Hacking W J, VanBavel E, Spaan J A
Department of Medical Physics and Informatics, University of Amsterdam, The Netherlands.
Am J Physiol. 1996 Jan;270(1 Pt 2):H364-75. doi: 10.1152/ajpheart.1996.270.1.H364.
Local vessel wall shear stress is considered to be important for vessel growth. This study is a theoretical investigation of how this mechanism contributes to the structure of a vascular network. The analyses and simulations were performed on vascular networks of increasing complexity, ranging from single-vessel resistance to large hexagonal networks. These networks were perfused by constant-flow sources, constant-pressure sources, or pressure sources with internal resistances. The mathematical foundation of the local endothelial shear stress and vessel wall adaptation was as follows: delta d/delta t = K*(tau-tau desired)*d, where d is vessel diameter, tau desired is desired shear stress, and K is a growth factor. Single vessels and networks with vessels in series developed stable optimal diameters when perfused at constant flow or with a constant-pressure source with internal resistance. However, when constant-pressure perfusion was applied, these vessels developed ever-increasing diameters or completely regressed. In networks with two vessels in parallel, only one; vessel attained an optimal diameter and the other regressed, irrespective of the nature of the perfusion source. Finally, large hexagonal networks regressed to a single vessel when perfused with a pressure source with internal resistance. The behavior was independent of variation in parameters, although the adaptation rate and the diameter of the final vessel were altered. Similar conclusions hold for models of vascular trees. We conclude that the effect of shear stress on vascular diameter alone does not lead to stable network structures, and additional factor(s) must be present.
局部血管壁剪切应力被认为对血管生长很重要。本研究是对该机制如何影响血管网络结构的理论探究。分析和模拟在复杂度不断增加的血管网络上进行，范围从单血管阻力到大型六边形网络。这些网络由恒流源、恒压源或具有内阻的压力源灌注。局部内皮剪切应力和血管壁适应性的数学基础如下：(\frac{\Delta d}{\Delta t}=K*(\tau - \tau_{desired})*d)，其中(d)是血管直径，(\tau_{desired})是期望的剪切应力，(K)是生长因子。单血管以及血管串联的网络在恒流灌注或使用具有内阻的恒压源灌注时会形成稳定的最佳直径。然而，当采用恒压灌注时，这些血管直径会不断增大或完全退化。在有两条平行血管的网络中，无论灌注源的性质如何，只有一条血管能达到最佳直径，另一条则退化。最后，当用具有内阻的压力源灌注时，大型六边形网络会退化为单血管。尽管适应速率和最终血管的直径会改变，但这种行为与参数变化无关。对于血管树模型也有类似结论。我们得出结论，仅剪切应力对血管直径的影响不会导致稳定的网络结构，必定还存在其他因素。
