Gas Flow in Occluded Respiratory Tree: A New Matrix-Based Approach

Abstract

Studies suggest that both the size of airways and the number of bifurcations of the respiratory tree provide the best structural design to accomplish its function. However, constrictions and occlusions due to inflammation and pulmonary edema of the airways can inhibit normal air flowing through the respiratory tree, affecting gas exchange. It results in heterogeneity in gas exchange (and pulmonary perfusion) with adverse risk factors. In this study, we propose a methodology based on the airway tree admittance (reciprocal of impedance) to study this problem. This methodology is distinct from the traditional quantification, based on overall impedance using lump parameter models, and applies to a matrix formed by admittances of each airway of the entire conducting part of the bronchial tree. The generated system admittance matrix is highly sparse in nature, and thus to solve the same system, a modified block-based LU decomposition method is proposed to improve the space–time tradeoff. Our approach enables the determination of the local ventilation pattern and reduces the misevaluation, mainly in the cases that characterize the early-stage obstructive disorders. The key finding of the present study is to show that how the position and intensity of local obstruction in an airway can affect the overall as well as regional ventilation which can lead to impaired gas exchange.