Solid stress inhibits the growth of multicellular tumor spheroids

Microencapsulation of small intestinal neuroendocrine neoplasm cells for tumor model studies

Basic cancer research is dependent on reliable in vitro and in vivo tumor models. The serotonin (5-HT) producing small intestinal neuroendocrine tumor cell line KRJ-1 has been used in in vitro proliferation and secretion studies, but its use in in vivo models has been hampered by problems related to the xeno-barrier and tumor formation. This may be overcome by the encapsulation of tumor cells into alginate microspheres, which can function as bioreactors and protect against the host immune system. We used alginate encapsulation of KRJ-1 cells to achieve long-term functionality, growth and survival. Different conditions, including capsule size, variations in M/G content, gelling ions (Ca(2+) /Ba(2+)) and microcapsule core properties, and variations in KRJ-1 cell condition (single cells/spheroids) were tested. Viability and cell growth was evaluated with MTT, and confocal laser scanner microscopy combined with LIVE/DEAD viability stains. 5-HT secretion was measured to determine functionality. Under all conditions, single cell encapsulation proved unfavorable due to gradual cell death, while encapsulation of aggregates/spheroids resulted in surviving, functional bioreactors. The most ideal spheroids for encapsulation were 200-350 μm. Long-term survival (>30 days) was seen with solid Ca(2+) /Ba(2+) microbeads and hollow microcapsules. Basal 5-HT secretion was increased (sixfold) after hollow microcapsule encapsulation, while Ca(2+) /Ba(2+) microbeads was associated with normal basal secretion and responsiveness to cAMP/PKA activation. In conclusion, encapsulation of KRJ-1 cells into hollow microcapsules produces a bioreactor with a high constitutively activate basal 5-HT secretion, while Ca(2+) /Ba(2+) microbeads provide a more stable bioreactor similar to non-encapsulated cells. Alginate microspheres technology can thus be used to tailor different functional bioreactors for both in vitro and in vivo studies.

Diversity of dynamics and morphologies of invasive solid tumors

Complex tumor-host interactions can significantly affect the growth dynamics and morphologies of progressing neoplasms. The growth of a confined solid tumor induces mechanical pressure and deformation of the surrounding microenvironment, which in turn influences tumor growth. In this paper, we generalize a recently developed cellular automaton model for invasive tumor growth in heterogeneous microenvironments [Y. Jiao and S. Torquato, PLoS Comput. Biol.7, e1002314 (2011)] by incorporating the effects of pressure. Specifically, we explicitly model the pressure exerted on the growing tumor due to the deformation of the microenvironment and its effect on the local tumor-host interface instability. Both noninvasive-proliferative growth and invasive growth with individual cells that detach themselves from the primary tumor and migrate into the surrounding microenvironment are investigated. We find that while noninvasive tumors growing in "soft" homogeneous microenvironments develop almost isotropic shapes, both high pressure and host heterogeneity can strongly enhance malignant behavior, leading to finger-like protrusions of the tumor surface. Moreover, we show that individual invasive cells of an invasive tumor degrade the local extracellular matrix at the tumor-host interface, which diminishes the fingering growth of the primary tumor. The implications of our results for cancer diagnosis, prognosis and therapy are discussed.

Pannexin1 drives multicellular aggregate compaction via a signaling cascade that remodels the actin cytoskeleton

Pannexin 1 (Panx1) is a novel gap junction protein shown to have tumor-suppressive properties. To model its in vivo role in the intratumor biomechanical environment, we investigated whether Panx1 channels modulate the dynamic assembly of multicellular C6 glioma aggregates. Treatment with carbenoxolone and probenecid, which directly and specifically block Panx1 channels, respectively, showed that Panx1 is involved in accelerating aggregate assembly. Experiments further showed that exogenous ATP can reverse the inhibitive effects of carbenoxolone and that aggregate compaction is sensitive to the purinergic antagonist suramin. With a close examination of the F-actin microfilament network, these findings show that Panx1 channels act as conduits for ATP release that stimulate the P(2)X(7) purinergic receptor pathway, in turn up-regulating actomyosin function. Using a unique three-dimensional scaffold-free method to quantify multicellular interactions, this study shows that Panx1 is intimately involved in regulating intercellular biomechanical interactions pivotal in the progression of cancer.

Mechanical compression drives cancer cells toward invasive phenotype

Uncontrolled growth in a confined space generates mechanical compressive stress within tumors, but little is known about how such stress affects tumor cell behavior. Here we show that compressive stress stimulates migration of mammary carcinoma cells. The enhanced migration is accomplished by a subset of "leader cells" that extend filopodia at the leading edge of the cell sheet. Formation of these leader cells is dependent on cell microorganization and is enhanced by compressive stress. Accompanied by fibronectin deposition and stronger cell-matrix adhesion, the transition to leader-cell phenotype results in stabilization of persistent actomyosin-independent cell extensions and coordinated migration. Our results suggest that compressive stress accumulated during tumor growth can enable coordinated migration of cancer cells by stimulating formation of leader cells and enhancing cell-substrate adhesion. This novel mechanism represents a potential target for the prevention of cancer cell migration and invasion.

