Cancer is a disease of dysregulated mechanics which alters cell behaviour, compromises tissue structure, and promotes tumour growth and metastasis. In the context of tumour progression, the most widely studied of biomechanical markers is matrix stiffness as tumour tissue is typically stiffer than healthy tissue. However, solid stress has recently been identified as another marker of tumour growth, with findings strongly suggesting that its role in cancer is distinct from that of stiffness. Owing to the relative infancy of the field which draws from diverse disciplines, a comprehensive knowledge of the relationships between solid stress, tumorigenesis, and metastasis is likely to provide new and valuable insights. In this review, we discuss the micro- and macro-scale biomechanical interactions that give rise to solid stresses, and also examine the techniques developed to quantify solid stress within the tumour environment. Moreover, by reviewing the effects of solid stress on tissues, cancer and stromal cells, and signalling pathways, we also detail its mode of action at each level of the cancer cascade.
Biomechanics: another facet of the tumour milieu
On the timeline of science, a century is but a blip. And yet, the astounding advances made in cancer research over the last 100 years have made oncology one of the most exciting fields in biomedicine. The history of cancer research suggests that, to date, the primary focus has been on the biochemical underpinnings of cancer. While the significance of such research is unequivocal, all living beings are also governed by principles extrinsic to biochemistry. The laws of physics have indeed been applied to the biological domain ever since the time of Aristotle who related biomechanics to phenomena as diverse as the motion of animals' bodies to peristalsis. Apart from playing a vital role in physiological functions, biomechanics are also at the heart of many pathologies including, but not limited to, cardiomyopathy , atherosclerosis , osteoarthritis , degenerative vascular disease , cataracts , and cancer .
In a biomechanics context, the tumour mechanical milieu differs markedly from that of healthy tissue. Indeed, one observes that the extracellular matrix (ECM) in the tumour microenvironment is typically stiffer than normal tissue [7–9]. This is especially true of breast and pancreatic tumours which, presenting a dense and cross-linked ECM, are characterised by a strong desmoplastic reaction . This increased stiffness has been shown to activate cell surface integrins which, in turn, up-regulates ECM stiffness and initiates a positive feedback loop which promotes the malignant phenotype in epithelial cells . Recently, results from our laboratory have also shown increased matrix stiffness to promote epithelial-to-mesenchymal (EMT) transition in cancer cells , and cancer cell stiffness has been strongly associated with invasiveness .
While studies investigating the effect of stiffness on tumour progression currently constitute the bulk of cancer biomechanics research, another mechanical cue, solid stress, has recently emerged as a key marker of solid tumour growth. Solid stress, which is negligible in most healthy tissues, develops within the tumour microenvironment as cancer and stromal cells proliferate, and ECM deposition increases [13–18]. Key to note is that while stiffness (E) is an inherent material property which describes resistance to deformation in response to a load, stress (σ) is a force per unit area. Despite these two markers being related through Hooke's law which states that stress is proportional to strain (ε), σ = E⋅ε, they are two distinct measures of tumour progression .
Defining the aetiology of solid stress
In contrast with the more commonly encountered interstitial fluid pressure, solid stress refers to the portion of tumour-induced loads which are borne by key solid structural components within the tumour microenvironment, namely collagen and hyaluronan. As illustrated in Figure 1, solid stresses are broadly composed of three components: tumour growth-induced stress, swelling stress, and externally applied stress . Tumour growth-induced stress arises due to the microstructural biomechanical interactions that are associated with cell growth, recruitment, and motility . As tumour and stromal cells proliferate and expand their local surroundings, they exert tensile stress on collagen fibres and increase the stiffness of their microenvironment due to a strain-stiffening effect . In this rigid environment, expansion is resisted and further cell proliferation results in compressive stresses which are largely borne by hyaluronan due to its compressive resistance . The rapid proliferation of cells also results in the formation of a peritumoural tensile-loaded collagen-rich capsule [20,21]. Apart from mitogenic activity, growth-induced stresses also accumulate due to cytoskeletal processes such as cancer-associated fibroblasts (CAFs) contracting and stressing the collagen-rich tumour ECM [22,23]. This ECM remodelling process has recently been accurately characterised in 3D matrices by our research group through a technique combining high-resolution microscopy and biophysical and modelling approaches . Cell–ECM interactions that occur during cancer and stromal cell locomotion are also thought to contribute to solid stresses . Strong evidence supporting the role of cancer and stromal cells in solid stress was provided by Stylianopoulos et al.  who found that depletion of both types of cells led to a reduction in solid stress.
Diverse components of solid stress.
