内皮源性舒张因子对血流自动调节的数学模型
Mathematical model for blood flow autoregulation by endothelium-derived relaxing factor
摘要：
流体切应力是心血管系统的重要调节因子，通过内皮衍生的舒张因子（EDRF），即一氧化氮。该机制涉及动脉壁中的生化反应。血管紧张性是血管自动调节的主要机制，对切应力的变化起负反馈作用。本文提出了一种新的恒跨壁压下动脉血流自动调节的数学模型。内皮源性舒张因子一氧化氮、动脉壁的多层结构和动力学扩散过程被考虑在内。对薄壁动脉的极限情况进行了分析研究。给出了线性化系统的稳定性条件。求出了原系统的精确定态解，并对自动调节系统进行了数值模拟。结果表明，动脉对初始径向扰动的适应性和系统对血流变化的响应向新的平衡态的过渡。
英文摘要：
The fluid shear stress is an important regulator of the cardiovascular system via the endothelium-derived relaxing factor (EDRF) that is Nitric Oxide. This mechanism involves biochemical reactions in an arterial wall. The autoregulation process is managed by the vascular tonus and gives the negative feedback for the shear stress changing. A new mathematical model for the autoregulation of a blood flow through arteria under the constant transmural pressure is presented. Endothelium-derived relaxing factor Nitric Oxide, the multi-layer structure of an arterial wall, and kinetic-diffusion processes are taken into consideration. The limit case of the thin-wall artery is analytically studied. The stability condition for a stationary point of the linearized system is given. The exact stationary solutions of the origin system are found. The numerical simulation for the autoregulation system is presented. It is shown the arteria adaptation to an initial radial perturbation and the transition of the system to new equilibrium state in response on the blood flow changing.
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