Theoretical study of Beloussov’s hyper-restoration hypothesis for mechanical regulation of morphogenesis

Taber, Larry A.

doi:10.1007/s10237-007-0106-x

Cited by 77 publications

(100 citation statements)

References 47 publications

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“…Beloussov (1998) has speculated that such behaviour causes a succession of developmental events to create form. Here, we adopt this idea and, as in a previous study (Taber 2008), speculate that the target stress evolves with time.…”

Section: (C) Morphomechanical Lawsmentioning

confidence: 85%

“…Here, we adopt this as a key assumption (for supporting arguments, see Taber 2008). So, the problem boils down to determining the functional form of a morphomechanical law in which the rate-of-growth tensor depends on the Cauchy stress tensor, i.e.…”

Section: (C) Morphomechanical Lawsmentioning

confidence: 99%

“…Following our previous study of the HR hypothesis (Taber 2008), we assume that the morphomechanical law has the relatively simple form…”

Section: (C) Morphomechanical Lawsmentioning

confidence: 99%

“…Previously, we used specialized forms of equations (3.7) and (3.8) to investigate the HR response of some basic problems in morphogenesis (Taber 2008). The main idea of the HR hypothesis is illustrated by the following one-dimensional example.…”

Section: Fundamental Behaviour In One Dimensionmentioning

confidence: 99%

“…The focus here is primarily on epithelia (cell sheets), which play important roles in embryonic development. In an earlier study (Taber 2008), we used mathematical modelling to examine a theory for epithelial morphogenesis based on a mathematical formulation of Beloussov's hyper-restoration (HR) hypothesis (Beloussov et al 1994;Beloussov 1998). According to this hypothesis, epithelia actively elongate in response to increased stress and shorten in response to decreased stress.…”

Section: Introductionmentioning

confidence: 99%

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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: 85%

Section: (C) Morphomechanical Lawsmentioning

confidence: 99%

“…Following our previous study of the HR hypothesis (Taber 2008), we assume that the morphomechanical law has the relatively simple form…”

Section: (C) Morphomechanical Lawsmentioning

confidence: 99%

Section: Fundamental Behaviour In One Dimensionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Towards a unified theory for morphomechanics

Taber

2009

Phil. Trans. R. Soc. A.

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Computational models for mechanics of morphogenesis

Wyczalkowski

Chen

Filas

et al. 2012

Birth Defects Research Pt C

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In the developing embryo, tissues differentiate, deform, and move in an orchestrated manner to generate various biological shapes driven by the complex interplay between genetic, epigenetic, and environmental factors. Mechanics plays a key role in regulating and controlling morphogenesis, and quantitative models help us understand how various mechanical forces combine to shape the embryo. Models allow for the quantitative, unbiased testing of physical mechanisms, and when used appropriately, can motivate new experimental directions. This knowledge benefits biomedical researchers who aim to prevent and treat congenital malformations, as well as engineers working to create replacement tissues in the laboratory. In this review, we first give an overview of fundamental mechanical theories for morphogenesis, and then focus on models for specific processes, including pattern formation, gastrulation, neurulation, organogenesis, and wound healing. The role of mechanical feedback in development is also discussed. Finally, some perspectives are given on the emerging challenges in morphomechanics and mechanobiology.

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Stress alleviation strategy in cancer treatment: Insights from a mathematical model

et al. 2018

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Tumors generate mechanical forces during growth and progression, which are able to compress blood and lymphatic vessels, reducing perfusion rates and creating hypoxia.Tumor vessels-while nourishing the tumor-are usually leaky and tortuous, which further decreases perfusion. Consequently, vessel leakiness together with vessel compression causes a uniformly elevated interstitial fluid pressure that hinder drug delivery and compromise therapeutic outcomes. To enhance treatment efficacy, stress alleviation and vascular normalization strategies have been developed to improve tumor perfusion and drug delivery. Stress alleviation strategy aim to decrease solid stress levels and reopen compressed blood vessels leading to improve perfusion and drug delivery. On the other hand, vascular normalization strategy aims to restore the abnormalities in tumor vasculature by decreasing vessel leakiness and thus enhance drug efficacy. Here, we employed a mathematical model to study the stress alleviation strategy using published experimental data and performing new experiments in mice bearing breast tumors. Specifically, we accounted for variations in tumor hydraulic conductivity, elastic modulus and swelling related to changes in extracellular matrix components induced by the anti-fibrotic and stress alleviating drug, tranilast. We showed that alleviation of mechanical stresses in tumors reduces the tumor interstitial fluid pressure to normal levels and increases the functionality of the tumor vasculature resulted in improved drug delivery and treatment outcome. Finally, we used model predictions to show that vascular normalization can be combined with stress alleviation to further improve therapeutic outcomes. K E Y W O R D Sbreast cancer, drug delivery, re-engineering cancer, tumor perfusion, vascular normalization

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Theoretical study of Beloussov’s hyper-restoration hypothesis for mechanical regulation of morphogenesis

Cited by 77 publications

References 47 publications

Towards a unified theory for morphomechanics

Towards a unified theory for morphomechanics

Computational models for mechanics of morphogenesis

Stress alleviation strategy in cancer treatment: Insights from a mathematical model

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