MODEL ANALYSIS OF ENDOTHELIUM-DEPENDENT VASOMOTION OF SMALL ARTERY
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摘要: 微循环是血液和组织之间发生物质交换的主要场所，它可以通过改变管径实现对血压、血流量的局部调节.血管内皮层对小动脉运动有重要的调节作用.本文基于连续介质假设，建立了内皮调节过程中主要活性物质在管壁中的扩散——反应动力学模型，并分析了非线性黏弹性血管的径向运动特性.利用该模型首先得到了内皮舒张因子一氧化氮（NO）、平滑肌细胞内钙离子（Ca2+）以及磷酸化肌球蛋白（actin-myosin complexes，AMC）在管壁内的的径向浓度分布；为分析内皮调节的动态过程，进一步对小动脉的被动舒张、血流量发生扰动时的管径响应分别进行了模拟.研究结果显示：当没有活性物质参与调节小动脉被动舒张时，管径无振荡发生；当血流量变化引起内皮调节时，内皮舒张因子NO浓度和管径均出现衰减振荡，振荡周期约60 s.分析认为内皮调节对壁面剪切力的反馈控制，可能是NO浓度和管径产生周期性振荡的原因.内皮调节过程呈现的频谱特征可以为血管内皮功能障碍的诊断提供帮助.Abstract: Metabolic substance exchange between blood and tissue occurs mainly in microcirculation, which can locally regulate blood pressure and blood flow by changing their diameters.Vascular endothelium plays an important role in the vasomotor regulation of small artery.In this paper, a model was adopted to study the endothelial regulation mechanism.Based on the continuum assumption, two layers of diffusion & kinetic processes of key agents in endothelial regulation were modeled, and the nonlinear viscoelastic properties of the wall material were considered in the computation of radial motion of small artery.The stationary distributions of nitric oxide (NO), calcium ion (Ca2+) and the contracting actinmyosin complexes (AMC) concentrations in the wall were firstly obtained;then the process of arterial passive dilation and the autoregulation process to the disturbance of blood flow were simulated.Numerical results showed that there was no oscillation of arterial diameter occurred during the passive dilation process.However, when there was a change in blood flow, the whole system transferred from the initial state to a new equilibrium state with slow damped oscillations.The oscillating period was about 60 s.It is supposed that the endothelial oscillation of artery diameter and NO concentration occurring during the dynamic regulating process is caused by the feedback control of shear stress.This oscillation characteristic can provide useful information for the diagnosis of endothelial dysfunction.
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Key words:
- shear stress /
- endothelial regulation /
- nitric oxide /
- diabetes /
- microcirculation
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图 3 内皮调节主要介质在管壁内的径向浓度分布
Figure 3. Stationary concentration distributions in the arterial wall of the key agents
图 5 NO浓度和管径随时间的变化
Figure 5. Time dependence of the changes of NO concentration and artery radius
图 7 内皮调节介质浓度随时间的变化($\eta = 0,Q = 1.25Q_0 )$
Figure 7. Variations of key agents' concentrations ($\eta = 0,Q = 1.25Q_0 )$
图 8 内皮调节过程的剪切力反馈控制
Figure 8. Feedback control of shear stress in the process of endothelial regulation
表 1 模型参数
Table 1. Model parameters
表 2 不同血流量条件下管径和壁面剪切力的响应
Table 2. Responses of vessel radius and shear stress under different flow conditions
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