of the prospective applications of viscoelastic independently tunable hydrogels in regenerative medicine.

(1)

Precise regulation of cell behavior: By independently adjusting viscoelasticity, researchers can fine-tune cell proliferation, migration, and differentiation, thus providing an optimal microenvironment for specific cells in regenerative medicine.

(2)

Personalized treatment schemes: Viscoelastic hydrogels with independent regulation can be customized according to the physiological conditions of individual patients. In particular, for tissue repair or organ regeneration, this allows for personalized material design tailored to specific diseases or injuries, further advancing the field of personalized regenerative medicine.^245,246

(3)

Improvement of organ models and organoid culture in vitro: Applying hydrogels with independently adjustable viscoelasticity in organ and organoid cultures in vitro can better simulate the in vivo microenvironment, enhancing the physiological relevance of the models and the accuracy of experimental results.^{109,117,241,244}

(4)

Regeneration of complex tissues and organs: These materials may provide a foundation for the regeneration of complex tissues or organs with multiple layers and components. More research is needed to gradually explore the appropriate viscoelastic parameters of materials for various tissue engineering applications.^247–249

Overall, viscoelastic independently adjustable hydrogels are expected to drive the development of regenerative medicine toward more refined, personalized, and complex system regeneration.

Authors’ Contributions

Q.Q.: Investigation, visualization, validation, and writing—original draft. Y.S.: Methodology and data curation. J.W.: Visualization and methodology. X.L.: Conceptualization. L.Z.: Conceptualization. H.Y.: Conceptualization. N.Z.: Conceptualization. K.Z.: Supervision. Z.Z.: Investigation, methodology, and funding acquisition. Y.B.: Writing—review and editing, project administration, funding acquisition, and conceptualization.

Footnotes

Funding Information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 82071144 and 82301117), the Innovation Research Team Project of Beijing Stomatological Hospital, Capital Medical University (Grant No. CXTD202203), the Beijing Stomatological Hospital, Capital Medical University Young Scientist Program (Grant No. YSP202010), and the Beijing Hospitals Authority Clinical Medicine Development Special Funding Support (Grant No. ZLRK202330).

Disclosure Statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this article.

References

Engler

, Sen

, Sweeney

, et al. Matrix elasticity directs stem cell lineage specification. Cell, 2006; 126(4):677–689; doi: 10.1016/j.ce.2006.06.044

Humphrey

, Dufresne

, Schwartz

. Mechanotransduction and extracellular matrix homeostasis. Nat Rev Mol Cell Biol, 2014; 15(12):802–812; doi: 10.1038/nrm3896

Discher

, Janmey

, Wang

Y-L

. Tissue cells feel and respond to the stiffness of their substrate. Science, 2005; 310(5751):1139–1143; doi: 10.1126/science.1116995

Whitehead

, Griffin

, Gionet-Gonzales

, et al. Hydrogel mechanics are a key driver of bone formation by mesenchymal stromal cell spheroids. Biomaterials, 2021; 269:120607; doi: 10.1016/j.biomaterials.2020.120607

, Yun

, Narsu

. A mathematical model for viscoelastic properties of biological soft tissue. Theory Biosci, 2022; 141(1):13–25; doi: 10.1007/s12064-021-00361-7

Tajvidi Safa

, Huang

, Kabla

, et al. Active viscoelastic models for cell and tissue mechanics. R Soc Open Sci, 2024; 11(4):231074; doi: 10.1098/rsos.231074

Snoeijer

, Pandey

, Herrada

, et al. The relationship between viscoelasticity and elasticity. Proc Math Phys Eng Sci, 2020; 476(2243):20200419; doi: 10.1098/rspa.2020.0419

Slater

, Li

, Indana

, et al. Transient mechanical interactions between cells and viscoelastic extracellular matrix. Soft Matter, 2021; 17(45):10274–10285; doi: 10.1039/d0sm01911a

Fan

, Adebowale

, Váncza

, et al. Matrix viscoelasticity promotes liver cancer progression in the pre-cirrhotic liver. Nature, 2024; 626(7999):635–642.

10.

Charrier

, Pogoda

, Wells

, et al. Control of cell morphology and differentiation by substrates with independently tunable elasticity and viscous dissipation. Nat Commun, 2018; 9(1):449; doi: 10.1038/s41467-018-02906-9

11.

Chaudhuri

, Cooper-White

, Janmey

, et al. Effects of extracellular matrix viscoelasticity on cellular behaviour. Nature, 2020; 584(7822):535–546; doi: 10.1038/s41586-020-2612-2

12.

Elosegui-Artola

. The extracellular matrix viscoelasticity as a regulator of cell and tissue dynamics. Curr Opin Cell Biol, 2021; 72:10–18; doi: 10.1016/j.ceb.2021.04.002

13.

Mao

, Shin

, Mooney

. Effects of substrate stiffness and cell-cell contact on mesenchymal stem cell differentiation. Biomaterials, 2016; 98:184–191; doi: 10.1016/j.biomaterials.2016.05.004

14.

Lai

, Geliang

, Bin

, et al. Effects of hydrogel stiffness and viscoelasticity on organoid culture: A comprehensive review. Mol Med, 2025; 31(1):83; doi: 10.1186/s10020-025-01131-7

15.

Baumgart

. Stiffness—an unknown world of mechanical science. Injury, 2000; 31(Suppl 2):B14–B23; doi: 10.1016/S0020-1383(00)80040-6

16.

, Dai

, Hong

. Recent advances in high-strength and elastic hydrogels for 3D printing in biomedical applications. Acta Biomater, 2019; 95:50–59; doi: 10.1016/j.actbio.2019.05.032

17.

Budday

, Sommer

, Holzapfel

, et al. Viscoelastic parameter identification of human brain tissue. J Mech Behav Biomed Mater, 2017; 74:463–476; doi: 10.1016/j.jmbbm.2017.07.014

18.

Liu

, Bilston

. On the viscoelastic character of liver tissue: Experiments and modelling of the linear behaviour. Biorheology, 2000; 37(3):191–201; doi: 10.1177/0006355X200003700300

19.

Miller

, Straight

, Palmer

. Inertial artifact in viscoelastic measurements of striated muscle: Modeling and experimental results. Biophys J, 2022; 121(8):1424–1434; doi: L 10.1016/j.bpj.2022.03.018

20.

Geerligs

, Peters

, Ackermans

, et al. Linear viscoelastic behavior of subcutaneous adipose tissue. Biorheology, 2008; 45(6):677–688; doi: 10.3233/BIR-2008-0517

21.

Mano

. Viscoelastic properties of bone: Mechanical spectroscopy studies on a chicken model. Mater Sci Eng C, 2005; 25(2):145–152; doi: 10.1016/j.msec.2005.01.017

22.

Bonifasi‐Lista

, Lakez

, Small

, et al. Viscoelastic properties of the human medial collateral ligament under longitudinal, transverse and shear loading. J Orthop Res, 2005; 23(1):67–76; doi: 10.1016/j.orthres.2004.06.002

23.

Huang

, Hoppe

, Kurtaliaj

, et al. Effects of tendon viscoelasticity on the distribution of forces across sutures in a model of tendon-to-bone repair. Int J Solids Struct, 2022; 250:111725; doi: 10.1016/j.ijsolstr.2022.111725

24.

Yang

, Sherman

, Gludovatz

, et al. On the tear resistance of skin. Nat Commun, 2015; 6(1):6649; doi: 10.1038/ncomms7649

25.

Lawless

, Sadeghi

, Temple

, et al. Viscoelasticity of articular cartilage: Analysing the effect of induced stress and the restraint of bone in a dynamic environment. J Mech Behav Biomed Mater, 2017; 75:293–301; doi: 10.1016/j.jmbbm.2017.07.040

26.

