Sheng C, Sarwal S N, Watts K C, Marble A E
Technical University of Nova Scotia, Halifax, Canada.
Med Biol Eng Comput. 1995 Jan;33(1):8-17. doi: 10.1007/BF02522938.
A quasi-one-dimensional non-linear mathematical model for the computation of the blood flow in the human systemic circulation is constructed. The morphology and physical modelling of the whole system (arteries, capillaries and veins) are completed by different methods for the different vessel generations. A hybrid method is used to solve the problem numerically, based on the governing equation (continuity, momentum and state equations), the input boundary conditions and the predetermined initial conditions. The two-step Lax-Wendroff finite-difference method is used to compute variables for each individual vessel, and the characteristic method is employed for the computation of internal boundary conditions of the vessel connection and the input and output system boundary conditions. Using this approach, blood flow, transmural pressure and blood velocity are computed at all vessel sites and for each time step. The pressure and flow waveforms obtained show reasonable agreement with clinical data and results reported in the literature. When an external conservative force field is applied to the system, the results computed from the model are intuitively correct. The term representing the external pressure added to the system by the muscle, which represents active control on the cardiovascular system, is also embodied in this model.
构建了一个用于计算人体体循环中血流的准一维非线性数学模型。对于不同代的血管，采用不同方法完成了整个系统（动脉、毛细血管和静脉）的形态学和物理建模。基于控制方程（连续性方程、动量方程和状态方程）、输入边界条件和预定初始条件，使用一种混合方法对问题进行数值求解。采用两步Lax-Wendroff有限差分法计算每个血管的变量，并采用特征线法计算血管连接的内部边界条件以及输入和输出系统边界条件。使用这种方法，可以计算出所有血管部位在每个时间步的血流、跨壁压力和血流速度。所获得的压力和流量波形与临床数据以及文献报道的结果显示出合理的一致性。当对系统施加外部保守力场时，从模型计算得到的结果直观上是正确的。该模型还体现了代表肌肉对心血管系统主动控制的、加到系统上的外部压力项。
