Large-deformation analysis of the elastic recoil of fibre layers in a Brinkman medium with application to the endothelial glycocalyx

• Published in: Journal of fluid mechanics 2006-05, Vol.554 (1), p.217-235
• Main Authors: HAN, YUEFENG, WEINBAUM, SHELDON, SPAAN, JOS A. E., VINK, HANS
• Format: Article
• Language: English
• Subjects: Biological and medical sciences; Blood vessels and receptors; Deformation; Fibers; Fundamental and applied biological sciences. Psychology; Rigidity; Shear stress; Vertebrates: cardiovascular system
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S0022112005007779

There is wide interest in the role of the endothelial surface layer (ESL) in transmitting blood shear stress to the intracellular cytoskeleton of the endothelial cell. However, very little is known about the mechanical properties of the glycocalyx or the flexural rigidity of the core proteins that comprise it. Vink, Duling & Spaan (FASEB J., vol. 13, 1999, p. A 11) measured the time-dependent restoration of the ESL after it had been nearly completely compressed by the passage of a white blood cell (WBC) in a tightly fitting capillary. Using this initial experiment, Weinbaum et al. (Proc. Natl. Acad. Sci. USA, vol. 100, 2003, p. 7988) predicted that the core proteins have a flexural rigidity EI of 700 pN nm$^{2}$, which is $\sim$1/20 the measured value for an actin filament. However, their analysis assumes small deflections and only the fibre motion is considered. In the present paper we report additional experiments and apply large-deformation theory for ‘elastica’ to describe the restoration of the fibres in a Brinkman medium which absorbs fluid as the ESL expands. We find that there are two phases in the fibre recoil: an initial phase for large compressions where the ESL thickness is $