Vappou

, Breton

, Choquet

, et al. Magnetic resonance elastography compared with rotational rheometry for in vitro brain tissue viscoelasticity measurement. MAGMA, 2007; 20(5–6):273–278; doi: 10.1007/s10334-007-0098-7

27.

Haji

, Mori

, Omori

, et al. Mechanical properties of the vocal fold. Acta Oto-Laryngol, 1992; 112(3):559–565; doi: 10.3109/00016489209137440

28.

Töyräs

, Nieminen

, Kröger

, et al. Bone mineral density, ultrasound velocity, and broadband attenuation predict mechanical properties of trabecular bone differently. Bone, 2002; 31(4):503–507; doi: 10.1007/s00158-024-03756-4

29.

Coluccino

, Peres

, Gottardi

, et al. Anisotropy in the viscoelastic response of knee meniscus cartilage. Jabfm, 2017; 15(1):77–83; doi: 10.5301/jabfm.5000319

30.

Troyer

, Puttlitz

. Human cervical spine ligaments exhibit fully nonlinear viscoelastic behavior. Acta Biomater, 2011; 7(2):700–709; doi: 10.1016/j.actbio.2010.09.003

31.

Netti

, D’amore

, Ronca

, et al. Structure-mechanical properties relationship of natural tendons and ligaments. J Mater Sci: Mater Med, 1996; 7(9):525–530; doi: 10.1007/BF00122175

32.

Tanaka

, Iwabuchi

, Rego

, et al. Dynamic shear behavior of mandibular condylar cartilage is dependent on testing direction. J Biomech, 2008; 41(5):1119–1123; doi: 10.1016/j.jbiomech.2007.12.012

33.

Jansen

, Birch

, Schiffman

, et al. Mechanics of intact bone marrow. J Mech Behav Biomed Mater, 2015; 50:299–307; doi: 10.1016/j.jmbbm.2015.06.023

34.

Pereira

, Caridade

, Frias

, et al. Biomechanical and cellular segmental characterization of human meniscus: Building the basis for tissue engineering therapies. Osteoarthritis Cartilage, 2014; 22(9):1271–1281; doi: 10.1016/j.joca.2014.07.001

35.

Barnes

, Lawless

, Shepherd

, et al. Viscoelastic properties of human bladder tumours. J Mech Behav Biomed Mater, 2016; 61:250–257; doi: 10.1016/j.jmbbm.2016.03.012

36.

Chintada

, Rau

, Goksel

. Nonlinear characterization of tissue viscoelasticity with acoustoelastic attenuation of shear waves. IEEE Trans Ultrason Ferroelectr Freq Control, 2022; 69(1):38–53; doi: 10.1109/TUFFC.2021.3105339

37.

Hatami-Marbini

. Viscoelastic shear properties of the corneal stroma. J Biomech, 2014; 47(3):723–728; doi: 10.1016/j.jbiomech.2013.11.019

38.

Kobayashi

, Okamura

, Tsukune

, et al. Non-minimum phase viscoelastic properties of soft biological tissues. J Mech Behav Biomed Mater, 2020; 110:103795; doi: 10.1016/j.jmbbm.2020.103795

39.

Tanaka

, Inubushi

, Koolstra

, et al. Comparison of dynamic shear properties of the porcine molar and incisor periodontal ligament. Ann Biomed Eng, 2006; 34(12):1917–1923; doi: 10.1007/s10439-006-9209-2

40.

Chan

. Measurements of vocal fold tissue viscoelasticity: Approaching the male phonatory frequency range. J Acoust Soc Am, 2004; 115(6):3161–3170; doi: 10.1121/1.1736272

41.

Chaudhuri

, Koshy

, Branco da Cunha

, et al. Extracellular matrix stiffness and composition jointly regulate the induction of malignant phenotypes in mammary epithelium. Nat Mater, 2014; 13(10):970–978; doi: 10.1038/nmat4009

42.

Malhotra

, Pan

, Rüther

, et al. Linear viscoelastic and microstructural properties of native male human skin and in vitro 3D reconstructed skin models. J Mech Behav Biomed Mater, 2019; 90:644–654; doi: 10.1016/j.jmbbm.2018.11.013

43.

Nam

, Hu

, Butte

, et al. Strain-enhanced stress relaxation impacts nonlinear elasticity in collagen gels. Proc Natl Acad Sci U S A, 2016; 113(20):5492–5497; doi: 10.1073/pnas.1523906113

44.

Fessel

, Snedeker

. Evidence against proteoglycan mediated collagen fibril load transmission and dynamic viscoelasticity in tendon. Matrix Biol, 2009; 28(8):503–510; doi: 10.1016/j.matbio.2009.08.002

45.

Mierke

. Viscoelasticity, like forces, plays a role in mechanotransduction. Front Cell Dev Biol, 2022; 10:789841; doi: 10.3389/fcell.2022.789841

46.

, Jeffreys

, Diba

, et al. Viscoelastic biomaterials for tissue regeneration. Tissue Eng Part C Methods, 2022; 28(7):289–300; doi: 10.1089/ten.TEC.2022.0040

47.

Martinez-Garcia

, de Hilster

RHJ

, Sharma

, et al. Architecture and composition dictate viscoelastic properties of organ-derived extracellular matrix hydrogels. Polymers (Basel), 2021; 13(18):3113; doi: 10.3390/polym13183113

48.

de Hilster

RHJ

, Sharma

, Jonker

, et al. Human lung extracellular matrix hydrogels resemble the stiffness and viscoelasticity of native lung tissue. Am J Physiol Lung Cell Mol Physiol, 2020; 318(4):L698–L704; doi: 10.1152/ajplung.00451.2019

49.

Nizamoglu

, de Hilster

, Zhao

, et al. An in vitro model of fibrosis using crosslinked native extracellular matrix-derived hydrogels to modulate biomechanics without changing composition. Acta Biomater, 2022; 147:50–62; doi: 10.1016/j.actbio.2022.05.031

50.

Tang

, Richardson

, Anseth

. Dynamic covalent hydrogels as biomaterials to mimic the viscoelasticity of soft tissues. Prog Mater Sci, 2021; 120:100738; doi: 10.1016/j.pmatsci.2020.100738

51.

Jannati

, Shahri

, Jafarzadeh

, et al. Non-newtonian pulsatile blood flow through the stenosed arteries: Comparison between the viscoelastic and elastic arterial wall in response to the alterations. Biomed Phys Eng Express, 2023; 9(6):65022; doi: 10.1088/2057-1976/ad0240

52.

Silver

, Horvath

, Foran

. Viscoelasticity of the vessel wall: The role of collagen and elastic fibers. Crit Rev Biomed Eng, 2001; 29(3):279–301; doi: 10.1615/critrevbiomedeng.v29.i3.10

53.

, Zhao

, Shi

, et al. Viscoelastic properties of human periodontal ligament: Effects of the loading frequency and location. Angle Orthod, 2019; 89(3):480–487; doi: 10.2319/062818-481.1

54.

Zhang

, Liu

, Feng

, et al. Rational design of viscoelastic hydrogels for periodontal ligament remodeling and repair. Acta Biomater, 2024; 174:69–90; doi: 10.1016/j.actbio.2023.12.017

55.

Ebihara

, Venkatesan

, Tanaka

, et al. Changes in extracellular matrix and tissue viscoelasticity in bleomycin–induced lung fibrosis: Temporal aspects. Am J Respir Crit Care Med, 2000; 162(4 Pt 1):1569–1576; doi: 10.1164/ajrccm.162.4.9912011

56.

Mierke

. Viscoelasticity acts as a marker for tumor extracellular matrix characteristics. Front Cell Dev Biol, 2021; 9:785138; doi: 10.3389/fcell.2021.785138

57.

Hartley

, Williams

, Mata

. comparison of the mechanical properties of ecm components and synthetic self‐assembling peptides. Adv Healthc Mater, 2025; 14(11):e2402385; doi: 10.1002/adhm.202402385

58.