Numerical simulation of a thermodynamically consistent four-species tumor growth model

In this paper, we develop a thermodynamically consistent four-species model of tumor growth on the basis of the continuum theory of mixtures. Unique to this model is the incorporation of nutrient within the mixture as opposed to being modeled with an auxiliary reaction-diffusion equation. The formulation involves systems of highly nonlinear partial differential equations of surface effects through diffuse-interface models. A mixed finite element spatial discretization is developed and implemented to provide numerical results demonstrating the range of solutions this model can produce. A time-stepping algorithm is then presented for this system, which is shown to be first order accurate and energy gradient stable. The results of an array of numerical experiments are presented, which demonstrate a wide range of solutions produced by various choices of model parameters.

Live cell division dynamics monitoring in 3D large spheroid tumor models using light sheet microscopy

Background

Multicellular tumor spheroids are models of increasing interest for cancer and cell biology studies. They allow considering cellular interactions in exploring cell cycle and cell division mechanisms. However, 3D imaging of cell division in living spheroids is technically challenging and has never been reported.

Results

Here, we report a major breakthrough based on the engineering of multicellular tumor spheroids expressing an histone H2B fluorescent nuclear reporter protein, and specifically designed sample holders to monitor live cell division dynamics in 3D large spheroids using an home-made selective-plane illumination microscope.

Conclusions

As illustrated using the antimitotic drug, paclitaxel, this technological advance paves the way for studies of the dynamics of cell divion processes in 3D and more generally for the investigation of tumor cell population biology in integrated system as the spheroid model.

TNF-α induced secretion of HMGB1 from non-immune canine mammary epithelial cells (MTH53A)

BACKGROUND

Mammary neoplasias are one of the most frequent and spontaneously occurring malignancies in dogs and humans. Due to the similar anatomy of the mammary gland in both species, the dog has become an important animal model for this cancer entity. In human breast carcinomas, the overexpression of a protein named high-mobility group box 1 (HMGB1) was reported. Cells of the immune system were described to release HMGB1 actively exerting cytokine function. Thereby it is involved in the immune system activation, tissue repair, and cell migration. Passive release of HMGB1 by necrotic cells at sites of tissue damage or in necrotic hypoxic regions of tumors induces cellular responses e.g. release of proinflammatory cytokines leading to elevated inflammatory response and neo-vascularization of necrotic tumor areas. Herein we investigated if a time-dependent stimulation with the separately applied proinflammatory cytokines TNF-α and IFN-γ can cause secretion of HMGB1 in a non-immune related HMGB1-non-secreting epithelial canine mammary cell line (MTH53A) derived from non-neoplastic tissue.

METHODS

The canine cell line was transfected with recombinant HMGB1 bicistronic expression vectors and stimulated after transfection with the respective cytokine independently for 6, 24 and 48 h. HMGB1 protein detection was performed by Western blot analysis and quantified a by enzyme-linked immunosorbent assay. Live cell laser scanning multiphoton microscopy of MTH53A cells expressing a HMGB1-GFP fusion protein was performed in order to examine, if secretion of HMGB1 under cytokine stimulating conditions is also visible by fluorescence imaging.

RESULTS

The observed HMGB1 release kinetics showed a clearly time-dependent manner with a peak release 24h after TNF-α stimulation, while stimulation with IFN-γ had only small effects on the HMGB1 release. Multiphoton HMGB1 live cell microscopy showed diffuse cell membrane structure changes 29 h after cytokine-stimulation but no clear secretion of HMGB1-GFP after TNF-α stimulation was visible.

CONCLUSION

Our results demonstrate that non-immune HMGB1-non-secreting cells of epithelial origin derived from mammary non-neoplastic tissue can be induced to release HMGB1 by single cytokine application. This indicates that tumor and surrounding tissue can be stimulated by tumor present inflammatory and necrotic cytokines to release HMGB1 acting as neo-vascularizing factor thus promoting tumor growth.

Down-regulation of DNA mismatch repair enhances initiation and growth of neuroblastoma and brain tumour multicellular spheroids

