17 Hydrogel Mechanics: Fundamentals, Strategies and State-of-the-art Design
Yiming Yuan
I. Introduction
Hydrogels represent a fascinating class of soft materials that combine the structural properties of crosslinked polymer networks with the fluid properties of water. These unique materials, consisting of water-swollen polymer networks, have garnered significant attention in various fields, from biomedical engineering to environmental applications. Their appeal lies in their remarkable similarity to biological tissues, making them particularly promising for applications such as tissue engineering scaffolds, medical implants, and wound dressings.
However, the journey to developing practically useful hydrogels has been marked by a significant challenge: their inherently poor mechanical properties. Conventional hydrogels, typically composed of single non-uniform networks of hydrophilic polymers, exhibit extremely low mechanical strength and toughness. To put this in perspective, while natural load-bearing tissues like skeletal muscles and cartilage demonstrate fracture energies of 2.5 kJ/m² and 1 kJ/m² respectively, traditional synthetic hydrogels barely achieve 10 J/m². This substantial gap in mechanical performance has long been a critical bottleneck in their practical applications.
The mechanical limitations of conventional hydrogels stem from several intrinsic characteristics. First, their network structure often suffers from inhomogeneity in both polymer density distribution and strand length between crosslinking points. This structural non-uniformity makes them particularly susceptible to stress concentration, leading to easy crack initiation. Second, these materials typically exhibit rubber-like elasticity without significant energy dissipation mechanisms, resulting in poor resistance to crack propagation. Furthermore, their high water content, while beneficial for biocompatibility, results in a low concentration of load-bearing polymer chains, contributing to their mechanical weakness.
Since the 2000s, the field has witnessed remarkable progress in addressing these limitations. Researchers have developed various innovative strategies to enhance the mechanical properties of hydrogels while maintaining their essential characteristics. These advances have not only led to the creation of mechanically robust hydrogels but have also deepened our understanding of their failure mechanisms and structure-property relationships.
The evolution of hydrogel design has progressed through several key innovations. Early approaches focused on improving network uniformity and introducing sliding crosslinks. This was followed by the groundbreaking development of double-network systems, which demonstrated that combining two contrasting networks could yield materials with exceptional mechanical properties. More recent advances have explored the incorporation of dynamic bonds, hierarchical structures, and even self-growing capabilities inspired by biological systems.
Today, state-of-the-art hydrogels can achieve remarkable mechanical properties: fracture energies reaching 200 kJ/m², elastic modulus ranging from sub-megapascal to hundreds of megapascals, and stretching ratios from several to hundreds of times their original length. These achievements have opened new possibilities for applications that were previously unthinkable with conventional hydrogels.
As we delve deeper into the design principles for strong and tough hydrogels, we will explore how various structural modifications at molecular and mesoscopic scales can be engineered to achieve desired mechanical properties. Understanding these principles is crucial not only for developing better materials but also for tailoring hydrogels for specific applications, from soft robotics to tissue engineering.
II. Concepts, Theories, and Principles[1]
i. Fundamental Mechanics of Basic Hydrogels
The mechanical behavior of hydrogels is fundamentally determined by their unique network structure and interactions with water molecules. Understanding these basic mechanics is crucial for developing enhanced hydrogel systems with superior mechanical properties.
Network Structure and Swelling Behavior
Hydrogels are characterized by their three-dimensional polymer networks containing crosslinks that enable water retention. The key structural parameters include:
- Network Mesh Size (ξ): Defines the space between crosslinking points, controlling water mobility and molecular diffusion.
- Polymer Volume Fraction (φ): Determines the water content and consequently affects mechanical properties.
- Crosslinking Density: Influences both elastic modulus and swelling capacity.
The swelling equilibrium in hydrogels results from the balance between osmotic forces drawing water into the network and elastic forces of the stretched polymer chains resisting expansion. This equilibrium significantly impacts mechanical properties, as higher water content typically results in reduced mechanical strength.