Sun

. The mechanics of fibrillar collagen extracellular matrix. Cell Rep Phys Sci, 2021; 2(8):100515; doi: 10.1016/j.xcrp.2021.100515

59.

Silver

, Kelkar

, Deshmukh

. Molecular basis for mechanical properties of ecms: Proposed role of fibrillar collagen and proteoglycans in tissue biomechanics. Biomolecules, 2021; 11(7):1018; doi: 10.3390/biom11071018

60.

Bertassoni

, Swain

. The contribution of proteoglycans to the mechanical behavior of mineralized tissues. J Mech Behav Biomed Mater, 2014; 38:91–104; doi: 10.1016/j.jmbbm.2014.06.008

61.

Sodhi

, Panitch

. Glycosaminoglycans in tissue engineering: A review. Biomolecules, 2020; 11(1):29; doi: 10.3390/biom11010029

62.

Bauer

, Gu

, Kwee

, et al. Hydrogel substrate stress-relaxation regulates the spreading and proliferation of mouse myoblasts. Acta Biomater, 2017; 62:82–90; doi: 10.1016/j.actbio.2017.08.041

63.

Chaudhuri

, Gu

, Klumpers

, et al. Hydrogels with tunable stress relaxation regulate stem cell fate and activity. Nat Mater, 2016; 15(3):326–334; doi: 10.1038/nmat4489

64.

Darnell

, Young

, Gu

, et al. Substrate stress‐relaxation regulates scaffold remodeling and bone formation in vivo. Adv Healthc Mater, 2017; 6(1):10.1002/adhm.201601185; doi: 10.1002/adhm.201601185

65.

Cameron

, Frith

, Cooper-White

. The influence of substrate creep on mesenchymal stem cell behaviour and phenotype. Biomaterials, 2011; 32(26):5979–5993; doi: 10.1016/j.biomaterials.2011.04.003

66.

Hsiao

S-H

, Hsu

S-h

. Synthesis and characterization of dual stimuli-sensitive biodegradable polyurethane soft hydrogels for 3D cell-laden bioprinting. ACS Appl Mater Interfaces, 2018; 10(35):29273–29287; doi: 10.1021/acsami.8b08362

67.

Huang

, Li

, Ma

, et al. Collagen hydrogel viscoelasticity regulates MSC chondrogenesis in a ROCK-dependent manner. Sci Adv, 2023; 9(6):eade9497; doi: 10.1126/sciadv.ade9497

68.

Liu

, Yu

, Yuan

, et al. Engineering the viscoelasticity of gelatin methacryloyl (gelma) hydrogels via small “dynamic bridges” to regulate bmsc behaviors for osteochondral regeneration. Bioact Mater, 2023; 25:445–459; doi: 10.1016/j.bioactmat.2022.07.031

69.

Walker

, Pringle

, Ciccone

, et al. Mind the viscous modulus: The mechanotransductive response to the viscous nature of isoelastic matrices regulates stem cell chondrogenesis. Adv Healthc Mater, 2024; 13(9):e2302571; doi: 10.1002/adhm.202302571

70.

Adebowale

, Gong

, Hou

, et al. Enhanced substrate stress relaxation promotes filopodia-mediated cell migration. Nat Mater, 2021; 20(9):1290–1299; doi: 10.1038/s41563-021-00981-w

71.

Cameron

, Frith

, Gomez

, et al. The effect of time-dependent deformation of viscoelastic hydrogels on myogenic induction and rac1 activity in mesenchymal stem cells. Biomaterials, 2014; 35(6):1857–1868; doi: 10.1016/j.biomaterials.2013.11.023

72.

Hurley

, Campbell

, Killgore

, et al. Measurement of viscoelastic loss tangent with contact resonance modes of atomic force microscopy. Macromolecules, 2013; 46(23):9396–9402; doi: 10.1021/ma401988h

73.

Mondal

. Part III: Characterization Tools and Techniques of Hydrogels. Springer International Publishing AG: Switzerland; 2019.

74.

Cacopardo

, Guazzelli

, Ahluwalia

. Characterizing and engineering biomimetic materials for viscoelastic mechanotransduction studies. Tissue Eng Part B Rev, 2022; 28(4):912–925; doi: 10.1089/ten.teb.2021.0151

75.

Schmidt

, Kiefer

, Dalgliesh

, et al. Nanoscopic interfacial hydrogel viscoelasticity revealed from comparison of macroscopic and microscopic rheology. Nano Lett, 2024; 24(16):4758–4765.

76.

, Harvey

, Begiristain

, et al. Measuring the elastic modulus of soft biomaterials using nanoindentation. J Mech Behav Biomed Mater, 2022; 133:105329; doi: 10.1016/j.jmbbm.2022.105329

77.

Shepherd

, Zhang

, Ovaert

, et al. Direct comparison of nanoindentation and macroscopic measurements of bone viscoelasticity. J Mech Behav Biomed Mater, 2011; 4(8):2055–2062; doi: 10.1016/j.jmbbm.2011.07.004

78.

, Liu

, Xu

, et al. Nanoscale characterization of dynamic cellular viscoelasticity by atomic force microscopy with varying measurement parameters. J Mech Behav Biomed Mater, 2018; 82:193–201; doi: 10.1016/j.jmbbm.2018.03.036

79.

Liu

, Zhang

, Chen

, et al. An afm-based model-fitting-free viscoelasticity characterization method for accurate grading of primary prostate tumor. IEEE Trans Nanobioscience, 2024; 23(2):319–327; doi: 10.1109/TNB.2024.3351768

80.

Efremov

, Okajima

, Raman

. Measuring viscoelasticity of soft biological samples using atomic force microscopy. Soft Matter, 2020; 16(1):64–81; doi: 10.1039/c9sm01020c

81.

Tripathy

, Berger

. Measuring viscoelasticity of soft samples using atomic force microscopy. J Biomech Eng, 2009; 131(9):94507; doi: 10.1115/1.3194752

82.

Poul

, Ormachea

, Gary

, et al. Comprehensive experimental assessments of rheological models’ performance in elastography of soft tissues. Acta Biomater, 2022; 146:259–273; doi: 10.1016/j.actbio.2022.04.047

83.

Perni

, Prokopovich

. Rheometer enabled study of cartilage frequency-dependent properties. Sci Rep, 2020; 10(1):20696; doi: 10.1038/s41598-020-77758-9

84.

Paimushin

, Kayumov

, Kholmogorov

. On the regularities of behavior of an elastic-viscoplastic composite under cyclic loading. Russ Math, 2019; 63(5):75–81; doi: 10.3103/S1066369X19050086

85.

Xia

, Xiao

, Pan

, et al. Microrheology, advances in methods and insights. Adv Colloid Interface Sci, 2018; 257:71–85; doi: 10.1016/j.cis.2018.04.008

86.

Mao

, Nielsen

, Ali

. Passive and active microrheology for biomedical systems. Front Bioeng Biotechnol, 2022; 10:916354; doi: 10.3389/fbioe.2022.916354

87.

Bergamaschi

, Taris

K-KH

, Biebricher

, et al. Viscoelasticity of diverse biological samples quantified by acoustic force microrheology (afmr). Commun Biol, 2024; 7(1):683; doi: 10.1038/s42003-024-06367-3

88.

Moore

, Caughey

, Meyer

, et al. In Vivo Viscoelastic Response (VisR) ultrasound for characterizing mechanical anisotropy in lower-limb skeletal muscles of boys with and without Duchenne muscular dystrophy. Ultrasound Med Biol, 2018; 44(12):2519–2530; doi: 10.1016/j.ultrasmedbio.2018.07.004

89.

