The wall traction induced by flowing red blood cells in model microvessels and its potential mechanotransduction*

There is evidence in early embryonic development, even well before advective oxygen transport is important, that the presence of red bloods cells \textit{per se} trigger essential steps of normal vascular development. For example, Lucitti {\it et al.}\ [{\it Development} {\bf 134}, 3317 (2007)] showed that sequestration of blood cells early in the development of a mouse, such that the hematocrit is reduced, suppresses normal vascular network development. Vascular development also provides a model for remodeling and angiogenesis. We consider the transient stresses associated with blood cells flowing in model microvessels of comparable diameter to those at early stages of development ($6\mu$m to $12\mu$m). A detailed simulation tool is used to show that passing blood cells present a significant fluctuating traction signature on the vessel wall, well above the mean stresses. This is particularly pronounced for slow flows ($\la 50\mu$m/s) or small diameters ($\la 7\mu$m), for which root-mean-square wall traction fluctuations can exceed their mean. These events potentially present mechanotranduction triggers that direct development or remodeling. Attenuation of such fluctuating tractions by a viscoelastic endothelial glycocalyx layer is also considered.