Swelling stress, the second class of solid stresses, is believed to arise as a result of microstructural interactions between collagen and hyaluronan . High fractions of the latter, typical of breast and pancreatic cancers, generate a high negative charge density due to the many negative charges along each hyaluronan chain . These negative charges have a twofold effect: they promote the immobilisation of large volumes of interstitial fluid and also cause electrostatic repulsion — collectively generating a swelling effect. This swelling stretches and stiffens surrounding collagen fibres which become loaded in tension. Owing to the increased stiffness, additional swelling is resisted and has the end effect of compressing the hyaluronan. These theoretical modes of action were confirmed experimentally by Voutouri et al.  who found that reduction in hyaluronan decreases tumour swelling to negligible levels, while collagen reduction facilitated increased swelling. Furthermore, decreasing or degrading collagen has been shown to reduce solid stress [17,29].
Externally applied stress acts at the tissue level and is a result of the force balance between the tumour and the surrounding host tissue [17,30]. Owing to the mechanical resistance provided by the host tissue, tumour growth generates a stress in the contacting host which is a function of its deformation and stiffness. As tumours grow under quasi-static equilibrium, the host tissue balances this load by exerting an equal and opposite force on the tumour. While omitting the effect of matrix-modifying agents such as matrix metalloproteinases, mathematical models have shown that for a growing tumour to overcome the growth-inhibiting effect of solid stress  and the physical resistance of the surrounding tissue, the stiffness of the solid tumour ought to exceed that of the host tissue by a factor of at least 1.5, thus possibly shielding tumour cells from increasing stress and conferring a competitive advantage to the tumour . This finding is consistent with the well-known fact that in vivo, solid tumour tissue is typically stiffer than host tissue . While externally applied stress is a passive source of stress when compared with growth-induced and swelling stress, its significance is not to be underestimated — it has been calculated that its contribution to the total solid stress state within a tumour exceeds 70% .
Diversity in approaches to quantifying solid stress
Despite the existence of a vast range of tools that measure tissue stiffness, techniques that enable researchers to quantify solid stress are limited. Because of this, many early studies used computational modelling to simulate the growth of tumours and calculate the resulting stresses. While subjectivity and a lack of standards have historically dogged the field, these models do generally concur that solid stresses are compressive in all directions within the tumour itself, yet, peritumourally, stresses are tensile in the circumferential orientation and compressive in the radial direction [33–35].
In 2003, Gordon et al.  sought to experimentally measure the stress induced by a growing multicellular brain tumour spheroid (MTS) in vitro. Growing the MTS in microbead-laden Matrigel, the authors imaged the tumour growth-induced displacement field using multiparticle tracking methods. By determining the hydrostatic pressure required to produce a displacement field which matched that caused by the growing MTS, they estimated the pressure in the MTS to be 50 Pa by the fourth day of growth.
Seeking to develop the first ex vivo method of solid stress measurement, Stylianopoulos et al.  drew inspiration from established protocols which are used to characterise growth-induced solid stress in brain, cardiac, and arterial tissues [37–39]. Slicing through 80% of the thickness of excised tumours, they report the gradual formation of a measurable opening at the location of the cut. Knowledge of the tumour material properties enabled the authors to subsequently translate the deformations into stresses (0.37–19 kPa). The concurrent bulging at the centre of the tumour (indicating the release of stored compressive strain energy in hyaluronan) and retraction of the periphery (due to the release of tensile strain energy stored in the peritumoural collagen capsule) correlates with the findings from earlier computational models [17,40].
The next evolution of solid stress measurement techniques came from Nia et al.  who refined the displacement-based measurement approach by incorporating high-resolution imaging into three distinct stress measurement methods. In the first method, excised murine tumours were cut in half and allowed to deform at the cut plane. The deformation normal to this plane was subsequently mapped using high-resolution ultrasound and converted into stress through a mathematical model (0.21 kPa in brain tumours to 7 kPa in pancreatic tumours). For smaller tumours, such as micro- and macro-metastases, a second more sensitive technique was developed whereby tumours were excised and cut into 100–500 µm thin slices. Owing to their thinness, the slices bend and buckle as they release stored stress and allow the measurement of small solid stresses using high-resolution ultrasound. The third and final method seeks to also measure externally applied stresses that are otherwise released upon tumour excision. Strikingly, Nia et al. achieved this by performing a core biopsy in a murine brain tumour still surrounded by the brain and cranium via a cranial window. The stress-relaxing deformations of both the biopsy void and core were subsequently measured and translated into stresses. Notably, the maximum stress measured 0.1 kPa, as compared with 0.02 kPa for biopsies obtained ex vivo, thus revealing a fivefold increase and highlighting the significant role played by the host tissue mechanical resistance.
