Deep Indentation and Puncture of a Rigid Cylinder Inserted into a Soft Solid

Herein, we study stress-strain diagrams of soft biological tissues such as animal skin, muscles and arteries by Finsler geometry (FG) modeling. The stress-strain diagram of these biological materials is always J-shaped and is composed of toe, heel, linear and failure regions. In the toe region, the stress is zero, and the length of this zero-stress region becomes very large (≃ 150%) in, for example, certain arteries. In this paper, we study long-toe diagrams using two-dimensional (2D) and 3D FG modeling techniques and Monte Carlo (MC) simulations. We find that except for the failure region, large-strain J-shaped diagrams are successfully reproduced by the FG models. This implies that the complex J-shaped curves originate from the interaction between the directional and positional degrees of freedom of polymeric molecules, as implemented in the FG model.

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

MRS Proceedings ◽

10.1557/proc-1060-ll05-07 ◽

2007 ◽

Vol 1060 ◽

Cited By ~ 2

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.

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PHOTOACOUSTIC VISCOELASTICITY IMAGING OF BIOLOGICAL TISSUES WITH INTENSITY-MODULATED CONTINUOUS-WAVE LASER

Journal of Innovative Optical Health Sciences ◽

10.1142/s1793545813500338 ◽

2013 ◽

Vol 06 (04) ◽

pp. 1350033 ◽

Cited By ~ 8

Author(s):

YUE ZHAO ◽

SIHUA YANG

Keyword(s):

Continuous Wave ◽

Biomechanical Properties ◽

Biological Tissues ◽

Phase Delay ◽

Continuous Wave Laser ◽

Absorption Coefficients ◽

Soft Solids ◽

Novel Technique ◽

Wave Laser ◽

The Relationship

In this paper, a novel photoacoustic viscoelasticity imaging (PAVEI) technique that provides viscoelastic information of biological tissues is presented. We deduced the process of photoacoustic (PA) effect on the basis of thermal viscoelasticity theory and established the relationship between the PA phase delay and the viscoelasticity for soft solids. By detecting the phase delay of PA signal, the viscoelasticity distribution of absorbers can be mapped. Gelatin phantoms with different densities and different absorption coefficients were used to verify the dependence of PAVEI measurements. Moreover, tissue mimicking phantoms mixed with fat and collagen at different concentrations were used to testify the feasibility of this technique with reliable contrast. Finally, the PAVEI was successfully applied to discrimination between biological tissue constituents. Our experimental results demonstrate that this novel technique has the potential for visualizing the anatomical and biomechanical properties of biological tissues.

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Mechanics of Biomacromolecular Networks Containing Folded Domains

Journal of Engineering Materials and Technology ◽

10.1115/1.2345442 ◽

2006 ◽

Vol 128 (4) ◽

pp. 509-518 ◽

Cited By ~ 25

Author(s):

H. Jerry Qi ◽

Christine Ortiz ◽

Mary C. Boyce

Keyword(s):

Network Model ◽

Single Molecule ◽

Large Strain ◽

Biological Membrane ◽

Biological Materials ◽

Biological Tissues ◽

Force Extension ◽

Stress Strain ◽

Strain Behavior ◽

Dimensional Network

The force-extension behavior of single modular biomacromolecules is known to exhibit a characteristic repeating pattern of a nonlinear rise in force with imposed displacement to a peak, followed by a significant force drop upon reaching the peak. This “saw-tooth” pattern is a result of stretch-induced unfolding of modules along the molecular chain and is speculated to play a governing role in the function of biological materials and structures. In this paper, constitutive models for the large strain deformation of networks of modular macromolecules are developed building directly from statistical mechanics based models of the single molecule force-extension behavior. The proposed two-dimensional network model has applicability to biological membrane skeletons and the three-dimensional network model emulates cytoskeletal networks, natural fibers, and soft biological tissues. Simulations of the uniaxial and multiaxial stress-strain behavior of these networks illustrate the macroscopic membrane and solid stretching conditions which activate unfolding in these microstructures. The models simultaneously track the evolution in underlying microstructural features with different macroscopic stretching conditions, including the evolution in molecular orientation and the forces acting on the constituent molecular chains and junctions. The effect of network pretension on the stress-strain behavior and the macroscopic stress and strain conditions which trigger unfolding are presented. The implications of the predicted stress-strain behaviors on a variety of biological materials are discussed.

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