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

Angiolo Farina1, Antonio Fasano2, Fabio Rosso1

  • 1Dipartimento di Matematica e Informatica "Ulisse Dini", Università degli Studi di Firenze, Viale Morgagni 67/a, 50134 Firenze, Italy.

Journal of Theoretical Biology
|November 19, 2022
PubMed
Summary

This study introduces a mathematical model for the Fåhræus effect, explaining how blood hematocrit decreases in small vessels. The model accurately predicts this phenomenon, validated by experimental data.

Keywords:
Blood flow in small vesselsBlood viscosityFåhræus–Lindqvist effectHematocrit levelMathematical modeling

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Area of Science:

  • Physiology
  • Biophysics
  • Fluid Dynamics

Background:

  • The Fåhræus effect describes the reduction in blood hematocrit within small blood vessels.
  • Understanding this phenomenon is crucial for comprehending blood microcirculation dynamics.

Purpose of the Study:

  • To develop a mathematical model that accurately reproduces the Fåhræus effect.
  • To provide a fluid dynamics-based explanation for the observed changes in relative hematocrit.

Main Methods:

  • Formulation of a mathematical model based on fluid dynamics principles.
  • Derivation of a formula linking relative hematocrit, reservoir hematocrit, and vessel diameter.
  • Validation of the model using experimental data from Barbee and Cokelet (1971).

Main Results:

  • The model successfully reproduces the Fåhræus effect, showing decreasing relative hematocrit with decreasing vessel diameter.
  • The derived formula demonstrates a strong correlation between hematocrit and vessel size.
  • Remarkable agreement was found between the model's predictions and experimental results.

Conclusions:

  • The proposed mathematical model offers a robust explanation for the Fåhræus effect in blood microcirculation.
  • The model's predictions align well with experimental observations and empirical formulas.
  • This work contributes to a deeper understanding of hemorheology in narrow vessels.