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Mechanics of lung cancer: A finite element model shows strain amplification during early tumorigenesis [1]

['Rebecca G. Zitnay', 'Department Of Biomedical Engineering', 'University Of Utah', 'Salt Lake City', 'Utah', 'United States Of America', 'Huntsman Cancer Institute', 'Michael R. Herron', 'Keith R. Carney', 'Department Of Oncological Sciences']

Date: 2022-11 

Abstract Early lung cancer lesions develop within a unique microenvironment that undergoes constant cyclic stretch from respiration. While tumor stiffening is an established driver of tumor progression, the contribution of stress and strain to lung cancer is unknown. We developed tissue scale finite element models of lung tissue to test how early lesions alter respiration-induced strain. We found that an early tumor, represented as alveolar filling, amplified the strain experienced in the adjacent alveolar walls. Tumor stiffening further increased the amplitude of the strain in the adjacent alveolar walls and extended the strain amplification deeper into the normal lung. In contrast, the strain experienced in the tumor proper was less than the applied strain, although regions of amplification appeared at the tumor edge. Measurements of the alveolar wall thickness in clinical and mouse model samples of lung adenocarcinoma (LUAD) showed wall thickening adjacent to the tumors, consistent with cellular response to strain. Modeling alveolar wall thickening by encircling the tumor with thickened walls moved the strain amplification radially outward, to the next adjacent alveolus. Simulating iterative thickening in response to amplified strain produced tracks of thickened walls. We observed such tracks in early-stage clinical samples. The tracks were populated with invading tumor cells, suggesting that strain amplification in very early lung lesions could guide pro-invasive remodeling of the tumor microenvironment. The simulation results and tumor measurements suggest that cells at the edge of a lung tumor and in surrounding alveolar walls experience increased strain during respiration that could promote tumor progression.

Author summary Lung cancer is the leading cause of cancer-related death in the world. Efforts to identify and treat patients early are hampered by an incomplete understanding of the factors that drive early lesion progression to invasive cancer. We aimed to understand the role of mechanical strain in early lesion progression. The lung is unique in that it undergoes cyclic stretch, which creates strain across the alveolar walls. Computational models have provided fundamental insights into the stretch-strain relationship in the lung. In order to map the strain experienced in the alveolar walls near a tumor, we incorporated a tumor into a tissue scale model of the lung under stretch. We used finite element modeling to apply physiological material behavior to the lung and tumor tissue. Based on reported findings and our measurements, tumor progression was modeled as stiffening of the tumor and thickening of the tumor-adjacent alveolar walls. We found that early tumors amplified the strain in the tumor-adjacent alveolar walls. Strain amplification also arose at the tumor edges. Simulating strain-mediated wall stiffening generated tracks of thickened walls. We experimentally confirmed the presence of tracks of thickened extracellular matrix in clinical samples of LUAD. Our model is the first to interrogate the alterations in strain in and around a tumor during simulated respiration and suggests that lung mechanics and strain amplification play a role in early lung tumorigenesis.

Citation: Zitnay RG, Herron MR, Carney KR, Potter S, Emerson LL, Weiss JA, et al. (2022) Mechanics of lung cancer: A finite element model shows strain amplification during early tumorigenesis. PLoS Comput Biol 18(10): e1010153. https://doi.org/10.1371/journal.pcbi.1010153 Editor: Philip K. Maini, Oxford, UNITED KINGDOM Received: April 29, 2022; Accepted: October 6, 2022; Published: October 24, 2022 Copyright: © 2022 Zitnay et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability: The authors confirm that all data underlying the findings are fully available without restriction. The MatLab code used to construct the lung lattice geometry has been uploaded to a publicly available repository: (https://github.com/MendozaLabHCI/TumorLungMechanics_2022). FEBio and FEBioStudio are open-source software projects. Installation packages and source code are freely available at https://febio.org/. The bulk lung constitutive model from Birzle et. al. was implemented in the release versions of FEBio and FEBioStudio. Funding: The research reported in this publication was supported by the National Institutes of Health under Award Number P30CA042014, and R01GM083925 (JAW), U24EB029007 (JAW), and R01CA255790 (MCM), as well as by the American Cancer Society RSG CSM130435 (MCM). The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIH.The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing interests: The authors have declared that no competing interests exist.

