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The flow of red blood cells through a narrow spleen-like slit
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Small slits between endothelial cells in the spleen are perhaps the smallest blood passages in the body, and red blood cells must deform significantly to pass through them. These slits have been posited to participate in the removal of senescent blood cells from the circulation, a key function of the spleen. One of the effects of red blood cell aging is an increased cytosol viscosity; relaxation time measurements suggest their interior viscosity can increase by up to a factor of 10 toward the end of their normal 120 day circulating lifetime. We employ a boundary integral model to simulate red blood cells as they deform sufficiently to flow through such a small passage, whether in the spleen or in a microfluidic device. Different flow rates and cytosol viscosities show three distinct behaviors. (1) For sufficiently slow flow, the pressure gradient is insufficient to overcome elastic resistance and the cell becomes jammed. (2) For faster flow, the cell passes the slit, though more slowly for higher cytosol viscosity. This can be hypothesized to facilitate recognition of senescent cells. (3) A surprising behavior is observed for high elastic capillary numbers, due either to high velocity or high cytosol viscosity. In this case, the cells infold within the slit, with a finger of low-viscosity plasma pushing deeply into the cell from its upstream side. Such infolding might provide an additional mechanism for jamming, and the sharpness of the resulting features would be expected to promote cell degradation. Linear analysis of a model system shows a similar instability, which is analyzed in regard to the cell flow. This linear analysis also suggests a similar instability for unphysiologically low cytosol viscosity. Simulations confirm that a similar infolding also occurs in this case, which intriguingly suggests that normal cytosol viscosities are in a range that is protective against such deformations.
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