Theoretical study of dynamics of arterial wall remodeling in response to changes in blood pressure

Rachev, Alexander; Stergiopulos, Nikolaos; Meister, J.‐J.

doi:10.1016/0021-9290(95)00108-5

Cited by 98 publications

(65 citation statements)

References 6 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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“…Baek et al (2006); Humphrey and Rajagopal (2002); Kroon and Holzapfel (2007a,b); Rachev et al (1996); Ryan and Humphrey (1999); Taber and Humphrey (2001); Watton et al (2004)). In the present paper, we propose a new theoretical model for the growth of human cerebral saccular aneurysms.…”

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confidence: 99%

A theoretical model for fibroblast-controlled growth of saccular cerebral aneurysms

Kroon

Holzapfel

2009

Journal of Theoretical Biology

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A new theoretical model for the growth of saccular cerebral aneurysms is proposed by extending the recent constitutive framework of Kroon and Holzapfel (J. Theor. Biol., 247:775-787, 2007). The continuous turnover of collagen is taken to be the driving mechanism in aneurysmal growth. The collagen production rate depends on the magnitude of the cyclic deformation of fibroblasts, caused by the pulsating blood pressure during the cardiac cycle. The volume density of fibroblasts in the aneurysmal tissue is taken to be constant throughout the growth process. The growth model is assessed by considering the inflation of an axisymmetric membranous piece of aneurysmal tissue, with material characteristics representative of a cerebral aneurysm. The diastolic and systolic states of the aneurysm are computed, together with its load-free state. It turns out that the value of collagen pre-stretch, that determines growth speed and stability of the aneurysm, is of pivotal importance. The model is able to predict aneurysms with typical berry-like shapes observed clinically, and the predicted wall stresses correlate well with the experimentally obtained ultimate stresses of this type of tissue. The model predicts that aneurysms should fail when reaching a size of about 1.2-3.6 mm, which is smaller than what has been clinically observed. With some refinements, the model may, however, be used to predict future growth of diagnosed aneurysms.

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“…Figure 1 shows the capability of the present model to represent analytically and accurately the typical exponential deformation of a variety of viscoelastic materials (Rachev et al 1996;Haslach Jr 2005;Tan et al 2008). The time dynamics response of the material is nonlinear, with a nonlinear beginning initial portion.…”

Section: Discussionmentioning

confidence: 99%