Introduction Lung cancer is the primary cause of cancer-related death worldwide [1]. New screening efforts aim to catch pre-cancerous and early-stage disease, when a surgical cure is possible [2]. However, even after surgical resection and treatment, 23% of patients with stage I or stage II disease suffer a local recurrence within 5 years [3]. Improving clinical management requires a better understanding of the factors that contribute to early lung tumor progression, including changes within the tumor microenvironment. Lung adenocarcinoma (LUAD) is the most common form of lung cancer. LUAD is initiated by oncogenic mutations in lung epithelial cells that line the alveoli. The mutations cause aberrant cell proliferation, causing transformed cells to fill the alveolar airspace and thicken the alveolar walls [4]. Oncogenic KRAS is the most common initiator of LUAD and accounts for ~30% of disease [5,6]. Additional mutations, such as loss of tumor suppressor TP53, and alterations in the tumor microenvironment contribute to the tumor’s progression to metastatic cancer [5,7,8]. The deposition of extracellular matrix (ECM) proteins like Tenascin-C and crosslinking of collagen promote metastasis and correlate with poor prognosis [9,10]. These ECM changes often accumulate into a desmoplastic stroma [11,12], which is associated with tumor stiffening and aggressiveness in many solid tumors [13–17]. Lung tumors are unique in that they develop in a soft tissue environment that undergoes regular cyclic stretch from respiration. The contribution of mechanical strain to early lung tumorigenesis is unknown. Alveolar surface area increases ~50% at total lung capacity, reached during deep inspiration or ventilation [18,19]. Live imaging has shown that alveolar segments elongate ~15% at inflation volumes near total lung capacity [20]. Both lung epithelial and stromal cells sense and respond to strain [21–23]. Strain can induce oncogenic cellular processes, such as growth factor and matrix production and cell proliferation and migration [24–30]. During lung injury, strain signaling for ECM deposition and cell proliferation drives tissue repair [31]. The process becomes pathological in pulmonary fibrosis. In this disease, persistently elevated strain creates a signaling loop for continuous cell proliferation and ECM deposition [32]. Fibrosis-associated scar tissue and alveolar wall thickening impair lung elasticity and lung function [33,34]. The desmoplastic stroma of late-stage LUAD resembles fibrosis [9,35], suggesting that elevated strain may play a role in LUAD pathogenesis. We hypothesized that early tumors locally amplify the strain in surrounding alveolar walls during respiration. Since direct measurement of localized strains in the intact lung is experimentally challenging, we mapped the strain environment around a lung tumor by computationally modeling the mechanics of the alveolar network. In order to determine the stress-strain behavior of individual alveoli in lung tissue containing a tumor, we developed a finite element model of the alveolar network. Previous lung models have characterized the material behavior and geometric distortions of the lung during respiration and fibrosis. Early constitutive lung models described the uni-axial stretch of bulk lung tissue [36–38]. Early network models with lattices of spring elements revealed the relationship between lung pressure and volume [39,40]. They showed that alveolar wall stress and stiffness control lung elasticity [39,40]. More recently, a geometric study of lung distortion showed that uni-axial stretch causes the alveolar walls to align parallel to the axis of stretch, rather than elongate [41]. The more physiological elongation-type deformations were captured by new constitutive models that applied bi-axial stretch to decellularized tissue [42] and incorporated pressure-volume changes in bulk lung [43]. While the model by Birzle et al. described native lung behavior [43], it did not allow for the investigation of heterogeneous alveoli deformation. We developed a tissue-scale finite element model of the lung using FEBio [44]. Previous continuum constitutive models characterized the heterogeneity in cell and alveoli responses to strain, but were based on uni-axial stretch experiments [45,46] or decellularized tissue [47]. Our model applies the physiological stress-strain relationship of lung tissue [43] to a network of a randomized hexagonal lattice of 3D shell elements [48]. The alveolar walls can undergo elongation, bending and shear. A tumor was incorporated in the center of the lattice using 3D solid elements. When we applied biaxial stretch to simulate physiological tension, we found that the tumor amplified strain in the alveolar walls adjacent to the tumor and in the tumor edge. Modifying the tumor to simulate the increased stiffness associated with late-stage disease resulted in greater strain amplification in alveolar walls. Measurements of alveolar walls in LUAD samples from mouse models and clinical cases showed that tumor-adjacent walls were thickened. When we incorporated thicker alveolar walls into our lung model, the thickening resulted in strain amplification that persisted farther away from the tumor radially. Iterative strain-dependent thickening generated tracks of thick walls. We identified similar tracks of ECM deposition at the invasive edge of human LUAD, suggesting that early lung lesions create local strain amplification that could contribute to tumor progression.

