# Forward Computational Modeling of Respiratory Airflow
## 4 Boundary Conditions and Simulation Methods
It was assumed that the boundary conditions at the distal outlets of the conducting airways could not be measured experimentally. Thus, an inverse modeling technique was utilized to get the global resistance and compliance values of the lungs. Using the global resistance and compliance values, the lung periphery was represented by a resistor and capacitor connected in series, driven by a time-dependent pressure value. While patient-specific 3D models have been utilized in some studies [57; 58; 59; 60], the results would not be physiologically accurate because of the heterogeneity in pressure, volume flow rate, resistance, and compliance at different regions of the lungs. Hence, utilizing global or constant values for the outlet parameters will not suffice for a valid analysis of the lung function, even more so for an injured lung. To understand correctly the relative differences in airflow characteristics, relatively varying boundary conditions must be utilized to mimic the inhomogeneity in the lung parenchyma [30; 32; 61]. Also, simulating the entire lung structure using only a few bifurcations might provide approximate pressure and velocity values in the central airway tree, but this method will not help in accurately understanding the distribution of flow in more peripheral regions of the lungs. Furthermore, the assumption of steady inspiratory flow at the inlet of the airway tree is not representative of physiological breathing. As such, oscillatory inspiratory flow and subject-specific outlet boundary conditions may be imposed on the airway tree model, to have a solution that more closely represents lung physiology. [PERSON] et al. [2] applied a novel image-based method utilizing subject-specific boundary conditions at the central airway tree endings (Figure 4). Two 3D-CT images taken at different time points during inflation were matched using a mass-preserving image registration technique and a map of regional ventilation was obtained. A 1D centerline airway tree was then generated from the distal conducting airway tree segmentation of the larger image using the volume-filling algorithm developed by [PERSON] et al. [43] that fills the lung lobes with bifurcating 1D trees. The 1D airway tree is then matched with the regional ventilation map to produce a 1D airflow having specified boundary conditions at each point. The boundary conditions at the start of the 1D airway tree were then imposed on the distal ends of the central airway tree. Uniform velocity and pressure boundary conditions were also implemented on this airway tree model simulation and compared to the patient-specific boundary model simulation. Large eddy simulation (LES) was utilized to capture transitional and turbulent flow in the central airway. The results showed that the distributions for pressure and velocity are more heterogenous for the patient-specific model than for the uniform velocity and uniform pressure boundary condition models (Figure 5). The uniform pressure boundary condition yielded a uniform pressure drop in all five lobes, the uniform velocity boundary condition yielded a greater pressure drop in the right middle lobe than the others, and the patient-specific boundary condition yielded a greater pressure drop in both the left lower lobe and the right lower lobe. The distribution in the patient-specific model was consistent with what is expected from the airflow distribution in heterogenous lung anatomy [2,16]. Figure 4: Workflow for attaining subject-specific boundary flow conditions at the distal airway tree [55]. Regional ventilation is obtained from the registration of two 3D images taken at different time points during inhalation, and matched to the structural 1D airway tree using the volume filling branching method. For both regional ventilation and the ventilation map, cool colors correspond to regions of high ventilation, while warm colors correspond to regions of low ventilation. For the volume-filling method, the five different colors correspond to distinct anatomic lobes.