Biomedical and physiological foundations of Blood Rheology Casson Model.
Human blood is not a simple homogeneous Newtonian fluid; it is a dense suspension of cellular elements (erythrocytes/RBCs, leukocytes, and platelets) suspended in an aqueous electrolyte-protein matrix (blood plasma). Erythrocytes comprise approximately 40% to 45% of total blood volume (normal hematocrit Hct). At low shear rates (γ̇ < 50 s⁻¹), red blood cells aggregate face-to-face into reversible, rouleaux structures and three-dimensional cellular networks stabilized by plasma fibrinogen and globulins. This cellular networking creates shear-thinning (pseudoplastic) non-Newtonian flow behavior and a finite yield stress τ_y below which blood resists flow. At elevated shear rates, rouleaux disperse into individual deformable biconcave discs that elongate and align with streamlines, causing apparent viscosity to asymptote toward a constant high-shear baseline. To mathematically characterize this non-Newtonian behavior, the Casson fluid model is the universally adopted standard: √τ = √μ_c · √γ̇ + √τ_y, where τ is shear stress, γ̇ is shear rate, μ_c is the Casson asymptotic plastic viscosity (Pa·s), and τ_y is the blood yield stress (Pa). In a cone-and-plate rotational rheometer, the shear rate is geometrically uniform throughout the entire wedge gap, providing ideal conditions to evaluate blood rheology. In this laboratory investigation, anti-coagulated whole blood at 37.0 °C is tested across shear rates from 16 to 196 s⁻¹ to determine Casson parameters.
Viva voce questions & analytical theory
What is the physical cause of blood shear-thinning at low shear rates?
At low shear rates, red blood cells aggregate into stacked coin-like rouleaux structures bound by plasma fibrinogen; as shear rate increases, hydrodynamic shear stresses break these rouleaux apart and deform individual erythrocytes into streamlined ellipsoids, decreasing flow resistance.
Why does a cone-and-plate rheometer produce a uniform shear rate?
The linear velocity of the rotating cone increases linearly with radius r (v = ω·r), but the gap height between the cone and plate also increases linearly with radius (h = r·tan θ). Because shear rate is velocity divided by gap height (γ̇ = v/h = ω/tan θ), the radius r cancels, making shear rate mathematically identical at every point in the fluid.
What physiological role does plasma fibrinogen play in blood rheology?
Fibrinogen is a large, asymmetrical 340 kDa plasma glycoprotein that adsorbs simultaneously onto adjacent erythrocyte membranes, acting as a molecular bridge that drives rouleaux aggregation and establishes the blood yield stress τ_y.
How does hematocrit affect whole blood viscosity?
Viscosity increases exponentially with hematocrit. In polycythemia (Hct > 55–60%), blood viscosity doubles or triples, drastically elevating vascular resistance and cardiac workload; in severe anemia (Hct < 25%), blood becomes less viscous, reducing peripheral vascular resistance.
What is the clinical significance of blood yield stress in microcirculatory stasis?
If perfusion pressure drops below the threshold needed to generate the yield stress τ_y in post-capillary venules, blood flow halts completely, resulting in microvascular stasis, thrombosis, and tissue infarction (as seen in septic shock and sickle cell crisis).
Why is blood treated as Newtonian in large arteries but non-Newtonian in microvessels?
In large arteries (aorta, femoral), shear rates typically exceed 200–500 s⁻¹, where blood viscosity plateaus at a constant asymptotic value (~3.5–4.0 cP); in microvessels and low-flow recirculating zones, shear rates drop below 50 s⁻¹, where non-Newtonian rouleaux dynamics dominate.
Experimental precautions and patient safety
- Always use a humidified solvent trap; blood drying around the cone perimeter creates enormous edge-drying torque artifacts.
- Ensure exact sample volume pipetting (500 μL); underfilling or overfilling the gap distorts the meniscus and invalidates shear geometry.
- Verify that anti-coagulated blood shows no microscopic clot formation or hemolysis before testing.
- Perform a high-shear preshear (300 s⁻¹ for 30 s) before each run to establish a reproducible uniform initial cellular dispersion state.
Theoretical assumptions & biological limits
- The Casson model is an empirical continuum approximation; it applies across 10 to 300 s⁻¹ but does not capture zero-shear viscoelasticity.
- Assumes homogeneous suspension, neglecting the Fahraeus-Lindqvist cell-free layer present in narrow channels.
- In-vitro rotational testing uses steady shear, whereas in-vivo arterial flow is pulsatile with oscillating shear directions.
- Blood samples age rapidly in vitro; measurements must be completed within 4 hours of venipuncture to avoid erythrocyte echinocyte crenation.