Olufsen M S, Peskin C S, Kim W Y, Pedersen E M, Nadim A, Larsen J
Department of Mathematics and Center for BioDynamics, Boston University, Massachusetts 02215, USA.
Ann Biomed Eng. 2000 Nov-Dec;28(11):1281-99. doi: 10.1114/1.1326031.
Blood flow in the large systemic arteries is modeled using one-dimensional equations derived from the axisymmetric Navier-Stokes equations for flow in compliant and tapering vessels. The arterial tree is truncated after the first few generations of large arteries with the remaining small arteries and arterioles providing outflow boundary conditions for the large arteries. By modeling the small arteries and arterioles as a structured tree, a semi-analytical approach based on a linearized version of the governing equations can be used to derive an expression for the root impedance of the structured tree in the frequency domain. In the time domain, this provides the proper outflow boundary condition. The structured tree is a binary asymmetric tree in which the radii of the daughter vessels are scaled linearly with the radius of the parent vessel. Blood flow and pressure in the large vessels are computed as functions of time and axial distance within each of the arteries. Comparison between the simulations and magnetic resonance measurements in the ascending aorta and nine peripheral locations in one individual shows excellent agreement between the two.
大的体动脉中的血流是通过从轴对称的纳维-斯托克斯方程推导出来的一维方程进行建模的，这些方程适用于顺应性和逐渐变细的血管中的流动。在最初几代大动脉之后截断动脉树，其余的小动脉和小动脉为大动脉提供流出边界条件。通过将小动脉和小动脉建模为结构化树，可以使用基于控制方程线性化版本的半解析方法来推导频域中结构化树的根阻抗表达式。在时域中，这提供了适当的流出边界条件。结构化树是一种二叉不对称树，其中子血管的半径与父血管的半径成线性比例。大血管中的血流和压力作为每个动脉内时间和轴向距离的函数进行计算。对一个个体的升主动脉和九个外周位置的模拟与磁共振测量之间的比较表明，两者之间具有极好的一致性。
