# Forward Computational Modeling of Respiratory Airflow
###### Abstract
This recoil decreases the volume of the thoracic cavity, leading to an increase in alveolar pressure relative to the atmosphere, and establishes a pressure gradient to move air out of the lung. These inspiratory and expiratory phases induce non-uniform volume changes throughout the lung tissues, because of the inherent heterogeneity in regional mechanical properties [9]. This distribution of airflow in the lungs (during spontaneous breathing) initiated by the pressure gradient is influenced by both resistance of the airway pathways and the compliance of the lung tissue. Several studies have relied on the symmetric [6] and asymmetric [10; 11; 12] airway trees to understand the distributions of airflow, ventilation, and other mechanical properties in the lungs, given their simplicity in structure, since both models assume regular dichotomous branching. The aforementioned Weibel model assumes symmetry in branch dimensions (i.e., length and diameter) and bifurcation angles of parent-daughter segments in a particular generation [6]. The generation number for each branch in the tree is assigned relative to its parent branch, with the trachea assigned as Generation 0. Each subsequent daughter branch is assigned a generation higher than the previous maternal branch. By contrast, the models of [PERSON] and co-workers [12; 13] assume asymmetry in bifurcation and branch dimension, based on a recursion index \(\Delta\). The trachea is assigned the highest order number, with one daughter branch an order lower and the other determined by an assigned value for \(\Delta\), representing the difference in order numbers for daughter branches of the same generation. For computational modeling, tracheebronchial trees generated using either symmetric or asymmetric designs are often modeled as a 1D flow field (i.e., axial), integrating governing equations for pressure-flow relationships over the cross-sectional area of the airway branches [10; 14]. Most airflow simulations of the lung focus on small subsections of the airway tree and/or a fixed mesh for tissue behavior [2; 15; 16; 17; 18]. Simulations using such models usually rely on the assumption of smooth cylindrical tubes for the airway branches [10] whereas the human airway cross-section is quite irregular in shape [17]. Moreover, the airway airflow simulations are often simplified, and do not accurately reflect the flow mechanics associated with heterogenous and irregular airway branching. Neither the [PERSON] nor Horsfield models account for the three-dimensional (3D) spatial arrangement of the airways. Furthermore, the design of both models is based on airway tree casts [12; 19], which may introduce geometric distortion to the parent-daughter branch angles and tissue structures. Given recent advancements in subject-specific in silico simulations for potential clinical decision-making [1], there is a need for more structurally and spatially realistic 3D models for predicting response to therapy or treatment outcomes, since the branching structural pattern of the airway tree influences the distribution of airflow. Not only will more advanced 3D geometric models be a significant improvement to understanding the mechanics of airflow in the lung, but they will also have utility for enabling high-fidelity simulations of airflow in diseased lungs, compared to the more conceptually idealized Weibel and Horsfield structures [10]. In this focused review of respiratory airflow modeling, we will summarize the techniques and limitations used for generating realistic, 3D geometric models of the mammalian lung, as well as various techniques used for computational airflow simulations based on mathematical and image-based geometric models, as well as the boundary conditions imposed. Fluid-structure interactions, and the nature of airflow (i.e., laminar, transitional, and turbulent), at different regions of the lung will be considered, as well as the impact of various assumed flow paradigms on ventilation distribution and other functional indices.