Dual scale porous medium model of lung congestion caused by tuberculosis

Abstract

Pulmonary tuberculosis is a chronic respiratory disease and lung infection that can be fatal if left untreated, as severe cases lead to compromised oxygen exchange at the alveolar level. This study uses a dual-scale porous medium model and computational methods to understand the nature of tuberculosis infection spread within the lungs and its effects on the alveolar oxygen exchange. The entire lung is modelled as a global, equivalent, heterogeneous porous medium comprising three zones with varying permeabilities that correspond to 23 generations of airflow branches. Airflow during each breathing cycle is simulated by solving transient mass and momentum transfer equations across the three zones of the global model. A separate local model is invoked in zone 3, to analyse oxygen exchange between the alveolar airflow and incoming capillary blood via mass transfer equations. The transient mass exchange equations are solved in the local model to yield the percentage of oxygen transferred to the blood. Tuberculosis spread – and hence, the congestion of the lung – is introduced by modifying the permeability and porosity of the global porous medium model. The impact of infection on the overall bloodstream oxygen content is evaluated by concurrent use of the global and local models. For the case with sudden reduction in immunity, severe infection condition is observed at \(\varvec{86\%}\) of the total infection spreading time and at \(\varvec{75\%}\) for the case with gradual reduction in immunity. For \(\varvec{40\%}\) increase in immunity beyond the \(\varvec{50\% \Gamma }\) stage, it is observed from the simulations that the severe infection situation is completely avoided, preventing any further tuberculosis spread.