On the mechanics of solids with a growing mass

Lubarda, Vlado A.; Hoger, Anne

doi:10.1016/s0020-7683(02)00352-9

Cited by 269 publications

(269 citation statements)

References 33 publications

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“…for example (Ambrosi and Mollica, 2002;Lubarda and Hoger, 2002). The elastic deformation of the material is given by an equation analogous to (9) but with the strain calculated from the displacement from the zero stress configuration, so that (after linearisation)…”

Section: Discussionmentioning

confidence: 99%

Biomechanical Modelling of Colorectal Crypt Budding and Fission

Edwards

Chapman

2007

Bull. Math. Biol.

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This paper presents a biomechanical model for the small pits, called crypts, that line the colon. A continuum approach is adopted, with the crypt epithelium modelled as a growing beam attached to the underlying lamina by cell bonds, which generate tension within the layer. These cell attachments are assumed to be viscoelastic thus allowing for cell progression along the crypt. It is shown that any combination of: an increase in net proliferation (i.e. cell production minus apoptosis), an enlargement of the proliferative compartment, an increase in the strength of the cellular attachment to the underlying lamina, or a change in the rate of cell growth or cell bonding may generate buckling of the tissue. These changes can all be generated by an activating mutation of the Wnt cascade, which is generally accepted to be the first genetic change in colorectal cancer, with subsequent deformation, budding, and crypt fission an observed feature of the adenomatous crypt.

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Section: Discussionmentioning

confidence: 99%

Biomechanical Modelling of Colorectal Crypt Budding and Fission

Edwards

Chapman

2007

Bull. Math. Biol.

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“…For a general orthotropic strain energydensity function, the components of are provided in Eq. (11.9) of Lubarda and Hoger (2002). For an isotropic material, a simplified expression is given in Eq.…”

Section: Appendix A: Computation Of Rotation Tensormentioning

confidence: 99%

Computational modeling of morphogenesis regulated by mechanical feedback

Ramasubramanian

Taber

2007

Biomech Model Mechanobiol

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Mechanical forces cause changes in form during embryogenesis and likely play a role in regulating these changes. This paper explores the idea that changes in homeostatic tissue stress (target stress), possibly modulated by genes, drive some morphogenetic processes. Computational models are presented to illustrate how regional variations in target stress can cause a range of complex behaviors involving the bending of epithelia. These models include growth and cytoskeletal contraction regulated by stress-based mechanical feedback. All simulations were carried out using the commercial finite element code ABAQUS, with growth and contraction included by modifying the zero-stress state in the material constitutive relations. Results presented for bending of bilayered beams and invagination of cylindrical and spherical shells provide insight into some of the mechanical aspects that must be considered in studying morphogenetic mechanisms.

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“…Although very difficult to validate, they are much more bio-physical and allow checking different hypotheses and design new experiments useful for a better understanding of the specific problem analyzed. Multiphasic formulations are usually used, including complex interactions between Mechanics, cells and volume growth in the framework of open systems [30,31].…”

Section: Mechanistic-based Approachesmentioning

confidence: 99%

Patches of Finite Elements for Singularly-Perturbed Diffusion Reaction Equations with Discontinuous Coefficients

Culpo

Falco

O’Riordan

2010

Progress in Industrial Mathematics at ECMI 2008

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Summary. Mechanical modeling of living tissues is currently one of the most crucial challenges in research for mechanical engineers and mathematicians. Mechanics is a key factor to understanding the mechanisms that regulate many biological processes, such as mitosis, migration, and differentiation. This work aims to present the most crucial aspects, in the authors' opinion, to approach this challenge.

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On the mechanics of solids with a growing mass

Cited by 269 publications

References 33 publications

Biomechanical Modelling of Colorectal Crypt Budding and Fission

Biomechanical Modelling of Colorectal Crypt Budding and Fission

Computational modeling of morphogenesis regulated by mechanical feedback

Patches of Finite Elements for Singularly-Perturbed Diffusion Reaction Equations with Discontinuous Coefficients

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