Viscoelastic Biomaterials Research Articles

Viscoelastic Mechanics: From Pathology and Cell Fate to Tissue Regeneration Biomaterial Development.

Viscoelasticity is the mechanical feature of living tissues and the cellular extracellular matrix (ECM) and has been recognized as an essential biophysical cue in cell function and fate regulation, tissue development and homeostasis maintenance, and disease progression. These findings provide new insights for the development of biomaterials with comparable viscoelastic properties as native ECMs and the tissue matrix, displaying promising applications in regeneration medicine. In this review, the relationship between matrix viscoelasticity and tissue functions (e.g., development and regeneration) in physiological conditions and disease progression (e.g., aging, degenerative, fibrosis, and tumor) in pathological conditions will be especially highlighted to figure out the potential therapeutic target for disease treatment and inspiration for tissue regeneration related biomaterial development. Furthermore, findings and an understanding of the cell response to ECM viscoelasticity and the mechanism behind it are comprehensively summarized to provide a pathophysiological basis for viscoelastic biomaterials design. The advances of viscoelastic biomaterials on defect tissue repair are also reviewed, suggesting the significance of the native matrix matchable microenvironment on tissue regeneration. Although challenging, tunable viscoelastic biomaterials that match the mechanical properties of native tissues and ECMs show great promise. They could promote tissue regeneration, treat degenerative diseases, and support the development of organoids and artificial organs.

Matrix Viscoelasticity Tunes the Mechanobiological Behavior of Chondrocytes.

In articular cartilage, the pericellular matrix acting as a specialized mechanical microenvironment modulates environmental signals to chondrocytes through mechanotransduction. Matrix viscoelastic alterations during cartilage development and osteoarthritis (OA) degeneration play an important role in regulating chondrocyte fate and cartilage matrix homeostasis. In recent years, scientists are gradually realizing the importance of matrix viscoelasticity in regulating chondrocyte function and phenotype. Notably, this is an emerging field, and this review summarizes the existing literatures to the best of our knowledge. This review provides an overview of the viscoelastic properties of hydrogels and the role of matrix viscoelasticity in directing chondrocyte behavior. In this review, we elaborated the mechanotransuction mechanisms by which cells sense and respond to the viscoelastic environment and also discussed the underlying signaling pathways. Moreover, emerging insights into the role of matrix viscoelasticity in regulating chondrocyte function and cartilage formation shed light into designing cell-instructive biomaterial. We also describe the potential use of viscoelastic biomaterials in cartilage tissue engineering and regenerative medicine. Future perspectives on mechanobiological comprehension of the viscoelastic behaviors involved in tissue homeostasis, cellular responses, and biomaterial design are highlighted. Finally, this review also highlights recent strategies utilizing viscoelastic hydrogels for designing cartilage-on-a-chip.

Development of Improved Confined Compression Testing Setups for Use in Stress Relaxation Testing of Viscoelastic Biomaterials.

The development of cell-based biomaterial alternatives holds significant promise in tissue engineering applications, but it requires accurate mechanical assessment. Herein, we present the development of a novel 3D-printed confined compression apparatus, fabricated using clear resin, designed to cater to the unique demands of biomaterial developers. Our objective was to enhance the precision of force measurements and improve sample visibility during compression testing. We compared the performance of our innovative 3D-printed confined compression setup to a conventional setup by performing stress relaxation testing on hydrogels with variable degrees of crosslinking. We assessed equilibrium force, aggregate modulus, and peak force. This study demonstrates that our revised setup can capture a larger range of force values while simultaneously improving accuracy. We were able to detect significant differences in force and aggregate modulus measurements of hydrogels with variable degrees of crosslinking using our revised setup, whereas these were indistinguishable with the convectional apparatus. Further, by incorporating a clear resin in the fabrication of the compression chamber, we improved sample visibility, thus enabling real-time monitoring and informed assessment of biomaterial behavior under compressive testing.

