# Numerical simulation of blood flow through microvascular capillary networks.Bull Math Biol 2009; 71(6):1520-41BM

A numerical method is implemented for computing blood flow through a branching microvascular capillary network. The simulations follow the motion of individual red blood cells as they enter the network from an arterial entrance point with a specified tube hematocrit, while simultaneously updating the nodal capillary pressures. Poiseuille's law is used to describe flow in the capillary segments with an effective viscosity that depends on the number of cells residing inside each segment. The relative apparent viscosity is available from previous computational studies of individual red blood cell motion. Simulations are performed for a tree-like capillary network consisting of bifurcating segments. The results reveal that the probability of directional cell motion at a bifurcation (phase separation) may have an important effect on the statistical measures of the cell residence time and scattering of the tube hematocrit across the network. Blood cells act as regulators of the flow rate through the network branches by increasing the effective viscosity when the flow rate is high and decreasing the effective viscosity when the flow rate is low. Comparison with simulations based on conventional models of blood flow regarded as a continuum indicates that the latter underestimates the variance of the hematocrit across the vascular tree.

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*Bulletin of Mathematical Biology,*vol. 71, no. 6, 2009, pp. 1520-41.

*Bull Math Biol*. 2009;71(6):1520-41.

*Bulletin of Mathematical Biology,*

*71*(6), pp. 1520-41. doi:10.1007/s11538-009-9412-z.

*Bull Math Biol.*2009;71(6):1520-41. PubMed PMID: 19267162.