Elastic Modulus and Network Parameters
The elastic response of hydrogels follows rubber elasticity theory for small deformations. The shear modulus (G) is proportional to the crosslinking density and temperature:
where ν represents the effective crosslink density, k is Boltzmann’s constant, and T is absolute temperature. However, real hydrogels often deviate from this ideal behavior due to:
- Network inhomogeneity
- Non-uniform chain length distribution
- Physical entanglements
- Non-affine deformation at large strains
Fracture Mechanisms and Energy Dissipation
The fracture behavior of conventional hydrogels is characterized by:
- Low Fracture Energy
- Typical values range from 1-10 J/m²
- Limited by the lack of energy dissipation mechanisms
- Crack propagation occurs easily once initiated
- Brittle Failure Mode
- Minimal plastic deformation before failure
- Limited crack-bridging capability
- Rapid crack propagation
- Stress Concentration Effects
- Network inhomogeneity acts as stress concentration points
- Local stress amplification leads to premature failure
- Crack initiation typically occurs at defect sites
Fatigue Resistance and Threshold Behavior
Under cyclic loading, conventional hydrogels exhibit:
- Low Fatigue Threshold
- Minimal resistance to crack propagation under cyclic loading
- Progressive network damage accumulation
- Limited self-healing capability
- Time-Dependent Behavior
- Viscoelastic effects due to polymer-water interactions
- Rate-dependent mechanical response
- Stress relaxation and creep phenomena
These fundamental mechanical characteristics of basic hydrogels highlight their limitations:
- Poor mechanical strength
- Limited energy dissipation
- Low fracture toughness
- Insufficient fatigue resistance
Understanding these limitations has driven the development of various design strategies to enhance hydrogel mechanical properties, which will be discussed in subsequent sections. Modern approaches focus on introducing multiple energy dissipation mechanisms and creating more uniform network structures to overcome these inherent weaknesses while maintaining the essential properties that make hydrogels valuable in various applications.
ii. Design Strategies for Tough Hydrogels
The development of tough hydrogels has seen remarkable progress through various innovative design strategies. These approaches can be categorized into three main types based on their swelling behavior and structural characteristics.
Elastic Hydrogels (λs > 1)
Elastic hydrogels, characterized by swelling ratios greater than 1 (λs > 1), represent a fundamental category in tough hydrogel design. These materials face inherent challenges due to their swelling nature, which typically reduces mechanical strength. However, two major strategies have emerged to enhance their toughness:
Topological Structure Design
- Slide-Ring Networks: These networks utilize figure-of-eight polyrotaxane crosslinks that can freely move along polymer chains, similar to pulleys. This mobility allows for more efficient stress distribution and increased extensibility.
- Homogeneous Networks: Utilizing well-defined tetrahedron-like PEG macromonomers creates networks with fewer spatial heterogeneities, improving failure strength and extensibility.
- Dense Entanglement Networks: By incorporating high concentrations of polymer with sparse crosslinks, these networks achieve both high modulus (~0.1 MPa) and good stretchability.
Double-Network (DN) Structure
The DN approach combines two contrasting networks:
- First Network: Rigid and brittle, typically a highly crosslinked polyelectrolyte
- Second Network: Soft and ductile, usually a sparsely crosslinked neutral polymer
- Working Mechanism: The brittle first network sacrificially breaks to dissipate energy while the ductile second network maintains structural integrity
- Achievements: Can reach fracture energies of several kilojoules per square meter while maintaining ~90% water content
Viscoelastic Hydrogels (λs < 1)
Viscoelastic hydrogels typically exhibit deswelling behavior (λs < 1) and incorporate dynamic bonds for energy dissipation.
Dual-Crosslinked Systems
These systems combine:
- Primary Network: Chemically crosslinked backbone
- Secondary Network: Physical crosslinks through various non-covalent interactions
- Key Features:
- Self-healing capability
- High mechanical strength (tensile strength up to several MPa)
- Significant energy dissipation through dynamic bond breaking/reformation
Dynamic Bonds
Various types of dynamic bonds can be incorporated:
- Ionic bonds
- Hydrogen bonds
- Metal-ligand coordination
- Hydrophobic interactions
- Host-guest interactions
The dynamic nature of these bonds provides:
- Stress relaxation mechanisms
- Self-healing properties
- Enhanced energy dissipation
- Improved toughness through sacrificial bond breaking
High-Order Structure Incorporation
This strategy involves introducing larger-scale structural elements to enhance mechanical properties.
