Simulation of Flow in the Human Upper Airways Modeled as a Piping System Using the Hydraulic Diameter


  • Thor Gudmund Weisz
  • Bernhard Müller
  • Reidar Kristoffersen



CFD, Hydraulic Diameter, Obstructive Sleep Apnea, Biomechanics


Obstructive sleep apnea (OSA) is a medical condition characterized by repetitive obstructions in the human upper airways during sleep. Recent estimates from the United States show that the condition impacts 15% to 20% of the adult population. OSA treatment can be subdivided into surgical and non-surgical approaches. Non-surgical approaches such as continuous positive airway pressure (CPAP) devices have the highest success rates when used correctly. However, these approaches have low patient compliance due to the invasive nature of the devices during sleep, leaving surgery as a viable alternative for many. Predicting the outcome of OSA surgery is difficult due to the complex nature of both the airways and the surgeries themselves. CFD modeling of the airways is a helpful way to gain valuable insights into the flow structures and the impact of individual surgeries on the airways. However, CFD is not a viable approach for each patient-specific case due to its time-consuming nature. A pragmatic model has been created to predict the outcome of OSA surgery on a patient-specific basis to produce valid surgical estimates fast to be used by non-CFD engineers. The model transforms the human upper airways into a piping system by applying the hydraulic diameter equation on geometries created from CT scans. This paper aims to validate the use of the hydraulic diameter given by Dh = 4 · (A / Pe), where A is the cross-sectional area and Pe is the wetted perimeter, on the complex geometries of the nasal cavity and to provide a novel equation for the hydraulic diameter in the nasal cavity. The proposed hydraulic diameter equation is given by Dh = CDh · (A / Pe) where CDh is the hydraulic diameter coefficient. Airflow has been simulated through a simplified geometry using CFD to validate the hydraulic diameter and find an updated equation. Pragmatic model simulations using the hydraulic diameter have been compared to the results from CFD simulations to assess the pragmatic model’s accuracy. The results showed that the original hydraulic diameter did not give entirely accurate results and that the novel equation using CDh = 3.71 gave the pragmatic model better accuracy for the validation cases. Tuning the parameter CDh for flow in an OSA patient’s upper airways, the pragmatic model succeeded in quite accurately reproducing the area-averaged pressure in the patient’s upper airways.