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Updated: Dec 20, 2025

In Vitro Model of Physiological and Pathological Blood Flow with Application to Investigations of Vascular Cell Remodeling

In Vitro Model of Physiological and Pathological Blood Flow with Application to Investigations of Vascular Cell Remodeling

Published on: November 3, 2015

A Microscale Mathematical Blood Flow Model for Understanding Cardiovascular Diseases.

Maria Hadjinicolaou¹, Eleftherios Protopapas²

¹Applied Mathematics Laboratory, School of Science and Technology, Hellenic Open University, Patras, Greece. hadjinicolaou@eap.gr.

Advances in Experimental Medicine and Biology

|May 30, 2020

Summary

This summary is machine-generated.

This study models blood plasma flow through red blood cells in capillaries using a Stokes flow model. The research provides an analytical solution for fluid dynamics within these microcirculatory systems.

Keywords:

Blood plasma Cardiovascular Inverted prolate Mathematical model Particle in cell Red blood cell Stokes flow Stream function

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Area of Science:

Fluid Dynamics
Biomedical Engineering
Microcirculation

Background:

Capillary blood flow involves complex interactions between plasma and red blood cells.
Modeling these microfluidic systems is crucial for understanding physiological and pathological conditions.

Purpose of the Study:

To develop an analytical model for blood plasma flow through a swarm of red blood cells in capillaries.
To obtain analytical expansions for flow velocity components using a stream function approach.

Main Methods:

Modeled flow as axisymmetric Stokes flow within inverted prolate spheroidal solid-fluid unitary cells.
Introduced a stream function satisfying the biharmonic equation (E⁴ψ = 0).
Employed Kelvin inversion to transform the problem into prolate spheroidal coordinates for solution.

Main Results:

Derived analytical expansions for velocity components based on the stream function.
The solution was obtained via inverse Kelvin transformation, accounting for the Stokes operator's behavior.
The final analytical solution for the stream function is presented as an R-separable series expansion.

Conclusions:

Successfully modeled blood plasma flow in a red blood cell swarm using a novel analytical approach.
The method provides a detailed understanding of fluid dynamics at the microcirculatory level.
The derived analytical solution offers a valuable tool for further research in hemorheology.