Schmitt

, Henni

, Cloutier

. Characterization of blood clot viscoelasticity by dynamic ultrasound elastography and modeling of the rheological behavior. J Biomech, 2011; 44(4):622–629; doi: 10.1016/j.jbiomech.2010.11.015

90.

Feng

, Qiu

, Chen

, et al. Viscoelastic characterization of soft tissue-mimicking gelatin phantoms using indentation and magnetic resonance elastography. J Vis Exp, 2022(183):10.3791/63770.

91.

Bilston

. Soft tissue rheology and its implications for elastography: Challenges and opportunities. NMR Biomed, 2018; 31(10):e3832; doi: 10.1002/nbm.3832

92.

Caponi

, Passeri

, Capponi

, et al. Non-contact elastography methods in mechanobiology: A point of view. Eur Biophys J, 2022; 51(2):99–104; doi: 10.1007/s00249-021-01567-9

93.

Garteiser

, Doblas

, Van Beers

. Magnetic resonance elastography of liver and spleen: Methods and applications. NMR Biomed, 2018; 31(10):e3891; doi: 10.1002/nbm.3891

94.

Asbach

, Klatt

, Hamhaber

, et al. Assessment of liver viscoelasticity using multifrequency mr elastography. Magn Reson Med, 2008; 60(2):373–379; doi: 10.1002/mrm.21636

95.

Riek

, Millward

, Hamann

, et al. Magnetic resonance elastography reveals altered brain viscoelasticity in experimental autoimmune encephalomyelitis. Neuroimage Clin, 2012; 1(1):81–90; doi: 10.1016/j.nicl.2012.09.003

96.

Urban

, Chen

, Fatemi

. A review of shearwave dispersion ultrasound vibrometry (SDUV) and its applications. Curr Med Imaging Rev, 2012; 8(1):27–36; doi: 10.2174/157340512799220625

97.

, Flé

, Bhatt

, et al. Viscoelasticity imaging of biological tissues and single cells using shear wave propagation. Front Phys, 2021; 9:666192; doi: 10.3389/fphy.2021.666192

98.

Eliahoo

, Setayesh

, Hoffman

, et al. Viscoelasticity in 3D cell culture and regenerative medicine: Measurement techniques and biological relevance. ACS Mater Au, 2024; 4(4):354–384; doi: 10.1021/acsmaterialsau.3c00038

99.

Ahmad

, Salman

, Khan

, et al. Versatility of hydrogels: From synthetic strategies, classification, and properties to biomedical applications. Gels, 2022; 8(3):167; doi: 10.3390/gels8030167

100.

Chaudhuri

. Viscoelastic hydrogels for 3D cell culture. Biomater Sci, 2017; 5(8):1480–1490; doi: 10.1039/c7bm00261k

101.

Zhu

, Wang

, et al. Metal-coordinated dynamics and viscoelastic properties of double-network hydrogels. Gels, 2023; 9(2):145; doi: 10.3390/gels9020145

102.

Yang

, Chen

, Zhao

, et al. Constructions and properties of physically cross-linked hydrogels based on natural polymers. Polym Rev, 2023; 63(3):574–612; doi: 10.1080/15583724.2022.2137525

103.

, Yan

, Dreiss

, et al. Injectable peg hydrogels with tissue‐like viscoelasticity formed through reversible alendronate–calcium phosphate crosslinking for cell–material interactions. Adv Healthc Mater, 2024; 13(22):e2400472; doi: 10.1002/adhm.202400472

104.

Lin

, Lou

, Xia

, et al. Cross‐linker architectures impact viscoelasticity in dynamic covalent hydrogels. . Adv Healthc Mater, 2024; 13(30):e2402059; doi: 10.1002/adhm.202402059

105.

Richardson

, Wilcox

, Randolph

, et al. Hydrazone covalent adaptable networks modulate extracellular matrix deposition for cartilage tissue engineering. Acta Biomater, 2019; 83:71–82; doi: 10.1016/j.actbio.2018.11.014

106.

Lee

H-P

, Gu

, Mooney

, et al. Mechanical confinement regulates cartilage matrix formation by chondrocytes. Nat Mater, 2017; 16(12):1243–1251; doi: 10.1038/nmat4993

107.

Indana

, Agarwal

, Bhutani

, et al. Viscoelasticity and adhesion signaling in biomaterials control human pluripotent stem cell morphogenesis in 3D culture. Adv Mater, 2021; 33(43):e2101966; doi: 10.1002/adma.202101966

108.

Nam

, Gupta

, Lee

H-P

, et al. Cell cycle progression in confining microenvironments is regulated by a growth-responsive trpv4-pi3k/akt-p27kip1 signaling axis. Sci Adv, 2019; 5(8):eaaw6171; doi: 10.1126/sciadv.aaw6171

109.

Bao

, Cui

, Wang

, et al. Carbon nanotubes promote the development of intestinal organoids through regulating extracellular matrix viscoelasticity and intracellular energy metabolism. ACS Nano, 2021; 15(10):15858–15873; doi: 10.1021/acsnano.1c03707

110.

Hughes

, Aykanat

, Pierini

, et al. DNA‐intercalating supramolecular hydrogels for tunable thermal and viscoelastic properties. Angew Chem Int Ed Engl, 2024; 63(45):e202411115; doi: 10.1002/anie.202411115

111.

Peng

, Hsiao

, Gupta

, et al. Dynamic matrices with DNA-encoded viscoelasticity for cell and organoid culture. Nat Nanotechnol, 2023; 18(12):1463–1473; doi: 10.1038/s41565-023-01483-3

112.

Jung

, Earmme

, Choi

S-H

. Effect of end-block chain length on rheological properties of aba triblock copolymer hydrogels. Korea-Aust Rheol J, 2021; 33(2):123–131; doi: 10.1007/s13367-021-0011-3

113.

McKinnon

, Domaille

, Cha

, et al. Biophysically defined and cytocompatible covalently adaptable networks as viscoelastic 3D cell culture systems. Adv Mater, 2014; 26(6):865–872; doi: 10.1002/adma.201303680

114.

Jay

, Shukair

, Langheinrich

, et al. Modulation of viscoelasticity and hiv transport as a function of ph in a reversibly crosslinked hydrogel. Adv Funct Mater, 2009; 19(18):2969–2977; doi: 10.1002/adfm.200900757

115.

Tong

, Yang

. Sliding hydrogels with mobile molecular ligands and crosslinks as 3D stem cell niche. Adv Mater, 2016; 28(33):7257–7263; doi: 10.1002/adma.201601484

116.

Seth

, Friedrichs

, Limasale

YDP

, et al. Interpenetrating polymer network hydrogels with tunable viscoelasticity and proteolytic cleavability to direct stem cells in vitro. Adv Healthc Mater, 2025; 14(9):e2402656; doi: 10.1002/adhm.202402656

117.

Johnick

, van

, Aarts

, et al. Co‐assembled supramolecular hydrogelators enhance glomerulogenesis in kidney organoids through cell‐adhesive motifs. Adv Funct Mater, 2024; 34(42):2404786; doi: 10.1002/adfm.202404786

118.

Yang

, Wei

, Loebel

, et al. Enhanced mechanosensing of cells in synthetic 3D matrix with controlled biophysical dynamics. Nat Commun, 2021; 12(1):3514; doi: 10.1038/s41467-021-23120-0

119.

Lou

, Stowers

, Nam

, et al. Stress relaxing hyaluronic acid-collagen hydrogels promote cell spreading, fiber remodeling, and focal adhesion formation in 3D cell culture. Biomaterials, 2018; 154:213–222; doi: 10.1016/j.biomaterials.2017.11.004

120.

Drozdov

, de Claville Christiansen

. Tuning the viscoelastic response of hydrogel scaffolds with covalent and dynamic bonds. J Mech Behav Biomed Mater, 2022; 130:105179; doi: 10.1016/j.jmbbm.2022.105179

121.

