Biomaterial Database

A theoretical model for the Fåhræus effect in medium-large microvessels. 2023

Angiolo Farina, and Antonio Fasano, and Fabio Rosso

Dipartimento di Matematica e Informatica "Ulisse Dini", Università degli Studi di Firenze, Viale Morgagni 67/a, 50134 Firenze, Italy. Electronic address: angiolo.farina@unifi.it.

This paper presents a mathematical model capable to reproduce a celebrated phenomenon in blood microcirculation known as Fåhræus effect, since its discovery by Robin Fåhræus (1929). This consists in a decaying of the relative hematocrit in small vessels as the vessel diameter decreases. The key point of the model is a formula, direct consequence of the basic principles of fluid dynamics, that links the relative hematocrit to the reservoir hematocrit and the vessel diameter, which confirms the observed behavior. To test the model we selected, among the few experiments carried on since then, those performed by Barbee and Cokelet (1971). The agreement is remarkable. An extended comparison is also carried out with a celebrated empirical formula proposed by Pries et al. (1992) to describe the same phenomenon.

UI	MeSH Term	Description	Entries
D008833	Microcirculation	The circulation of the BLOOD through the MICROVASCULAR NETWORK.	Microvascular Blood Flow,Microvascular Circulation,Blood Flow, Microvascular,Circulation, Microvascular,Flow, Microvascular Blood,Microvascular Blood Flows,Microvascular Circulations
D008955	Models, Cardiovascular	Theoretical representations that simulate the behavior or activity of the cardiovascular system, processes, or phenomena; includes the use of mathematical equations, computers and other electronic equipment.	Cardiovascular Model,Cardiovascular Models,Model, Cardiovascular
D001783	Blood Flow Velocity	A value equal to the total volume flow divided by the cross-sectional area of the vascular bed.	Blood Flow Velocities,Flow Velocities, Blood,Flow Velocity, Blood,Velocities, Blood Flow,Velocity, Blood Flow
D001809	Blood Viscosity	The internal resistance of the BLOOD to shear forces. The in vitro measure of whole blood viscosity is of limited clinical utility because it bears little relationship to the actual viscosity within the circulation, but an increase in the viscosity of circulating blood can contribute to morbidity in patients suffering from disorders such as SICKLE CELL ANEMIA and POLYCYTHEMIA.	Blood Viscosities,Viscosities, Blood,Viscosity, Blood
D006400	Hematocrit	The volume of packed RED BLOOD CELLS in a blood specimen. The volume is measured by centrifugation in a tube with graduated markings, or with automated blood cell counters. It is an indicator of erythrocyte status in disease. For example, ANEMIA shows a low value; POLYCYTHEMIA, a high value.	Erythrocyte Volume, Packed,Packed Red-Cell Volume,Erythrocyte Volumes, Packed,Hematocrits,Packed Erythrocyte Volume,Packed Erythrocyte Volumes,Packed Red Cell Volume,Packed Red-Cell Volumes,Red-Cell Volume, Packed,Red-Cell Volumes, Packed,Volume, Packed Erythrocyte,Volume, Packed Red-Cell,Volumes, Packed Erythrocyte,Volumes, Packed Red-Cell
D055806	Microvessels	The finer blood vessels of the vasculature that are generally less than 100 microns in internal diameter.	Microvasculature,Microvascular Network,Microvascular Networks,Microvessel,Network, Microvascular,Networks, Microvascular