Influence of adhesion on oscillatory indentations of viscoelastic biomaterials by a rigid cone

Abstract Steady-state responses in oscillatory indentation tests are widely adopted to evaluate the viscoelastic behavior of cells and tissues. In such tests, the adhesion of biomaterials is commonly neglected, which leads to significant inaccuracy in extracting the mechanical properties. In this article, by introducing the interfacial adhesion described by Lennard-Jones potential, we develop a finite element method to simulate the oscillatory indentation on a viscoelastic half-space. Under a sinusoidal displacement excitation by a rigid cone, it is found that the reaction force evolves sinusoidally at the same frequency but having some phase shift. Interfacial adhesion magnifies the amplitude of force vibration while weakens the average strength. The phase shift is eased in the case of weak adhesion, but turns aggravated once the strength of adhesion exceeds a critical value. The present study can provide guidance for the development of oscillatory indentation tests on viscoelastic materials, and extract more precisely their mechanical properties.

De novo design of modular protein hydrogels with programmable intra- and extracellular viscoelasticity

Relating the macroscopic properties of protein-based materials to their underlying component microstructure is an outstanding challenge. Here, we exploit computational design to specify the size, flexibility, and valency of de novo protein building blocks, as well as the interaction dynamics between them, to investigate how molecular parameters govern the macroscopic viscoelasticity of the resultant protein hydrogels. We construct gel systems from pairs of symmetric protein homo-oligomers, each comprising 2, 5, 24, or 120 individual protein components, that are crosslinked either physically or covalently into idealized step-growth biopolymer networks. Through rheological assessment, we find that the covalent linkage of multifunctional precursors yields hydrogels whose viscoelasticity depends on the crosslink length between the constituent building blocks. In contrast, reversibly crosslinking the homo-oligomeric components with a computationally designed heterodimer results in viscoelastic biomaterials exhibiting fluid-like properties under rest and low shear, but solid-like behavior at higher frequencies. Exploiting the unique genetic encodability of these materials, we demonstrate the assembly of protein networks within living mammalian cells and show via fluorescence recovery after photobleaching (FRAP) that mechanical properties can be tuned intracellularly in a manner similar to formulations formed extracellularly. We anticipate that the ability to modularly construct and systematically program the viscoelastic properties of designer protein-based materials could have broad utility in biomedicine, with applications in tissue engineering, therapeutic delivery, and synthetic biology.

Evaluation of Non-Cross Linked Xeno-Free Hyaluronic Acid Solutions as Visco Elastic Biomaterials.

Hyaluronic acid (HA) is a naturally occurring biodegradable, high molecular weight, non-sulfated glycosaminoglycan (GAG) polymer known for its excellent biocompatibility. HA-based products are widely used as viscosupplements, dermal fillers, and ophthalmic lubricants in clinical settings. Although animal and bacterial-derived HA are commonly reported, plant-sourced HA is not frequently reported. In this study, we have evaluated various viscoelastic properties of one such plant-based HA solution and propose them as an alternative to existing animal/bacteria-sourced HA. The viscoelastic properties of plant-sourced HA solution of various concentrations (0.1%, 0.5%, 1%, and 2% in PBS) were studied using a rheometer at 37°C. Flow curves, amplitude sweep studies, and frequency sweep studies were performed and compared for all HA solutions. The HA solutions displayed shear-thinning behavior, which is an important characteristic of an injectable biomaterial. The 0.1 and 0.5% HA were found to have viscoelastic properties appropriate for eye lubricants, while 1 and 2% HA solutions showed properties suitable for soft tissue fillers. Frequency sweep studies indicated that all the samples are typically viscoelastic liquids with a loss modulus (G″) higher than the storage modulus (G'). This indicated that the samples needed further processing like crosslinking of HA or using higher molecular weight HA to be suitable as viscosupplements. However, the frequency sweep studies also indicated that these solutions can be used as soft tissue fillers of any type based on the G' and tan δ values. The plant-sourced HA solutions are found to exhibit good shear-thinning properties with viscoelastic properties suitable for eye lubricants and soft tissue fillers. However, to be used as viscosupplements, the viscoelastic properties of HA solutions have to be further modified through non-toxic crosslinking strategies, and hydrophobic derivatives as well as by using high molecular weight HAs.

