Dutta A, Tarbell J M
Physiological Transport Studies Laboratory, The Pennsylvania State University, University Park, PA USA.
J Biomech Eng. 1996 Feb;118(1):111-9. doi: 10.1115/1.2795936.
Two different non-Newtonian models for blood, one a simple power law model exhibiting shear thinning viscosity, and another a generalized Maxwell model displaying both shear thinning viscosity and oscillatory flow viscoelasticity, were used along with a Newtonian model to simulate sinusoidal flow of blood in rigid and elastic straight arteries. When the spring elements were removed from the viscoelastic model resulting in a purely viscous shear thinning fluid, the predictions of flow rate and WSS were virtually unaltered. Hence, elasticity of blood does not appear to influence its flow behavior under physiological conditions in large arteries, and a purely viscous shear thinning model should be quite realistic for simulating blood flow under these conditions. When a power law model with a high shear rate Newtonian cutoff was used for sinusoidal flow simulation in elastic arteries, the mean and amplitude of the flow rate were found to be lower for a power law fluid compared to a Newtonian fluid experiencing the same pressure gradient. The wall shear stress was found to be relatively insensitive to fluid rheology but strongly dependent on vessel wall motion for flows driven by the same pressure gradient. The effect of wall motion on wall shear stress could be greatly reduced by matching flow rate rather than pressure gradient. For physiological flow simulation in the aorta, an increase in mean WSS but a reduction in peak WSS were observed for the power law model compared to a Newtonian fluid model for a matched flow rate waveform.
使用了两种不同的血液非牛顿模型，一种是表现出剪切稀化粘度的简单幂律模型，另一种是既表现出剪切稀化粘度又表现出振荡流粘弹性的广义麦克斯韦模型，同时还使用了牛顿模型来模拟刚性和弹性直动脉中的血液正弦流动。当从粘弹性模型中移除弹簧元件，从而得到一种纯粘性的剪切稀化流体时，流量和壁面剪应力（WSS）的预测值几乎没有改变。因此，在大动脉的生理条件下，血液的弹性似乎不会影响其流动行为，并且对于在这些条件下模拟血液流动，纯粘性剪切稀化模型应该是相当现实的。当使用具有高剪切率牛顿截止的幂律模型来模拟弹性动脉中的正弦流动时，发现与经历相同压力梯度的牛顿流体相比，幂律流体的流量平均值和幅值更低。对于由相同压力梯度驱动的流动，发现壁面剪应力对流体流变学相对不敏感，但强烈依赖于血管壁运动。通过匹配流量而不是压力梯度，可以大大降低壁面运动对壁面剪应力的影响。对于主动脉中的生理流动模拟，与匹配流量波形的牛顿流体模型相比，幂律模型观察到平均壁面剪应力增加但峰值壁面剪应力降低。
