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Sinuosities in vascular structures

Published online by Cambridge University Press:  13 December 2007

J.-B. Masson  and
J.-L. Martin
J.-B. Masson*
Affiliation:
Laboratoire d'Optique et Biosciences, École Polytechnique, CNRS UMR 7645, INSERM U696, 91128 Palaiseau, France
J.-L. Martin
Affiliation:
Laboratoire d'Optique et Biosciences, École Polytechnique, CNRS UMR 7645, INSERM U696, 91128 Palaiseau, France
*
jean-baptiste.masson@polytechnique.fr

Abstract

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In most organs, depending on the scale, the nature of the heart pump, the geometry and topology of the organ, some of the blood vessels tend to exhibit sinuous trajectories. We describe a part of this sinuous behavior, including partial biological and strong physical effects in a global physical framework. We will voluntarily focus on physical and topological effects. This study is performed on the vitelline membrane of the chicken embryo. Crossing angles, sinuosity, and the oscillation amplitude of the vascular system are analyzed. Surprisingly, the equation of river meandering dynamics is found to model the sinuosities in the vascular system, and an extension of this equation to non planar case is able to explain the effect of tissue global curvature on the vascular system. Results of this study could lead to a new understanding of the interplay between biological signaling and physical effects in determining the vascular pattern in different tissues.

Keywords

Type
Research Article
Information
The European Physical Journal - Applied Physics , Volume 40 , Issue 3 , December 2007 , pp. 351 - 356
Copyright
© EDP Sciences, 2007

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