Continuum Scale Non Newtonian Particle Transport Model for Haemorheology -- Implementation and Validation

TL;DR

This paper introduces a continuum scale non-Newtonian particle transport model for red blood cells, implemented in FOAM, validated against analytical solutions, and demonstrating physiologically relevant cell migration and viscosity modulation.

Contribution

The paper presents a novel continuum scale model for red blood cell transport that integrates modern rheology models and is validated for vascular flow simulations.

Findings

Red blood cell migration occurs on physiologically relevant timescales in small vessels.

The model accurately predicts non-Newtonian viscosity modulation by haematocrit.

The implementation is available as open-source code for further research.

Abstract

We present a continuum scale particle transport model for red blood cells following collision arguments in a diffusive flux formulation. The model is implemented in FOAM, in a framework for haemodynamics simulations. Modern mechanistic rheology models are implemented and tested. The model is verified against a known analytical solution and shows excellent agreement for high quality meshes and good agreement for typical meshes as used in vascular flow simulations. Simulation results for different size and time scales show that migration of red blood cells does occur on physiologically relevany timescales on small vessels below 1 mm and that the haematocrit concentration modulates the non-Newtonian viscosity. This model forms part of a multi-scale approach to haemorheology and model parameters will be derived from meso-scale simulations using multi-component Lattice-Boltzmann methods. The code, haemoFoam, is made available for interested researchers.