In a paradigm shift for solid stress measurement, Nieskoski et al.  successively developed a piezoelectric transducer-based technique which forgoes displacement data. To circumvent the inability of a piezoelectric transducer to discriminate between fluid and solid stresses, the authors added a retractable sheath to their transducer that enabled the individual measurement of total tissue stress (TTS) and interstitial fluid pressure (IFP) in pancreatic tumours. Reasoning that TTS is equal to the arithmetic sum of IFP and solid stress, their measurements of TTS and IFP allowed the indirect quantification of solid stress (6.6 kPa — in remarkably good agreement with Nia et al. ).
Effects of solid stress on the tissue level
Solid stress has implications on the whole tissue level. Firstly, as tumour growth exerts compressive forces on the surrounding organ, it would seem intuitive that this may result in organ function impairment. Yet surprisingly, while the detrimental effects of tumour growth on spinal cord compression have been well described [42–45], much remains to be uncovered in regard to other organs.
Another significant effect of solid stress at the tissue level is the compression of intratumoural blood vessels [32,46]. This occurs when stromal hyaluronan is stressed in compression beyond its maximum strain energy capacity and any additional compressive stress is transmitted to neighbouring structurally weak tumour vessels . Consequently, regions of the tumour may experience reduced perfusion, a condition which, in turn, promotes hypoxia, poor immunosurveillance, and reduced drug delivery [32,47,48]. To varying extents, these factors are all associated with enhanced tumour progression [32,47,48]. As such, in recent years, preclinical studies have demonstrated how targeting solid stress development may improve anti-cancer drug efficacy. Indeed, Zhang et al.  recently demonstrated that the reduction in solid stress in pancreatic tumours led to improved delivery of nanomedicine. In another study which highlights the therapeutic potential of solid stress alleviation, Chauhan et al.  analysed the inhibition of angiotensin signalling. Focussing on breast and pancreatic tumours, the authors observed both lower levels of CAFs and their pro-fibrotic signalling, collectively leading to less dense matrices and reduced solid stress . As a result, tumour blood vessels were decompressed, and both oxygenation and chemotherapeutic drug delivery were improved .
Upstream of angiotensin signalling is the transforming growth factor-β (TGF-β) pathway. It is thought that activation of exogenous ECM-bound latent TGF-β is directly regulated by intracellular and extracellular tensions [50–53]. This process has been linked to fibroblast activation [52,54], tumour progression, and metastasis [55–57], as well as collagen  and hyaluronan production . Our research group has shown that the ability of pancreatic stellate cells (PSCs) to activate latent TGF-β may be suppressed through the administration of all-trans retinoic acid (ATRA) . We also determined that ATRA treatment in hepatic stellate cells down-regulates their synthesis of collagen, a key component of solid stress . This finding therefore potentially opens up new avenues for drugs that modulate the pro-tumorigenic role of solid stress.
Effects of solid stress on the cellular level
Investigations on the effects of solid stress are also being extended to the cellular level largely through the use of tumour spheroids embedded in gel matrices [31,62,63]. In their seminal study, Helmlinger et al.  employed a colon cancer tumour spheroid model to demonstrate that compression led to inhibition of spheroid growth and decreased cell proliferation. More recently, similar findings were reported by Cheng et al.  and Delarue et al.  in their independent studies which focussed on compression of tumour spheroids. As Figure 2 illustrates, the studies propose that the observed reduced cell proliferation is regulated by the intrinsic mitotic apoptosis pathway  and the cell cycle inhibitor p27kip1 .
Compression leads to reduced tumour spheroid growth due to apoptosis induction and reduced cell proliferation.
Along with cancer cells, solid stress may also influence the behaviour of other cells pertaining to the tumour microenvironment. A study by Fernández-Sánchez et al.  investigated the effects of compression on healthy mouse colon cells through the implantation of magnets and magnetic liposomes. They demonstrated how the applied compressive force led to tumorigenic signalling in healthy cells. Kalli et al.  also found that compression led to increased pancreatic fibroblast activation, resulting in a desmoplastic response. They observed higher levels of expression of fibrosis-associated proteins such as collagen I, fibronectin I, and periostin. Similar to results from our laboratory which indicate the existence of a positive mechanical feedback loop between increased stromal stiffness and PSC activation , this may suggest that a positive feedback loop also exists between solid stress in tumours and ECM production by fibroblasts. The relation (or lack thereof) between the two mechanical quantities, however, remains untested.
