Computational and experimental time domain, one dimensional models of air wave propagation in human airways

Abstract

The scientific literature on airflow in the respiratory system is usually associated with rigid ducts. Many studies have been conducted in the frequency domain to assess respiratory system mechanics. Time-domain analyses appear more independent from the hypotheses of periodicity, required by frequency analysis, providing data that are simpler to interpret since features can be easily associated to time. However, the complexity of the bronchial tree makes 3-D simulations too expensive computationally, limiting the analysis to few generations. 1-D modelling in space-time variables has been extensively applied to simulate blood pressure and flow waveforms in arteries, providing a good compromise between accuracy and computational cost. This work represents the first attempt to apply this formulation to study pulse waveforms in the human bronchial tree. Experiments have been carried out, in this work, to validate the model capabilities in modelling pressure and velocity waveforms when air pulses propagate in flexible tubes with different mechanical and geometrical properties. The experiments have shown that the arrival of reflected air waves occurs in correspondence of the theoretical timing once the wave speed is known. Reflected backward compression waves have generated an increase of pressure (P) and decrease of velocity (U) while expansion backward waves have produced a decrease of P and increase of U according to the linear analysis of wave reflections. The experiments have demonstrated also the capabilities of Wave intensity analysis (WIA), an analytical technique used to study wave propagation in cardiovascular system, in separating forward and backward components of pressure and velocity also for the air case. After validating the 1-D modelling in space and time variables, several models for human airways have been considered starting from simplified versions (bifurcation trachea- main bronchi, series of tubes) to more complex systems up to seven generations of bifurcations according to both symmetrical and asymmetrical models. Calculated pressures waveforms in trachea are shown to change accordingly to both peripheral resistance and compliance variations, suggesting a possible non-invasive assessment of peripheral conditions. A favourable comparison with typical pressure and flow waveforms from impulse oscillometry system, which has recently been introduced as a clinical diagnostic technique, is also shown. The results suggested that a deeper investigation of the mechanisms underlying air wave propagation in lungs could be a useful tool to better understand the differences between normal and pathologic conditions and how pathologies may affect the pattern of pressure and velocity waveforms.