Bootsma

, Fitzgerald

, Free

, et al. 3D printing of an interpenetrating network hydrogel material with tunable viscoelastic properties. J Mech Behav Biomed Mater, 2017; 70:84–94; doi: 10.1016/j.jmbbm.2016.07.020

122.

Zhao

, Xue

, Burns

, et al. Viscoelastic supramolecular hyaluronan-peptide cross-linked hydrogels. Biomacromolecules, 2024; 25(7):3946–3958; doi: 10.1021/acs.biomac.4c00095

123.

Carberry

, Rao

, Anseth

. Phototunable viscoelasticity in hydrogels through thioester exchange. Ann Biomed Eng, 2020; 48(7):2053–2063; doi: 10.1007/s10439-020-02460-w

124.

Kazemirad

, Heris

, Mongeau

. Viscoelasticity of hyaluronic acid‐gelatin hydrogels for vocal fold tissue engineering. J Biomed Mater Res B Appl Biomater, 2016; 104(2):283–290; doi: 10.1002/jbm.b.33358

125.

Martinez-Garcia

, Valk

, Sharma

, et al. Adipose tissue-derived stromal cells alter the mechanical stability and viscoelastic properties of gelatine methacryloyl hydrogels. Int J Mol Sci, 2021; 22(18):10153; doi: 10.3390/ijms221810153

126.

Cacopardo

, Guazzelli

, Nossa

, et al. Engineering hydrogel viscoelasticity. J Mech Behav Biomed Mater, 2019; 89:162–167; doi: 10.1016/j.jmbbm.2018.09.031

127.

Charbonier

, Indana

, Chaudhuri

. Tuning viscoelasticity in alginate hydrogels for 3D cell culture studies. Curr Protoc, 2021; 1(5):e124; doi: 10.1002/cpz1.124

128.

Chester

, Lee

, Wagner

, et al. Elucidating the combinatorial effect of substrate stiffness and surface viscoelasticity on cellular phenotype. J Biomed Mater Res A, 2022; 110(6):1224–1237; doi: 10.1002/jbm.a.37367

129.

Tan

, Huang

, Ayers

, et al. Modulating viscoelasticity, stiffness, and degradation of synthetic cellular niches via stoichiometric tuning of covalent versus dynamic noncovalent cross-linking. ACS Cent Sci, 2018; 4(8):971–981; doi: 10.1021/acscentsci.8b00170

130.

Fagioli

, Pavoni

, Logrippo

, et al. Linear viscoelastic properties of selected polysaccharide gums as function of concentration, ph, and temperature. J Food Sci, 2019; 84(1):65–72; doi: 10.1111/1750-3841.14407

131.

Nam

, Stowers

, Lou

, et al. Varying peg density to control stress relaxation in alginate-peg hydrogels for 3D cell culture studies. Biomaterials, 2019; 200:15–24; doi: 10.1016/j.biomaterials.2019.02.004

132.

Hafeez

, Aldana

, Duimel

, et al. Molecular tuning of a benzene‐1, 3, 5‐tricarboxamide supramolecular fibrous hydrogel enables control over viscoelasticity and creates tunable ecm‐mimetic hydrogels and bioinks. Adv Mater, 2023; 35(24):e2207053; doi: 10.1002/adma.202207053

133.

, Ruan

, Huang

, et al. Harnessing the potential of hydrogels for advanced therapeutic applications: Current achievements and future directions. Signal Transduct Target Ther, 2024; 9(1):166; doi: 10.1038/s41392-024-01852-x

134.

Lou

, Friedowitz

, Will

, et al. Predictably engineering the viscoelastic behavior of dynamic hydrogels via correlation with molecular parameters. Adv Mater, 2021; 33(51):e2104460; doi: 10.1002/adma.202104460

135.

Chaudhuri

, Gu

, Darnell

, et al. Substrate stress relaxation regulates cell spreading. Nat Commun, 2015; 6(1):6364; doi: 10.1038/ncomms7365

136.

Narita

, Mayumi

, Ducouret

, et al. Viscoelastic properties of poly (vinyl alcohol) hydrogels having permanent and transient cross-links studied by microrheology, classical rheometry, and dynamic light scattering. Macromolecules, 2013; 46(10):4174–4183; doi: 10.1021/ma400600f

137.

Chrisnandy

, Blondel

, Rezakhani

, et al. Synthetic dynamic hydrogels promote degradation-independent in vitro organogenesis. Nat Mater, 2022; 21(4):479–487; doi: 10.1038/s41563-021-01136-7

138.

Loebel

, Ayoub

, Galarraga

, et al. Tailoring supramolecular guest–host hydrogel viscoelasticity with covalent fibrinogen double networks. J Mater Chem B, 2019; 7(10):1753–1760; doi: 10.1039/C8TB02593B

139.

Kaewprasit

, Kobayashi

, Damrongsakkul

. Thai silk fibroin gelation process enhancing by monohydric and polyhydric alcohols. Int J Biol Macromol, 2018; 118(Pt B):1726–1735; doi: 10.1016/j.ijbiomac.2018.07.017

140.

Moheimani

, Stealey

, Neal

, et al. Tunable viscoelasticity of alginate hydrogels via serial autoclaving. Adv Healthc Mater, 2024; 13(32):e2401550; doi: 10.1002/adhm.202401550

141.

Rosales

, Anseth

. The design of reversible hydrogels to capture extracellular matrix dynamics. Nat Rev Mater, 2016; 1(2):15012–15015; doi: 10.1038/natrevmats.2015.12

142.

, Song

, Soto

, et al. Viscoelastic extracellular matrix enhances epigenetic remodeling and cellular plasticity. Nat Commun, 2025; 16(1):4054; doi: 10.1101/2024.04.14.589442

143.

Grolman

, Weinand

, Mooney

. Extracellular matrix plasticity as a driver of cell spreading. Proc Natl Acad Sci U S A, 2020; 117(42):25999–26007; doi: 10.1073/pnas.2008801117

144.

Raines

. The extracellular matrix can regulate vascular cell migration, proliferation, and survival: Relationships to vascular disease. Int J Exp Pathol, 2000; 81(3):173–182; doi: 10.1046/j.1365-2613.2000.00155.x

145.

, Lin

, Huang

, et al. 3D spatiotemporal mechanical microenvironment: A hydrogel‐based platform for guiding stem cell fate. Adv Mater, 2018; 30(49):e1705911; doi: 10.1002/adma.201705911

146.

Wang

, Hashemi

, Stratton

, et al. The effect of physical cues of biomaterial scaffolds on stem cell behavior. Adv Healthc Mater, 2021; 10(3):e2001244; doi: 10.10.1002/adhm.202001244

147.

Jiang

, Xu

, Chen

, et al. Impact of hydrogel elasticity and adherence on osteosarcoma cells and osteoblasts. Adv Healthc Mater, 2020; 9(4):e2000054; doi: 10.1002/adhm.202000054

148.

Alonso-Nocelo

, Raimondo

, Vining

, et al. Matrix stiffness and tumor-associated macrophages modulate epithelial to mesenchymal transition of human adenocarcinoma cells. Biofabrication, 2018; 10(3):35004; doi: 10.1088/1758-5090/aaafbc

149.

, Han

, Yang

, et al. Viscoelastic cell microenvironment: Hydrogel‐based strategy for recapitulating dynamic ecm mechanics. Adv Funct Materials, 2021; 31(24):2100848; doi: 10.1002/adfm.202100848

150.

Huang

, Huang

, Xiao

, et al. Viscoelasticity in natural tissues and engineered scaffolds for tissue reconstruction. Acta Biomater, 2019; 97:74–92; doi: 10.1016/j.actbio.2019.08.013

151.

Liu

, Zhang

, Dong

, et al. Effect of viscoelastic properties of cellulose nanocrystal/collagen hydrogels on chondrocyte behaviors. Front Bioeng Biotechnol, 2022; 10:959409; doi: 10.3389/fbioe.2022.959409

152.

