Lung Tissue Viscoelasticity

Abstract

The viscoelastic properties of connective tissues play fundamental roles in the functioning of many organs and organisms as well as in the interactions of these macroscopic biosystems with the complex environment they live in. An emerging view exists that the viscoelastic properties of the extracellular matrix of the lung reflect, to a large extent, the underlying complexity of its structure. This chapter summarizes the phenomenological description of lung tissue viscoelasticity and its relation to tissue composition and structure. In particular, it is shown that the constitutive equation and, hence, the stress relaxation of the lung tissue follows a power law functional form. The constituents of the connective tissue mainly determine the proportionality constants, whereas the complex structural organization of the tissue is responsible for the power law and the numerical value of the exponent. It is argued that the power law constitutive equation develops from the complexity of the structure and the interactions among the components. A concise mathematical description of the constitutive equation of the lung tissue can be based on fractional calculus, which is related to the fractal properties of the collagen‐elastin fiber network embedded in the proteoglycan matrix.

Constant-phase descriptions of canine lung, chest wall, and total respiratory system viscoelasticity: Effects of distending pressure

“…Independent of any model description, the frequency-dependence observed in the impedance of the lungs, chest wall, and total respiratory system is consistent with complex viscoelasticity (Suki et al, 1994; Suki and Lutchen, 2006). In addition, the pressure-dependence of the Z L and Z rs spectra occurring at lower frequencies of oscillation is consistent stiffening of the lung parenchyma, which may arise from progressive recruitment of collagen fibrils in the connective tissue matrix as they bear more load with increases in lung volume (Bates, 2007; Maksym and Bates, 1997a; Suki and Bates, 2011a).…”

“…This behavior is a common feature in nearly all biological tissues (Fung, 1993), and is thought to arise from the coupling of dissipative and elastic processes at the level of stress-bearing elements. This coupling may arise from the unfolding (i.e., reptation) of collagen and elastin fibers (Suki et al, 1994; Suki and Bates, 2008; Suki and Lutchen, 2006), surface forces at the air-liquid interface (Mora et al, 2000), cyclic recruitment and derecruitment (Kaczka et al, 2011a; Kaczka et al, 2005), as well as cross-bridge cyclic between actin and myosin in airway smooth muscle or other contractile elements in the parenchyma (Fredberg et al, 1993; Fredberg et al, 1996; Kapanci et al, 1974). …”

“…This property is often described in biological tissues, such as the lung parenchyma or chest wall, using constitutive equations characterizing dynamic stress-relaxation or creep (Suki et al, 1994). Macroscopically, the stress response (σ) to a step increase in strain (ε) is often expressed in the time-domain using a power law of the form (Hildebrandt, 1969; Suki and Lutchen, 2006): $$\sigma \left(t\right)=a{t}^{-\beta }$$ where t is time, a is a constant, and β is the stress-relaxation exponent. In the frequency-domain, systems which exhibit power law stress-relaxation can be partitioned into components corresponding to energy dissipation and energy storage according to the ratio of stress to strain (Suki and Lutchen, 2006): $$\frac{\sigma \left(\omega \right)}{\epsilon \left(\omega \right)}=jG{\omega }^{\beta }+H{\omega }^{\beta }$$ where j is the unit imaginary number (i.e., √–1), ω is the angular frequency (i.e., ω = 2π f ), and G and H are the loss and storage moduli, respectively.…”

A Spring–Dashpot System for Modelling Lung Tumour Motion in Radiotherapy

“…A thorough description of modelling lung tissue properties taking into account viscoelastic non-linear stress-strain behaviour can be found in Refs [19,20]. However, the focus of this work is the spatio-temporal relationship between abdominal motion and that of a tumour embedded in the lung tissue.…”