Optimal occlusion uniformly partitions red blood cells fluxes within a microvascular network.

Sheng-Ping L. Hwang,Van M. Savage,Shenyinying Tu,Kyung In Baek,Andrew Pietersen,Marcus Roper,Shyr-Shea Chang,Yu-Hsiu Liu,Tzung K. Hsiai

doi:10.1371/journal.pcbi.1005892

Abstract

In animals, gas exchange between blood and tissues occurs in narrow vessels, whose diameter is comparable to that of a red blood cell. Red blood cells must deform to squeeze through these narrow vessels, transiently blocking or occluding the vessels they pass through. Although the dynamics of vessel occlusion have been studied extensively, it remains an open question why microvessels need to be so narrow. We study occlusive dynamics within a model microvascular network: the embryonic zebrafish trunk. We show that pressure feedbacks created when red blood cells enter the finest vessels of the trunk act together to uniformly partition red blood cells through the microvasculature. Using mathematical models as well as direct observation, we show that these occlusive feedbacks are tuned throughout the trunk network to prevent the vessels closest to the heart from short-circuiting the network. Thus occlusion is linked with another open question of microvascular function: how are red blood cells delivered at the same rate to each micro-vessel? Our analysis shows that tuning of occlusive feedbacks increase the total dissipation within the network by a factor of 11, showing that uniformity of flows rather than minimization of transport costs may be prioritized by the microvascular network.

Highlights

Vascular networks transport oxygen, carbon dioxide and sugars within animals
Red blood cells are tightly squeezed within the finest vessels, meaning that these vessels account for as much as half of the total transport costs within the arterial network
As a direct demonstration of the tradeoff between minimizing the cost of transport and tuning occlusion to route red blood cells uniformly, we show that the optimal distribution of occlusive feedbacks that uniformizes red blood cell partitioning increases hydraulic dissipation in the network 11 fold compared with a network in which the smallest measured occlusive feedbacks occur within each vessel

Summary

Introduction

Exchange of both nutrients and gases occurs primarily in narrow vessels (e.g. capillaries) that are typically organized into reticulated networks. The narrowest vessels are comparable in diameter to red blood cells, forcing cells to squeeze through the vessels. The rate at which energy must be expended to maintain a constant flow of blood through a vessel is inversely proportional to the 4th power of the vessel radius. Experiments in which cells are deformed using optical tweezers, or by being pushed through synthetic micro-channels have shown that the extreme deformability of mammalian red blood cells requires continous ATP powered-remodeling of the connections between membrane and cytoskeleton. Chemical as well as hydraulic power inputs are needed to maintain flows through microvessels [6, 7]

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