Journal Article

A 2D constrained mixture model for arterial adaptations to large changes in flow, pressure and axial stretch

Rudolph L. Gleason and Jay D. Humphrey

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 22, issue 4, pages 347-369
Published in print December 2005 | ISSN: 1477-8599
Published online December 2005 | e-ISSN: 1477-8602 | DOI:
A 2D constrained mixture model for arterial adaptations to large changes in flow, pressure and axial stretch

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  • Applied Mathematics
  • Biomathematics and Statistics


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Soft tissue growth and remodelling (G&R) are achieved through highly complex, temporally regulated mechanisms that lead to the adaptation of structurally significant cells and extracellular matrix proteins. Herein we present a constrained mixture model to describe vascular adaptations in response to large perturbations in luminal flow rate, transmural pressure and axial extension. In the associated simulations, G&R occur in evolving loaded (i.e. current) configurations. Although several hypotheses are employed with regard to vasoregulatory mechanisms and rates of growth and turnover of individual constituents, the main hypothesis is that each structural constituent is produced within a range of homeostatic stresses (or stretches). As a result, although material that was produced in one configuration may have the same mechanical behaviour as that produced in another configuration, these materials will possess different natural configurations and contribute a different structural response to the mixture. Our simulations illustrate how, by simply evolving the reference states of individual constituents, blood vessels can adapt their structure and function to restore wall stresses.

Keywords: vascular remodelling; mechanotransduction; stress-mediated growth; mixture theory

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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