Qiao

, Fulmore

, Schaffer

, et al. Substrate stress relaxation regulates neural stem cell fate commitment. Proc Natl Acad Sci U S A, 2024; 121(28):e2317711121; doi: 10.1073/pnas.2317711121

153.

Sacco

, Vaneman

, Gomez

. Extracellular matrix viscoelasticity regulates tgfβ1‐induced epithelial‐mesenchymal transition and apoptosis via integrin linked kinase. J Cell Physiol, 2024; 239(2):e31165; doi: 10.1002/jcp.31165

154.

Lan

, Liu

, et al. Matrix viscoelasticity tunes the mechanobiological behavior of chondrocytes. Cell Biochem Funct, 2024; 42(7):e4126; doi: 10.1002/cbf.4126

155.

Bernero

, Zauchner

, Müller

, et al. Interpenetrating network hydrogels for studying the role of matrix viscoelasticity in 3D osteocyte morphogenesis. Biomater Sci, 2024; 12(4):919–932; doi: 10.1039/d3bm01781h

156.

Khalili

, Ahmad

. A review of cell adhesion studies for biomedical and biological applications. Int J Mol Sci, 2015; 16(8):18149–18184; doi: 10.3390/ijms160818149

157.

Choi

, Gonzalez

, Ho

, et al. Cell-cell adhesion impacts epithelia response to substrate stiffness: Morphology and gene expression. Biophys J, 2022; 121(2):336–346; doi: 10.1016/j.bpj.2021.11.2887

158.

Kamranvar

, Rani

, Johansson

. Cell cycle regulation by integrin-mediated adhesion. Cells, 2022; 11(16):2521; doi: 10.3390/cells11162521

159.

Marozas

, Anseth

, Cooper-White

. Adaptable boronate ester hydrogels with tunable viscoelastic spectra to probe timescale dependent mechanotransduction. Biomaterials, 2019; 223:119430; doi: 10.1016/j.biomaterials.2019.119430

160.

Cao

, Lin

, Driscoll

, et al. A chemomechanical model of matrix and nuclear rigidity regulation of focal adhesion size. Biophys J, 2015; 109(9):1807–1817; doi: 10.1016/j.bpj.2015.08.048

161.

Sun

, Hou

, Chu

, et al. Soft overcomes the hard: Flexible materials adapt to cell adhesion to promote cell mechanotransduction. Bioact Mater, 2022; 10:397–404; doi: 10.1016/j.bioactmat.2021.08.026

162.

Zhong

, Yang

, Liao

, et al. Matrix stiffness-regulated cellular functions under different dimensionalities. Biomater Sci, 2020; 8(10):2734–2755; doi: 10.1039/c9bm01809c

163.

Mandal

, Gong

, Rylander

, et al. Opposite responses of normal hepatocytes and hepatocellular carcinoma cells to substrate viscoelasticity. Biomater Sci, 2020; 8(7):2040–1328; doi: 10.1039/c9bm01339c

164.

Gong

, Szczesny

, Caliari

, et al. Matching material and cellular timescales maximizes cell spreading on viscoelastic substrates. Proc Natl Acad Sci U S A, 2018; 115(12):E2686–E2695; doi: 10.1073/pnas.1716620115

165.

, Xu

, Cheng

. The motor-clutch model in mechanobiology and mechanomedicine. Mechanobiol Med, 2024; 2(3):100067; doi: 10.1016/j.mbm.2024.100067

166.

, Xu

, Liu

. An overview of substrate stiffness guided cellular response and its applications in tissue regeneration. Bioact Mater, 2022; 15:82–102; doi: 10.1016/j.bioactmat.2021.12.005

167.

Zhang

, Wang

, Sun

, et al. Dynamic hydrogels with viscoelasticity and tunable stiffness for the regulation of cell behavior and fate. Materials (Basel), 2023; 16(14):5161; doi: 10.3390/ma16145161

168.

, Wang

, Yang

, et al. A viscoelastic chitosan-modified three-dimensional porous poly (l-lactide-co-ε-caprolactone) scaffold for cartilage tissue engineering. J Biomater Sci Polym Ed, 2012; 23(1–4):405–424; doi: 10.1163/092050610X551970

169.

Lee

, Alisafaei

, Adebawale

, et al. The nuclear piston activates mechanosensitive ion channels to generate cell migration paths in confining microenvironments. Sci Adv, 2021; 7(2):eabd4058; doi: 10.1126/sciadv.abd4058

170.

Chester

, Kathard

, Nortey

, et al. Viscoelastic properties of microgel thin films control fibroblast modes of migration and pro-fibrotic responses. Biomaterials, 2018; 185:371–382; doi: 10.1016/j.biomaterials.2018.09.012

171.

Lee

H-P

, Stowers

, Chaudhuri

. Volume expansion and trpv4 activation regulate stem cell fate in three-dimensional microenvironments. Nat Commun, 2019; 10(1):529; doi: 10.1038/s41467-019-08465-x

172.

Saraswathibhatla

, Indana

, Chaudhuri

. Cell–extracellular matrix mechanotransduction in 3D. Nat Rev Mol Cell Biol, 2023; 24(7):495–516; doi: 10.1038/s41580-023-00583-1

173.

Yamada

, Sixt

. Mechanisms of 3D cell migration. Nat Rev Mol Cell Biol, 2019; 20(12):738–752; doi: 10.1038/s41580-019-0172-9

174.

Isomursu

, Park

K-Y

, Hou

, et al. Directed cell migration towards softer environments. Nat Mater, 2022; 21(9):1081–1090; doi: 10.1038/s41563-022-01294-2

175.

Saei Arezoumand

, Alizadeh

, Pilehvar-Soltanahmadi

, et al. An overview on different strategies for the stemness maintenance of mscs. Artif Cells Nanomed Biotechnol, 2017; 45(7):1255–1271; doi: 10.1080/21691401.2016.1246452

176.

Zhao

, Lin

, Wang

. Maintenance and modulation of stem cells stemness based on biomaterial designing via chemical and physical signals. Appl Mater Today, 2020; 19:100614; doi: 10.1016/j.apmt.2020.100614

177.

, Zhang

, Enhe

, et al. Bioactive nanoparticle reinforced alginate/gelatin bioink for the maintenance of stem cell stemness. Mater Sci Eng C Mater Biol Appl, 2021; 126:112193; doi: 10.1016/j.msec.2021.112193

178.

Madl

, LeSavage

, Dewi

, et al. Maintenance of neural progenitor cell stemness in 3D hydrogels requires matrix remodelling. Nat Mater, 2017; 16(12):1233–1242; doi: 10.1038/nmat5020

179.

Jiang

, Tian

, Wang

, et al. Regulation mechanisms and maintenance strategies of stemness in mesenchymal stem cells. Stem Cell Rev Rep, 2024; 20(2):455–483; doi: 10.1007/s12015-023-10658-33

180.

Liu

, Da Ling

, Liang

, et al. Viscoelasticity of ecm and cells—origin, measurement and correlation. Mechanobiol Med, 2024; 2(4):100082; doi: 10.1016/j.mbm.2024.100082

181.

Lin

, He

, Feng

, et al. Self-renewal or quiescence? Orchestrating the fate of mesenchymal stem cells by matrix viscoelasticity via PI3K/Akt-CDK1 pathway. Biomaterials, 2021; 279:121235; doi: 10.1016/j.biomaterials.2021.121235

182.

Gao

, Liu

, Wang

, et al. Biomaterials regulates bmscs differentiation via mechanical microenvironment. Biomater Adv, 2024; 157:213738; doi: 10.1016/j.bioadv.2023.213738

183.

