Numerical Simulation of Non-Newtonian Hemodynamics in the Sickle Cell Mouse Carotid Artery Open Access
Guerrero, Chloe (Spring 2026)
Abstract
Sickle cell disease (SCD) is characterized by a significant alteration in blood rheology due to the presence of polymerized hemoglobin (HbS) within erythrocytes, leading to increased viscosity and impaired cellular deformability. This study utilizes computational fluid dynamics (CFD) to investigate the resulting hemodynamics within the mouse carotid artery. Using high-resolution geometry derived from magnetic resonance angiography (MRA), we implement a non-Newtonian Carreau constitutive model to characterize the shear-thinning behavior of HbSS blood.
The simulations specifically examine the impact of altered rheology on wall shear stress (WSS) distributions and flow patterns that contribute to chronic arterial remodeling and vaso-occlusion. By comparing Newtonian approximations with generalized Newtonian formulations, we quantify the degree to which non-Newtonian effects dominate in low-shear regions of the carotid bifurcation. Our results demonstrate that the elevated viscosity profile of HbSS blood significantly modifies the local mechanical environment, providing a quantitative framework for understanding the biophysical drivers of vascular complications in SCD models.
Table of Contents
Chapter I: Introduction
Chapter II: Sickle Cell Disease: Biological Context & Pathophysiology
2.1 Blood Composition
2.1.1 Plasma
2.1.2 Formed Elements
2.1.2.1 Erythrocytes
2.1.2.2 Leukocytes
2.1.2.3 Platelets
2.2 Sickle Cell Disease
2.2.1 Hemoglobin Structure and Function
2.2.2 Hemoglobin Allosteric States and Cooperativity
2.2.2.1 Oxygen Dissociation Curve
2.2.2.2 2,3-Biphosphoglycerate
2.2.3 Sickle Hemoglobin Pathophysiology
Chapter III: Mathematical & Rheological Framework
3.1 Introduction to Continuum Hemodynamics
3.1.1 The Navier–Stokes Equations
3.1.1.1 Mass Conservation and the Incompressibility Constraint
3.1.1.2 Momentum Conservation
3.2 Blood Rheology
3.2.1 Mechanical Properties and Modeling Assumptions
3.2.1.1 Viscosity and Shear-Thinning Behavior
3.2.1.2 Viscoelasticity and Thixotropy
3.2.1.3 Yield Stress
3.2.1.4 Scale Effects and the Fåhræus–Lindqvist Effect
3.2.2 Fluid Model Classification
3.2.2.1 Newtonian Fluids
3.2.2.2 Generalized Newtonian Fluids
3.2.3 Rheological Model Selection
3.2.3.1 Power-Law Model
3.2.3.2 Carreau-Yasuda & Carreau Model
3.2.3.3 Cross Model
Chapter IV: Numerical Approximations
4.1 Geometric Reconstruction & Mesh Generation
4.1.1 Image Segmentation and Surface Reconstruction
4.1.2 Volumetric Mesh Generation
4.2 Finite Element Methods
4.2.1 Variational Formulation of the Navier–Stokes System
4.2.1.1 Galerkin Discretization and Finite Element Spaces
4.2.1.2 Treatment of Non-Newtonian Viscosity
4.2.1.3 Picard Iteration for the Steady Nonlinear System
4.2.2 Time Discretization and Linearization for the Unsteady Simulations
4.2.2.1 Boundary Conditions
4.2.2.2 Wall Shear Stress Computation
4.3 Physiological Parameters and Rheological Modeling
4.4 Boundary Condition Specification
4.5 Simulation Design and Validation Strategy
4.5.1 Physics Sensitivity: Newtonian versus Carreau Rheology
4.5.2 Temporal Sensitivity: Steady versus Unsteady Formulations
4.5.3 Algorithmic Validation: Picard Convergence in the Steady Cases
4.6 FEniCS Implementation
Chapter V: Results & Discussion
5.1 Steady-State Hemodynamic Baseline
5.1.1 Steady-State Velocity and Pressure Fields
5.1.2 Steady-State Wall Shear Stress Distribution
5.2 Unsteady-State Hemodynamic Analysis
5.2.1 Unsteady Velocity and Pressure Fields
5.2.2 Statistical Distribution of Wall Shear Stress
5.2.3 Localized WSS Signatures & Arterial Geometry
5.3 Rheological Feedback Mechanisms
5.3.1 Spatial Distribution of the Shear Rate Field
5.3.2 Effective Viscosity Distribution
5.4 Clinical Implications for SCD Pathophysiology
5.4.1 Vaso-occlusive Risk and the Zero-Shear Plateau
5.4.2 Endothelial Damage and Intensified Wall Shear Stress
5.4.3 Concluding Remarks on Model Fidelity
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