The bronchial tree plays a main role in the human respiratory system because the air distribution throughout the lungs and gas exchange with blood occur in the airways whose dimensions vary from several centimeters to micrometers. Organization of about 60,000 conducting airways and 33 million respiratory airways in a limited space results in a complex structure. Due to this inherent complexity and a high number of airways, using target-oriented dimensional reduction is inevitable. In addition, there is no general reduced-order model for various types of problems. This necessitates coming up with an appropriate model from a variety of different reduced-order models to solve the desired problem. Lumped formulation, trumpet, or typical path model of whole or parts of bronchial tree are frequently used reduced-order models. On the other hand, using any of these models results in underestimation of flow heterogeneity leading to inaccurate prediction of the systems whose mechanisms depend on the fluid heterogeneity. In this study, a simple robust model combining mechanistic and non-mechanistic modeling approaches of the bronchial tree is proposed which overcomes the limitations of the previous reduced-order models and gives the same results of a detailed mechanistic model for the first time. This model starts from an accurate multi-branching model of conducting and respiratory airways (i.e., the base model) and suggests a proxy model of conducting airway and reduced-order model of respiratory airways based on the base model to significantly reduce computational cost while retaining the accuracy. The combination of these models suggests various reduced-order surrogate models of the human bronchial tree for different problems. The applications and limitations of each reduced-order model are also discussed. The accuracy of the proposed model in the prediction of fluid heterogeneity has been examined by the simulation of multi-breath inert gas washout because the alveolar slope is the reflection of fluid heterogeneity where the computational time decreases from 121 h (using the base model) to 4.8 s (using the reduced-order model). A parallel strategy for solving the equations is also proposed which decreases run time by 0.18 s making the model suitable for real-time applications. Furthermore, the ability of the model has been evaluated in the modeling of asthmatic lung as an instance of abnormal lungs, and in the modeling of O2–CO2 exchange as an instance of nonlinear reacting systems. The results indicate that the proposed model outperforms previous models based on accuracy, robustness, and run time.

Graphic abstract

中文翻译：

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人支气管树中流体流动和传质的各种降阶替代模型

支气管树在人体呼吸系统中起着主要作用，因为整个肺部的空气分布和与血液的气体交换发生在尺寸从几厘米到微米不等的气道中。在有限的空间内组织约 60,000 条导气管和 3300 万条呼吸管，导致结构复杂。由于这种固有的复杂性和大量的气道，使用面向目标的降维是不可避免的。此外，对于各种类型的问题，没有通用的降阶模型。这需要从各种不同的降阶模型中提出适当的模型来解决所需的问题。整体或部分支气管树的集总公式、喇叭或典型路径模型是常用的降阶模型。另一方面，使用这些模型中的任何一个都会导致对流动异质性的低估，从而导致对其机制取决于流体异质性的系统的不准确预测。在这项研究中，提出了一种结合支气管树机械和非机械建模方法的简单稳健模型，克服了先前降阶模型的局限性，并首次给出了与详细机械模型相同的结果。该模型从传导气道和呼吸气道的精确多分支模型（即基础模型）开始，并在基础模型的基础上提出传导气道代理模型和呼吸气道降阶模型，以显着降低计算成本，同时保留准确性。这些模型的组合提出了针对不同问题的人类支气管树的各种降阶代理模型。还讨论了每个降阶模型的应用和局限性。由于肺泡斜率是流体非均质性的反映，计算时间从 121 小时（使用基础模型）减少到4.8 s（使用降阶模型）。还提出了一种求解方程的并行策略，该策略将运行时间减少了 0.18 秒，使模型适用于实时应用。此外，该模型的能力已在哮喘肺建模中作为异常肺的一个实例进行了评估，以及作为非线性反应系统实例的 O2-CO2 交换建模。结果表明，所提出的模型在准确性、鲁棒性和运行时间方面优于以前的模型。

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