Multicellular tumour spheroid (MCTS) cultures are excellent model systems for simulating the development and microenvironmental conditions of in vivo tumour growth. Many documented cell lines can generate differentiated MCTS when cultured in suspension or in a non-adhesive environment. While physiological and biochemical properties of MCTS have been extensively characterized, insight into the events and conditions responsible for initiation of these structures is lacking. MCTS are formed by only a small subpopulation of cells during surface-associated growth but the processes responsible for this differentiation are poorly understood and have not been previously studied experimentally. Analysis of gene expression within spheroids has provided clues but to date it is not known if the observed differences are a cause or consequence of MCTS growth. One mechanism linked to tumourigenesis in a number of cancers is genetic instability arising from impaired DNA mismatch repair (MMR). This study aimed to determine the role of MMR in MCTS initiation and development. Using surface-associated N2a and CHLA-02-ATRT culture systems we have investigated the impact of impaired MMR on MCTS growth. Analysis of the DNA MMR genes MLH1 and PMS2 revealed both to be significantly down-regulated at the mRNA level compared with non-spheroid-forming cells. By using small interfering RNA (siRNA) against these genes we show that silencing of MLH1 and PMS2 enhances both MCTS initiation and subsequent expansion. This effect was prolonged over several passages following siRNA transfection. Down-regulation of DNA MMR can contribute to tumour initiation and progression in N2a and CHLA-02-ATRT MCTS models. Studies of surface-associated MCTS differentiation may have broader applications in studying events in the initiation of cancer foci.

Stress clamp experiments on multicellular tumor spheroids

The precise role of the microenvironment on tumor growth is poorly understood. Whereas the tumor is in constant competition with the surrounding tissue, little is known about the mechanics of this interaction. Using a novel experimental procedure, we study quantitatively the effect of an applied mechanical stress on the long-term growth of a spheroid cell aggregate. We observe that a stress of 10 kPa is sufficient to drastically reduce growth by inhibition of cell proliferation mainly in the core of the spheroid. We compare the results to a simple numerical model developed to describe the role of mechanics in cancer progression.

Morphological changes in early melanoma development: influence of nutrients, growth inhibitors and cell-adhesion mechanisms

Current diagnostic methods for skin cancers are based on some morphological characteristics of the pigmented skin lesions, including the geometry of their contour. The aim of this article is to model the early growth of melanoma accounting for the biomechanical characteristics of the tumor micro-environment, and evaluating their influence on the tumor morphology and its evolution. The spatial distribution of tumor cells and diffusing molecules are explicitly described in a three-dimensional multiphase model, which incorporates general cell-to-cell mechanical interactions, a dependence of cell proliferation on contact inhibition, as well as a local diffusion of nutrients and inhibiting molecules. A two-dimensional model is derived in a lubrication limit accounting for the thin geometry of the epidermis. First, the dynamical and spatial properties of planar and circular tumor fronts are studied, with both numerical and analytical techniques. A WKB method is then developed in order to analyze the solution of the governing partial differential equations and to derive the threshold conditions for a contour instability of the growing tumor. A control parameter and a critical wavelength are identified, showing that high cell proliferation, high cell adhesion, large tumor radius and slow tumor growth correlate with the occurrence of a contour instability. Finally, comparing the theoretical results with a large amount of clinical data we show that our predictions describe accurately both the morphology of melanoma observed in vivo and its variations with the tumor growth rate. This study represents a fundamental step to understand more complex microstructural patterns observed during skin tumor growth. Its results have important implications for the improvement of the diagnostic methods for melanoma, possibly driving progress towards a personalized screening.

Selection of brain metastasis-initiating breast cancer cells determined by growth on hard agar

An approach that facilitates rapid isolation and characterization of tumor cells with enhanced metastatic potential is highly desirable. Here, we demonstrate that plating GI-101A human breast cancer cells on hard (0.9%) agar selects for the subpopulation of metastasis-initiating cells. The agar-selected cells, designated GI-AGR, were homogeneous for CD44(+) and CD133(+) and five times more invasive than the parental GI-101A cells. Moreover, mice injected with GI-AGR cells had significantly more experimental brain metastases and shorter overall survival than did mice injected with GI-101A cells. Comparative gene expression analysis revealed that GI-AGR cells were markedly distinct from the parental cells but shared an overlapping pattern of gene expression with the GI-101A subline GI-BRN, which was generated by repeated in vivo recycling of GI-101A cells in an experimental brain metastasis model. Data mining on 216 genes shared between GI-AGR and GI-BRN breast cancer cells suggested that the molecular phenotype of these cells is consistent with that of cancer stem cells and the aggressive basal subtype of breast cancer. Collectively, these results demonstrate that analysis of cell growth in a hard agar assay is a powerful tool for selecting metastasis-initiating cells in a heterogeneous population of breast cancer cells, and that such selected cells have properties similar to those of tumor cells that are selected based on their potential to form metastases in mice.

The role of the microenvironment in tumor growth and invasion

Mathematical modeling and computational analysis are essential for understanding the dynamics of the complex gene networks that control normal development and homeostasis, and can help to understand how circumvention of that control leads to abnormal outcomes such as cancer. Our objectives here are to discuss the different mechanisms by which the local biochemical and mechanical microenvironment, which is comprised of various signaling molecules, cell types and the extracellular matrix (ECM), affects the progression of potentially-cancerous cells, and to present new results on two aspects of these effects. We first deal with the major processes involved in the progression from a normal cell to a cancerous cell at a level accessible to a general scientific readership, and we then outline a number of mathematical and computational issues that arise in cancer modeling. In Section 2 we present results from a model that deals with the effects of the mechanical properties of the environment on tumor growth, and in Section 3 we report results from a model of the signaling pathways and the tumor microenvironment (TME), and how their interactions affect the development of breast cancer. The results emphasize anew the complexities of the interactions within the TME and their effect on tumor growth, and show that tumor progression is not solely determined by the presence of a clone of mutated immortal cells, but rather that it can be 'community-controlled'.