Viscoelastic Biomaterials for Tissue Regeneration.

The extracellular matrix (ECM) mechanical properties regulate key cellular processes in tissue development and regeneration. The majority of scientific investigation has focused on ECM elasticity as the primary mechanical regulator of cell and tissue behavior. However, all living tissues are viscoelastic, exhibiting both solid- and liquid-like mechanical behavior. Despite increasing evidence regarding the role of ECM viscoelasticity in directing cellular behavior, this aspect is still largely overlooked in the design of biomaterials for tissue regeneration. Recently, with the emergence of various bottom-up material design strategies, new approaches can deliver unprecedented control over biomaterial properties at multiple length scales, thus enabling the design of viscoelastic biomaterials that mimic various aspects of the native tissue ECM microenvironment. This review describes key considerations for the design of viscoelastic biomaterials for tissue regeneration. We provide an overview of the role of matrix viscoelasticity in directing cell behavior toward regenerative outcomes, highlight recent strategies utilizing viscoelastic hydrogels for regenerative therapies, and outline remaining challenges, potential solutions, and emerging applications for viscoelastic biomaterials in tissue engineering and regenerative medicine. Impact statement All living tissues are viscoelastic. As we design viscoelastic biomaterials for tissue engineering and regenerative medicine, we must understand the effect of matrix viscoelasticity on in vitro cell behavior and in vivo regenerative outcomes. Engineering the next generation of biomaterials with tunable viscoelasticity to direct cell and tissue behavior will contribute to the development of in vitro tissue models and in vivo regenerative therapies to address unmet clinical needs.

Tensile creep mechanical behavior of periodontal ligament: A hyper-viscoelastic constitutive model

ObjectiveIn orthodontic treatment, the biomechanical response of periodontal ligament (PDL) induces tooth movement. Coupling modeling of PDL can effectively reflect its biomechanical response. The nonlinear creep mechanical behavior of PDL was studied by uniaxial tensile creep test and a new hyper-viscoelastic constitutive model. Two coupling modeling methods with limitations were excluded. MethodsPDL specimens were prepared from the central incisors of pig mandible. The theoretical step function was replaced by static loading with a total loading time of 1 s. The creep loading with the constant stresses of 0.05, 0.1, and 0.15 MPa was selected and kept unchanged for 1000 s. The instantaneous hyperelastic mechanical behavior and time-dependent nonlinear viscoelastic mechanical behavior of PDL were characterized by coupled instantaneous third-order Ogden hyperelastic and time-dependent nonlinear creep models. ResultsThe results showed that the instantaneous elastic curve of PDL increases in the form of hyperelastic index. The creep strain and creep compliance curves increase rapidly before 200s, and then increase slowly in steady state. The creep strain increased with an increase in the constant stress; conversely, the creep compliance decreased with an increase in the constant stress. The results showed that the experimental data were highly consistent with the hyper-viscoelastic constitutive model (R2>0.97). SignificanceWe normalize the framework of hyper-viscoelastic coupling modeling (Instantaneous hyperelastic model + time-dependent nonlinear viscoelastic model). Which can be extended to other nonlinear viscoelastic biomaterials.

Time-resolved in situ synchrotron-microCT: 4D deformation of bone and bone analogues using digital volume correlation

