Mathematical modelling of ventilation–perfusion mismatch in lung function

Impaired pulmonary gas exchange in respiratory diseases is caused by a large extent by the physiological mechanism of ventilation-perfusion (V/Q) mismatch.This study is aimed at developing a mathematical modelling framework to quantify regional ventilation, pulmonary perfusion and oxygen transport by coupled nonlinear differential equations.A novel model called Adaptive Ventilation-Perfusion Coupling Model (AVPCM) is proposed which is numerically solved using the Finite Difference Method (FDM) with an implicit Crank-Nicolson time integration scheme, which guarantees stability and accuracy of the calculations.The accuracy at which the simulation results achieved prediction of V/Q mismatch (92.8%), estimation of oxygen saturation (91.3%), prediction of the regional ventilation (89.7%) and the mean prediction error (13.5%) were lower than that of a conventional compartmental