Micromagnetorotation effects in micropolar magnetohydrodynamic blood flow through stenosis

This study presents a numerical investigation of a 3D micropolar magnetohydrodynamic (MHD) blood flow through stenosis, with and without the effects of micromagnetorotation (MMR). MMR refers to the magnetic torque caused by the misalignment of the magnetization of magnetic particles in the fluid with the magnetic field, which affects the internal rotation (microrotation) of these particles. Blood can be modeled as a micropolar fluid with magnetic particles due to the magnetization of erythrocytes. In this manner, this study analyzes important flow features, i.e., streamlines, vorticity, velocity, microrotation, wall shear stress, and pressure drop under varying stenosis, hematocrit levels, and magnetic fields, using two newly developed transient OpenFOAM solvers epotMicropolarFoam and epotMMRFoam. Results indicate that micropolar effects become more pronounced at severe stenosis due to the significant reduction in artery size, resulting also in higher wall shear stress and pressure drop. Furthermore, when MMR is disregarded, the magnetic field does not significantly alter blood flow, regardless of its intensity, due to the minimal impact of the Lorentz force on blood. Conversely, MMR substantially affects blood flow, particularly at higher hematocrit levels and severe stenoses, leading to reductions of up to 30% in velocity and vorticity and up to 99.9% in microrotation and higher wall shear stress and pressure drop. Simultaneously, any vortices or disturbances are dampened. These findings underscore the critical role of MMR (which was ignored so far) in altering flow behavior in stenosed arteries, suggesting that it should be considered in future MHD micropolar blood flow studies.

💡 Research Summary

This paper presents a comprehensive three‑dimensional numerical investigation of blood flow through stenosed arteries, modeled as a micropolar magnetohydrodynamic (MHD) fluid. The novelty lies in the explicit inclusion of the micromagnetorotation (MMR) term, which accounts for the magnetic torque generated when the magnetization of suspended magnetic particles (e.g., hemoglobin‑containing erythrocytes) is misaligned with an external magnetic field. By contrast, conventional MHD studies of blood consider only the Lorentz force; because blood’s electrical conductivity is low, the Lorentz force alone cannot explain experimentally observed reductions in flow velocity under strong magnetic fields.

The authors construct an idealized cylindrical artery of length L = 10 cm and radius R = 2 mm, embedding two stenotic segments: a moderate 50 % narrowing (length 0.2 L) and a severe 80 % narrowing (length 0.8 L). A uniform pressure gradient drives the flow in the axial direction, while a transverse magnetic field of magnitude B = 1 T, 3 T, or 8 T is applied. Hematocrit levels of 45 % and 60 % are examined to represent normal and elevated red‑cell concentrations.

Governing equations combine the continuity equation, the linear momentum balance, the microrotation balance, and Maxwell’s equations, augmented by the Shizawa‑Tanahashi MMR term. Two custom OpenFOAM solvers are developed: epotMicropolarFoam (micropolar MHD without MMR) and epotMMRFoam (micropolar MHD with MMR). Both solvers employ second‑order temporal discretization and third‑order spatial schemes; mesh‑independence studies confirm convergence within 1 % error. Validation against analytical solutions for MHD micropolar Poiseuille flow (Aslani et al.) shows excellent agreement.

Four modeling scenarios are compared: (i) Newtonian blood, (ii) micropolar blood, (iii) MHD micropolar blood without MMR, and (iv) MHD micropolar blood with MMR. Key findings include:

1. Micropolar effects become pronounced as stenosis severity increases. The rotational viscosity (μ_r) and coupling parameter (K) raise wall shear stress (WSS) by 20–40 % and shift velocity profiles toward the centerline.

2. MHD without MMR: Even at 8 T, the Lorentz force produces negligible changes (<2 %) in velocity, vorticity, microrotation, WSS, or pressure drop, confirming that blood’s low conductivity limits electromagnetic influence.

3. MHD with MMR: Inclusion of the MMR torque dramatically alters the flow. Microrotation is suppressed by up to 99.9 %, leading to a substantial increase in effective viscosity. Consequently, axial velocity and vorticity drop by up to 30 %, especially for the 80 % stenosis at 60 % hematocrit under 8 T. Wall shear stress rises by 25–40 % and pressure drop across the stenosis grows by 15–35 %.

4. Vortex attenuation: Strong MMR dampens the recirculation zones that normally appear downstream of a severe stenosis, thereby stabilizing the flow. This damping aligns with clinical observations of reduced turbulence during high‑field MRI or magnetic hyperthermia treatments.

5. Parametric trends: The impact of MMR scales with magnetic field strength, hematocrit, and stenosis severity. At low hematocrit (45 %) and mild stenosis (50 %), the effect is modest; at high hematocrit (60 %) and severe stenosis (80 %), the flow resistance can more than double.

The authors discuss the implications for biomedical engineering. In magnetic drug targeting or magnetic hyperthermia, neglecting MMR could lead to underestimation of flow resistance, misprediction of drug residence time, and inaccurate thermal dose calculations. The presented solvers provide a flexible platform for extending the analysis to patient‑specific geometries, pulsatile pressure waveforms, and multi‑phase blood models (e.g., core‑micropolar / near‑wall Newtonian).

In conclusion, the study demonstrates that micromagnetorotation is a dominant mechanism governing blood dynamics under strong magnetic fields, especially in narrowed vessels and at elevated hematocrit. Future hemodynamic modeling and magnetic‑based therapeutic design should incorporate the MMR term to achieve realistic predictions of velocity, shear stress, and pressure losses.