Respiratory exhalation/inhalation models and prediction of airborne infection risk in an aircraft cabin
Airborne disease transmission has always been a topic of wide interest in various fields for decades. The transmission of airborne disease starts when the infectious agents such as the influenza virus or Mycobacterium tuberculosis are exhaled from an infected person. The infectious agents are then dispersed and finally inhaled by a susceptible person. The transmission of infectious diseases in indoor environments, especially in aircraft cabins may represent great risk as they have high occupant density and need to be investigated. With the recent advancements, Computational Fluid Dynamics (CFD) has become a powerful tool for predicting the transmission of airborne diseases in indoor environments. The CFD simulations need precise thermo-fluid boundary conditions for the exhalation/inhalation during various respiratory events and reliable flow models to accurately predict the transport of the infectious agents. ^ The present study first developed exhalation/inhalation models for coughing, breathing and talking. The study conducted measurements on the exhaled/inhaled flow rate, flow direction and area of mouth/nose opening with human subjects. The flow rate variation over time can be defined as a combination of gamma functions for a cough; sinusoidal function for breathing, and a constant for talking process. The variables required to define these flow rate functions can be obtained from the physiological details of a person. The direction of the exhalation jet and the area of mouth/nose opening did not vary significantly during these processes. Though variation among people existed but had no correlation with the physiological details of a person. Thus a mean value for these parameters can be used as boundary condition. In summary, a set of mathematical equations were developed to provide the flow boundary conditions to the CFD simulations for the coughing, breathing and talking processes. The equations account for the variation in the flow boundary conditions with time and people. ^ The droplets exhaled by an infectious person are the carriers of infectious agents. The transport of these expiratory droplets in an aircraft was investigated using the CFD methods. The developed exhalation/inhalation boundary conditions were used. A seven-row, twin-aisle, fully-occupied cabin with index passenger seated at the center was investigated. The droplets exhaled were from a single cough, a single breath and a 15-s talk of the index passenger. The droplets were tracked by using Lagrangian method and their evaporation was modeled. It was found that the bulk airflow pattern in the cabin played the most important role on the droplet transport. The droplets were contained in the row before, at, and after the index patient within 30 s and dispersed uniformly to all the seven rows in 4 minutes. For the cough case, the total airborne droplet fraction reduced to 48%, 32%, 20%, and 12% after 1, 2, 3 and 4 minutes respectively. Similar observations were made for the breathing and talking cases. ^ The study further developed methods to predict the spatial and temporal distribution of expiratory droplets for any flight duration based on the 4 minutes of CFD simulations. The CFD simulations indicated that the local droplet concentrations were higher in the zone, where the expiratory droplets first reached. The droplets concentration then reduced due to the constant dispersion and removal of the droplets from the outlets. The variation in the droplet concentration in the vicinity of the passengers with time indicated that the droplets got well mixed in the cabin in 3 minutes, thus perfectly mixed conditions can be assumed beyond 3 minutes. The droplets from multiple exhalations from the index passenger were found to follow similar tracks. This indicates that the airflow in most of the cabin was steady. It is proposed that the concentration of the droplets in a zone can be obtained by adding the concentrations in the zone from all the exhalations taken place until that time provided with a time shift. Finally, the amount of droplets inhaled by the susceptible passengers was calculated for 4 hours of flight duration under three scenarios. ^ The study used the deterministic and probabilistic approaches (Wells Riley equation) to quantify the risk of infection based on the inhaled infectious dose. The inhaled dose was calculated using the amount of inhaled droplets and the infectious dose contained in a droplet. A case with index passenger suffering with influenza was analyzed. For the deterministic approach, the amount of influenza virus ribonucleic acid (RNA) particle inhaled by each passenger was calculated. For the probabilistic approach, the risk of infection for each passenger was evaluated based on the amount of inhaled quanta. The effectiveness of masks in reducing the risk of infection was also explored. ^
Qingyan Chen, Purdue University.