Digital volume correlation (DVC) in combination with high-resolution micro-computed tomography (microCT) imaging and in situ mechanical testing is gaining popularity for quantifying 3D full-field strains in bone and biomaterials. However, traditional in situ time-lapsed (i.e., interrupted) mechanical testing cannot fully capture the dynamic strain mechanisms in viscoelastic biological materials. The aim of this study was to investigate the time-resolved deformation of bone structures and analogues via continuous in situ synchrotron-radiation microCT (SR-microCT) compression and DVC to gain a better insight into their structure-function relationships. Fast SR-microCT imaging enabled the deformation behaviour to be captured with high temporal and spatial resolution. Time-resolved DVC highlighted the relationship between local strains and damage initiation and progression in the different biostructures undergoing plastic deformation, bending and/or buckling of their main microstructural elements. The results showed that SR-microCT continuous mechanical testing complemented and enhanced the information obtained from time-lapsed testing, which may underestimate the 3D strain magnitudes as a result of the stress relaxation occurring in between steps before image acquisition in porous biomaterials. Altogether, the findings of this study highlight the importance of time-resolved in situ experiments to fully characterise the time-dependent mechanical behaviour of biological tissues and biomaterials and to further explore their micromechanics under physiologically relevant conditions. Statement of significanceTime-resolved synchrotron X-ray tomography in combination with in situ mechanical testing provided the first four-dimensional analysis of the mechanical deformation of bone and bone analogues. To unravel the interplay of damage initiation and progression with local deformation, digital volume correlation was used to map the local strain field while microstructural changes were tracked with high temporal and spatial resolution. The results highlighted the importance of fast imaging and time-resolved in situ experiments to capture the real deformation of complex porous materials to fully characterize the local strain-damage relationship. The findings are notably improving the understanding of time-dependent mechanical behaviour of bone tissue, with the potential to be extend to highly viscoelastic biomaterials and soft tissues.

Resonant acoustic rheometry for non-contact characterization of viscoelastic biomaterials

Resonant Acoustic Rheometry (RAR) is a new, non-contact technique to characterize the mechanical properties of soft and viscoelastic biomaterials, such as hydrogels, that are used to mimic the extracellular matrix in tissue engineering. RAR uses a focused ultrasound pulse to generate a microscale perturbation at the sample surface and tracks the ensuing surface wave using pulse-echo ultrasound. The frequency spectrum of the resonant surface waves is analyzed to extract viscoelastic material properties. In this study, RAR was used to characterize fibrin, gelatin, and agarose hydrogels. Single time point measurements of gelled samples with static mechanical properties showed that RAR provided consistent quantitative data and measured intrinsic material characteristics independent of ultrasound parameters. RAR was also used to longitudinally track dynamic changes in viscoelastic properties over the course of fibrin gelation, revealing distinct phase and material property transitions. Application of RAR was verified using finite element modeling and the results were validated against rotational shear rheometry. Importantly, RAR circumvents some limitations of conventional rheology methods and can be performed in a high-throughput manner using conventional labware. Overall, these studies demonstrate that RAR can be a valuable tool to noninvasively quantify the viscoelastic mechanical properties of soft hydrogel biomaterials.

Effects of extracellular matrix viscoelasticity on cellular behaviour.

Substantial research over the past two decades has established that extracellular matrix (ECM) elasticity, or stiffness, affects fundamental cellular processes, including spreading, growth, proliferation, migration, differentiation and organoid formation. Linearly elastic polyacrylamide hydrogels and polydimethylsiloxane (PDMS) elastomers coated with ECM proteins are widely used to assess the role of stiffness, and results from such experiments are often assumed to reproduce the effect of the mechanical environment experienced by cells in vivo. However, tissues and ECMs are not linearly elastic materials-they exhibit far more complex mechanical behaviours, including viscoelasticity (a time-dependent response to loading or deformation), as well as mechanical plasticity and nonlinear elasticity. Here we review the complex mechanical behaviours of tissues and ECMs, discuss the effect of ECM viscoelasticity on cells, and describe the potential use of viscoelastic biomaterials in regenerative medicine. Recent work has revealed that matrix viscoelasticity regulates these same fundamental cell processes, and can promote behaviours that are not observed with elastic hydrogels in both two- and three-dimensional culture microenvironments. These findings have provided insights into cell-matrix interactions and how these interactions differentially modulate mechano-sensitive molecular pathways in cells. Moreover, these results suggest design guidelines for the next generation of biomaterials, with the goal of matching tissue and ECM mechanics for in vitro tissue models and applications in regenerative medicine.