Xie

, Xiao

, Shu

, et al. Cell response to mechanical microenvironment cues via rho signaling: From mechanobiology to mechanomedicine. Acta Biomater, 2023; 159:1–20; doi: 10.1016/j.actbio.2023.01.039

184.

Zhang

, Chu

, Wang

, et al. Effects of matrix stiffness on the differentiation of multipotent stem cells. Curr Stem Cell Res Ther, 2020; 15(5):449–461; doi: 10.2174/1574888X15666200408114632

185.

Guo

, Du

, Quan

, et al. Effects of biophysical cues of 3D hydrogels on mesenchymal stem cells differentiation. J Cell Physiol, 2021; 236(4):2268–2275; doi: 10.1002/jcp.30042+

186.

Roth

, Huang

, Navarro

, et al. Tunable hydrogel viscoelasticity modulates human neural maturation. Sci Adv, 2023; 9(42):eadh8313; doi: 10.1126/SCIADV.ADH8313

187.

Blatchley

, Hall

, Wang

, et al. Hypoxia and matrix viscoelasticity sequentially regulate endothelial progenitor cluster-based vasculogenesis. Sci Adv, 2019; 5(3):eaau7518; doi: 10.1126/sciadv.aau7518

188.

Argentati

, Morena

, Tortorella

, et al. Insight into mechanobiology: How stem cells feel mechanical forces and orchestrate biological functions. Int J Mol Sci, 2019; 20(21):5337; doi: 10.3390/ijms20215337

189.

Wolfenson

, Yang

, Sheetz

. Steps in mechanotransduction pathways that control cell morphology. Annu Rev Physiol, 2019; 81(1):585–605; doi: 10.1146/annurev-physiol-021317-121245

190.

Cao

, Tian

, et al. A hierarchical mechanotransduction system: From macro to micro. Adv Sci (Weinh), 2024; 11(11):e2302327; doi: 10.1002/advs.202302327

191.

Agarwal

, Lee

H-P

, Smeriglio

, et al. A dysfunctional trpv4–gsk3β pathway prevents osteoarthritic chondrocytes from sensing changes in extracellular matrix viscoelasticity. Nat Biomed Eng, 2021; 5(12):1472–1484; doi: 10.1038/s41551-021-00691-3

192.

Batan

, Peters

, Schroeder

, et al. Hydrogel cultures reveal transient receptor potential vanilloid 4 regulation of myofibroblast activation and proliferation in valvular interstitial cells. Faseb J, 2022; 36(5):e22306; doi: 10.1096/fj.202101863R

193.

Murthy

, Dubin

, Patapoutian

. Piezos thrive under pressure: Mechanically activated ion channels in health and disease. Nat Rev Mol Cell Biol, 2017; 18(12):771–783; doi: 10.1038/nrm.2017.92

194.

, Si

, Huang

, et al. Mechanical regulation of stem-cell differentiation by the stretch-activated piezo channel. Nature, 2018; 555(7694):103–106; doi: 10.1038/nature25744

195.

Wong

, Lenzini

, Bargi

, et al. Controlled deposition of 3D matrices to direct single cell functions. Adv Sci (Weinh), 2020; 7(20):2001066; doi: 10.1002/advs.202001066

196.

Trompeter

, Gardinier

, DeBarros

, et al. Insulin-like growth factor-1 regulates the mechanosensitivity of chondrocytes by modulating trpv4. Cell Calcium, 2021; 99:102467; doi: 10.1016/j.ceca.2021.102467

197.

Jin

, Jan

Y-N

. Mechanosensitive ion channels: Structural features relevant to mechanotransduction mechanisms. Annu Rev Neurosci, 2020; 43(1):207–229; doi: 10.1146/annurev-neuro-070918-050509

198.

Ranade

, Syeda

, Patapoutian

. Mechanically activated ion channels. Neuron, 2015; 87(6):1162–1179; doi: 10.1016/j.neuron.2015.08.032

199.

Sun

, Guo

, Fässler

. Integrin-mediated mechanotransduction. J Cell Biol, 2016; 215(4):445–456; doi: 10.1083/jcb.201609037

200.

Romero

, Le Clainche

, Gautreau

. Actin polymerization downstream of integrins: Signaling pathways and mechanotransduction. Biochem J, 2020; 477(1):1–21; doi: 10.1042/bcj20170719

201.

Mishra

, Manavathi

. Focal adhesion dynamics in cellular function and disease. Cell Signal, 2021; 85:110046; doi: 10.1016/j.cellsig.2021.110046

202.

Ang

, He

, Qiu

, et al. Targeting integrin pathways: Mechanisms and advances in therapy. Signal Transduct Target Ther, 2023; 8(1):1–42; doi: 10.1038/s41392-022-01259-6

203.

Chopra

, Murray

, Byfield

, et al. Augmentation of integrin-mediated mechanotransduction by hyaluronic acid. Biomaterials, 2014; 35(1):71–82; doi: 10.1016/j.biomaterials.2013.09.066

204.

Wang

, Ji

, Wang

, et al. Matrix stiffness regulates osteoclast fate through integrin-dependent mechanotransduction. Bioact Mater, 2023; 27:138–153; doi: 10.1016/j.bioactmat.2023.03.014

205.

Martino

, Perestrelo

, Vinarský

, et al. Cellular mechanotransduction: From tension to function. Front Physiol, 2018; 9:824; doi: 10.3389/fphys.2018.00824

206.

Geiger

, Spatz

, Bershadsky

. Environmental sensing through focal adhesions. Nat Rev Mol Cell Biol, 2009; 10(1):21–33; doi: 10.1038/nrm2593

207.

Sharip

, Kunz

. Mechanosignaling via Integrins: Pivotal players in liver fibrosis progression and therapy. Cells, 2025; 14(4):266; doi: 10.3390/cells14040266

208.

Wang

, Yang

, Han

, et al. Cell mechanical microenvironment for cell volume regulation. J Cell Physiol, 2020; 235(5):4070–4081; doi: 10.1002/jcp.29341

209.

Xie

, Huck

, Bao

. Unveiling the intricate connection: Cell volume as a key regulator of mechanotransduction. Annu Rev Biophys, 2024; 53(1):299–317; doi: 10.1146/annurev-biophys-030822-035656

210.

Kollmannsberger

, Fabry

. Linear and nonlinear rheology of living cells. Annu Rev Mater Res, 2011; 41(1):75–97; doi: 10.1146/annurev-matsci-062910-100351

211.

Deng

, Trepat

, Butler

, et al. Fast and slow dynamics of the cytoskeleton. Nat Mater, 2006; 5(8):636–640; doi: 10.1038/nmat1685

212.

Perdikaris

, Karniadakis

. Fractional-order viscoelasticity in one-dimensional blood flow models. Ann Biomed Eng, 2014; 42(5):1012–1023; doi: 10.1007/s10439-014-0970-3

213.

Nam

, Lee

, Brownfield

, et al. Viscoplasticity enables mechanical remodeling of matrix by cells. Biophys J, 2016; 111(10):2296–2308; doi: 10.1016/j.bpj.2016.10.002

214.

Bursac

, Lenormand

, Fabry

, et al. Cytoskeletal remodelling and slow dynamics in the living cell. Nat Mater, 2005; 4(7):557–561; doi: 10.1038/nmat1404

215.

Desprat

, Richert

, Simeon

, et al. Creep function of a single living cell. Biophys J, 2005; 88(3):2224–2233; doi: 10.1529/biophysj.104.050278

216.

, Huang

, Liu

, et al. A viscoelastic-stochastic model of cell adhesion considering matrix morphology and medium viscoelasticity. Soft Matter, 2024; 20(36):7270–7283; doi: 10.1039/d4sm00740a

217.

Cai

, Zhou

, Luo

, et al. Modeling and optimization of nonlinear viscoelastic behavior for tissue-engineered blood vessels. Tissue Eng Part C Methods, 2025; 31(5):191–202; doi: 10.1089/ten.tec.2025.0039

218.

