A volumetric model for growth of arterial walls with arbitrary geometry and loads

Rodríguez, J. C.; Ruigómez, José María Goicolea; Gabaldón, Felipe

doi:10.1016/j.jbiomech.2006.05.002

Cited by 42 publications

(32 citation statements)

References 21 publications

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“…In general, it is convenient to express the stress tensors in terms of convected coordinates, which rotate with the material (Taber 2004). Growth laws of the form of equation (3.7) have been used in prior models for the cardiovascular system (Rachev et al 1996;Taber 1998;Rodriguez et al 2007;Alford et al 2008). Usually, the target stress is taken as constant, which seems to work reasonably well for functional adaptation of mature tissues.…”

Section: (C) Morphomechanical Lawsmentioning

confidence: 99%

Towards a unified theory for morphomechanics

Taber

2009

Phil. Trans. R. Soc. A.

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Mechanical forces are closely involved in the construction of an embryo. Experiments have suggested that mechanical feedback plays a role in regulating these forces, but the nature of this feedback is poorly understood. Here, we propose a general principle for the mechanics of morphogenesis, as governed by a pair of evolution equations based on feedback from tissue stress. In one equation, the rate of growth (or contraction) depends on the difference between the current tissue stress and a target (homeostatic) stress. In the other equation, the target stress changes at a rate that depends on the same stress difference. The parameters in these morphomechanical laws are assumed to depend on stress rate. Computational models are used to illustrate how these equations can capture a relatively wide range of behaviours observed in developing embryos, as well as show the limitations of this theory. Specific applications include growth of pressure vessels (e.g. the heart, arteries and brain), wound healing and sea urchin gastrulation. Understanding the fundamental principles of tissue construction can help engineers design new strategies for creating replacement tissues and organs in vitro.

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Section: (C) Morphomechanical Lawsmentioning

confidence: 99%

Towards a unified theory for morphomechanics

Taber

2009

Phil. Trans. R. Soc. A.

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“…This results in a complex morphological organization of the cellular components of the middle layer, composed of smooth muscle cells and collagen mesh ECM, whose design will trace circumferential and longitudinal lines, giving to vascular tissue an anisotropic mechanical behavior condition. (Rodriguez, 2007). The primary ice spontaneous nucleation happen at random in many sites of ECM, Muldrew.…”

Section: X-ray Diffractionmentioning

confidence: 99%

X Ray Diffraction: An Approach to Structural Quality of Biological Preserved Tissues in Tissue Banks

Campos¹,

Saldías²,

Sanchez³

et al. 2012

Current Frontiers in Cryopreservation

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“…Taber and Eggers 1996;Taber 1998;Rodriguez et al 2007;Kuhl et al 2007) are based on the model proposed by Skalak et al (1982), Rodriguez et al (1994). In these models, a growth stimulus is translated into a growth tensor, which describes the growth of infinitesimal tissue elements in a virtual, isolated state.…”

Section: Volumetric Growth and Residual Stressmentioning

confidence: 99%

A model for arterial adaptation combining microstructural collagen remodeling and 3D tissue growth

Machyshyn

Bovendeerd

Ven

et al. 2010

Biomech Model Mechanobiol

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Long-term adaptation of soft tissues is realized through growth and remodeling (G&R). Mathematical models are powerful tools in testing hypotheses on G&R and supporting the design and interpretation of experiments. Most theoretical G&R studies concentrate on description of either growth or remodeling. Our model combines concepts of remodeling of collagen recruitment stretch and orientation suggested by other authors with a novel model of general 3D growth. We translate a growth-induced volume change into a change in shape due to the interaction of the growing tissue with its environment. Our G&R model is implemented in a finite element package in 3D, but applied to two rotationally symmetric cases, i.e., the adaptation towards the homeostatic state of the human aorta and the development of a fusiform aneurysm. Starting from a guessed non-homeostatic state, the model is able to reproduce a homeostatic state of an artery with realistic parameters. We investigate the sensitivity of this state to settings of initial parameters. In addition, we simulate G&R of a fusiform aneurysm, initiated by a localized degradation of the matrix of the healthy artery. The aneurysm stabilizes in size soon after the degradation stops.

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A volumetric model for growth of arterial walls with arbitrary geometry and loads

Cited by 42 publications

References 21 publications

Towards a unified theory for morphomechanics

Towards a unified theory for morphomechanics

X Ray Diffraction: An Approach to Structural Quality of Biological Preserved Tissues in Tissue Banks

A model for arterial adaptation combining microstructural collagen remodeling and 3D tissue growth

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