Mathematical modeling and simulations for large-strain J-shaped diagrams of soft biological tissues

Koibuchi, Hiroshi; Mitsuhashi, Kazuhiko; Ghosh, Swapan K.

doi:10.1101/275206

2018

DOI: 10.1101/275206

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Mathematical modeling and simulations for large-strain J-shaped diagrams of soft biological tissues

Hiroshi Koibuchi

Kazuhiko Mitsuhashi

Swapan K. Ghosh

Abstract: 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 techni… Show more

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Cited by 4 publications

References 47 publications

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A Biomimetic Nonwoven-Reinforced Hydrogel for Spinal Cord Injury Repair

et al. 2022

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In clinical trials, new scaffolds for regeneration after spinal cord injury (SCI) should reflect the importance of a mechanically optimised, hydrated environment. Composite scaffolds of nonwovens, self-assembling peptides (SAPs) and hydrogels offer the ability to mimic native spinal cord tissue, promote aligned tissue regeneration and tailor mechanical properties. This work studies the effects of an aligned electrospun nonwoven of P11-8—enriched poly(ε-caprolactone) (PCL) fibres, integrated with a photo-crosslinked hydrogel of glycidylmethacrylated collagen (collagen-GMA), on neurite extension. Mechanical properties of collagen-GMA hydrogel in compression and shear were recorded, along with cell viability. Collagen-GMA hydrogels showed J-shaped stress–strain curves in compression, mimicking native spinal cord tissue. For hydrogels prepared with a 0.8-1.1 wt.% collagen-GMA concentration, strain at break values were 68 ± 1–81 ± 1% (±SE); maximum stress values were 128 ± 9–311 ± 18 kPa (±SE); and maximum force values were 1.0 ± 0.1–2.5 ± 0.1 N (±SE). These values closely mimicked the compression values for feline and porcine tissue in the literature, especially those for 0.8 wt.%. Complex shear modulus values fell in the range 345–2588 Pa, with the lower modulus hydrogels in the range optimal for neural cell survival and growth. Collagen-GMA hydrogel provided an environment for homogenous and three-dimensional cell encapsulation, and high cell viability of 84 ± 2%. Combination of the aligned PCL/P11-8 electrospun nonwoven and collagen-GMA hydrogel retained fibre alignment and pore structure, respectively, and promoted aligned neurite extension of PC12 cells. Thus, it is possible to conclude that scaffolds with mechanical properties that both closely mimic native spinal cord tissue and are optimal for neural cells can be produced, which also promote aligned tissue regeneration when the benefits of hydrogels and electrospun nonwovens are combined.

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A Biomimetic Nonwoven-Reinforced Hydrogel for Spinal Cord Injury Repair

et al. 2022

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Monte Carlo Study of Rubber Elasticity on the Basis of Finsler Geometry Modeling

et al. 2019

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Configurations of the polymer state in rubbers, such as so-called isotropic (random) and anisotropic (almost aligned) states, are symmetric/asymmetric under space rotations. In this paper, we present numerical data obtained by Monte Carlo simulations of a model for rubber formulations to compare these predictions with the reported experimental stress–strain curves. The model is defined by extending the two-dimensional surface model of Helfrich–Polyakov based on the Finsler geometry description. In the Finsler geometry model, the directional degree of freedom σ → of the polymers and the polymer position r are assumed to be the dynamical variables, and these two variables play an important role in the modeling of rubber elasticity. We find that the simulated stresses τ sim are in good agreement with the reported experimental stresses τ exp for large strains of up to 1200 % . It should be emphasized that the stress–strain curves are directly calculated from the Finsler geometry model Hamiltonian and its partition function, and this technique is in sharp contrast to the standard technique in which affine deformation is assumed. It is also shown that the obtained results are qualitatively consistent with the experimental data as influenced by strain-induced crystallization and the presence of fillers, though the real strain-induced crystallization is a time-dependent phenomenon in general.

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Generalized Finsler Geometry and the Anisotropic Tearing of Skin

Clayton

2023

Symmetry

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A continuum mechanical theory with foundations in generalized Finsler geometry describes the complex anisotropic behavior of skin. A fiber bundle approach, encompassing total spaces with assigned linear and nonlinear connections, geometrically characterizes evolving configurations of a deformable body with the microstructure. An internal state vector is introduced on each configuration, describing subscale physics. A generalized Finsler metric depends on the position and the state vector, where the latter dependence allows for both the direction (i.e., as in Finsler geometry) and magnitude. Equilibrium equations are derived using a variational method, extending concepts of finite-strain hyperelasticity coupled to phase-field mechanics to generalized Finsler space. For application to skin tearing, state vector components represent microscopic damage processes (e.g., fiber rearrangements and ruptures) in different directions with respect to intrinsic orientations (e.g., parallel or perpendicular to Langer’s lines). Nonlinear potentials, motivated from soft-tissue mechanics and phase-field fracture theories, are assigned with orthotropic material symmetry pertinent to properties of skin. Governing equations are derived for one- and two-dimensional base manifolds. Analytical solutions capture experimental force-stretch data, toughness, and observations on evolving microstructure, in a more geometrically and physically descriptive way than prior phenomenological models.

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Mathematical modeling and simulations for large-strain J-shaped diagrams of soft biological tissues

Cited by 4 publications

References 47 publications

A Biomimetic Nonwoven-Reinforced Hydrogel for Spinal Cord Injury Repair

A Biomimetic Nonwoven-Reinforced Hydrogel for Spinal Cord Injury Repair

Monte Carlo Study of Rubber Elasticity on the Basis of Finsler Geometry Modeling

Generalized Finsler Geometry and the Anisotropic Tearing of Skin

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