Inflation instability in the lung: an analytical model of a thick-walled alveolus with wavy fibres under large deformations

Abstract

Inflation of hollow elastic structures can become unstable and exhibit a runaway phenomenon if the tension in their walls does not rise rapidly enough with increasing volume. Biological systems avoid such inflation instability for reasons that remain poorly understood. This is best exemplified by the lung, which inflates over its functional volume range without instability. The goal of this study was to determine how the constituents of lung parenchyma determine tissue stresses that protect alveoli from instability-related overdistension during inflation. We present an analytical model of a thick-walled alveolus composed of wavy elastic fibres, and investigate its pressure–volume behaviour under large deformations. Using second-harmonic generation imaging, we found that collagen waviness follows a beta distribution. Using this distribution to fit human pressure–volume curves, we estimated collagen and elastin effective stiffnesses to be 1247 kPa and 18.3 kPa, respectively. Furthermore, we demonstrate that linearly elastic but wavy collagen fibres are sufficient to achieve inflation stability within the physiological pressure range if the alveolar thickness-to-radius ratio is greater than 0.05. Our model thus identifies the constraints on alveolar geometry and collagen waviness required for inflation stability and provides a multiscale link between alveolar pressure and stresses on fibres in healthy and diseased lungs.

Mechanics of lung cancer: A finite element model shows strain amplification during early tumorigenesis

“…The relationship between force and displacement of our test lattice and the Birzle rectangular prism [37] was approximately linear for displacement values of 0-15,000 μm (0-50% strain), consistent with previous findings that demonstrate an approximately linear stress-strain relationship for bulk lung within the physiological strain range (Fig. S1, [38,41,42]). The neo-Hookean constitutive model was assigned to the lung lattice model.…”

“…The microindentation measurement was of decellularized lung tissue, but applied physiological stretch (~20%, [43]) to better represent native tissue. A linear stress-strain response has been demonstrated in bulk lung under physiological stretch [38,41,42]. However, the microindentation of decellularized lung tissue resulted in a non-linear force-displacement relationship [43].…”

Computational lung modelling in respiratory medicine

“…During inspiration, the collagen fibres are recruited via fibre re-orientation and straightening, exhibiting a strain-stiffening behaviour [20,23]. The variability in collagen fibre undulations and diameter leads to a wide range of time-constants in the viscoelastic behaviour of lung parenchyma [24]. Both quasistatic and dynamic collagen testing, in which tissue strips of the lung are treated with collagenase to isolate the contributions of collagen, has been reported [25][26][27].…”

Modeling the influence of gravity and the mechanical properties of elastin and collagen fibers on alveolar and lung pressure–volume curves

“…This gradient, in turn, influences regional lung expansion according to the orientation of the subject 18 . At the scale of individual alveoli, regional lung expansion is determined by the spatial distribution of alveolar compliance 19 , which determines how each alveolus expands due to a change in local transpulmonary pressure 2 . Alveolar compliance itself is determined at the scale of the alveolar septal wall by surface tension at the air–liquid interface and by the extracellular matrix (ECM) that consists predominantly of a network of collagen and elastin fibers 20 , 21 .…”

“…Accordingly, our goal in the present study is to develop a computational model of the lung that incorporates the key multi-scale processes alluded to above in a way that accurately explains the P–V behavior of the normal lung. The starting point for this study is an analytical model of the mechanical behavior of a single alveolus we recently developed 2 . This previous model represents each alveolus as a thick-walled spherical shell in which wavy collagen fibers are embedded, providing important insight into the factors that determine the inflation stability of the alveolus 2 , but it does not account for the way in which the P–V curve is impacted by regional heterogeneities due either to gravity or to inherent regional variability in intrinsic tissue mechanics.…”