An efficient and accurate method for modeling nonlinear fractional viscoelastic biomaterials

Computational biomechanics plays an important role in biomedical engineering: using modeling to understand pathophysiology, treatment and device design. While experimental evidence indicates that the mechanical response of most tissues is viscoelastic, current biomechanical models in the computational community often assume hyperelastic material models. Fractional viscoelastic constitutive models have been successfully used in literature to capture viscoelastic material response; however, the translation of these models into computational platforms remains limited. Many experimentally derived viscoelastic constitutive models are not suitable for three-dimensional simulations. Furthermore, the use of fractional derivatives can be computationally prohibitive, with a number of current numerical approximations having a computational cost that is O(NT2) and a storage cost that is O(NT) (NT denotes the number of time steps). In this paper, we present a novel numerical approximation to the Caputo derivative which exploits a recurrence relation similar to those used to discretize classic temporal derivatives, giving a computational cost that is O(NT) and a storage cost that is fixed over time. The approximation is optimized for numerical applications, and an error estimate is presented to demonstrate the efficacy of the method. The method, integrated into a finite element solid mechanics framework, is shown to be unconditionally stable in the linear viscoelastic case. It was then integrated into a computational biomechanical framework, with several numerical examples verifying the accuracy and computational efficiency of the method, including in an analytic test, in an analytic fractional differential equation, as well as in a computational biomechanical model problem.

Effect of viscoelasticity on interfacial stress transfer mechanism in the biocomposites: A theoretical study of viscoelastic shear lag model

Biocomposite with regularly staggered alignment microstructure is frequently observed in natural biological tissues, and exhibits superior mechanical behavior. Owing to their viscoelastic nature, biocomposites exhibit stress rate-dependent stiffness function and mechanical behavior. In this paper, a linear viscoelastic shear lag model (SLM) is proposed to illustrate the micromechanical behavior of biocomposites under triangular loading pulse. Theoretical and numerical results are derived to predict the deformation and stress transfer between fibers and interfibrous matrix while the biocomposite is transiently stretched. The results from the analytical and numerical solutions demonstrate that how the fiber overlap length and loading rate affect the stress transfer and mechanical properties of biocomposites. The structure-property correlation is illustrated for viscoelastic biomaterials under transient loading, and existence of characteristic length of soft matter with viscoelastic property is involved in load transfer mechanism between the adjacent reinforcements in transient regime, which optimizes the load transfer mechanism between the adjacent reinforcements. Furthermore, we found that discontinuous fibril model could ensure large relative sliding deformation, helping dissipate energy, protecting fibril from overall damage, and achieving high ductility and high toughness, which can provide beneficial design strategies for engineering fiber reinforced composites.

Quantitative Nanomechanical Properties of the Cuticle of the Multicolored Asian Lady Beetle Using the Modulus Mapping Technique

Biomaterials are essentially complex viscoelastic composites whose mechanical properties are related to their inter hierarchical structure. Nanoindentation can be used to investigate local material properties by employing a small probe to induce local surface deformation. This technique is recognized as an effective mechanical testing method for biomaterials, facilitating the measurement of time-dependent and viscoelastic mechanical properties. However, it is very difficult to acquire accurate mechanical properties for viscoelastic biomaterials using quasi- static nanoindentation testing techniques due to surface size effects, indenter shape, and force frequency and loading function. However, the dynamic nanoindentation approach has been successfully used to accurately investigate the viscoelastic mechanical properties of some materials. The application of small sinusoidal loading in nanoindentation has been used to investigate the dynamic characteristics of viscoelastic materials, including the storage modulus (Eʹ), loss modulus (E“) and loss tangent (tan δ). The objective of this study was to measure the viscoelastic properties of the cuticle of Harmonia axyridis Pallas (multicolored Asian lady beetle) by modulus mapping techniques on different color zones, the black spot region (BSR) and orange region (OR). Herein, the results are discussed in the context of the cuticle microstructure. Twodimensional (2-D) spatial distributions of Eʹ and E“ were mapped as functions of frequency in different color zones of Harmonia axyridis Pallas with the aim of shedding light on the nanomechanical properties of key structural features.

