Formulation and scaling of refractive index-matched non-Newtonian blood analogues for optical flow studies

Blood is a complex non-Newtonian fluid exhibiting shear-thinning and viscoelastic behaviour. Experimental modelling of arterial flows is essential for cardiovascular disease research, yet many in-vitro studies approximate blood as Newtonian due to practical constraints. Recent computational and limited experimental work has demonstrated this assumption can lead to significant differences in velocity and wall shear stress estimations. While non-Newtonian analogues have been used, studies often omit scaling methodology or rely on dimensionless numbers neglecting shear-dependent behaviour, reducing physiological relevance. This work addresses these limitations with an approach for formulating, characterizing, and scaling a refractive index (RI) matched non-Newtonian analogue for optical-based flow measurements, composed of water, glycerol, urea and xanthan gum (XG). Urea offers an inexpensive, safe alternative to salts like sodium iodide, enabling RI adjustment while maintaining physiologically relevant viscosities. The literature suggests small concentrations of XG can be added to induce shear-thinning and viscoelastic behaviour, though rheology is sensitive to batch variability, temperature, and pH. Rheological characterization revealed that achieving physiologically relevant shear-thinning behaviour required higher XG concentrations than anticipated, reinforcing the need for rheological characterization of each preparation. For the first time, a four-component analogue was formulated that matches both the RI needed for optical studies, and the power-law exponent of whole blood, enabling dynamic scaling that accounts for shear-dependent viscosity within a power-law representation of blood rheology. Results indicate that characterization of each analogue fluid is necessary, as previously reported ratios and properties cannot be assumed. Although demonstrated for arterial flows, the framework is applicable to a broader range of shear-thinning systems. This study provides a framework for future non-Newtonian optical-based haemodynamic investigations that improves representation of shear-dependent rheology through rheological characterization and dynamic similitude.