An Analytical Model for Estimating Alveolar Wall Elastic Moduli From Lung Tissue Uniaxial Stress-Strain Curves

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.

A Bioinspired in vitro Lung Model to Study Particokinetics of Nano-/Microparticles Under Cyclic Stretch and Air-Liquid Interface Conditions

“…Due to remaining limitations of the “optimum” BETA membrane with respect to thickness and stiffness (ca. 100-fold reduction needed to match alveolar basement membrane) (Polio et al, 2018 ; Doryab et al, 2019 ; Bou Jawde et al, 2020 ), we attempted to improve the performance characteristics of the membrane by expanding the previously tested range of PCL/gelatin mixing ratios. For this, new membranes were manufactured with PCL concentration larger than the previously explored upper limit of 10% [w/v solvent], namely 15% PCL mixed with 6, 8, and 10% [w/v] ( Figure 2A ).…”

“…As mentioned above, one of the main advantages of the PDMS membranes is their high mechano-elasticity with Young's modulus of ≈1–3 MPa (Wang et al, 2014 ), which is still ca. 100-fold larger than that of alveolar tissue with 3–6 kPa (Polio et al, 2018 ; Bou Jawde et al, 2020 ). Since the previously derived optimized BETA membrane (PCL/gelatin = 9.35%/6.34% [w/v solvent] or P/G = 9.35/6.34) (Doryab et al, 2020 ) has an initial Young's modulus of 9.0 ± 1.9 MPa (prior dissolution of gelatin), the present study tested the hypothesis that an increased PCL concentration of 15% (rather than 6–10% as tested previously) will result in a more elastic membrane.…”

“…While the BETA membrane is more biomimetic than most other membranes currently available due to the low WCA (68°) and 3D interconnectivity of the pores, the BETA membrane still has a ca. 100-fold higher elastic modulus and thickness of the alveolar tissue and basement membrane, respectively (Polio et al, 2018 ; Doryab et al, 2019 ; Bou Jawde et al, 2020 ). The former is expected to alter cell physiology as compared to lung conditions and the latter may result in bias transbarrier transport studies.…”

Application of lung microphysiological systems to COVID-19 modeling and drug discovery: a review

“…Therefore, it should be considered that the elasticity changes with the disease state in some of these components. Lung elasticity is determined by the elastin content, patterning and the level of collagen isotypes [ 143 – 148 ]. The restructuring and remodeling of ECM is dependent on matrix metalloproteinases (MMP) regulated by tissue inhibitors of metalloproteinases (TIMP) [ 144 , 149 , 150 ] and involves the collagens to a much greater extent than elastin [ 145 ].…”

“…The restructuring and remodeling of ECM is dependent on matrix metalloproteinases (MMP) regulated by tissue inhibitors of metalloproteinases (TIMP) [ 144 , 149 , 150 ] and involves the collagens to a much greater extent than elastin [ 145 ]. The ability to vary the elasticity of the substrate is especially important in a COVID model, since ARDS induces specific patterns of lung remodeling initiated by macrophages and continued by myofibroblasts [ 144 ], and ECM stiffening is a characteristic of senescence caused by interstitial fibrosis, alveolar septal cell loss and septal thinning [ 115 , 116 , 143 , 151 ]. The ECM structure also influences the regulation of inflammation, since ECM pore size can affect the M1/M2 differentiation of macrophages [ 152 ].…”