Interaction of human plasma proteins with thin gelatin-based hydrogel films: a QCM-D and ToF-SIMS study.

In the fields of surgery and regenerative medicine, it is crucial to understand the interactions of proteins with the biomaterials used as implants. Protein adsorption directly influences cell-material interactions in vivo and, as a result, regulates, for example, cell adhesion on the surface of the implant. Therefore, the development of suitable analytical techniques together with well-defined model systems allowing for the detection, characterization, and quantification of protein adsorbates is essential. In this study, a protocol for the deposition of highly stable, thin gelatin-based films on various substrates has been developed. The hydrogel films were characterized morphologically and chemically. Due to the obtained low thickness of the hydrogel layer, this setup allowed for a quantitative study on the interaction of human proteins (albumin and fibrinogen) with the hydrogel by Quartz Crystal Microbalance with Dissipation Monitoring (QCM-D). This technique enables the determination of adsorbant mass and changes in the shear modulus of the hydrogel layer upon adsorption of human proteins. Furthermore, Secondary Ion Mass Spectrometry and principal component analysis was applied to monitor the changed composition of the topmost adsorbate layer. This approach opens interesting perspectives for a sensitive screening of viscoelastic biomaterials that could be used for regenerative medicine.

A Mathematical Model for Analyzing the Elasticity, Viscosity, and Failure of Soft Tissue: Comparison of Native and Decellularized Porcine Cardiac Extracellular Matrix for Tissue Engineering

The clinical success of tissue-engineered constructs commonly requires mechanical properties that closely mimic those of the human tissue. Determining the viscoelastic properties of such biomaterials and the factors governing their failure profiles, however, has proven challenging, although collecting extensive data regarding their tensile behavior is straightforward. The easily calculated Young's modulus remains the most reported mechanical measure, regardless of its limitations, even though single-relaxation-time (SRT) models can provide much more information, which remain scarce due to a lack of manageable tools for implementing these models. We developed an easy-to-use algorithm for applying the Zener SRT model and determining the elastic moduli, viscosity, and failure profiles of materials under different mechanical tests in a user-independent manner. The algorithm was validated on the data resulting from tensile tests on native and decellularized porcine cardiac tissue, previously suggested as a promising scaffold material for cardiac tissue engineering. This analysis yields new and more accurate measurements such as the elastic moduli and viscosity, the model's relaxation time, and information on the factors governing the materials' failure profiles. These measurements indicate that the viscoelasticity and strength of the decellularized acellular extracellular matrix (ECM) are similar to those of native tissue, although its elasticity and apparent viscosity are higher. Nonetheless, reseeding and culturing the ECM with mesenchymal stem cells was shown to partially restore the mechanical properties lost after decellularization. We propose this algorithm as a platform for soft-tissue analysis that can provide comparable and unbiased measures for characterizing viscoelastic biomaterials commonly used in tissue engineering.

Electric-field-enhanced nutrient consumption in dielectric biomaterials that contain anchorage-dependent cells

