A model of lung parenchyma stress relaxation using fractional viscoelasticity

• Lung parenchyma viscoelasticity was studied via stress relaxation.
• Stress relaxation studies were conducted on freshly exercised inflated pig lungs.
• Fractional order and integer order viscoelastic models were compared.
• Fractional standard linear solid was the best among four-parameter models.

Some pulmonary diseases and injuries are believed to correlate with lung viscoelasticity changes. Hence, a better understanding of lung viscoelastic models could provide new perspectives on the progression of lung pathology and trauma. In the presented study, stress relaxation measurements were performed to quantify relaxation behavior of pig lungs. Results have uncovered certain trends, including an initial steep decay followed by a slow asymptotic relaxation, which would be better described by a power law than exponential decay. The fractional standard linear solid (FSLS) and two integer order viscoelastic models – standard linear solid (SLS) and generalized Maxwell (GM) – were used to fit the stress relaxation curves; the FSLS was found to be a better fit. It is suggested that fractional order viscoelastic models, which have nonlocal, multi-scale attributes and exhibit power law behavior, better capture the lung parenchyma viscoelastic behavior.