Fluid shear stress regulates the invasive potential of glioma cells via modulation of migratory activity and matrix metalloproteinase expression

Background

Glioma cells are exposed to elevated interstitial fluid flow during the onset of angiogenesis, at the tumor periphery while invading normal parenchyma, within white matter tracts, and during vascular normalization therapy. Glioma cell lines that have been exposed to fluid flow forces in vivo have much lower invasive potentials than in vitro cell motility assays without flow would indicate.

Methodology/Principal Findings

A 3D Modified Boyden chamber (Darcy flow through collagen/cell suspension) model was designed to mimic the fluid dynamic microenvironment to study the effects of fluid shear stress on the migratory activity of glioma cells. Novel methods for gel compaction and isolation of chemotactic migration from flow stimulation were utilized for three glioma cell lines: U87, CNS-1, and U251. All physiologic levels of fluid shear stress suppressed the migratory activity of U87 and CNS-1 cell lines. U251 motility remained unaltered within the 3D interstitial flow model. Matrix Metalloproteinase (MMP) inhibition experiments and assays demonstrated that the glioma cells depended on MMP activity to invade, and suppression in motility correlated with downregulation of MMP-1 and MMP-2 levels. This was confirmed by RT-PCR and with the aid of MMP-1 and MMP-2 shRNA constructs.

Conclusions/Significance

Fluid shear stress in the tumor microenvironment may explain reduced glioma invasion through modulation of cell motility and MMP levels. The flow-induced migration trends were consistent with reported invasive potentials of implanted gliomas. The models developed for this study imply that flow-modulated motility involves mechanotransduction of fluid shear stress affecting MMP activation and expression. These models should be useful for the continued study of interstitial flow effects on processes that affect tumor progression.

Contour instabilities in early tumor growth models

Recent tumor growth models are often based on the multiphase mixture framework. Using bifurcation theory techniques, we show that such models can give contour instabilities. Restricting to a simplified but realistic version of such models, with an elastic cell-to-cell interaction and a growth rate dependent on diffusing nutrients, we prove that the tumor cell concentration at the border acts as a control parameter inducing a bifurcation with loss of the circular symmetry. We show that the finite wavelength at threshold has the size of the proliferating peritumoral zone. We apply our predictions to melanoma growth since contour instabilities are crucial for early diagnosis. Given the generality of the equations, other relevant applications can be envisaged for solving problems of tissue growth and remodeling.

Perspectives on biological growth and remodeling

The continuum mechanical treatment of biological growth and remodeling has attracted considerable attention over the past fifteen years. Many aspects of these problems are now well-understood, yet there remain areas in need of significant development from the standpoint of experiments, theory, and computation. In this perspective paper we review the state of the field and highlight open questions, challenges, and avenues for further development.

Investigating the steady state of multicellular spheroids by revisiting the two-fluid model

In this paper we examine the steady state of tumour spheroids considering a structure in which the central necrotic region contains an inner liquid core surrounded by dead cells that keep some mechanical integrity. This partition is a consequence of assuming that a finite delay is required for the degradation of dead cells into liquid. The phenomenological assumption of constant local volume fraction of cells is also made. The above structure is coupled with a simple mechanical model that views the cell component as a viscous fluid and the extracellular liquid as an inviscid fluid. By imposing the continuity of the normal stress throughout the whole spheroid, we show that a steady state can exist only if the forces on cells at the outer boundary (provided e.g. by a surface tension) are intense enough, and in such a case we can compute the stationary radius. By giving reasonable values to the parameters, the model predicts that the stationary radius decreases with the external oxygen concentration, as expected from experimental observations.

Establishing diagnostic features for identifying the mucosa and submucosa of normal and cancerous gastric tissues by multiphoton microscopy

BACKGROUND

Establishing diagnostic features is essential and significant for developing multiphoton endoscopy to make an early diagnosis of gastric cancer at the cellular level. Until now, these diagnostic features have not been clearly described and understood.

DESIGN

Study of diagnostic features based on multiphoton microscopy (MPM).

OBJECTIVE

Establishing diagnostic features to identify the mucosa and submucosa of human normal and cancerous gastric tissues by investigating their multiphoton microscopic images.

SETTING

Fujian Normal University and Fujian Provincial Tumor Hospital.

PATIENTS

Ten pairs of normal and cancerous specimens were obtained from 10 patients (ages 51-68 years) undergoing radical gastrectomy.

INTERVENTIONS

MPM was performed on specimens.

MAIN OUTCOME MEASUREMENTS

Establishment of diagnostic features.

