Mynard Jonathan P, Valen-Sendstad Kristian
Biomedical Simulation Laboratory, Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON, Canada.
Heart Research, Clinical Sciences, Murdoch Childrens Research Institute, Parkville, VIC, Australia.
Int J Numer Method Biomed Eng. 2015 Jul;31(7):e02717. doi: 10.1002/cnm.2717. Epub 2015 Apr 29.
In reduced-order (0D/1D) blood or respiratory flow models, pressure losses at junctions are usually neglected. However, these may become important where velocities are high and significant flow redirection occurs. Current methods for estimating losses rely on relatively complex empirical equations that are only valid for specific junction geometries and flow regimes. In pulsatile multi-directional flows, switching between empirical equations upon reversing flow may introduce unrealistic discontinuities in simulated haemodynamic waveforms. Drawing from work by Bassett et al. (SAE Trans 112:565-583, 2003), we therefore developed a unified method (Unified0D) for estimating loss coefficients that can be applied to any junction (i.e. any number of branches at any angle) and any flow regime. Discontinuities in simulated waveforms were avoided by extending Bassett et al.'s control volume-based method to incorporate a 'pseudodatum' supplier branch, an imaginary effective vessel containing all inflow to the junction. Energy exchange between diverging flow streams was also accounted for empirically. The formulation was validated using high resolution computational fluid dynamics in a wide range flow conditions and junction configurations. In a pulsatile 1D simulation exhibiting transitions between four different flow regimes, the new formulation produced smooth transitions in calculated pressure losses.
在降阶（0D/1D）血液或呼吸流模型中，连接处的压力损失通常被忽略。然而，在流速较高且出现显著的流动转向时，这些压力损失可能变得很重要。当前估计损失的方法依赖于相对复杂的经验方程，这些方程仅对特定的连接几何形状和流动状态有效。在脉动多向流中，当流动反向时在经验方程之间切换可能会在模拟的血流动力学波形中引入不切实际的不连续性。因此，借鉴巴塞特等人（《汽车工程师学会会刊》112:565 - 583，2003年）的研究成果，我们开发了一种统一方法（Unified0D）来估计损失系数，该方法可应用于任何连接处（即任何角度的任何分支数量）和任何流动状态。通过扩展巴塞特等人基于控制体积的方法，纳入一个“伪基准”供应分支（一个包含所有流入连接处的假想有效血管），避免了模拟波形中的不连续性。还通过经验考虑了分流之间的能量交换。该公式在广泛的流动条件和连接配置下使用高分辨率计算流体动力学进行了验证。在一个展示四种不同流动状态之间转换的脉动1D模拟中，新公式在计算的压力损失中产生了平滑的转换。