Microphase Separation
- Forms distinct polymer-rich and polymer-poor domains
- Enhances energy dissipation through multiple length scales
- Examples include polyampholyte hydrogels with bicontinuous networks
- Achieves high toughness (fracture energy ~4 kJ/m²) and good self-healing
Microcrystals and Microfibres
- Created through methods like freeze-thawing or mechanical stretching
- Provides additional energy dissipation mechanisms
- Enhances crack resistance through:
- High chain density in crystalline domains
- Crack deflection by oriented fibers
- Transformation of crystals to fibrils under loading
Organic-Inorganic Nanocomposites
- Incorporates hard inorganic components (nanoparticles, nanotubes, nanosheets)
- Creates strong interfaces for effective load transfer
- Requires careful control of swelling mismatch between components
- Can achieve high strength (σf > 0.1 MPa) and toughness (Γ > 2 kJ/m²)
Each strategy offers unique advantages and can be combined to create hydrogels with tailored mechanical properties. The choice of strategy depends on the specific application requirements, such as:
- Required mechanical properties
- Environmental conditions
- Self-healing needs
- Processing constraints
- Application-specific requirements
The success of these strategies has led to hydrogels with mechanical properties approaching or even exceeding those of natural tissues, opening new possibilities in biomedical applications and soft robotics.
iii. Fatigue Resistance
Fatigue resistance represents a critical yet often overlooked aspect of hydrogel mechanical properties. While considerable attention has been given to static mechanical properties such as strength and toughness, the ability to withstand repeated loading cycles is paramount for practical applications. Understanding and improving fatigue resistance is essential for developing hydrogels that can maintain their performance over extended periods of use, particularly in demanding applications such as tissue engineering and soft robotics.
Mechanisms of Fatigue in Hydrogels
The fatigue behavior of hydrogels is governed by several interconnected mechanisms that operate at different scales. At the molecular level, network chain scission plays a fundamental role in fatigue development. During cyclic loading, covalent bonds within the polymer network experience repeated stress, leading to progressive breaking of these bonds. This process results in the accumulation of permanent damage within the network structure, gradually degrading the mechanical properties of the hydrogel over time.
Physical bond disruption represents another significant mechanism contributing to fatigue. Non-covalent interactions, including hydrogen bonds, ionic interactions, and hydrophobic associations, can break down under repeated loading. While these interactions are often reversible in nature, the recovery process may not keep pace with the loading frequency, leading to progressive deterioration of the network structure. The dynamic nature of these physical bonds creates a complex interplay between damage accumulation and self-healing processes.
Water migration effects further complicate the fatigue behavior of hydrogels. Under cyclic loading, local dehydration can occur in stressed regions, creating inhomogeneous water distribution throughout the material. This phenomenon leads to the formation of stress concentration zones, which can accelerate material degradation. The movement of water molecules during loading-unloading cycles can also affect the local mechanical properties and contribute to the overall fatigue response.
The progression of fatigue failure typically begins with crack initiation at network defects or stress concentration points. The presence of network heterogeneities and local variations in water content can significantly influence where these cracks first appear. Once initiated, crack propagation occurs under repeated loading-unloading cycles, with the rate of progression dependent on multiple factors including loading frequency, strain amplitude, environmental conditions, and the underlying network architecture.
Strategies for Enhancing Fatigue Resistance
Network architecture design serves as a fundamental approach to improving fatigue resistance. The development of homogeneous network structures helps minimize stress concentration points and reduces the probability of crack initiation. This can be achieved through carefully controlled polymerization conditions and optimization of crosslinking density. The uniformity of the network structure plays a crucial role in distributing applied loads more evenly throughout the material, thereby reducing local stress concentrations that could lead to premature failure.
Multiple network systems represent an advanced strategy for enhancing fatigue resistance. These systems typically incorporate sacrificial networks that can break down under stress while maintaining the integrity of the primary load-bearing network. Double network hydrogels exemplify this approach, where a rigid first network can undergo controlled breakdown to dissipate energy while a more flexible second network maintains structural integrity. This design principle has proven particularly effective in creating materials that can withstand repeated loading cycles without catastrophic failure.
The integration of dynamic bonds into hydrogel networks provides another powerful strategy for improving fatigue resistance. These reversible crosslinks can break and reform during loading cycles, enabling self-healing capabilities during rest periods. Supramolecular interactions and dynamic covalent bonds offer mechanisms for stress relaxation through bond reformation, effectively distributing and dissipating applied loads. The incorporation of crystalline domains can further enhance this effect by providing additional physical crosslinks that can undergo reversible transformation under stress.
