A model of lung parenchyma stress relaxation using fractional viscoelasticity

Abstract

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.

Sound transmission in porcine thorax through airway insonification

“…The values of material properties of muscle tissue were based on previous studies [10, 44, 46, 55]. According to those studies, the soft muscle tissue was considered viscoelastic [16], and the Voigt model was used.…”

“…Von Gierke et al [55] carried out experiments on the human thigh and upper arm, in which the skin surface was excited by a vibrating piston with different frequencies, and propagation of surface waves was measured using stroboscopy. The soft tissue in many previous studies was considered a viscoelastic medium [10, 16], and the viscous and elastic material parameter values were estimated based on experimental measurements. On the other hand, Garner et al [14] studied human bone viscoelastic properties over a wide range of frequencies.…”

Stability and resonance conditions of second-order fractional systems

“…The transfer function (6) can be used in mechanical engineering to model behavior of viscoelastic systems, where models with fractional damping part based on springs and dash-pots are widely used, for example by Gaul et al (1991), Schiessel et al (1995), Lewandowski and Chorazyczewski (2010), Moreau et al (2010), Meral et al (2010), Castaldo (2013), Grzesikiewicz et al (2013), Dai et al (2015), Zopf (2015), Zerpa et al (2015), and Cataldo (2015). Hence, constitutive equations with fractional derivatives permit noncausal responses provoked by transient vibrations of a damping model to be avoided (Gaul et al, 1991).…”

“…Hence, constitutive equations with fractional derivatives permit noncausal responses provoked by transient vibrations of a damping model to be avoided (Gaul et al, 1991). The fractional standard linear solid model of the lung parenchyma viscoelastic behavior compared to an integer model shows a better fit of stress relaxation curves (Dai et al, 2015). Moreover, a mathematical model of viscoelasticity using fractional order derivatives is successfully applied to model the dielectric behavior of materials by Wharmby et al (2014).…”

“…thermal diffusion (Battaglia et al, 2001;Wang, 2010;Gabano and Poinot, 2011;Datsko, 2012;Battaglia et al, 2012;Victor et al, 2013;Maachou et al, 2014;Sierociuket et al, 2015); . viscoelastic materials (Moreau et al, 2002;Deng, 2004;Meral et al, 2010;Castaldo, 2013;Grzesikiewicz et al, 2013;Dai et al, 2015;Xu et al, 2015;Zerpa et al, 2015;Zopf, 2015); . hydrodynamics (Tarasov, 2005);…”