Mathematical Modeling of Blood Flow in Stenosed Arteries

Mathematical modelling of blood flow in stenosed arteries seeks to describe the transport of an incompressible, often non-Newtonian fluid through vessels narrowed by plaque or constrictive lesions. By combining constitutive equations for blood rheology with the Navier–Stokes equations and appropriate boundary conditions, researchers can predict velocity fields, pressure gradients and wall shear stresses that underlie disease progression and treatment outcomes. Geometric descriptions of stenotic plaques range from idealized cosine shapes to irregular, patient-specific reconstructions, capturing the influence of stenosis severity and eccentricity on haemodynamics. Unsteady (pulsatile) simulations incorporate cardiac waveform dynamics, while steady-state analyses yield insight into critical pressure drops and recirculation zones. Extensions to magnetohydrodynamics (MHD) and hybrid nanofluid models enable investigation of electromagnetic control and targeted drug-carrier behaviour. Such models inform stent design, non-invasive diagnostic tools and therapeutic strategies aimed at restoring physiological flow and minimising thrombogenic risk.

Research from Nature Portfolio

Recent studies have examined the impact of Lorentz force on pulsatile flow of a non-Newtonian Casson fluid in a constricted channel using Darcy’s law. Numerical solutions employing the vorticity–streamfunction approach reveal that increasing magnetic field intensity reduces the size of separation regions, flattens the streamwise velocity profile and affords control over wall shear stress in both steady and oscillatory regimes. These findings underscore the potential of electromagnetic modulation to mitigate adverse haemodynamic features in stenotic vessels.

Mathematical Modeling of Blood Flow in Stenosed Arteries publication trend

The graph below shows the total number of articles in mathematical modeling of blood flow in stenosed arteries across all publications each year (not limited to Nature Index journals).

Technical terms

Stenosis: A localised narrowing of the arterial lumen that alters flow resistance and shear patterns.

Non-Newtonian fluid: A fluid whose viscosity varies with shear rate, used to capture the shear-thinning behaviour of blood.

Casson fluid model: A constitutive rheological model describing yield stress and shear-thinning of blood under low shear conditions.

Hartmann number: A dimensionless parameter expressing the ratio of electromagnetic force to viscous force in magnetohydrodynamic flow.

Wall shear stress: The tangential force per unit area exerted by blood on the vessel wall, critical for endothelial function and lesion development.

Darcy’s law: A phenomenological relation describing flow through a porous medium, adapted here to model flow in constricted or permeable vessel regions.

References

1. Numerical simulation of unsteady generic Newtonian blood flow and heat transfer through discrepant shaped dilatable arterial stenosis. Results in Engineering (2023).
2. Impact of Lorentz force on the pulsatile flow of a non-Newtonian Casson fluid in a constricted channel using Darcy’s law: a numerical study. Scientific Reports (2020).
3. Computer Simulations of EMHD Casson Nanofluid Flow of Blood through an Irregular Stenotic Permeable Artery: Application of Koo-Kleinstreuer-Li Correlations. Nanomaterials (2023).
4. Finite Difference Computation of Au‐Cu/Magneto‐Bio‐Hybrid Nanofluid Flow in an Inclined Uneven Stenosis Artery. Complexity (2022).