Experimental studies and mathematical modeling of the viscoelastic rheology of tracheobronchial mucus from respiratory healthy patients.

Background: Tracheobronchial mucus plays a crucial role in pulmonary function by providing protection against inhaled pathogens. Due to its composition of water, mucins, and other biomolecules, it has a complex viscoelastic rheological behavior. This interplay of both viscous and elastic properties has not been fully described yet. In this study, we characterize the rheology of human mucus using oscillatory and transient tests. Based on the transient tests, we describe the material behavior of mucus under stress and strain loading by mathematical models.

Methods: Mucus samples were collected from clinically used endotracheal tubes. For rheological characterization, oscillatory amplitude-sweep and frequency-sweep tests, and transient creep-recovery and stress-relaxation tests were performed. The results of the transient test were approximated using the Burgers model, the Weibull distribution, and the six-element Maxwell model. The three-dimensional microstructure of the tracheobronchial mucus was visualized using scanning electron microscope imaging.

Results: Amplitude-sweep tests showed storage moduli ranging from 0.1 Pa to 10,000 Pa and a median critical strain of 4%. In frequency-sweep tests, storage and loss moduli increased with frequency, with the median of the storage modulus ranging from 10 Pa to 30 Pa, and the median of the loss modulus from 5 Pa to 14 Pa. The Burgers model approximates the viscoelastic behavior of tracheobronchial mucus during a constant load of stress appropriately (R² of 0.99), and the Weibull distribution is suitable to predict the recovery of the sample after the removal of this stress (R² of 0.99). The approximation of the stress-relaxation test data by a six-element Maxwell model shows a larger fit error (R² of 0.91).

Conclusions: This study provides a detailed description of all process steps of characterizing the rheology of tracheobronchial mucus, including sample collection, microstructure visualization, and rheological investigation. Based on this characterization, we provide mathematical models of the rheological behavior of tracheobronchial mucus. These can now be used to simulate mucus flow in the respiratory system through numerical approaches.