Bangasser

, Shamsan

, Chan

, et al. Shifting the optimal stiffness for cell migration. Nat Commun, 2017; 8(1):15313; doi: 10.1038/ncomms15313

219.

Bangasser

, Rosenfeld

, Odde

. Determinants of maximal force transmission in a motor-clutch model of cell traction in a compliant microenvironment. Biophys J, 2013; 105(3):581–592; doi: 10.1016/j.bpj.2013.06.027

220.

Chan

, Odde

. Traction dynamics of filopodia on compliant substrates. Science, 2008; 322(5908):1687–1691; doi: 10.1126/science.1163595

221.

Hassan

, Qin

Y-X

, Komatsu

, et al. Utilization of finite element analysis for articular cartilage tissue engineering. Materials (Basel), 2019; 12(20):3331; doi: 10.3390/ma12203331

222.

Schipani

, Nolan

, Lally

, et al. Integrating finite element modelling and 3D printing to engineer biomimetic polymeric scaffolds for tissue engineering. Connect Tissue Res, 2020; 61(2):174–189; doi: 10.1080/03008207.2019.1656720

223.

Karcher

, Lammerding

, Huang

, et al. A three-dimensional viscoelastic model for cell deformation with experimental verification. Biophys J, 2003; 85(5):3336–3349; doi: 10.1016/S0006-3495(03)74753-5

224.

Fellner

, Heshmat

, Werginz

, et al. A finite element method framework to model extracellular neural stimulation. J Neural Eng, 2022; 19(2):022001; doi: 10.1088/1741-2552/ac6060

225.

Smit

. Finite element models of osteocytes and their load-induced activation. Curr Osteoporos Rep, 2022; 20(2):127–140; doi: 10.1007/s11914-022-00728-9

226.

, Torres

, Hakim

, et al. Collagen-and hyaluronic acid-based hydrogels and their biomedical applications. Mater Sci Eng R Rep, 2021; 146:100641; doi: 10.1016/j.mser.2021.100641

227.

Cao

, Duan

, Zhang

, et al. Current hydrogel advances in physicochemical and biological response-driven biomedical application diversity. Signal Transduct Target Ther, 2021; 6(1):426; doi: 10.1038/s41392-021-00830-x

228.

Lázaro

, Alonso

, Rodriguez

, et al. Characterization of the viscoelastic properties of hyaluronic acid. Biorheology, 2018; 55(1):41–50; doi: 10.3233/BIR-180174

229.

, Ni

, Shi

, et al. Enhancing BMSC chondrogenesis with a dynamic viscoelastic hyaluronan hydrogel loaded with kartogenin for cartilage repair. Int J Biol Macromol, 2025; 312:144042; doi: 10.1016/j.ijbiomac.2025.144042

230.

Hong

, Wan

, Park

, et al. Rheological characteristics of hyaluronic acid fillers as viscoelastic substances. Polymers (Basel), 2024; 16(16):2386; doi: 10.3390/polym16162386

231.

Antoine

, Vlachos

, Rylander

. Review of collagen i hydrogels for bioengineered tissue microenvironments: Characterization of mechanics, structure, and transport. Tissue Eng Part B Rev, 2014; 20(6):683–696; doi: 10.1089/ten.TEB.2014.0086

232.

Vijayalekha

, Anandasadagopan

, Pandurangan

. An overview of collagen-based composite scaffold for bone tissue engineering. Appl Biochem Biotechnol, 2023; 195(7):4617–4636; doi: 10.1007/s12010-023-04318-y

233.

Fan

, Ren

, Emmert

, et al. The use of collagen-based materials in bone tissue engineering. Int J Mol Sci, 2023; 24(4):3744; doi: 10.3390/ijms24043744

234.

Chen

, Zhang

, Huang

, et al. DNA-encoded dynamic hydrogels for 3D bioprinted cartilage organoids. Mater Today Bio, 2025; 31:101509; doi: 10.1016/j.mtbio.2025.101509

235.

Liu

, Li

, Chen

, et al. Bone ecm-like 3D printing scaffold with liquid crystalline and viscoelastic microenvironment for bone regeneration. ACS Nano, 2022; 16(12):21020–21035; doi: 10.1021/acsnano.2c08699

236.

Habanjar

, Diab-Assaf

, Caldefie-Chezet

, et al. 3D cell culture systems: Tumor application, advantages, and disadvantages. Int J Mol Sci, 2021; 22(22):12200; doi: 10.3390/ijms222212200

237.

Pragnere

, Courtial

E-J

, Dubreuil

, et al. Tuning viscoelasticity and stiffness in bioprinted hydrogels for enhanced 3D cell culture: A multi-scale mechanical analysis. J Mech Behav Biomed Mater, 2024; 159:106696; doi: 10.1016/j.jmbbm.2024.106696

238.

Liu

, Li

, et al. Viscoelastic hydrogels regulate adipose-derived mesenchymal stem cells for nucleus pulposus regeneration. Acta Biomater, 2024; 180:244–261; doi: 10.1016/j.actbio.2024.04.017

239.

Zhang

, Li

, Tian

, et al. Harnessing mechanical stress with viscoelastic biomaterials for periodontal ligament regeneration. Adv Sci (Weinh), 2024; 11(18):e2309562; doi: 10.1002/advs.202309562

240.

Zhang

, Jia

, Liu

, et al. A viscoelastic alginate-based hydrogel network coordinated with spermidine for periodontal ligament regeneration. Regen Biomater, 2023; 10:rbad009; doi: 10.1093/rb/rbad009

241.

Chen

, Liu

, McDaniel

, et al. Viscoelasticity of hyaluronic acid hydrogels regulates human pluripotent stem cell‐derived spinal cord organoid patterning and vascularization. Adv Healthc Mater, 2024; 13(32):e2402199; doi: 10.1002/adhm.202402199

242.

Wyle

, Lu

, Hepfer

, et al. The role of biophysical factors in organ development: Insights from current organoid models. Bioengineering (Basel), 2024; 11(6):619; doi: 10.3390/bioengineering11060619

243.

Sato

, Vries

, Snippert

, et al. Single lgr5 stem cells build crypt-villus structures in vitro without a mesenchymal niche. Nature, 2009; 459(7244):262–265; doi: 10.1038/nature07935

244.

Elosegui-Artola

, Gupta

, Najibi

, et al. Matrix viscoelasticity controls spatiotemporal tissue organization. Nat Mater, 2023; 22(1):117–127; doi: 10.1038/s41563-022-01400-4

245.

Neves

, Rodrigues

, Reis

, et al. Current approaches and future perspectives on strategies for the development of personalized tissue engineering therapies. Expert Rev Precis Med Drug Dev, 2016; 1(1):93–108; doi: 10.1080/23808993.2016.1140004

246.

Armstrong

, Stevens

. Emerging technologies for tissue engineering: From gene editing to personalized medicine. Tissue Eng Part A, 2019; 25(9–10):688–692; doi: 10.1089/ten.tea.2019.0026

247.

Kang

, Zeng

, Varghese

. Functionally graded multilayer scaffolds for in vivo osteochondral tissue engineering. Acta Biomater, 2018; 78:365–377; doi: 10.1016/j.actbio.2018.07.039

248.

Yang

, Lin

, Rothrauff

, et al. Multilayered polycaprolactone/gelatin fiber-hydrogel composite for tendon tissue engineering. Acta Biomater, 2016; 35:68–76; doi: 10.1016/j.actbio.2016.03.004

249.

Jin

, Wang

, Yang

, et al. Multilayered hydrogel scaffold construct with native tissue matched elastic modulus: A regenerative microenvironment for urethral scar-free healing. Biomaterials, 2025; 312:122711; doi: 10.1016/j.biomaterials.2024.122711