Towards a universal law for blood flow

TL;DR

This paper proposes a universal law for blood flow based on local RBCs concentration, supported by a non-local diffusion model, advancing the understanding of blood flow dynamics in simple geometries and potentially in complex networks.

Contribution

It introduces a universal law for blood flow that depends on local RBCs concentration and a non-local diffusion equation, providing a new theoretical framework.

Findings

Universal law holds at given local RBCs concentration

Non-local diffusion equation matches full simulations

Applicable to shear and pressure driven flows

Abstract

Despite decades of research on blood flow, an analogue of Navier-Stokes equations that accurately describe blood flow properties has not been established yet. The reason behind this is that the properties of blood flow seem \`a priori non universal as they depend on various factors such as global concentration of red blood cells (RBCs) and channel width. Here, we have discovered a universal law when the stress and strain rate are measured at a given local RBCs concentration. However, the local concentration must be determined in order to close the problem. We propose a non-local diffusion equation of RBCs concentration that agrees with the full simulation. The universal law is exemplified for both shear and pressure driven flows. While the theory is restricted to a simplistic geometry (straight channel) it provides a fundamental basis for future research on blood flow dynamics and could lead to the development of a new theory that accurately describes blood flow properties under various conditions, such as in complex vascular networks.