Quasi‐dynamic breathing model of the lung incorporating viscoelasticity of the lung tissue

We advanced a novel model to calculate viscoelastic lung compliance and airflow resistance in presence of mucus, accounting for the quasi‐linear viscoelastic stress–strain response of the parenchyma (alveoli) tissue. We adapted a continuum‐based numerical modeling approach for the lung, integrating the fluid mechanics of the airflow within individual generations of the bronchi and alveoli. The model accounts for elasticity of the deformable bronchioles, resistance to airflow due to the presence of mucus within the bronchioles, and subsequent mucus flow. Simulated quasi‐dynamic inhalation and expiration cycles were used to characterize the net compliance and resistance of the lung, considering the rheology of the mucus and viscoelastic properties of the parenchyma tissue. The structure and material properties of the lung were identified to have an important contribution to the lung compliance and airflow resistance. The secondary objective of this work was to assess whether a higher frequency and smaller volume of harmonic air flow rate compared to a normal ventilator breathing cycle enhanced mucus outflow. Results predict, lower mucus viscosity and higher excitation frequency of breathing are favorable for the flow of mucus up the bronchi tree, towards the trachea. This work advanced a physics‐based quasi‐dynamic breathing model integrating both the viscoelastic and non‐linear hyperelastic constitutive descriptions of the lung parenchyma tissue. Viscoelastic resistance was developed as a function of mucus volume by calibrating the empirical Kelvin‐Voigt‐based breathing model to the physics‐based quasi‐dynamic breathing model. This work reconciled the measured lung volume‐pressure data with the mechanics‐based constitutive description of tissue stress for lung parenchyma under a generalized three‐dimensional stress state.