Elasticity Models for the Spherical Indentation of Gels and Soft Biological Tissues

2007 ◽  
Vol 1060 ◽  
Author(s):  
David C. Lin ◽  
Emilios K. Dimitriadis ◽  
Ferenc Horkay
Keyword(s):  
Soft Matter ◽  
Nonlinear Models ◽  
Large Strain ◽  
Van Der Waals ◽  
Biological Tissues ◽  
Cartilage Tissue ◽  
Poly Vinyl Alcohol ◽  
Spherical Indentation ◽  
Small Strains ◽  
Single Term

ABSTRACTAFM micro- or nanoindentation is a powerful technique for mapping the elasticity of materials at high resolution. When applied to soft matter, however, its accuracy is equivocal. The sources of the uncertainty can be methodological or analytical in nature. In this paper, we address the lack of practicable nonlinear elastic contact models, which frequently compels the use of Hertzian models in analyzing force curves. We derive and compare approximate force-indentation relations based on a number of hyperelastic general strain energy functions. These models were applied to existing data from the spherical indentation of native mouse cartilage tissue as well as chemically crosslinked poly(vinyl alcohol) gels. For the biological tissue, the Fung and single-term Ogden models were found to provide the best fit of the data while the Mooney-Rivlin and van der Waals models were most suitable for the synthetic gels. The other models (neo-Hookean, two-term reduced polynomial, Fung, van der Waals, and Hertz) were effective to varying degrees. The Hertz model proved to be acceptable for the synthetic gels at small strains (<20% for the samples tested). Although this finding supports the generally accepted view that many soft elastic materials can be assumed to be linear elastic at small strains, we propose the use of the nonlinear models when evaluating the large-strain indentation response of gels and tissues.

Spherical indentation load-relaxation of soft biological tissues

2006 ◽  
Vol 21 (8) ◽  
pp. 2003-2010 ◽  
Author(s):  
Jason M. Mattice ◽  
Anthony G. Lau ◽  
Michelle L. Oyen ◽  
Richard W. Kent
Keyword(s):  
Costal Cartilage ◽  
Kidney Tissue ◽  
Biological Tissues ◽  
Indentation Load ◽  
Spherical Indentation ◽  
Load Relaxation ◽  
Soft Biological Tissues ◽  
Long Time ◽  
Constant Displacement ◽  
Soft Biological Materials

Elastic-viscoelastic correspondence was used to generate displacement–time solutions for spherical indentation testing of soft biological materials with time-dependent mechanical behavior. Boltzmann hereditary integral operators were used to determine solutions for indentation load-relaxation following a constant displacement rate ramp. A “ramp correction factor” approach was used for routine analysis of experimental load-relaxation data. Experimental load-relaxation tests were performed on rubber, as well as kidney tissue and costal cartilage, two hydrated soft biological tissues with vastly different mechanical responses. The experimental data were fit to the spherical indentation ramp-relaxation solutions to obtain values of short- and long-time shear modulus and of material time constants. The method is used to demonstrate linearly viscoelastic responses in rubber, level-independent indentation results for costal cartilage, and age-independent indentation results for kidney parenchymal tissue.

4. States of matter

2014 ◽  
pp. 51-69
Author(s):  
Peter Atkins
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Liquid Crystals ◽  
Magnetic Resonance ◽  
Equation Of State ◽  
Soft Matter ◽  
Van Der Waals ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
Van Der Waals Equation ◽  
Intermediate States

‘States of matter’ describes the three traditional states — gas, liquid, and solid — and the models used to predict and understand their behaviour. The van der Waals equation of state captures many of the properties of real gases. The classical way of studying the motion of molecules in liquids is to measure its viscosity. Techniques include neutron scattering and nuclear magnetic resonance. X-ray diffraction is used to determine the structures of solids. Intermediate states of matter — where liquid meets gas and liquid meets solid — are also considered. Examples include supercritical fluids, soft matter such as liquid crystals, and graphene, a remarkable and essentially two-dimensional material.

Poroelastic Indentation Analysis for Hydrated Biological Tissues

2006 ◽  
Vol 975 ◽  
Author(s):  
Michelle L. Oyen ◽  
Amanpreet K. Bembey ◽  
Andrew J. Bushby
Keyword(s):  
Indentation Test ◽  
Biological Tissues ◽  
Time Dependent ◽  
Spherical Indentation ◽  
Indentation Creep ◽  
Polar Solvents ◽  
Viscoelastic Analysis ◽  
Wide Range ◽  
Indentation Problem

ABSTRACTIndentation techniques are employed for the measurement of mechanical properties of a wide range of materials. In particular, techniques focused at small length-scales, such as nanoindentation and AFM indentation, allow for local characterization of material properties in heterogeneous materials including natural tissues and biomimetic materials. Typical elastic analysis for spherical indentation is applicable in the absence of time-dependent deformation, but is inappropriate for materials with time-dependent responses. Recent analyses for the viscoelastic indentation problem, based on elastic-viscoelastic correspondence, have begun to address the issue of time-dependent deformation during an indentation test. The viscoelastic analysis has been shown to fit experimental indentation data well, and has been demonstrated as useful for characterization of viscoelasticity in polymeric materials and in hydrated mineralized tissues. However, a viscoelastic analysis is not necessarily sufficient for multi-phase materials with fluid flow. In the current work, a poroelastic analysis—based on fluid motion through a porous elastic network—is used to examine spherical indentation creep responses of hydrated biological materials. Both analytical and finite element approaches are considered for the poroelastic Hertzian indentation problem. Modeling results are compared with experimental data from nanoindentation of hydrated bone immersed in water and polar solvents (ethanol, methanol, acetone). Baseline (water-immersed) bone responses are characterized using the poroelastic model and numerical results are compared with altered hydration states due to polar solvents.