Role of Hierarchical Structures
The implementation of hierarchical structures in hydrogel design represents a sophisticated approach to enhancing fatigue resistance. At the molecular level, careful consideration of polymer chemistry and crosslinking density provides the foundation for mechanical stability. The incorporation of microscale features, such as fiber reinforcement and controlled phase separation, creates additional mechanisms for energy dissipation and crack deflection. At the macroscale, gradient structures and oriented elements can help distribute loads more effectively throughout the material.
The synergistic effects achieved through hierarchical design are particularly noteworthy. By integrating multiple toughening mechanisms across different length scales, hydrogels can achieve superior fatigue resistance through complementary energy dissipation pathways. This multi-scale approach creates multiple barriers to crack propagation while maintaining the material’s ability to recover from repeated loading cycles.
Performance Metrics and Testing
The evaluation of fatigue resistance requires comprehensive testing protocols and careful analysis of multiple performance metrics. Cyclic loading tests conducted at various strain amplitudes and frequencies provide essential data about material behavior under repeated stress. The measurement of fatigue threshold values helps determine the maximum stress or strain that a hydrogel can withstand indefinitely without failure.
Crack propagation analysis offers valuable insights into the material’s resistance to fatigue-induced damage. By monitoring crack growth rates and determining threshold energy release rates, researchers can better understand the mechanisms of fatigue resistance and predict material lifetime under specific loading conditions. This information is crucial for designing hydrogels that meet the demanding requirements of various applications.
The development of standardized testing methods and performance metrics continues to evolve, reflecting the growing importance of fatigue resistance in hydrogel applications. These methods must account for the complex interplay between mechanical loading, water content, and environmental conditions that characterize real-world applications.
The pursuit of enhanced fatigue resistance in hydrogels represents an ongoing challenge in materials science. Success in this area requires careful consideration of multiple design aspects and their interactions, from molecular architecture to macroscale structure. Recent advances have led to the development of hydrogels capable of withstanding thousands of loading cycles while maintaining their mechanical integrity, marking significant progress toward their implementation in demanding applications such as tissue engineering, soft robotics, and biomedical devices.
III. Discussion of Some Peer-Reviewed Papers
i. Anti-Swelling Anisotropic Conductive Hydrogel for Implantable Electronic Tendon[2]
Key Innovations and Design Principles
Novel Fabrication Strategy
The researchers developed an innovative dual-process approach combining drying-induced strengthening mechanism and pre-stretching regulated ordered arrangement. This strategy successfully created a hydrogel with:
- Dense and stable interconnected polymer network
- Hierarchically anisotropic structure
- High water content (72.5 wt%) matching natural tendons
- Excellent anti-swelling properties (<3% swelling)
Material Selection and Synergistic Effects
The hydrogel composition was carefully designed with three key components:
- Poly(vinyl alcohol) (PVA): Main matrix
- Provides tunable crystalline structure
- Ensures good biocompatibility
- Enables effective rehydration
- Cellulose nanofiber (CNF): Reinforcing filler
- Acts as collagen-mimicking building blocks
- Enhances mechanical properties
- Provides rich hydrogen bond sites
- PEDOT:PSS: Conductive component
- Enables electrical conductivity
- Maintains good hydrophilicity
- Ensures uniform dispersion
Critical Performance Analysis
Mechanical Properties
The optimized PCPP-SD&S hydrogel achieved exceptional mechanical performance:
Property | Value | Comparison to Control |
---|---|---|
Tensile Strength | 3.71 MPa | 1.9× higher |
Elastic Modulus | 1.1 MPa | 2.4× higher |
Toughness | 9.86 MJ•m⁻³ | 2.6× higher |
Elongation at Break | 505% | Comparable |
Stability and Anti-Swelling
The hydrogel demonstrated remarkable stability:
- Maintained stable water content (~72.5 wt%) for over 72 hours
- Showed minimal swelling (<3%) in physiological conditions
- Preserved mechanical properties in aqueous environments
- Exhibited reliable conductivity over extended periods
Biocompatibility
Comprehensive biocompatibility testing revealed:
- Excellent cell viability (>80% after 48h)