Interestingly, Kalli et al.  also highlight the pro-migratory role of solid stress by noting that secretion of growth differentiation factor 15 was induced in fibroblasts  following compression. This was shown to be crucial for triggering migration of pancreatic cancer cells when co-cultured with fibroblasts . The influence of solid stress on tumour cell migration was also investigated by Tse et al.  who assessed the response of breast cancer cell monolayers to compression. They found that as compression was increased, aggressive cell lines became increasingly migratory, invasive, and exhibited increased cytoskeletal rearrangement. The authors also observed that peripheral cells assumed a leader cell phenotype, characterised by directional migration and filopodia formation.
An alternative hypothesis is that cancer cell migration and invasion is promoted by mechanotransduction of tension at focal adhesions. The application of tensile solid stress to focal adhesions is, in fact, likely to tie in with recent research from our group which implicates stretching of the R8 domain in the talin molecule (a key component of focal adhesions) in the triggering of the detachment of deleted in liver cancer 1 (DLC1) [68,69]. Since deactivation of DLC1 is linked to increased cancer cell migration and invasion , solid stress may thus play an additional and direct role in tumour progression and phenotypic behaviour.
This behavioural dependency on the stress state at focal adhesions may, in future, create new opportunities wherein cellular responses are regulated by tailoring the physical environment with which cells interact. Our results demonstrate that in addition to matrix rigidity, cells also sense the length of ligands that tether them to their matrix and respond accordingly . Substrates engineered to incorporate longer adhesive tethers may thus be used as a platform to probe cells in a low stress environment as these require greater stretching before being able to bear tensile loads, with the reverse being true for shorter tethers. This would have profound implications for organoid/tissue engineering as well the latest endeavours to mimic human organs for drug design (organ-on-a-chip).
Effects of solid stress on the molecular level
Given the evidence on the ability of solid stress to regulate cell behaviour, it is evident that solid stress plays a central role in subcellular signalling pathways. Indeed, Bailey et al.  determined that compression activates the sonic hedgehog (SHH) pathway in pancreatic stromal cells, in turn, promoting a desmoplastic reaction via enhanced proliferation and activation of fibroblasts. Decreased solid stress, indicated by increased vessel patency, has also been linked to SHH inhibition by Stylianopoulos et al. . In their concluding remarks, Mpekris et al.  go one step further and propose that SHH inhibition represents an attractive therapeutic strategy to alleviate solid stress as it involves direct targeting of fibroblasts rather than downstream ECM proteins.
While the body of work regarding the subcellular effects of solid stress in cancer cells remains in its infancy, much can be learnt from its known effects on other non-cancerous cell lines. Case in point, recent work by Benham-Pyle et al.  has shown that increased matrix tension leads to increased nuclear localisation of yes-associated protein (YAP) in quiescent kidney epithelial cells. Together with TEAD transcription factors, this can lead to the activation of target genes implicated in proliferation (fibroblast growth factor and Ki67) and apoptosis evasion (Birc5) . Moreover, the authors concluded that stretch-induced YAP activation in quiescent cells prompted their re-entry into cell cycling and up-regulated proliferation . Nuclear translocation of YAP homologue was also observed in Drosophila cells under stretch . Hinting at its possible relevance to tumour-induced solid stresses, YAP signalling has recently been linked to the intracellular response to tumour stiffness as well as tumour progression in humans [10,75–77]. Within this context, our laboratory recently showed that nuclear translocation and activation of YAP following mechanical activation is regulated by focal adhesion kinase (FAK) . However, the role of FAK in mechanotransduction pathways involving solid stress remains unknown.
An additional pathway frequently associated with cancer progression is the Wnt/β-catenin pathway [79–83] and Fernández-Sánchez et al.  elucidated how solid stress is likely one of its regulators. In their study, solid stress was shown to increase phosphorylation of Ret kinase, consequently inactivating glycogen synthase kinase-3β (a component of the β-catenin destruction complex) and phosphorylating β-catenin at Y564. The end effect was elevated levels of free β-catenin which translocated to the nucleus, resulting in up to a threefold increase in expression of its tumour-promoting target genes: Myc, Zeb1, and Axin2 . In another study, authors also observed how stretching led to β-catenin-induced G1-S cell cycle transition of quiescent cells . This was attributed to greater transcriptional activation of β-catenin target genes such as Cyclin D1, Aurora A, and Cdc 25 . While concurring on strain-induced phosphorylation of β-catenin Y564, further research by the same group associated this with Src tyrosine kinase rather than Ret kinase . This may be explained by their use of stretch rather than compression, as was used in Fernández-Sánchez et al. .
