Abstract
The non-linear stress-strain behavior of uniaxially-stretched lung parenchyma is thought to be an emergent phenomenon arising from the ensemble behavior of its microscopic constituents. Such behavior includes the alignment and elongation of randomly oriented alveolar walls with initially flaccid fibers in the direction of strain. To account for the link between microscopic wall behavior and the macroscopic stress-strain curve, we developed an analytical model that represents both alignment and elongation of alveolar walls during uniaxial stretching. The model includes the kinetics and mechanical behavior of randomly oriented elastic alveolar walls that have a bending stiffness at their intersections. The alignment and stretch of the walls following incremental stretch of the tissue were determined based on energy minimization, and the total stress was obtained by differentiating the total energy density with respect to strain. The stress-strain curves predicted by the model were comparable to curves generated by a previously published numerical alveolar network model. The model was also fit to experimentally measured stress-strain curves in parenchymal strips obtained from mice with decreased lung collagen content, and from young and aged mice. This yielded estimates for the elastic modulus of an alveolar wall, which increased with age from 4.4 to 5.9 kPa (p = 0.043), and for the elastic modulus of fibers within the wall, which increased with age from 311 to 620 kPa (p = 0.001). This demonstrates the possibility of estimating alveolar wall mechanical properties in biological soft tissue from its macroscopic behavior given appropriate assumptions about tissue structure.
Highlights
The macroscopic mechanical behavior of a biological tissue such as the lung parenchyma arises from the ensemble behavior of its microscopic constituents (Suki and Bates, 2011)
We investigated the effects of aging on alveolar wall tensile and bond-bending moduli by fitting lung tissue stress-strain curves obtained in young (n = 5; 5 months) and old (n = 6; 19, and 24 months) mice
We developed an analytical model of lung parenchymal tissue mechanics that links uniaxial stress-strain behavior at the level of the tissue strip to the alignment and elongation of alveolar walls
Summary
The macroscopic mechanical behavior of a biological tissue such as the lung parenchyma arises from the ensemble behavior of its microscopic constituents (Suki and Bates, 2011). The progressive recruitment of collagen fibers with increasing strain has been modeled for lung parenchymal tissue (Maksym and Bates, 1997), human vein, fascia, tympanic membrane, rabbit papillary muscle (Decraemer et al, 1980), and ligament (Liao and Belkoff, 1999) Both recruitment and fiber reorientation were simultaneously taken into account by Lanir (1979). The stress-strain behavior of the individual tissue constituents themselves must be taken into account for a complete understanding of tissue mechanics Determining this behavior experimentally is challenging because of the tiny length scales involved, but Sacks was able to determine fiber orientation using small-angle light scattering and numerically solved the constitutive equations to estimate the stress-strain behavior of individual collagen fibers (Sacks, 2003). They interact with each other and with other components of the ECM through electrostatic forces arising, for example, from negatively charged proteoglycans (PGs) that exert repulsive forces on each other (Cavalcante et al, 2005; Ritter et al, 2009)
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