# Forward Computational Modeling of Respiratory Airflow
## 4 Boundary Conditions and Simulation Methods
DNS has the highest accuracy, resolving all flow structures, but has extremely high computational cost, hence it is used for simplified flow problems. Airflow is considered fully developed or developing based on the extent to which the velocity profile is formed. A fully developed airflow region can be assumed at any point in the airway segment where the length from the entrance (\(L_{e}\)) is far greater than the diameter of the segment. More specifically, a fully developed region can be assumed at a length greater than (\(L_{e}\)) (Equations (13) and (14)), the distance where the shear stress reaches 2% of the fully developed value [54]. \[\frac{L_{e}}{d}=0.05\;\text{Re},\;\text{Re}\;<2000\;(\text{Turbulent flow}) \tag{13}\]  
\[\frac{L_{e}}{d}=50\;\text{Re},\;\text{Re}\;>2000\;(\text{Turbulent flow}) \tag{14}\]  
Steady inspiratory flow at the inlet is often assumed using various volume flow rate or pressure values, and uniform pressure or velocity at the outlets for simplicity. The resulting solutions from these simulations, albeit mathematically accurate, are not physiologically representative of the mechanical function of the lungs nor are they subject-specific. Nonetheless, they can be utilized to give insights into the changes in structure and function of healthy vs. injured lung cases. Depending on the aim of the study, there are several computational simplifications that may also be implemented. For analyzing the relationship of structural and functional alterations in healthy vs. severe asthmatic lungs, [PERSON] et al. [55] utilized the Galerkin finite element method to discretize the airway tree and imposed a steady inspiratory flow rate of 3.27 \(\times\) 10\({}^{-4}\) m\({}^{3}\) s\({}^{-1}\) (about 20 L min\({}^{-1}\)) and non-uniform flow rates at the outlets. This inspiratory flow rate value is equivalent to the peak flow rate of a sinusoidal waveform with a tidal volume of 0.5 L and a period of 4.8 s. It was concluded that constricted airways in asthmatic patients contribute to higher wall shear stress, elevated pressure drop, and an increase in particle deposition [55]. Although unsteady inspiratory inlet value is ideal, a steady inlet value will suffice for this analysis because the goal is to determine the differences in airflow characteristics as a function of the changes in airway structure. [PERSON] et al. [23] performed a similar simulation by utilizing a User Defined Function (UDF) to simulate airflow in 8 bifurcations of the airway tree obtained from [PERSON]'s modified Horsfield model. To achieve this, the entry boundary conditions (inlet flow rate) were 15, 30, and 75 L min\({}^{-1}\), while the exit boundary conditions at the airway tree endings were imposed on their truncated homologs and set to a relative pressure of zero. [PERSON] et al. suggested that setting the boundary values of the truncated homologs to relative pressures of zero is unimportant in a bid to understand the relative difference in airflow behavior in different airways [23]. Since the same structure was utilized for all three simulations, the outlet boundary values need to be the same. And since the goal of the study was to understand the impact of changes in inlet flow rate on airflow mechanics, these assumptions suffice. Another approach for forward computational simulation of the respiratory system entails utilizing results from inverse modeling. [PERSON] et al. [56] utilized image-based anatomical models of three female human subjects sectioned into subject-specific image-based 3D conducting airways and 1D distal generic airways [56]. The conducting airways were segmented from the 3D CT image scans using SimVascular (an open-source software, [[https://simvascular.github.io/](https://simvascular.github.io/)]([https://simvascular.github.io/](https://simvascular.github.io/)), accessed on 22 November 2024) and spanned the trachea to the most distal conducting airways visible from the CT scan. However, simulations were only performed for a few generations (8, 11, and 9 for the three models utilized).