论文标题
血管网络中血流模拟的非线性总参数模型
Nonlinear lumped-parameter models for blood flow simulations in networks of vessels
论文作者
论文摘要
为了解决与复杂网络中血流建模相关的计算效率问题，我们得出了一个非线性集总参数模型的家族，用于偏离公认的一维模型的血流中的血流。这些0D模型必须保留原始1D模型的重要非线性特性：压力面积关系的非线性和表征0D模型的压力依赖性参数，电阻$ r $和电感$ l $，该$ l $是根据时间依赖性的横截面面积定义的，受压力变化。我们介绍了合适的耦合条件，通过0D连接连接0D船只，并构建保留原始1D网络拓扑的0D网络。然后将新衍生的非线性0D模型应用于几个动脉网络，并将预测的结果与（i）参考1D结果进行比较，以验证模型并评估其在所有容器中以较低的计算成本进行验证的压力和流动波形的良好近似值的能力，该计算成本在CPU时间和（ii）范围内衡量的0D范围，以衡量的是0D，以衡量的是（ii），以衡量的是（ii），包括（ii），累加了（ii），累积了（ii），以衡量范围，以衡量范围，包括（ii），包括（ii），以衡量的是，在范围内汇总了范围，以衡量范围，以衡量范围，以衡量范围，包括（ii），以衡量的是，包括（ii），在范围内汇总了范围的范围。与1D结果的协议条款。
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.
