Abstract
We simulate deformable red blood cells in the microcirculation using the immersed boundary method with a cytoskeletal model that incorporates structural details revealed by tomographic images. The elasticity of red blood cells is known to be supplied by both their lipid bilayer membranes, which resist bending and local changes in area, and their cytoskeletons, which resist in-plane shear. The cytoskeleton consists of spectrin tetramers that are tethered to the lipid bilayer by ankyrin and by actin-based junctional complexes. We model the cytoskeleton as a random geometric graph, with nodes corresponding to junctional complexes and with edges corresponding to spectrin tetramers such that the edge lengths are given by the end-to-end distances between nodes. The statistical properties of this graph are based on distributions gathered from three-dimensional tomographic images of the cytoskeleton by a segmentation algorithm. We show that the elastic response of our model cytoskeleton, in which the spectrin polymers are treated as entropic springs, is in good agreement with the experimentally measured shear modulus. By simulating red blood cells in flow with the immersed boundary method, we compare this discrete cytoskeletal model to an existing continuum model and predict the extent to which dynamic spectrin network connectivity can protect against failure in the case of a red cell subjected to an applied strain. The methods presented here could form the basis of disease- and patient-specific computational studies of hereditary diseases affecting the red cell cytoskeleton.
Highlights
Red cells possess a lipid membrane and cytoskeleton that together enclose a viscous cytoplasm characterized by a high concentration of hemoglobin
Red blood cells are responsible for delivering oxygen to tissues throughout the body
Far from being rigid bodies, red blood cells adopt biconcave disk shapes at equilibrium, parachute-like shapes as they move between large vessels and small capillaries, and more extreme shapes as they traverse the endothelial slits of the spleen
Summary
Red cells possess a lipid membrane and cytoskeleton that together enclose a viscous cytoplasm characterized by a high concentration of hemoglobin. The elastic properties of the cell can be separated into contributions from the lipid bilayer, which supplies bending rigidity and resistance to local changes in area, and from the cytoskeleton, which is a polymer network of spectrin tetramers connected at actin-based junctional complexes that supplies shear resistance. In previous work [1], we used a continuum neo-Hookean model [2] to describe the coupled membrane-cytoskeleton system, and we simulated the behavior of red cells in flow using the immersed boundary method, a numerical method for fluid-structure interaction problems [3]. Continuum models correctly predict that red cells “remember” the positions of their biconcave dimples [6], but on the other hand there is evidence that the cytoskeleton is constantly remodeling [7] so that the reference configuration changes over time, a property not taken into account in standard neo-Hookean continuum models. Characterizing the cytoskeletal mechanics in detail, including the nature of network remodeling, is crucial for understanding the red cell’s exceptional deformability [7] and for explaining the experimental effects of repeated osmotic swelling and shrinking on red cell elasticity [10]
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