RESULTS

MPM has the ability to exhibit not only the mucosal and submucosal microstructures of normal and cancerous gastric tissues but also the distribution and content of abnormal cells in these 2 layers. More importantly, it can provide the diagnostic features to qualitatively and quantitatively differentiate between normal and cancerous gastric tissues.

LIMITATIONS

The selection bias and preparation of specimen.

CONCLUSIONS

These findings provide the groundwork for further establishing diagnostic criteria.

Downregulation of a newly identified laminin, laminin-3B11, in vascular basement membranes of invasive human breast cancers

Laminins present in the basement membranes (BM) of blood vessels are involved in angiogenesis and other vascular functions that are critical for tumor growth and metastasis. Two major vascular laminins, the α4 (laminin-411/421) and α5 (laminin-511/521) types, have been well characterized. We recently found a third type of vascular laminin, laminin-3B11, consisting of the α3B, β1 and γ1 chains, and revealed its biological activity. Laminin-3B11 potently stimulates vascular endothelial cells to extend lamellipodial protrusions. To understand the roles of laminin-3B11 in blood vessel functions and tumor growth, we examined localization of the laminin α3B chain in normal mammary glands and breast cancers, in comparison with the α4 and α5 laminins. In the immunohistochemical analysis, the α3B laminin was co-localized with the α4 and α5 laminins in the BM of venules and capillaries of normal breast tissues, but α3B was scarcely detected in vessels near invasive breast carcinoma cells. In contrast, the α4 laminin was overexpressed in capillaries of invasive carcinomas, where a large number of macrophages were found. The α5 laminin appeared to be weakly downregulated in cancer tissues, especially in capillary vessels. Furthermore, our in vitro analysis indicated that TNF-α significantly suppressed the laminin α3B expression in vascular endothelial cells, while it, as well as IL-1β and TGF-α, upregulated the α4 expression. These results suggest that Lm3B11/3B21 may be required for normal mature vessels and interfere with tumor angiogenesis.

Cancer cell invasion is enhanced by applied mechanical stimulation

Metastatic cells migrate from the site of the primary tumor, through the stroma, into the blood and lymphatic vessels, finally colonizing various other tissues to form secondary tumors. Numerous studies have been done to identify the stimuli that drive the metastatic cascade. This has led to the identification of multiple biochemical signals that promote metastasis. However, information on the role of mechanical factors in cancer metastasis has been limited to the affect of compliance. Interestingly, the tumor microenvironment is rich in many cell types including highly contractile cells that are responsible for extensive remodeling and production of the dense extracellular matrix surrounding the cancerous tissue. We hypothesize that the mechanical forces produced by remodeling activities of cells in the tumor microenvironment contribute to the invasion efficiency of metastatic cells. We have discovered a significant difference in the extent of invasion in mechanically stimulated verses non-stimulated cell culture environments. Furthermore, this mechanically enhanced invasion is dependent upon substrate protein composition, and influenced by topography. Finally, we have found that the protein cofilin is needed to sense the mechanical stimuli that enhances invasion. We conclude that other types of mechanical signals in the tumor microenvironment, besides the rigidity, can enhance the invasive abilities of cancer cells in vitro. We further propose that in vivo, non-cancerous cells located within the tumor micro-environment may be capable of providing the necessary mechanical stimulus during the remodeling of the extracellular matrix surrounding the tumor.

Toward an Ising model of cancer and beyond

The holy grail of tumor modeling is to formulate theoretical and computational tools that can be utilized in the clinic to predict neoplastic progression and propose individualized optimal treatment strategies to control cancer growth. In order to develop such a predictive model, one must account for the numerous complex mechanisms involved in tumor growth. Here we review the research work that we have done toward the development of an 'Ising model' of cancer. The Ising model is an idealized statistical-mechanical model of ferromagnetism that is based on simple local-interaction rules, but nonetheless leads to basic insights and features of real magnets, such as phase transitions with a critical point. The review begins with a description of a minimalist four-dimensional (three dimensions in space and one in time) cellular automaton (CA) model of cancer in which cells transition between states (proliferative, hypoxic and necrotic) according to simple local rules and their present states, which can viewed as a stripped-down Ising model of cancer. This model is applied to study the growth of glioblastoma multiforme, the most malignant of brain cancers. This is followed by a discussion of the extension of the model to study the effect on the tumor dynamics and geometry of a mutated subpopulation. A discussion of how tumor growth is affected by chemotherapeutic treatment, including induced resistance, is then described. We then describe how to incorporate angiogenesis as well as the heterogeneous and confined environment in which a tumor grows in the CA model. The characterization of the level of organization of the invasive network around a solid tumor using spanning trees is subsequently discussed. Then, we describe open problems and future promising avenues for future research, including the need to develop better molecular-based models that incorporate the true heterogeneous environment over wide range of length and time scales (via imaging data), cell motility, oncogenes, tumor suppressor genes and cell-cell communication. A discussion about the need to bring to bear the powerful machinery of the theory of heterogeneous media to better understand the behavior of cancer in its microenvironment is presented. Finally, we propose the possibility of using optimization techniques, which have been used profitably to understand physical phenomena, in order to devise therapeutic (chemotherapy/radiation) strategies and to understand tumorigenesis itself.

