Fung Y C, Liu S Q
Department of AMES/Bioengineering, University of California, San Diego, La Jolla 92093-0412.
J Biomech Eng. 1993 Feb;115(1):1-12. doi: 10.1115/1.2895465.
The endothelium lining human arteries is a continuum of endothelial cells. The flowing blood imposes a shear stress on the endothelium. To compute the internal stress in the endothelium, we use two alternative hypotheses: 1) The cell content is fluid-like so that at steady-state it has no shear stress. 2) The cell content is solid-like. Under hypothesis No. 1, the membrane tension in the upper cell membrane grows in the direction opposite to the blood flow at a rate equal to the blood shear stress. At the junction of two neighboring cells the membrane tension in the downstream cell is transmitted partly to the basal lamina, and partly to the upstream cell. The transmission depends on the osmotic or static pressure difference between the cell and blood. If the static pressure difference is zero, the tension in the upper cell membrane will accumulate upstream. At other values of static pressure, the cell membrane tension may increase, decrease, or fluctuate along the vessel depending on the inclination of the side walls of the cells at the junctions. To determine the sidewall inclinations, we propose to use the complementary energy theorem. Under hypothesis No. 2, the cell content can bear shear, which tends to reduce the cell membrane tension; but the cell membrane tension accumulation phenomenon discussed above remains valid. These results are used to analyze the interaction of the cell membrane and cell nucleus; and the effect of turbulences in the flow on causing large fluctuations in cell membrane tension and vertical oscillations of the nuclei. The implication of tensile stress on the permeability of the cell membrane is discussed. We conclude that for the study of mass transport and stress fibers in the endothelial cells, one should consider the interaction of neighboring endothelial cells as a continuum, and shift attention from the shear stress in the blood to the principal stresses in the cells.
衬于人体动脉的内皮是由内皮细胞构成的连续体。流动的血液对内皮施加剪切应力。为了计算内皮中的内应力，我们采用两种不同的假设：1）细胞内容物呈流体状，因此在稳态时没有剪切应力。2）细胞内容物呈固体状。在假设1下，上层细胞膜中的膜张力在与血流相反的方向上以等于血液剪切应力的速率增长。在两个相邻细胞的连接处，下游细胞中的膜张力部分传递到基底层，部分传递到上游细胞。这种传递取决于细胞与血液之间的渗透压或静压差。如果静压差为零，上层细胞膜中的张力将在上游积累。在其他静压差值下，细胞膜张力可能会沿着血管增加、减少或波动，这取决于连接处细胞侧壁的倾斜度。为了确定侧壁倾斜度，我们建议使用余能定理。在假设2下，细胞内容物能够承受剪切力，这倾向于降低细胞膜张力；但上述细胞膜张力积累现象仍然成立。这些结果用于分析细胞膜与细胞核的相互作用；以及血流中的湍流对导致细胞膜张力大幅波动和细胞核垂直振荡的影响。讨论了拉应力对细胞膜通透性的影响。我们得出结论，对于研究内皮细胞中的物质运输和应力纤维，应该将相邻内皮细胞的相互作用视为一个连续体，并将注意力从血液中的剪切应力转移到细胞中的主应力上。
