Sinuosities in vascular structures

Laboratoire d'Optique et Biosciences, École Polytechnique, CNRS UMR 7645, INSERM U696, 91128 Palaiseau, France

Corresponding author: jean-baptiste.masson@polytechnique.fr

Received: 16 February 2007
Revised: 1 July 2007
Accepted: 11 September 2007
Published online: 13 December 2007

Abstract

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.