Biomechanical forces shape the tumor microenvironment

The importance of the tumor microenvironment in cancer progression is indisputable, yet a key component of the microenvironment--biomechanical forces--remains poorly understood. Tumor growth and progression is paralleled by a host of physical changes in the tumor microenvironment, such as growth-induced solid stresses, increased matrix stiffness, high fluid pressure, and increased interstitial flow. These changes to the biomechanical microenvironment promote tumorigenesis and tumor cell invasion and induce stromal cells--such as fibroblasts, immune cells, and endothelial cells--to change behavior and support cancer progression. This review highlights what we currently know about the biomechanical forces generated in the tumor microenvironment, how they arise, and how these forces can dramatically influence cell behavior, drawing not only upon studies directly related to cancer and tumor cells, but also work in other fields that have shown the effects of these types of mechanical forces vis-à-vis cell behaviors relevant to the tumor microenvironment. By understanding how all of these biomechanical forces can affect tumor cells, stromal cells, and tumor-stromal crosstalk, as well as alter how tumor and stromal cells perceive other extracellular signals in the tumor microenvironment, we can develop new approaches for diagnosis, prognosis, and ultimately treatment of cancer.

Coupled mathematical model of tumorigenesis and angiogenesis in vascular tumours

OBJECTIVES

Mathematical models are useful for studying vascular and avascular tumours, because these allow for more logical experimental design and provide valuable insights into the underlying mechanisms of their growth and development. The processes of avascular tumour growth and the development of capillary networks through tumour-induced angiogenesis have already been extensively investigated, albeit separately. Despite the clinical significance of vascular tumours, few studies have combined these approaches to develop a single comprehensive growth and development model.

MATERIALS AND METHODS

We develop a continuum-based mathematical model of vascular tumour growth. In the model, angiogenesis is initiated through the release of angiogenic growth factors (AGFs) by cells in the hypoxic regions of the tumour. The nutrient concentration within the tumour reflects the influence of capillary growth and invasion induced by AGF.

RESULTS AND CONCLUSIONS

Parametric and sensitivity studies were performed to evaluate the influence of different model parameters on tumour growth and to identify the parameters with the most influence, which include the rates of proliferation, apoptosis and necrosis, as well as the diffusion of sprout tips and the size of the region affected by angiogenesis. An optimization was performed for values of the model parameters that resulted in the best agreement with published experimental data. The resulting model solution matched the experimental data with a high degree of correlation (r = 0.85).

Forcing form and function: biomechanical regulation of tumor evolution

Cancer cells exist in a constantly evolving tissue microenvironment of diverse cell types within a proteinaceous extracellular matrix. As tumors evolve, the physical forces within this complex microenvironment change, with pleiotropic effects on both cell- and tissue-level behaviors. Recent work suggests that these biomechanical factors direct tissue development and modulate tissue homeostasis, and, when altered, crucially influence tumor evolution. In this review, we discuss the biomechanical regulation of cell and tissue homeostasis from the molecular, cellular and tissue levels, including how modifications of this physical dialogue could contribute to cancer etiology. Because of the broad impact of biomechanical factors on cell and tissue functions, an understanding of tumor evolution from the biomechanical perspective should improve risk assessment, clinical diagnosis and the efficacy of cancer treatment.

Bioengineered 3D platform to explore cell-ECM interactions and drug resistance of epithelial ovarian cancer cells

The behaviour of cells cultured within three-dimensional (3D) structures rather than onto two-dimensional (2D) culture plastic more closely reflects their in vivo responses. Consequently, 3D culture systems are becoming crucial scientific tools in cancer cell research. We used a novel 3D culture concept to assess cell-matrix interactions implicated in carcinogenesis: a synthetic hydrogel matrix equipped with key biomimetic features, namely incorporated cell integrin-binding motifs (e.g. RGD peptides) and the ability of being degraded by cell-secreted proteases (e.g. matrix metalloproteases). As a cell model, we chose epithelial ovarian cancer, an aggressive disease typically diagnosed at an advanced stage when chemoresistance occurs. Both cell lines used (OV-MZ-6, SKOV-3) proliferated similarly in 2D, but not in 3D. Spheroid formation was observed exclusively in 3D when cells were embedded within hydrogels. By exploiting the design flexibility of the hydrogel characteristics, we showed that proliferation in 3D was dependent on cell-integrin engagement and the ability of cells to proteolytically remodel their extracellular microenvironment. Higher survival rates after exposure to the anti-cancer drug paclitaxel were observed in cell spheroids grown in hydrogels (40-60%) compared to cell monolayers in 2D (20%). Thus, 2D evaluation of chemosensitivity may not reflect pathophysiological events seen in patients. Because of the design flexibility of their characteristics and their stability in long-term cultures (28 days), these biomimetic hydrogels represent alternative culture systems for the increasing demand in cancer research for more versatile, physiologically relevant and reproducible 3D matrices.

