Traditionally, the arteries in mammals are viewed as the tubes with elastic wall, whose elasticity could be slowly (during a minute) tuned to change its diameter thereby regulating regional blood supply. Recent findings showed that an artery is a much more sophisticated organ, which can change elasticity of vascular wall within a fraction of a second during a cardiac cycle due to activation of its smooth muscles manifested by generation of arterial action potentials. The rapid variations in elasticity of vascular wall resulted in three basic modes of arterial pulsing: passive, active, and intermediate. The latter is characterized by counteraction of dilation force of arterial pressure and the contractile one of smooth muscle in arterial wall, which can result in seemingly “rigid” artery of constant diameter. The prevalence of any of these forces results in active or passive pulsing modes. Existence of various pulsing modes raises the question of their effect on the main function of blood vessels, i.e., the transport of blood. The aim of this study is to assess the effect of various modes of arterial pulsing on hydraulic impedance of major arteries. The linearized Navier–Stokes equation was employed to develop a model of pulsatile flow of viscous incompressible fluid at small velocity via a conduit artery with the walls of variable or constant elasticity. An essential feature of the developed model is the shape of variable pressure drop applied to the ends of arterial segment, which simulates the real changes in arterial pressure during the heartbeat. Here, it is modeled by periodic (systolic) positive bell-shaped impulses with maxima corresponding to systolic arterial pressure, while the minimal plateau level refers to diastolic arterial pressure. The model assesses the changes in arterial hydraulic impedance during a cardiac cycle relatively to the stable level corresponding to constant blood flow driven by persistent pressure drop. Within intermediate variety of pulsing modes between the active and passive ones, the approximation of rigid arterial segment with infinite elasticity of arterial wall showed that hydraulic impedance in rigid artery is not constant due to inertial properties of the flowing blood. In passive pulsing mode characterized with constant elasticity of arterial wall, the diameter of artery changes in parallel with systolic pressure applied to the ends of arterial segment. At this, the overall change of hydraulic resistance is negative. In active pulsing mode, elasticity of arterial wall varies at different phase shifts relative to arterial pressure due to periodic contractions and relaxation of the smooth muscles in arterial wall. An important feature of active mode is possibility to decrease the hydraulic impedance during the front of arterial pressure. Various experimental modes of artery pulsing can be mathematically simulated. The passive and active modes of pulsing as well as a broad variety of intermediate pulsing modes with various phase shifts between arterial pressure and its diameter result in potency of the arteries to tune its performance in order to meet the regional circulatory requirements. The model showed that active arterial pulsing can diminish the arterial hydraulic impedance and contribute to the work needed for circulation thereby helping the pumping action of the heart.

Graphical abstract

中文翻译：

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以各种模式脉动的主要动脉血流的流体动力学模型

传统上，哺乳动物的动脉被视为具有弹性壁的管，其弹性可以缓慢（在一分钟内）调整以改变其直径，从而调节区域血液供应。最近的研究结果表明，动脉是一种更复杂的器官，由于其平滑肌的激活，表现为动脉动作电位的产生，它可以在心动周期中的几分之一秒内改变血管壁的弹性。血管壁弹性的快速变化导致动脉搏动的三种基本模式：被动、主动和中间。后者的特点是动脉压力的扩张力和动脉壁平滑肌的收缩力相互抵消，导致看似“刚性”的恒定直径动脉。任何这些力的普遍存在都会导致主动或被动脉冲模式。各种脉冲模式的存在提出了它们对血管主要功能，即血液输送的影响的问题。本研究的目的是评估各种动脉搏动模式对主要动脉水力阻抗的影响。线性化的 Navier-Stokes 方程用于开发粘性不可压缩流体以小速度通过具有可变或恒定弹性壁的导管动脉的脉动流动模型。所开发模型的一个基本特征是应用于动脉段末端的可变压降的形状，它模拟了心跳期间动脉压的真实变化。这里，它由周期性（收缩）正钟形脉冲建模，最大值对应于收缩动脉压，而最小平台水平指的是舒张动脉压。该模型评估心动周期中动脉液压阻抗相对于稳定水平的变化，该稳定水平对应于持续压降驱动的恒定血流。在主动和被动脉动模式之间的中间变化中，刚性动脉段与动脉壁无限弹性的近似表明，由于流动血液的惯性特性，刚性动脉中的水力阻抗不是恒定的。在以动脉壁弹性恒定为特征的被动脉动模式下，动脉直径的变化与施加于动脉段末端的收缩压平行。此时，液压阻力的整体变化为负。在主动脉冲模式下，由于动脉壁平滑肌的周期性收缩和松弛，动脉壁的弹性相对于动脉压力以不同的相移变化。主动模式的一个重要特征是可以降低动脉压前沿期间的液压阻抗。可以在数学上模拟动脉搏动的各种实验模式。被动和主动脉动模式以及在动脉压力与其直径之间具有各种相移的多种中间脉动模式导致动脉有能力调整其性能以满足区域循环需求。

图形概要