One-dimensional modelling of pulse wave propagation in human airway bifurcations in space-time variables

Abstract

Airflow in the respiratory system is complicated as it goes through various regions with different geometries and mechanical properties. Three-dimensional (3-D) simulations are typically limited to local areas of the system because of their high computational cost. On the other hand, the one-dimensional (1-D) equations of flow in compliant tubes offer a good compromise between accuracy and computational cost when a global assessment of airflow in the system is required. The aim of the current study is to apply the 1-D formulation in space and time variables to study the propagation of a pulse wave in human airways; first in a simple system composed of just one bifurcation, trachea-main bronchi, according to the symmetrical Weibel model. Then extending the system to include a further generation, the bronchi branches. Pulse waveforms carry information about the functionality and morphology of the respiratory system and the 1-D modelling, in terms of space and time variables, represents an innovative approach for respiratory response interpretation. 1-D modelling in space-time variables has been extensively applied to simulate blood pressure and flow in the cardiovascular system. This work represents the first attempt to apply this formulation to study pulse waveforms in the human bronchial tree.