The role of anisotropy and fiber dispersion in the mechanics and remodeling of biological tissues
<p>In many soft biological tissues mechanical strength and anisotropy are determined primarily by the presence of fibers, in particular collagen. </p> <p>When an isotropic material is subject to a uniaxial tension, the principal strain transverse to the direction of applied load is...
| Main Authors: | , |
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| Format: | Thesis |
| Language: | English |
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2015
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| _version_ | 1826342863148941312 |
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| author | Melnik, A Goriely, A |
| author2 | Goriely, A |
| author_facet | Goriely, A Melnik, A Goriely, A |
| author_sort | Melnik, A |
| collection | OXFORD |
| description | <p>In many soft biological tissues mechanical strength and anisotropy are determined primarily by the presence of fibers, in particular collagen. </p> <p>When an isotropic material is subject to a uniaxial tension, the principal strain transverse to the direction of applied load is always negative. However, in fiber reinforced materials the transverse principal strain can change its sign as the load increases, passing through the zero-points, known as <em>perversions</em>. We investigate how the number of perversions in a material reinforced by two symmetrically aligned families of distributed fibers depends both on the degree of fiber dispersion and the model used for fiber dispersion. Angular integration and three variants of the generalized structure tensor approach are considered and discussed. The study of perversions clearly demonstrates the qualitative difference between these approaches in the case of high dispersion of fibers. The results suggest that this difference is primarily due to the way compressive fibers are modeled. </p> <p>Fiber alignment in biological tissues is created and maintained by the cells, which respond to mechanical stimuli arising from properties of the surrounding material. This coupling between mechanical anisotropy and tissue remodeling can be modeled in nonlinear elasticity by a fiber-reinforced hyperelastic material where remodeling is represented as the change in fiber orientation. We study analytically a simple model of fiber reorientation in a rectangular elastic tissue reinforced by two symmetrically arranged families of fibers subject to constant external loads. In this model, the fiber direction tends to align with the maximum principal stretch or strain. We characterize the global behaviour of the system for all material parameters and applied loads, and show that provided the fibers are tensile initially, the system converges to a stable equilibrium, which corresponds to either complete or intermediate fiber alignment.</p> <p>Finally, we consider a model for the coupled growth and fiber reorientation in an elastic incompressible disk. The dynamics of our model is extremely sensitive to the initial condition and characterized by an infinite number of equilibrium states of fiber arrangement. We observed that the stress-induced fiber reorientation and growth laws used in our model produce specific fiber orientation pattern, which suggest a possible mechanism for self-organisation.</p> |
| first_indexed | 2024-03-06T22:16:50Z |
| format | Thesis |
| id | oxford-uuid:53a76408-54e3-45bf-98c1-0c409ac454ac |
| institution | University of Oxford |
| language | English |
| last_indexed | 2025-03-11T23:38:01Z |
| publishDate | 2015 |
| record_format | dspace |
| spelling | oxford-uuid:53a76408-54e3-45bf-98c1-0c409ac454ac2025-03-11T14:34:26ZThe role of anisotropy and fiber dispersion in the mechanics and remodeling of biological tissuesThesishttp://purl.org/coar/resource_type/c_db06uuid:53a76408-54e3-45bf-98c1-0c409ac454acTissues--Mechanical propertiesElasticity--Mathematical modelsBiomechanicsApplied mathematicsMechanics, Applied--MathematicsEnglishORA Deposit2015Melnik, AGoriely, AGoriely, A<p>In many soft biological tissues mechanical strength and anisotropy are determined primarily by the presence of fibers, in particular collagen. </p> <p>When an isotropic material is subject to a uniaxial tension, the principal strain transverse to the direction of applied load is always negative. However, in fiber reinforced materials the transverse principal strain can change its sign as the load increases, passing through the zero-points, known as <em>perversions</em>. We investigate how the number of perversions in a material reinforced by two symmetrically aligned families of distributed fibers depends both on the degree of fiber dispersion and the model used for fiber dispersion. Angular integration and three variants of the generalized structure tensor approach are considered and discussed. The study of perversions clearly demonstrates the qualitative difference between these approaches in the case of high dispersion of fibers. The results suggest that this difference is primarily due to the way compressive fibers are modeled. </p> <p>Fiber alignment in biological tissues is created and maintained by the cells, which respond to mechanical stimuli arising from properties of the surrounding material. This coupling between mechanical anisotropy and tissue remodeling can be modeled in nonlinear elasticity by a fiber-reinforced hyperelastic material where remodeling is represented as the change in fiber orientation. We study analytically a simple model of fiber reorientation in a rectangular elastic tissue reinforced by two symmetrically arranged families of fibers subject to constant external loads. In this model, the fiber direction tends to align with the maximum principal stretch or strain. We characterize the global behaviour of the system for all material parameters and applied loads, and show that provided the fibers are tensile initially, the system converges to a stable equilibrium, which corresponds to either complete or intermediate fiber alignment.</p> <p>Finally, we consider a model for the coupled growth and fiber reorientation in an elastic incompressible disk. The dynamics of our model is extremely sensitive to the initial condition and characterized by an infinite number of equilibrium states of fiber arrangement. We observed that the stress-induced fiber reorientation and growth laws used in our model produce specific fiber orientation pattern, which suggest a possible mechanism for self-organisation.</p> |
| spellingShingle | Tissues--Mechanical properties Elasticity--Mathematical models Biomechanics Applied mathematics Mechanics, Applied--Mathematics Melnik, A Goriely, A The role of anisotropy and fiber dispersion in the mechanics and remodeling of biological tissues |
| title | The role of anisotropy and fiber dispersion in the mechanics and remodeling of biological tissues |
| title_full | The role of anisotropy and fiber dispersion in the mechanics and remodeling of biological tissues |
| title_fullStr | The role of anisotropy and fiber dispersion in the mechanics and remodeling of biological tissues |
| title_full_unstemmed | The role of anisotropy and fiber dispersion in the mechanics and remodeling of biological tissues |
| title_short | The role of anisotropy and fiber dispersion in the mechanics and remodeling of biological tissues |
| title_sort | role of anisotropy and fiber dispersion in the mechanics and remodeling of biological tissues |
| topic | Tissues--Mechanical properties Elasticity--Mathematical models Biomechanics Applied mathematics Mechanics, Applied--Mathematics |
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