Passage and blockage of microfluidic channels of different sizes by iRBC in the ring, trophozoite, and schizont stages of infection. The flow goes from the right to the left. Reprinted with permission from Shelby et al., “A microfluidic model for single-cell capillary obstruction by Plasmodium falciparum-infected erythrocytes,” Proc. Natl. Acad. Sci. U.S.A. 100, 14618–14622 (2003). Copyright 2003 The National Academy of Sciences, U.S.A.
The healthy RBC and the ring-stage iRBC have the same biconcave shape described by Eq. (9) , with the smallest and largest thickness being and . The spatial coordinates are marked in microns.
The cell geometries at (a) the early trophozoite stage, with , and (b) the late trophozoite stage, with .
The iRBC has a spheroidal shape at the schizont stage, with diameter and thickness .
Tank-treading: temporal evolution of the cell length L and width W for . Three of our simulations, at coarse and fine spatial resolutions with and without bending, are compared with the result of Sui et al., 53 which does not include bending elasticity.
(a) The average RBC length and width as functions of the capillary number Ca. (b) The dimensionless frequency f of tank-treading, scaled by the shear rate K, as a function of the capillary number Ca.
Schematic of the computational domain. The overall dimensions of the channel are , and , with three segments of equal length . The narrow section in the middle has a width , and for the narrow, medium, and wide channels.
The trajectories of RBCs through the narrow channel ( ) for three values of the shear modulus Gs . The insets show top-view snapshots of the cell during the transit with color contours of the local stretching γ of Eq. (11) , at and for (red arrows) and at for (blue arrow).
The transit time tt , made dimensionless by T, as a function of the membrane shear modulus Gs for the three channels.
Steady-state shape of the iRBC in the early trophozoite, late trophozoite, and schizont stages after it blocks the narrow channel ( ). The length of the tongue lt , defined as the distance between the cell front and the channel entry and scaled by the channel length L, is plotted as a function of the excess surface area ratio se . Color contours of the surface stretching γ are also shown in the insets.
The transit time tt through the medium and wide channels as functions of the excess surface area ratio se . The transit time is scaled by T.
Trajectories of the schizont-stage iRBC in the wide channel ( ) with a parasite of different sizes. R = 0 indicates a baseline case without parasite, and the insets are snapshots of the parasite configuration for the other two trajectories.
Dimensions of the healthy and infected red cell in different stages. denotes the excess surface area ratio of the cell, where a is the effective cell radius defined as the radius of a sphere having the volume V of the cell. The last column indicates the dimensions of the parasite.
The passage and blockage of healthy and infected red blood cells through microfluidic channels of different size.
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