Poster Q3 - Microscale Strain-Stiffening of Lung Parenchyma with and without tumors revealed by the Crystal Ribcage Platform

Introduction: Lung conditions, including cancer, significantly remodel the structure of the lung at organ, cellular, and molecular length scales, altering its mechanical properties and in turn influencing disease development, progression, diagnosis, and treatment response (Science, 2020; Nature BME, 2016). Spatial variations in stiffness may, in turn, lead to ventilatory heterogeneities and ventilation-perfusion mismatch (Intensive Care Medicine, 2009). Previously, measuring variations in lung stiffness across sub-alveolar distances and under physiologically realistic conditions was unachievable. However, our recent innovation (Nature Methods, 2023), the crystal ribcage (Fig. 1(a)), allows us to image functioning lungs at optical resolution while maintaining control over physiological factors like air and vascular pressures. Utilizing this technology, we developed a data-driven, multiscale network model that processes images taken at different distending pressures to create precise maps of the lung’s stiffness in absolute units. Our validated model produces detailed maps that reveal the lung’s mechanical properties at sub-alveolar scales, both in health and disease. We find that the lung and lung tumors exhibit (i) significant heterogeneities in stiffness at sub-alveolar scales, (ii) pronounced strain stiffening, (iii) heteroscedastic increases in stiffness variability with inflation, and (iv) significant elevation of the lung tumor’s stiffness and strain-stiffening compared to normal tissue. This method provides a quantitative tool for assessing the stiffness changes induced by disease, offering new insights into mechanotransduction in lung tissues.

Materials and

Methods: Our methodology combines novel empirical and computational models for studying the mechanical properties of murine lungs in both health and cancer. Following an established protocol, we first induced primary lung tumors in C57BL/6 mice expressing tdTomato. With the ex vivo lung inside the crystal ribcage, which mimics the lung's natural boundary conditions, we then captured high-resolution, confocal-microscopic images of the lung inflated to different pressures under quasi-static conditions. We then constructed a finite-element model of the whole lung, the geometry of which was extracted from microCT images of the lung using Bayesian methods (Fig. 1(b)), and subsequently calibrated the finite-element model’s mechanical properties to recapitulate the lung’s organ-scale behavior within the crystal ribcage (Fig. 1(c)). These simulations were crucial in determining the material properties that accurately reproduce the organ’s mechanical response. Next, applying image registration (MICCAI, 2012), we measured the organ’s cellular-scale deformation induced by stepwise reductions in air pressure. Through a sophisticated analytical approach based on the Adjoint-Weighted Equation (Int J Num Methods Engineering, 2010) formulation of the inverse-elasticity problem, we recovered maps of the tissue stiffness in absolute units, yielding novel measurements of the mechanical properties of the lung at sub-alveolar length scales. The outcomes of these simulations and models were statistically analyzed to evaluate changes in strain and stiffness across different lung conditions and pressures, highlighting the significant impact of pathology on lung mechanics.

Results, Conclusions, and Discussions: The finite-element model recapitulates the lung’s pressure-distension curve measured in the crystal ribcage (Fig. 1(e)). Applying the complete model to images of the lung in the crystal ribcage (Fig. 1(d)), we find that the registered displacements at alveolar length scales allow us to accurately reconstruct the lung’s geometry in the low-pressure reference configuration (Fig. 1(e)). Subsequent estimates of the lung’s strain demonstrate that the tumor deforms less than the surrounding tissue (Fig. 1(f)). From maps of the lung’s stiffness in absolute units (Fig. 1(g)), we find that our estimates (5-15 kPa) are in good agreement with AFM studies (JoVE, 2011) while revealing significant heterogeneities at alveolar scales. We also find the tumor was consistently stiffer than surrounding healthy tissue across all tested pressures. Furthermore, we find that the lung exhibits pronounced strain stiffening, with stiffnesses increasing by 1.75x in normal tissue and by 6x in primary tumors (Fig. 1(h) and Fig. 1(i)(ii)). At higher pressures, the tumor's stiffness was significantly greater than that of normal tissue, reaching nearly 5 times the stiffness of nearby tissues, illustrating the severe impact of cancer on lung mechanics. Moreover, the variance in stiffness also increased with pressure, indicating greater heterogeneity in cancerous tissues compared to normal tissues (Fig. 1(i)(ii)). These findings align with our hypothesis that variations in collagen arrangement and cross-linking contribute to increased tissue stiffness, particularly in cancer where the extracellular matrix is denser and more cross-linked. The model also predicts a reduction in stiffness in the peritumor region compared to normal tissue. These findings suggest the tumor not only alters its immediate environment but potentially affects the mechanical properties of its surroundings, including regions not directly associated with tumor mass. Tumors may thus cause V/Q-mismatch by reducing ventilation of nearby regions. Our model has not only validated known mechanical behaviors of lung tissues, such as strain stiffening and heterogeneity under stress, but has also revealed new evidence that lung cancer likewise exhibits and alters these properties. This comprehensive methodological framework supports the detailed study of lung biomechanics with implications for understanding disease mechanisms and therapeutic responses at sub-alveolar resolution.

Acknowledgements (Optional):

References:
1 Nia, H. T., Munn, L. L. & Jain, R. K. Physical traits of cancer. Science 370, eaaz0868 (2020). https://doi.org:doi:10.1126/science.aaz0868
2 Nia, H. T. et al. Solid stress and elastic energy as measures of tumour mechanopathology. Nature Biomedical Engineering 1, 0004 (2016). https://doi.org:10.1038/s41551-016-0004
3 Glenny, R. W. Determinants of regional ventilation and blood flow in the lung. Intensive Care Medicine 35,
1833-1842 (2009). https://doi.org:10.1007/s00134-009-1649-3
4 Banerji, R. et al. Crystal ribcage: a platform for probing real-time lung function at cellular resolution. Nature Methods (2023). https://doi.org:10.1038/s41592-023-02004-9
5 Heinrich, M. P., Jenkinson, M., Brady, S. M. & Schnabel, J. A. in Medical Image Computing and Computer-Assisted Intervention – MICCAI 2012 115-122 (Springer Berlin Heidelberg, 2012).
6 Albocher, U., Oberai, A. A., Barbone, P. E. & Harari, I. Adjoint-weighted equation for inverse problems of incompressible plane-stress elasticity. Computer methods in applied mechanics and engineering 198, 2412-2420 (2009). https://doi.org:10.1016/j.cma.2009.02.034
7 Barbone, P. E. et al. Adjoint‐weighted variational formulation for the direct solution of inverse problems of general linear elasticity with full interior data. International journal for numerical methods in engineering 81, 1713-1736 (2010).
8 Liu, F. & Tschumperlin, D. J. Micro-Mechanical Characterization of Lung Tissue Using Atomic Force Microscopy. Journal of Visualized Experiments (2011). https://doi.org:10.3791/2911