A novel approach to quantify ventilation heterogeneity in occluded bronchial tree based on lung admittance

Obstructions in airways result in significant alterations in ventilation distribution and consequently reduce the ventilation to perfusion ratio, affecting gas exchange. This study presents a lumped parameter-based model to quantify the spatial ventilation distribution using constructal theory. An extension of the existing theory is made for the conductive bronchial tree and is represented in matrix frame incorporated with airway admittances. The proposed lung admittance model has a greater advantage over the existing methodologies based on lung impedance, as it can be applicable for both fully and partially blocked regions. We proved the well-posedness of the problem, and the generated matrix is highly sparse in nature. A modified block decomposition method is implemented for symmetric and asymmetric trees of various obstructions 0 : 20 : 100 % to reduce the memory size. The asymmetry is considered in every left branch of the bronchial tree recursively, following the mathematical relations: L-i,L-2j = gamma L-i,L-2j+1 and D-i,D-2j = gamma D-i,D-2j+1, where L and D are the length, diameter of the jth branch at ith generation, respectively, for gamma is an element of 0.9 : 0.01 : 1.0. It is observed that relative flow rate (Q(i,j)/Q(i,j )(healthy)) decreases exponentially with the generation index. In tidal breathing, the regional ventilation pattern is found to vary spatially instead of spatio-temporally. The comparison of our result with the clinical data is found to be accurate when 40% or more obstruction is considered in the proximal region (observed in asthma). Moreover, this predicts an increment of lung impedance by 6%, which can be used for further improvement of clinical observations.