Background and objective: The paper describes a mathematical model of blood flow in capillaries with accounting for the endothelial surface layer (ESL).
Method: The influence of ESL is modeled by a boundary layer with zero flow velocity. Finite element modeling and an analytical approach based on the homogenization of the core region of blood flow occupied by erythrocytes are developed to describe the resistance of a capillary. The reliability of the results obtained is verified for different values of the discharge hematocrit and vessel diameter using known in vivo data.
Results: The proposed approach is applied to the numerical simulation of blood circulation in a capillary network of the germinal matrix of infants born at 25 gestational weeks. The influence of the hematocrit level and effective thickness of ESL on the resistance of the capillary network of the germinal matrix of preterm infants is studied. It was found that a decrease in the effective thickness of ESL in the capillary network (and/or a decrease in the hematocrit) leads to reducing the resistance of the capillary network.
Conclusion: A decrease in the effective thickness of ESL in the capillary network leads to an increase in the pressure drop in arterioles, which may be considered as an additional risk factor for hemorrhages in fragile blood vessels within the germinal matrix.
Keywords: Endothelial surface layer; Finite element method; Mathematical modeling of cerebral blood circulation.
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