Mechanics of pulmonary airways: Linking structure to function through constitutive modeling, biochemistry, and histology

Abstract

Breathing involves fluid-solid interactions in the lung; however, the lack of experimental data inhibits combining the mechanics of air flow to airway deformation, challenging the understanding of how biomaterial constituents contribute to tissue response. As such, lung mechanics research is increasingly focused on exploring the relationship between structure and function. To address these needs, we characterize mechanical properties of porcine airways using uniaxial tensile experiments, accounting for bronchial orientation- and location- dependency. Structurally-reinforced constitutive models are developed to incorporate the role of collagen and elastin fibers embedded within the extrafibrillar matrix. The strain-energy function combines a matrix description (evaluating six models: compressible NeoHookean, unconstrained Ogden, uncoupled Mooney-Rivlin, incompressible Ogden, incompressible Demiray and incompressible NeoHookean), superimposed with non-linear fibers (evaluating two models: exponential and polynomial). The best constitutive formulation representative of all bronchial regions is determined based on curve-fit results to experimental data, accounting for uniqueness and sensitivity. Glycosaminoglycan and collagen composition, alongside tissue architecture, indicate fiber form to be primarily responsible for observed airway anisotropy and heterogeneous mechanical behavior. To the authors' best knowledge, this study is the first to formulate a structurally-motivated constitutive model, augmented with biochemical analysis and microstructural observations, to investigate the mechanical function of proximal and distal bronchi. Our systematic pulmonary tissue characterization provides a necessary foundation for understanding pulmonary mechanics; furthermore, these results enable clinical translation through simulations of airway obstruction in disease, fluid-structure interaction insights during breathing, and potentially, predictive capabilities for medical interventions. STATEMENT OF SIGNIFICANCE: The advancement of pulmonary research relies on investigating the biomechanical response of the bronchial tree. Experiments demonstrating the non-linear, heterogeneous, and anisotropic material behavior of porcine airways are used to develop a structural constitutive model representative of proximal and distal bronchial behavior. Calibrated material parameters exhibit regional variation in biomaterial properties, initially hypothesized to originate from tissue constituents. Further exploration through biochemical and histological analysis indicates mechanical function is primarily governed by microstructural form. The results of this study can be directly used in finite element and fluid-structure interaction models to enable physiologically relevant and more accurate computational simulations aimed to help diagnose and monitor pulmonary disease.

Keywords: Biochemistry; Constitutive modeling; Histology; Lung mechanics; Material behavior; Tissue characterization.

Figure 1:

Schematic of study design. A) Three regions of porcine airway were evaluated, including trachea, large bronchi, and small bronchi. B) For each region, samples were orientated along the circumferential or axial direction, with fibers aligned along the axial direction. C) The stress-strain response was curve-fit to a structure-based constitutive model that included a description for the fibers and extrafibrillar matrix. D) Methods for model selection, whereby circumferential samples informed the matrix model, which was combined with a fiber model to fit axial samples.

Figure 2:

Average stress-stretch curves for each sample orientation and region. Generally, axial samples displayed greater strain-stiffening than circumferential samples. For clarity, standard error of the mean is shown for the small bronchi.

Figure 3:

Representative uniaxial stress-stretch data of circumferential (A-C) and axial (D-F) specimens fit to various constitutive models. Model parameters were fit for each region separately (A and D: trachea, B and E: large bronchi, C and F: small bronchi). Circumferential samples were fit to homogenous compressible and incompressible non-linear matrix models, with incompressible Demiray providing the best fit based on high R², low residual error, and sensitivity analysis (top row, black line). Axial tissues were fit to fiber-reinforced exponential or polynomial function, with incompressible Demiray for the matrix. Fibers were best described with an exponential strain-energy function (bottom row, black line). Incompressible NeoHookean (black line, B-C) and polynomial model (blue line, D-E) poorly represented experimental data. Comparable fit performances are visible in reduced stress-strain range insets.

Figure 4:

Average ± standard error of means of incompressible Demiray model parameters (μ, β, k₁ and k₂) determined by fit to circumferentially oriented samples (solid bars) or in combination with a fiber description for axially-oriented samples (striped bars). Regional differences for μ and β were similar for both circumferentially and axially oriented specimens (trachea (T), large bronchi (LB), and small bronchi (SB)). k₁ and k₂ fiber parameters were determined from axially oriented specimens. Regional differences were observed for both fiber parameters. *p<0.001, ^p=0.003.

Figure 5:

Percent stress contribution from fiber (dotted lined bars)and matrix (solid bars) components. Fiber contribution was greater than the matrix contribution in the trachea (T) and large bronchi (LB). Stress contribution was evenly distributed between matrix and fibers in the small bronchi (SB). *p<0.002.

Figure 6:

A) For circumferential samples, a strong correlation was observed between bulk tissue modulus E and matrix modulus μ. B) For axial samples, a strong correlation was observed between bulk tissue modulus and fiber stiffness k₁. Data for all three regions shown.

Figure 7:

Results from sensitivity analysis. A-C) Incompressible Demiray model shown with average model parameters represented by the solid black line. Deviations in model parameters μ, β by ± 1 standard deviation are shown by colored dashed lines. D-F) Combined exponential fiber and incompressible Demiray matrix fit with average model parameters (solid black line) and deviations of μ, β, k₁, k₂ by ± 1 standard deviation. One parameter was varied (colored, dotted lines) while others were held fixed to the average value.

Figure 8:

Glycosaminoglycans (GAG) and collagen content of soft tissue (submucosa and mucosa) normalized by dry weight (average ± standard deviation for all three regions: trachea (T), large bronchi (LB) and small bronchi (SB)). Generally, GAG and DNA content increased from proximal to distal regions (*p<0.001). Conversely, regional differences were not significant (n.s.) for collagen content.

Figure 9:

Representative histological samples stained with Masson’s Trichrome, where collagen fibers are blue and elastin fibers appear red. Fibers in the trachea were crimped, while fibers in the small bronchi appeared to be taut and straightened.