- Significant reduction in protein adsorption
- Minimal inflammatory response in vivo
- No significant fibrous capsule formation after implantation
Applications and Future Perspectives
Demonstrated Applications
- Real-time Motion Monitoring
- Successfully detected joint movements underwater
- Maintained stable sensing performance over 600 cycles
- Demonstrated reliable strain sensitivity (GF = 0.88-1.30)
- Artificial Tendon Replacement
- Effectively restored joint mobility in animal models
- Enabled real-time monitoring of joint rehabilitation
- Showed promising recovery in rat tendon defect models
Limitations and Future Directions
- Long-term Studies Needed
- Extended in vivo performance evaluation
- Degradation behavior assessment
- Long-term biocompatibility studies
- Optimization Opportunities
- Further enhancement of mechanical properties
- Improved sensing capabilities
- Integration with tissue regeneration strategies
- Clinical Translation
- Scale-up manufacturing considerations
- Sterilization protocol development
- Regulatory compliance requirements
Significance and Impact
This work represents a significant advancement in:
- Hydrogel design for load-bearing applications
- Anti-swelling strategies for implantable materials
- Integration of sensing capabilities in artificial tissues
- Biomimetic approaches for tendon replacement
The combination of high mechanical strength, excellent anti-swelling properties, and real-time sensing capabilities makes this hydrogel system a promising candidate for next-generation implantable electronic tendons and other biomedical applications.
ii. High-Strength, Low-Friction Hydrogel for Articular Cartilage Applications[3]
Key Innovations and Design Principles
Novel Material Design Strategy
The researchers developed a biocompatible composite hydrogel using three key components:
- PVA (Polyvinyl alcohol)
- Forms crystalline domains
- Provides basic network structure
- Enables physical crosslinking
- Chitosan
- Forms interpenetrating network
- Contributes to hydrogen bonding
- Enhances biocompatibility
- Sodium Alginate
- Introduces ionic interactions
- Reduces friction coefficient
- Maintains biocompatibility
Fabrication Process Innovation
The synthesis involved a two-step approach:
- Freeze-thaw cycling (3 times) of PVA/chitosan mixture
- Subsequent soaking in sodium alginate solution
This process created multiple physical crosslinking mechanisms:
- Crystalline domains
- Hydrogen bonds
- Ionic interactions
Critical Performance Analysis
Mechanical Properties
The optimized hydrogel achieved exceptional performance:
Property | Value | Comparison to Control |
---|---|---|
Compressive Strength | 141 MPa | ~94× higher |
Tensile Strength | 7.4 MPa | ~31× higher |
Young’s Modulus | 2.4 MPa | ~71× higher |
Elongation at Break | 515% | ~3.5× higher |
Tribological Properties
Key achievements in friction reduction:
- Coefficient of friction: 0.044
- Lower than natural cartilage (0.11)
- Superior to commercial alternatives:
- Cobalt-chromium alloy (0.15)
- Ceramic (0.12)
Structural Characteristics
The hydrogel demonstrated optimal structural properties:
- Porosity: 70.6 ± 1.8% (matching natural cartilage range of 60-80%)
- Water content: 58.6 wt%
- Uniform pore structure (~2.5 μm)
- High gel fraction (85.0%)
Applications and Limitations
Advantages
- Biocompatibility
- 100% cell viability
- Non-toxic components
- Green synthesis process
- Mechanical Stability
- High creep resistance
- 93% recovery efficiency
- Excellent fatigue resistance
- Practical Benefits
- Simple fabrication process
- Commercially available materials
- Scalable production potential
Current Limitations
- Structural Issues
- Isotropic structure (vs. natural cartilage’s anisotropic structure)
- Lack of hierarchical organization
- Biological Integration
- Absence of bioactive molecules
- No growth factors
- Limited cell integration capability
- Clinical Translation Gaps**
- Need for osteointegration studies
- Long-term stability unknown
- In vivo performance validation required
Future Research Directions
Immediate Priorities
- Development of anisotropic structures
- Integration of bioactive molecules
- Long-term stability studies
Long-term Goals
- Optimization of hierarchical assembly
- Enhancement of tissue integration
- Clinical validation studies
Impact and Significance
This work represents a significant advancement in:
- Hydrogel design for load-bearing applications
- Friction reduction in artificial cartilage
- Biocompatible material synthesis
- Physical crosslinking strategies
The combination of high strength, low friction, and excellent biocompatibility makes this hydrogel system a promising candidate for articular cartilage replacement and other biomedical applications.