Rho/ROCK signalling, typically implicated in the pro-motility and mesenchymal response of both healthy and cancer cells to matrix stiffness, may also be a downstream effect of solid stress [67,76,85–87]. Evidence for this was provided by Boyle et al.  who showed how compression of HEK-293T cells at both the cellular and tissue levels led to increased Rho/ROCK signalling, actomyosin contractility, proliferation, and a shift towards a more mesenchymal phenotype.
Another potent, if controversial, process in the cancer cascade is EMT. The associated increase in cancer cell motility and invasion is, among other soluble factors, regulated by interleukin 6 (IL-6) signalling . This pathway has, for the first time, recently been linked to solid stress . Apart from significantly increasing IL-6-mediated EMT in clear cell renal cell carcinoma tissues, solid stress was also found to drive a positive feedback mechanism that enhanced EMT and tumour progression via the Akt/GSK-3β/β-catenin signalling pathway .
Finally, it should be noted that protein-encoding genes are not the only downstream targets of transcriptional activation induced by solid stress. Kim et al.  found that expression of microRNA was also altered by compression of breast cancer cells and cancer-associated fibroblasts. Tellingly, they found that over a quarter of up-regulated microRNAs were associated with processes such as apoptosis evasion and proliferation. They also noted that miR-4769-5p and miR-4446-3p, down-regulators of tumour suppression genes, were heavily up-regulated in both breast cancer cells and cancer-associated fibroblasts — thus presenting potential as potent therapeutic targets .
Conclusion and future perspectives
Despite its very recent emergence, it is already evident that solid stress plays a key regulatory role at all levels of the cancer cascade. Owing to its novelty and distinct mode of action, solid stress may potentially contribute much to the development of new therapeutic targets, and as such, beckons for increased research into its effects on tumour growth and invasion.
The importance of accurate and relevant solid stress quantification cannot be understated as its results provide critical context for successive experimental work. In this regard, computational models which characterise tumour-induced stresses are of great value as they circumvent many practical obstacles associated with the development of physical tools. Steps must, however, be taken to avoid user judgement tainting the predictive power of such models. In particular, the boundless range of constitutive relations used to describe the mechanical properties of healthy and tumour tissue necessitates the standardisation of mechanical testing methods. In addition, experimental validation of these computational findings ought to become less of a rarity. With regard to experimental methods for solid stress quantification, it is clear that their current scarcity may be explained by the infancy of the field. As things stand, measurement of solid stress is a fragmented endeavour — some studies omit entire components such as externally applied stress, while others only focus on one type of stress (compression) and ignore others (tension). Studies that set out to paint a complete picture should therefore become a priority.
Regarding the analysis of the effects of solid stress on tissues and cells, most studies only investigate one type of stress, typically compression. However, both computational models and physical methods have shown the tumour microenvironment to be characterised by a complex and heterogeneous stress state that involves both tension and compression [13,17]. Different types of stress have already been shown to result in different responses, both in a tumour context [64,84], and not . Accordingly, studies which investigate the effects of solid stress need to mimic the complex and multi-component in vivo stress state with greater fidelity. The same reasoning may also be extended to studies that analyse cancer cells or CAFs in isolation. Research has demonstrated how CAFs and cancer cells interact synergistically, ultimately promoting tumour progression [56,65]. While studies on single cell lines are of undeniable value, these findings highlight the need for research on the effect of solid stress on the behaviour of CAFs and cancer cells in co-culture and vice versa.
Mechanical interactions between cells, ECM, and tissues, at both the micro- and macro-scale, are responsible for the accumulation of solid stress.
A diverse range of characterisation techniques has revealed the presence of a heterogeneous and anisotropic stress state within the tumour environment.
Solid stress is directly implicated in all levels of the cancer cascade, be it through tissue deformation, regulation of cell behaviour (proliferation, phenotype, and invasiveness), and mediation of signalling pathways (SHH, YAP, β-catenin, Rho/ROCK, and IL-6).
all-trans retinoic acid
deleted in liver cancer 1
epithelial to mesenchymal
focal adhesion kinase
interstitial fluid pressure
multicellular tumour spheroid
pancreatic stellate cell
transforming growth factor-β
total tissue stress
A.V. planned, wrote the original draft, and reviewed and edited the article. E.M.E. wrote the original draft. A.d.R.H. supervised, reviewed, and edited the article.
This work was funded by the European Research Council grant ERC 282051 (ForceRegulation). The work was partially funded by the Endeavour Scholarship Scheme (Malta). Scholarships are part-financed by the European Union — European Social Fund (ESF) — Operational Programme II — Cohesion Policy 2014–2020 ‘Investing in human capital to create more opportunities and promote the well-being of society’.
The Authors declare that there are no competing interests associated with the manuscript.