Quantifying the non-Newtonian effects of pulsatile hemodynamics in tubes

Abstract

• A new hemorheological constitutive TEVP model able to reproduce experimental data. • Pulsating hemodynamic conditions are studied. • At high pressure-gradient, RBC aggregation primarily affects hysteresis phenomena. • The streamwise normal stress is the dominant stress component. • Inelastic models underestimate the kinematic phase-lag compared to the TEVP model. We investigate in silico the pulsatile blood flow in straight, rigid tubes using an elasto-viscoplastic, constitutive model coupled with thixotropy (TEVP) (Varchanis et al., 2019; Giannokostas et al., 2020). In addition to blood viscoelasticity, our model accounts for RBC aggregation through a kinetic equation that describes the level of blood structure at any instance and the viscoplasticity at stasis conditions. We evaluate the model parameters using steady, simple shear, and transient multi-shear rheometric experiments for human physiological subjects with normal blood aggregation. Then, we accurately reproduce previous experimental results (Thurston, 1975; Bugliarello and Sevilla, 1970; Thurston, 1976; Womersley, 1955) and provide reliable predictions for the pressure, stress, and velocity fields. We also investigate blood flow under sinusoidal and experimentally determined waveforms of the pressure-gradient with different frequencies, amplitudes, and patterns, providing a thorough parametric study. We find that the streamwise normal stress is of considerable magnitude. This stress component stretches the RBCs and their aggregates in the flow direction. Commonly used inelastic hemorheological models (e.g., Casson and Newtonian) cannot predict this. Typical values of the time-averaged wall normal-stress are found in the range of 2 Pa − 30 Pa , which are an order of magnitude larger than the corresponding wall shear-stress for the same hemodynamic conditions. The inelastic models systematically underestimate the shear-stress and overestimate the mean velocity. Finally, the TEVP model accurately predicts the phase-lags between the pressure-gradient and the flow-rate, and between the pressure-gradient and the structure-parameter for the whole range of the frequencies expressed in terms of the Womersley number, indicating its physical completeness and robustness.