This research contribution addresses electric-field stimulation of intra-tissue mass transfer and cell proliferation in viscoelastic biomaterials. The unsteady state reaction–diffusion equation is solved according to the von Kármán–Pohlhausen integral method of boundary layer analysis when nutrient consumption and tissue regeneration occur in response to harmonic electric potential differences across a parallel-plate capacitor in a dielectric-sandwich configuration. The partial differential mass balance with diffusion and electro-kinetic consumption contains the Damköhler (Λ 2) and Deborah (De) numbers. Zero-field and electric-field-sensitive Damköhler numbers affect nutrient boundary layer growth. Diagonal elements of the 2nd-rank diffusion tensor are enhanced in the presence of weak electric fields, in agreement with the formalism of equilibrium and nonequilibrium thermodynamics. Induced dipole polarization density within viscoelastic biomaterials is calculated via the real and imaginary components of the complex dielectric constant, according to the Debye equation, to quantify electro-kinetic stimulation. Rates of nutrient consumption under zero-field conditions are described by third-order kinetics that include local mass densities of nutrients, oxygen, and attached cells. Thinner nutrient boundary layers are stabilized at shorter dimensionless diffusion times when the zero-field intra-tissue Damköhler number increases above its initial-condition-sensitive critical value [i.e., {Λ 2 zero-field} critical ≥ 53, see Eq. (23)], such that the biomaterial core is starved of essential ingredients required for successful proliferation. When tissue regeneration occurs above the critical electric-field-sensitive intra-tissue Damköhler number, the electro-kinetic contribution to nutrient consumption cannot be neglected. The critical electric-field-sensitive intra-tissue Damköhler number is proportional to the Deborah number.

Stress-sensitive tissue regeneration in viscoelastic biomaterials subjected to modulated tensile strain

This research contribution addresses the mechanochemistry of intra-tissue mass transfer for nutrients, oxygen, growth factors, and other essential ingredients that anchorage-dependent cells require for successful proliferation on biocompatible surfaces. The unsteady state reaction–diffusion equation (i.e., modified diffusion equation) is solved according to the von Kármán–Pohlhausen integral method of boundary layer analysis when nutrient consumption and tissue regeneration are stimulated by harmonically imposed stress. The mass balance with diffusion and stress-sensitive kinetics represents a rare example where the Damköhler and Deborah numbers appear together in an effort to simulate the development of mass transfer boundary layers in porous viscoelastic biomaterials. The Boltzmann superposition integral is employed to calculate time-dependent strain in terms of the real and imaginary components of dynamic compliance for viscoelastic solids that transmit harmonic excitation to anchorage-dependent cells. Rates of nutrient consumption under stress-free conditions are described by third-order kinetics which include local mass densities of nutrients, oxygen, and attached cells that maintain dynamic equilibrium with active protein sites in the porous matrix. Thinner nutrient mass transfer boundary layers are stabilized at shorter dimensionless diffusion times when the stress-free intra-tissue Damköhler number increases above its initial-condition-sensitive critical value. The critical stress-sensitive intra-tissue Damköhler number, above which it is necessary to consider the effect of harmonic strain on nutrient consumption and tissue regeneration, is proportional to the Deborah number and corresponds to a larger fraction of the stress-free intra-tissue Damköhler number in rigid biomaterials.

Nonlinear viscoelastic biomaterials: meaningful characterization and engineering inspiration

Nonlinear mechanical properties play an important role in numerous biological functions, for instance the locomotion strategy used by terrestrial gastropods. We discuss the progress made toward bioinspired snail-like locomotion and the pursuit of an engineered fluid that imitates the nonlinear viscoelastic properties of native gastropod pedal mucus. The rheological behavior of native pedal mucus is characterized using an oscillatory deformation protocol known as large amplitude oscillatory shear, and we review recently developed techniques for appropriately describing nonlinear viscoelastic behavior. Although materials that exhibit purely elastic and purely viscous nonlinearities are amenable to standard techniques for characterization, pedal mucus samples (and biomaterials in general) are viscoelastic, exhibiting both elastic and viscous nonlinear responses simultaneously and requiring advanced techniques for characterization. We reveal the utility of these new methods by examining trail mucus from the terrestrial slug Limax maximus using oscillatory shear rheology. Material responses which previously could only be described mathematically, with little physical insight, can now be interpreted with familiar language such as strain-stiffening/softening and shear-thickening/thinning. The new methodology is applicable to any complex material that can be tested using imposed oscillatory deformations. We have developed data-analysis software to enable wider use of this framework within and beyond the biomaterials community. The functionality of this software is outlined here.

Forced vibration analysis of harmonically excited nonlinear viscoelastic biomaterials

Forced vibration analysis of harmonically excited nonlinear viscoelastic biomaterials