iii. High-Strength Injectable Supramolecular Hydrogel for Tooth-Extraction Wound Healing[4]
Key Innovations and Design Principles
Novel Material Design
The researchers developed a supramolecular hydrogel using 2-amino-2′-fluoro-2′-deoxyadenosine (2-FA) as the key molecular gelator, featuring:
- Multi-hydrogen-bonding System
- Double NH2 groups
- 2′-F atoms
- Water molecules
- Forms strong physical crosslinks
- Unique Structural Properties
- Low molecular weight (<300)
- Self-assembling capability
- 3D porous network structure
- Dense and stable interconnections
Material Performance
Key achievements:
- Storage modulus: >1 MPa at 5.0 wt%
- Rapid sol-gel transition: seconds at 37°C
- Excellent shear-thinning behavior
- Long-term stability: >10 months
Critical Performance Analysis
3.2.1 Mechanical Properties
The hydrogel demonstrated exceptional mechanical performance:
Property | Value | Notes |
---|---|---|
Storage Modulus | >1 MPa | At 5.0 wt% concentration |
Compressive Strain | >80% | Without breaking |
Compressive Strength | 0.2 MPa | At 5.0 wt% |
Thermal Stability | >38°C | At concentrations >2.5 wt% |
Injectable Properties
Key features:
- Rapid shear-thinning
- Self-healing capability
- Quick recovery (97.45% recovery)
- Immediate gelation at injection site
Biological Performance
- Biocompatibility
- No cytotoxicity at therapeutic concentrations
- Good hemocompatibility
- Rapid biodegradation
- Antimicrobial Activity
- Effective against both G(+) and G(-) bacteria
- Novel “secondary messenger storm” mechanism
- Disrupts bacterial carbon-nitrogen balance
Applications in Tooth-Extraction Wound Healing
Key Advantages
- Wound Management
- Rapid hemostasis
- Excellent space maintenance
- Controlled degradation
- Tissue Healing
- Enhanced bone formation
- Reduced inflammatory response
- Better wound closure
- Clinical Benefits
- Easy application
- Minimal invasion
- Better healing outcomes than commercial alternatives
3.3.2 Healing Mechanism
The hydrogel promotes healing through:
- Maintaining blood clot stability
- Regulating macrophage activity
- Inhibiting excessive osteoclast formation
- Providing antimicrobial protection
Limitations and Future Directions
Current Limitations
- Material Properties
- Concentration-dependent performance
- Temperature sensitivity
- Limited control over degradation rate
- Clinical Translation
- Need for larger scale trials
- Sterilization protocol development
- Cost considerations
3.4.2 Future Research Directions
- Material Optimization
- Tunable degradation rates
- Enhanced mechanical properties
- Improved temperature stability
- Clinical Development
- Long-term efficacy studies
- Comparative effectiveness research
- Regulatory compliance studies
Impact and Significance
This work represents significant advancement in:
- Supramolecular hydrogel design
- Injectable biomaterials
- Dental wound healing
- Antimicrobial strategies
The combination of high strength, injectability, and biological functionality makes this hydrogel system a promising candidate for dental applications and potentially other biomedical uses.
IV. Additional Video
Here is a video that shows a highly tough hydrogel with high crack-propergation resistance [2]
V. References
[1] Li X, Gong JP. Design principles for strong and tough hydrogels. Nat Rev Mater 2024, 9(6): 380-398.
[2] Li N, Yu Q, Duan S, Du Y, Shi X, Li X, et al. Anti‐Swelling, High‐Strength, Anisotropic Conductive Hydrogel with Excellent Biocompatibility for Implantable Electronic Tendon. Adv Funct Mater 2023, 34(12).
[3] Luo C, Guo A, Zhao Y, Sun X. A high strength, low friction, and biocompatible hydrogel from PVA, chitosan and sodium alginate for articular cartilage. Carbohydr Polym 2022, 286: 119268.
[4] Wang Z, Zhang Y, Yin Y, Liu J, Li P, Zhao Y, et al. High-Strength and Injectable Supramolecular Hydrogel Self-Assembled by Monomeric Nucleoside for Tooth-Extraction Wound Healing. Adv Mater 2022, 34(13): e2108300.