# Forward Computational Modeling of Respiratory Airflow
## 4 Boundary Conditions and Simulation Methods
This work is made available under the terms of the Creative Commons Attribution CC BY 4.0 ([[https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/)]([https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/))). Figure 5: Velocity vectors (pink) and pressure drop distributions in a three-dimensional model with: (**a**) patient-specific; (**b**) uniform velocity; and (**c**) uniform pressure boundary conditions at the distal airway outlets. The patient-specific boundary condition yielded a greater pressure drop in the left lower lobe and the right lower lobe compared with the uniform velocity condition, the uniform velocity boundary condition yielded a greater pressure drop in the right middle lobe than the others, and the uniform pressure boundary condition yielded a uniform pressure drop across all five lobes. From reference [2], with permission. The patient-specific boundary condition at the distal end of the airway tree is a flow rate boundary condition. From the CT intensity at the distal airways for the images acquired, the air fraction at each voxel can be calculated as [62; 63]:  
\[\beta_{\text{air}}(x)=\frac{\text{HU}_{\text{tissue}}-I(x)}{\text{HU}_{\text{ tissue}}-\text{HU}_{\text{air}}} \tag{15}\]  
where \(\beta_{\text{air}}(x)\) and \(I(x)\) represent the air fraction and image intensity at a given voxel location \(x\). \(\text{HU}_{\text{tissue}}\) (parenchyma and blood) and \(\text{HU}_{\text{air}}\) represent the Hounsfield units for tissue (+65) and air (\(-1000\)), respectively. The value of the air fraction at each distal voxel is multiplied by the reference volume of a CT image voxel to get the volumes of air at any two-time points during inflation. The difference in volumes over the difference in time gives the air flow rate at each distal airway tree ending [16]. [PERSON] and coworkers [5; 16], as well as [PERSON] and coworkers [5; 64; 65] proposed a more detailed computational framework. In addition to performing simulations using the gray level values from the image scans for the patient-specific boundary conditions, a free-form deformation and a soft tissue deformation technique can be utilized to attain subject specific boundary conditions. For the free-form deformation, images at two time points (\(t_{1}\) and \(t_{2}\)) during inflation are acquired and the image at \(t_{1}\) is embedded with a finite element mesh. The 3D image at \(t_{1}\) is then transformed into the \(t_{2}\) image and the change (transformation) in the volume is assumed to be equivalent to airflow. Hence, the rate of change in volume from \(t_{1}\) to \(t_{2}\) is utilized as the flow boundary condition. The free-form deformation technique assumes that although there is a change in lung tissue form and structure, there exists no net change in tissue volume hence the volume change seen during inflation is attributed to air. The soft tissue deformation technique is used in calculating local expanding boundary pressure through finite deformation elasticity values of stress and strain of the lung parenchyma. The modeling framework was formulated to link equations for large deformation of the lung tissue to equations for airway flow and pressure at different regions in the airway tree. Furthermore, the breathing cycle (inspiration and expiration) either during spontaneous breathing or assisted breathing via a mechanical ventilator not only involves airflow through the airway tree but also airway tissue deformation (contraction or expansion) at different regions. Hence, CFD simulations closer to physiological reality would include some form of fluid-structure interaction (FSI) [66; 67] which is lacking in some of these studies. [PERSON] et al. developed and deployed an FSI technique that utilizes a finite volume-based and element-based structural dynamics method with a dynamic level-set meshing algorithm [68]. This FSI technique is triple based with the fluid domain, the airway structure domain, and a moving mesh.