The non-linear mechanical properties of soft engineered biological tissues determined by finite spherical indentation

2008 ◽  
Vol 11 (5) ◽  
pp. 585-592 ◽  
Author(s):  
Martijn A.J. Cox ◽  
Debby Gawlitta ◽  
Niels J.B. Driessen ◽  
Cees W.J. Oomens ◽  
Frank P.T. Baaijens
Keyword(s):  
Mechanical Properties ◽  
Biological Tissues ◽  
Spherical Indentation ◽  
Non Linear

scholarly journals Preparation and Characterization of Poly(vinyl alcohol)-chondroitin Sulphate Hydrogel as Scaffolds for Articular Cartilage Regeneration

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Shivani Nanda ◽  
Nikhil Sood ◽  
B. V. K. Reddy ◽  
Tanmay S. Markandeywar
Keyword(s):  
Articular Cartilage ◽  
Chondroitin Sulphate ◽  
Articular Surface ◽  
Rheological Behaviour ◽  
Cartilage Regeneration ◽  
Cartilage Tissue ◽  
Poly Vinyl Alcohol ◽  
Cross Linking ◽  
Articular Cartilage Regeneration

The aim of the study was to develop PVA-CS hydrogel scaffolds using glutaraldehyde as a cross-linking agent by chemical cross-linking method in order to obtain biomimetic scaffolds for articular cartilage regeneration. The introduction of PVA enhances the mechanical and bioadhesive properties to the native tissue while chondroitin sulphate enhances the glycosaminoglycan content of extracellular matrix. The role of hydrogel as cartilage regeneration scaffold was evaluated by swelling study, porosity, rheological behaviour, in vitro degradation, and quantification of released chondroitin sulphate. In vivo results showed that cross-linked hydrogels repaired defects with no sign of inflammation as it was well anchored to tissue in the formation of new articular surface. It may be concluded that the addition of chondroitin sulphate to the PVA polymer develops a novel composite with significant applications in cartilage tissue engineering.

ON FIXED-STRESS AND FIXED-STRAIN SOLUTION SCHEMES FOR LARGE STRAIN POROELASTICITY APPLIED TO SOFT BIOLOGICAL TISSUES

2021 ◽  
Author(s):  
José Luís Medeiros Thiesen ◽  
Bruno Klahr ◽  
Thiago André Carniel ◽  
Eduardo Fancello
Keyword(s):  
Large Strain ◽  
Biological Tissues ◽  
Soft Biological Tissues

Dynamic hyaluronic acid hydrogel with covalent linked gelatin as an anti-oxidative bioink for cartilage tissue engineering

2021 ◽  
Author(s):  
Wen Shi ◽  
Fang Fang ◽  
Yunfan Kong ◽  
Sydney E Greer ◽  
Mitchell A Kuss ◽  
...  
Keyword(s):  
Tissue Engineering ◽  
Hyaluronic Acid ◽  
Therapeutic Option ◽  
Phenylboronic Acid ◽  
Cartilage Tissue Engineering ◽  
Covalent Bond ◽  
Cartilage Tissue ◽  
Poly Vinyl Alcohol ◽  
Extracellular Matrix Components

Abstract Cartilage tissue engineering has arisen as a promising therapeutic option for degenerative joint diseases, such as osteoarthritis, in the hope of restoring the structure and physiological functions. Hydrogels are promising biomaterials for developing engineered constructs for cartilage regeneration. However, such cell-laden constructs could be exposed to elevated levels of reactive oxygen species (ROS) in the inflammatory microenvironment after being implanted into injured joints, which may affect their phenotype and normal functions and thereby hinder the regeneration efficacy. To attenuate ROS induced side effects, a multifunctional hydrogel with an innate anti-oxidative ability was produced in this study. The hydrogel was rapidly formed through a dynamic covalent bond between phenylboronic acid grafted hyaluronic acid (HA-PBA) and poly (vinyl alcohol) (PVA) and was further stabilized through a secondary crosslinking between the acrylate moiety on HA-PBA and the free thiol group from thiolated gelatin. The hydrogel is cyto-compatible and injectable and can be used as a bioink for 3D bioprinting. The viscoelastic properties of the hydrogels could be modulated through the hydrogel precursor concentration. The presence of dynamic covalent linkages contributed to its shear-thinning property and thus good printability of the hydrogel, resulting in the fabrication of a porous grid construct and a meniscus like scaffold at high structural fidelity. The bioprinted hydrogel promoted cell adhesion and chondrogenic differentiation of encapsulated rabbit adipose derived mesenchymal stem cells. Meanwhile, the hydrogel supported robust deposition of extracellular matrix components, including glycosaminoglycans and type II collagen, by embedded mouse chondrocytes in vitro. Most importantly, the hydrogel could protect encapsulated chondrocytes from ROS induced downregulation of cartilage-specific anabolic genes (ACAN and COL2) and upregulation of a catabolic gene (MMP13) after incubation with H2O2. Furthermore, intra-articular injection of the hydrogel in mice revealed adequate stability and good biocompatibility in vivo. These results demonstrate that this hydrogel can be used as a novel bioink for the generation of 3D bioprinted constructs with anti-ROS ability to potentially enhance cartilage tissue regeneration in a chronic inflammatory and elevated ROS microenvironment.

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