Discussion This research interrogated how a tumor in an expanding lung could influence cellular-level strain. We incorporated a tumor into a geometric model of the lung to predict and map strains in the tumor microenvironment. Our results demonstrated that the strain experienced by alveolar walls near the tumor and at the edge of early tumors is larger than that experienced in healthy lung tissue. The model also predicted that tumor stiffening associated with tumor progression would lead to additional strain amplification that could exacerbate the altered mechanical environment. Alveolar wall thickening observed around a tumor in the lung would displace the strain amplification to the next adjacent alveolus further into the tumor microenvironment and could progressively lead to the formation of thick fiber tracks associated with tumor invasion. Our finding of strain amplification at the earliest stage of lung cancer, before the onset of fibrotic remodeling, suggests that mechanical signaling at the tumor edge could promote early lung tumor progression. The strain amplification identified in our lung tumor model would be sensed by tumor cells at the invasive front and fibroblasts in the immediate neighborhood. We expect that some strain amplification would also occur with benign lung tumors, although to a lesser extent since benign tumors exhibit abnormal growth and thickening but retain an alveolar structure. Stretch activates cell signaling through voltage-gated ion channels and focal adhesions [61]. Epithelial cells sense and respond to the magnitude of strain energy with transcriptional induction of oncogenic behavior: cell proliferation, survival, stemness, and migration [32,62–64]. The in vivo consequence of strain to the disease progression of benign and cancerous lesions remains to be determined. Fibroblasts respond to strain with increased matrix production and can remodel ECM to construct matrix tracks [54,65,66]. In vitro, low strains of 5–10% were found to reduce proliferation, matrix production, and myofibroblast differentiation [67], while strains at 20–30% increased fibroblast proliferation and matrix production [24,68]. This suggests that strain amplification in the lung could push the strain to a magnitude that causes fibroblasts to deposit matrix. We found that modeling matrix deposition as alveolar wall thickening pushes the strain amplification further out into the tumor microenvironment, which suggests that altered mechanical tension may create a feedforward loop of strain and matrix deposition. Such feedforward loops have been described in progressive pulmonary fibrosis, where fibrotic remodeling by activated fibroblasts further promotes fibrosis [32,69] and in glioblastoma, in which stiffness-sensing tumor cells deposit and remodel the ECM [16]. We also found that progressive strain-dependent thickening of alveolar walls can generate tracks of thick walls emanating in a radial pattern out from the tumor. Tracks of aligned ECM, including those composed of collagen, fibronectin, and Tenascin-C are a signature of invasive cancer and can serve as a conduit for tumor cell dissemination [55,57,59,70–72]. Tumor cells preferentially invade along aligned fibers and we observed tumor cells populated along Tenascin-C tracks in early human LUAD. Together, these results suggest that strain amplification in early lung cancer may initiate Tenascin-C-containing matrix deposition, which creates tracks of matrix that promote tumor cell invasion. Our modeling approach allowed us to test how the presence of a tumor alters the magnitude and spatial distribution of strain in lung tissue. Tissue scale lung mechanics have previously been modeled using either network or constitutive models. Network lung models have employed 2- or 3-dimensional lattices of spring elements to assess strain in individual alveolar walls. The models revealed the relationships between lung pressure, volume, and alveolar stress [39] and between lung elasticity and alveolar wall stiffness and distortion [40,41,48,73]. Constitutive lung models have applied strain energy functions based on the behavior of bulk lung tissue in uni-axial tensile tests [36–38] and the pressure-volume changes that occur at physiological stretch [43]. Our geometric model reflects the normal and tumor geometries observed in mouse models and human histopathology (Fig 1, [21]) as well as realistic material properties established in a constitutive model normal lung tissue [43]. Lung parenchyma is homogenous and isotropic [74], therefore the strain energy function derived from bulk material characterization is applicable to our lung lattice model without consideration of tissue orientation. Parameter optimization of our lung model for the range strain matching physiological respiration yielded a lung tissue modulus of 35 kPa and a linear stress-strain response. The modulus was consistent with the reported 30–50 kPa measured by microindentation [42]. The microindentation measurement was of decellularized lung tissue, but applied physiological stretch (~20%, [42]) to better represent native tissue. A linear stress-strain response has been demonstrated in bulk lung under physiological stretch [48–50]. However, the microindentation of decellularized lung tissue resulted in a non-linear force-displacement relationship [42]. The non-linear stress-strain response in decellularized tissue is expected, given that a stress-strain relationship solely dependent on ECM is nonlinear [41,75,76]. We assumed that the tumor was space-filling within the designated alveoli and that the alveolar walls could not be broken, did not have natural variations in width, and were constructed of homogenous material. In our model, all the alveolar walls are vertical. In the native lung, the angle of these walls vary. This geometric limitation of wall angles would influence the angles of the junctions between alveoli and thus alter the patterns of strain amplification. While these simplifications enabled computation and the initial discoveries of strain amplification, the assumptions could be relaxed in future models to understand strain during tumor progression. A limitation of the 2.5D model, compared to the 3D lung, is that the junctions between the alveoli and the top and bottom surface of the alveolar sheet are modeled as uniformly perpendicular to the plane of the sheet. This restricts the angle of strain with respect to the tumor, and may predict more uniform tracks than might be observed with a randomized 3-dimensional geometry. In invasive LUAD, the tumor grows to occupy new alveolar spaces and invades through breaks in the basement membrane layer around the tumor [77,78]. Our assumption that the integrity of the alveolar walls is maintained around the tumor constrains the tumor size and distributes the tension throughout the edge of the tumor. In normal lung, alveolar walls exhibit variable widths in which thin walls exhibit more strain than thicker walls [45]. Such heterogeneity could lead to even greater strain amplification in alveoli adjacent to the tumor when the alveoli are comprised of thinner walls. Highly elevated strain could lead to alveolar wall rupture, observed in histological sections (Fig 1, [79]), and would change the local strain distribution. In our model, we assumed the thickened alveolar walls adjacent to a tumor had the same material properties as the regular width alveolar wall. However, oncogenic remodeling, including the deposition of new ECM proteins, ECM alignment, and crosslinking, likely stiffens the alveolar walls [33]. Thus, our model likely underestimated the impact of alveolar wall remodeling around the tumor. The identification of tumor-induced strain amplification in the tumor microenvironment underscores the importance of future research into strain and mechanotransduction in lung cancer. If strain amplification promotes ECM deposition and tumor invasion, signatures of strain-sensitivity could serve as a new marker to distinguish indolent from aggressive early lesions and strain-induced ECM remodeling may be a new therapeutic target for blocking progression.