Gene expression profiles in 3D tumor analogs indicate compressive strain differentially enhances metastatic potential

Non-physiological mechanobiological stimuli typically occur in tumors and are considered to promote cancer spreading. Non-fluid related pressure (solid stress), which arises as tumors grow against adjacent tissues, is among the least studied endogenous stimuli due to challenges in replicating the in vivo environment. To this end, the novel devices well-pressor and the videomicroscopy-compatible optic-pressor were developed to exert precise compressive strain on cells in 3D gels in absence of other mechanical stimuli and soluble gradients. Glioblastoma (U87, HGL21) and breast cancer (MDA-MB-231) cells in 1% agarose hydrogels were exposed to 50% compressive strain for 3 h (0.25-0.05 kPa). Live imaging showed that cells elongate and deflect vertically to the load. This stimulation is shown for the first time to differentially regulate metastasis-associated genes. Furthermore, a group of differentially expressed genes was identified in all cell types, both by microarrays and confirmed by RT-PCR for select genes (caveolin-1, integrin-β1, Rac1), indicating shared response mechanisms. These genes are functionally linked and involved in decreasing cell-cell contact, increasing ECM degradation, and ultimately promoting invasion. Caveolin could orchestrate these responses while the uPA and PI3K/Akt systems could play major roles. Future work will focus on specific molecular partnerships under compression and their impact on cancer progression.

In silico estimates of the free energy rates in growing tumor spheroids

The physics of solid tumor growth can be considered at three distinct size scales: the tumor scale, the cell-extracellular matrix (ECM) scale and the sub-cellular scale. In this paper we consider the tumor scale in the interest of eventually developing a system-level understanding of the progression of cancer. At this scale, cell populations and chemical species are best treated as concentration fields that vary with time and space. The cells have chemo-mechanical interactions with each other and with the ECM, consume glucose and oxygen that are transported through the tumor, and create chemical by-products. We present a continuum mathematical model for the biochemical dynamics and mechanics that govern tumor growth. The biochemical dynamics and mechanics also engender free energy changes that serve as universal measures for comparison of these processes. Within our mathematical framework we therefore consider the free energy inequality, which arises from the first and second laws of thermodynamics. With the model we compute preliminary estimates of the free energy rates of a growing tumor in its pre-vascular stage by using currently available data from single cells and multicellular tumor spheroids.

Dissecting cancer through mathematics: from the cell to the animal model

This Timeline article charts progress in mathematical modelling of cancer over the past 50 years, highlighting the different theoretical approaches that have been used to dissect the disease and the insights that have arisen. Although most of this research was conducted with little involvement from experimentalists or clinicians, there are signs that the tide is turning and that increasing numbers of those involved in cancer research and mathematical modellers are recognizing that by working together they might more rapidly advance our understanding of cancer and improve its treatment.

Nonlinear modelling of cancer: bridging the gap between cells and tumours

Despite major scientific, medical and technological advances over the last few decades, a cure for cancer remains elusive. The disease initiation is complex, and including initiation and avascular growth, onset of hypoxia and acidosis due to accumulation of cells beyond normal physiological conditions, inducement of angiogenesis from the surrounding vasculature, tumour vascularization and further growth, and invasion of surrounding tissue and metastasis. Although the focus historically has been to study these events through experimental and clinical observations, mathematical modelling and simulation that enable analysis at multiple time and spatial scales have also complemented these efforts. Here, we provide an overview of this multiscale modelling focusing on the growth phase of tumours and bypassing the initial stage of tumourigenesis. While we briefly review discrete modelling, our focus is on the continuum approach. We limit the scope further by considering models of tumour progression that do not distinguish tumour cells by their age. We also do not consider immune system interactions nor do we describe models of therapy. We do discuss hybrid-modelling frameworks, where the tumour tissue is modelled using both discrete (cell-scale) and continuum (tumour-scale) elements, thus connecting the micrometre to the centimetre tumour scale. We review recent examples that incorporate experimental data into model parameters. We show that recent mathematical modelling predicts that transport limitations of cell nutrients, oxygen and growth factors may result in cell death that leads to morphological instability, providing a mechanism for invasion via tumour fingering and fragmentation. These conditions induce selection pressure for cell survivability, and may lead to additional genetic mutations. Mathematical modelling further shows that parameters that control the tumour mass shape also control its ability to invade. Thus, tumour morphology may serve as a predictor of invasiveness and treatment prognosis.

