Embolization: critical thrombus height, shear rates, and pulsatility. Patency of blood vessels

The present article builds on elementary fluid dynamics and previous analyses by the author to delineate approximate boundaries of mural thrombus height Hp, maximum shear rate gamma Max, and flow pulsatility beyond which thrombi are subject to either very high or very low probabilities of embolization. A thrombus height of approximately 0.1 mm emerges as a critical dividing line: Below it, the maximum embolizing shear stress tau s is independent of thrombus height and varies only linearly with shear rate. Above it, tau s quickly approaches a strong quadratic dependence on both thrombus height and shear rate: tau s approximately (Hp gamma)2, significantly increasing the likelihood of an embolizing event. By contrast, convective-diffusive removal of blood components during the initial stages of thrombus formation varies only weakly with gamma 1/3 in all but the smallest vessels. These maximum embolizing stresses are due principally to fluid drag. Acceleration (pulsatile) forces only begin to make their presence felt at gamma less than 500 s-1 and reach parity with fluid drag at gamma approximately 10 s-1, i.e., at a level where the presence of pulsatility is questionable. The results are used to provide maps of domains with high and low probabilities of an embolytic event and of vessel patency. The maps reveal that relatively modest changes in shear rate and/or vessel lumen can cause shifts from high to low likelihood of vessel patency, opening up possible ways of controlling blockage by manipulation of these variables.