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olid stress and tissue stiffness affect tumour growth, invasion, metastasis and treatment. Unlike stiffness, which can be precisely mapped in tumours, the measurement of solid stresses is challenging. Here, we show that 2D spatial maps of the solid stress and the resulting elastic energy in excised or in situ tumours with arbitrary shapes and a wide range of sizes can be obtained via three distinct and quantitative techniques that rely on the measurement of tissue displacement after disruption of the confining structures. Application of these methods in models of primary tumours and metastasis revealed that (i) solid stress depends on both cancer cells and their microenvironments, (ii) solid stress increases with tumour size and (iii) mechanical confinement by the surrounding tissue substantially contributes to intratumoral solid stress. Further study of the genesis and consequences of solid stress, facilitated by the engineering principles presented here, may lead to new discoveries and therapies.

Increased tissue stiffness is a widely accepted and actively studied biomechanical property of fibrotic tumours and has been linked to several hallmarks of cancer, including growth, metabolism, invasion and metastasis 1,2,3,4,5,6,7 . However, the abnormal mechanics of tumours are not limited to tissue stiffening. We recently demonstrated that solid stress represents a new mechanopathology that is consistently elevated in mouse and human tumours 8,9 . Solid stress is distinct from interstitial fluid pressure, as the former is contained in—and transmitted by—solid and elastic elements of the extracellular matrix and cells rather than fluids 10 . Therefore, tumours are not only more rigid than many normal tissues, but cancer cells also produce and are exposed to these physical forces. Composed of a combination of tension and compression, these forces are significant in tumours, but negligible in most normal tissues.

Early evidence for the existence of solid stress in tumours came from the discovery that blood and lymphatic vessels are mechanically compressed 11,12,13 . This can contribute to hypoxia 9,14 ,promote tumour progression and decrease the efficacy of chemo-, radio- and immunotherapies 15 . In addition to these physiological consequences, forces can directly affect tumour biology: the exogenous application of solid stress in vivo can mechanically stimulate tumorigenic pathways, increasing β-catenin signalling in colon epithelia 16 , and the controlled application of compressive forces in vitro affects the growth8 of cancer cells and promotes their collective migration 17 . Strategies designed to reduce solid stress and decompress blood vessels by reducing levels of collagen and hyaluronic acid 14,18,19 have led to therapeutic approaches for enhancing the efficiency of conventional anticancer treatments and are currently being tested in clinical trials 20,21 .

Despite the important implications of solid stress and the immense potential for finding new mechanically activated pathways and targets, there are currently no high-resolution methods for quantifying solid stress in experimental or human tumours. Unlike stiffness, which can be measured using widely available multiscale techniques, measuring solid stress in biological tissues has proved challenging. Previous studies in our laboratory 8,9 , based on previous observations22,23 that arterial wall tissue relaxes if the contained forces are surgically released, demonstrated the presence of residual tissue stresses in tumours. However, this approach is based on a partial cut through a spherical model of the tumour, which makes the precise release of solid stress and the measurement of the ensuing deformation challenging. This method is also limited to bulk estimation of solid stress and is not applicable in situ. The optical-depth limitations of alternative imaging-based methods, such as fluorescent oil microdroplet injection 24 and single-molecule fluorescent force sensors 25 , restrict their use to cellular- and subcellular-scale force detection.

We have developed experimental and mathematical frameworks to provide 2D mapping of solid stress in tumours (planar-cut method), sensitive estimations of the solid stress in small tumours with small magnitudes of solid stress, as is the case for metastatic lesions (slicing method), and in situ quantification of solid stress in tumours, which retains the effects of the normal surrounding tissues (needle-biopsy method). All three methods are based on the concept of releasing the solid stress in a controlled way with a defined geometry and then quantifying the stress-induced deformation via high-resolution ultrasonography or optical microscopy. Given the specific topography of the stress relaxation and the geometric and material properties of the tumour, solid stress and discharged elastic energy are estimated using mathematical modelling. Applying these methods to multiple mouse cancer models in primary and metastatic settings has led to the following findings: (i) solid stress and elastic energy may differ between primary and metastatic settings, as they depend on both cancer-cell type and their microenvironment; (ii) tumours with higher elastic energy are not necessarily stiffer, and the stiffer tumours do not necessarily have higher elastic energy; (iii) solid stress increases with tumour size; and (iv) the normal tissue surrounding a tumour substantially contributes to intratumoral solid stress.


Nature Biomedical Engineering





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Biomedical Engineering