Supporting information S1 Fig. Parameter optimization for lung lattice. Force-Displacement relationship of the Birzle, et al. constitutive model [43] and the neo-Hookian approximation (Modulus = 35 kPa, Poisson Ratio = 0.25). The assessed range of displacement values reflected physiological strains. Displacement of 15,000 μm = 50% applied stretch. Displacement of 15,000 μm = 50% applied stretch. https://doi.org/10.1371/journal.pcbi.1010153.s001 (TIF) S2 Fig. Calculated lung modulus by indentation agrees with experimental AFM results. A. Schematic of simulated indentation. A spherical rigid body represents the AFM tip and a solid volume matches the Birzle, et al. constitutive model [43]. The rigid body is displaced vertically at an indentation depth (d) equivalent to the sphere radius (r), 2.5 μm. B. Visualization of the rigid sphere and associated reaction force in the initial position above the material and C. after displacement into the material. https://doi.org/10.1371/journal.pcbi.1010153.s002 (TIF) S3 Fig. Strain ratio increases with tumor modulus. A. Distribution of alveolar wall strain in the normal lung model (no tumor) under 20% applied stretch. The 8 layers of alveoli around the edge of the modeling domain were excluded from the calculations to avoid edge effects. Median Lagrange shell strain is 20.51%, which corresponds to a strain ratio of 0.93. B. Strain ratio in the tumor-adjacent alveolar walls (Fig 3D–3F wall 1). Boxes are 25th percentile to 75th percentile with the median marked by the central line. Red lines show the median Lagrange shell strain for the 2 kPa and 20 kPa tumors at 20% stretch (29.8% and 32.5%), which correspond to strain ratio 1.4 and 1.5. C. Relationship between tumor modulus and strain ratio for applied stretch values of 5, 20, and 50%. The strain ratios for large tumor modulus values converged at 1.7 with 50% stretch, 1.5 with 20% stretch, and 1.3 with 5% stretch. https://doi.org/10.1371/journal.pcbi.1010153.s003 (TIF) S4 Fig. Overall strain in the system redistributes during strain-mediated alveolar wall thickening. A. Region of interest including 5,432 elements selected for analysis around the tumor includes ~15 layers of alveoli. B. Distribution of Lagrange shell strain in all selected elements in the normal lung and after each simulation iteration of 20% applied stretch and shell-thickening in Fig 6A). C. Colormaps of Lagrange strain in alveolar walls around the tumor during strain-mediated thickening. Lattice is positioned to match the orientation of the tumor in Fig 6A. https://doi.org/10.1371/journal.pcbi.1010153.s004 (TIF) S1 Table. Mesh Convergence Values. https://doi.org/10.1371/journal.pcbi.1010153.s005 (DOCX)

Acknowledgments We thank the FEBio development team for their continued efforts to develop, improve and support the FEBio software.

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