To address the issue of computational efficiency related to the modelling of blood flow in complex networks, we derive a family of nonlinear lumped-parameter models for blood flow in compliant vessels departing from a well-established one-dimensional model. These 0D models must preserve important nonlinear properties of the original 1D model: the nonlinearity of the pressure-area relation and the pressure-dependent parameters characterizing the 0D models, the resistance $R$ and the inductance $L$, defined in terms of a time-dependent cross-sectional area subject to pressure changes. We introduce suitable coupling conditions to join 0D vessels through 0D junctions and construct 0D networks preserving the original 1D network topology. The newly derived nonlinear 0D models are then applied to several arterial networks and the predicted results are compared against (i) the reference 1D results, to validate the models and assess their ability to reproduce good approximations of pressure and flow waveforms in all vessels at a much lower computational cost, measured in terms of CPU time, and (ii) the linear 0D results, to evaluate the improvement gained by including certain nonlinearities in the 0D models, in terms of agreement with the 1D results.
翻译:为了解决与复杂网络血液流动建模有关的计算效率问题,我们从复杂的网络中得出一组非线性单幅参数模型,用于从一个成熟的一维模型出发的符合要求的船舶的血液流动。这些0D模型必须保留原 1D 模型重要的非线性非线性特性:压力区域关系的非线性和以0D 模型、抗力美元和降压值为特征的压力依赖参数,该模型的定义是以受压力变化影响的时间依赖跨截面区域为定义的。我们引入了适当的组合条件,以便通过0D 交叉点加入0D 船只,并建造0D 网络以维护原1D 网络表层。这些新得出的非线性0D 模型随后应用于几个动画网,并将预测结果与(一) 参考 1D 结果进行比较,以验证模型并评估其在所有船舶中以低得多的计算成本复制良好压力近似值和流动波形的能力,以CPU时间衡量,以及(二) 线性0D结果,以评价与1 D 模型中的某些非线性结果的改进情况。