Progress technology in microencapsulation methods for cell therapy

Cell encapsulation in microcapsules allows the in situ delivery of secreted proteins to treat different pathological conditions. Spherical microcapsules offer optimal surface-to-volume ratio for protein and nutrient diffusion, and thus, cell viability. This technology permits cell survival along with protein secretion activity upon appropriate host stimuli without the deleterious effects of immunosuppressant drugs. Microcapsules can be classified in 3 categories: matrix-core/shell microcapsules, liquid-core/shell microcapsules, and cells-core/shell microcapsules (or conformal coating). Many preparation techniques using natural or synthetic polymers as well as inorganic compounds have been reported. Matrix-core/shell microcapsules in which cells are hydrogel-embedded, exemplified by alginates capsule, is by far the most studied method. Numerous refinement of the technique have been proposed over the years such as better material characterization and purification, improvements in microbead generation methods, and new microbeads coating techniques. Other approaches, based on liquid-core capsules showed improved protein production and increased cell survival. But aside those more traditional techniques, new techniques are emerging in response to shortcomings of existing methods. More recently, direct cell aggregate coating have been proposed to minimize membrane thickness and implants size. Microcapsule performances are largely dictated by the physicochemical properties of the materials and the preparation techniques employed. Despite numerous promising pre-clinical results, at the present time each methods proposed need further improvements before reaching the clinical phase.

Growing heterogeneous tumors in silico

An in silico tool that can be utilized in the clinic to predict neoplastic progression and propose individualized treatment strategies is the holy grail of computational tumor modeling. Building such a tool requires the development and successful integration of a number of biophysical and mathematical models. In this paper, we work toward this long-term goal by formulating a cellular automaton model of tumor growth that accounts for several different inter-tumor processes and host-tumor interactions. In particular, the algorithm couples the remodeling of the microvasculature with the evolution of the tumor mass and considers the impact that organ-imposed physical confinement and environmental heterogeneity have on tumor size and shape. Furthermore, the algorithm is able to account for cell-level heterogeneity, allowing us to explore the likelihood that different advantageous and deleterious mutations survive in the tumor cell population. This computational tool we have built has a number of applications in its current form in both predicting tumor growth and predicting response to treatment. Moreover, the latent power of our algorithm is that it also suggests other tumor-related processes that need to be accounted for and calls for the conduction of new experiments to validate the model's predictions.

Multi-scale models of cell and tissue dynamics

Cell and tissue movement are essential processes at various stages in the life cycle of most organisms. The early development of multi-cellular organisms involves individual and collective cell movement; leukocytes must migrate towards sites of infection as part of the immune response; and in cancer, directed movement is involved in invasion and metastasis. The forces needed to drive movement arise from actin polymerization, molecular motors and other processes, but understanding the cell- or tissue-level organization of these processes that is needed to produce the forces necessary for directed movement at the appropriate point in the cell or tissue is a major challenge. In this paper, we present three models that deal with the mechanics of cells and tissues: a model of an arbitrarily deformable single cell, a discrete model of the onset of tumour growth in which each cell is treated individually, and a hybrid continuum-discrete model of the later stages of tumour growth. While the models are different in scope, their underlying mechanical and mathematical principles are similar and can be applied to a variety of biological systems.

Quantitative measurement of blood flow using perfusion CT for assessing clinicopathologic features and prognosis in patients with rectal cancer

PURPOSE

The ability to evaluate clinicopathologic features and prognosis before surgery by contrast-enhanced CT would be valuable for managing rectal cancer. This study was designed to evaluate the clinical usefulness of perfusion CT in patients with rectal cancer before surgery.

METHODS

Forty-four consecutive patients (27 men, 17 women; median age, 63.6 years) with rectal cancer underwent perfusion CT before surgery. We retrospectively investigated the correlations between tumor blood flow generated by perfusion CT and clinicopathologic features.

RESULTS

There was a significant correlation between blood flow and wall invasion (P = 0.04). Well-differentiated tumors showed significantly higher blood flow than moderately differentiated tumors (P = 0.03). There was a significant tendency for tumors with low blood flow to show lymph node metastasis (P = 0.0005), vascular invasion (P = 0.004), lymphatic invasion (P = 0.04), and distant metastasis (P = 0.0005). For blood flow, accuracy was 75% for detection of tumors with lymph node metastasis if the cutoff point was set at 55 ml/100 g per minute. Patients with high blood flow tumors survived significantly longer than those with low blood flow tumors (P = 0.002).

CONCLUSIONS

Blood flow of rectal cancers may be useful to evaluate pathologic features and prognosis before surgery.

Small Agarose Microcapsules with Cell-Enclosing Hollow Core for Cell Therapy: Transplantation of Ifosfamide-Activating Cells to the Mice with Preestablished Subcutaneous Tumor

Cell transplantation after enclosing in microcapsules has been studied as an alternative approach for treatment of wide variety of diseases. In the present study, we examined the feasibility of using agarose microcapsules, having a cell-enclosing hollow core of 100–150 μm in diameter and agarose gel membrane of about 20 μm in thickness, as a device for the methodology. We enclosed cells that had been genetically engineered to express cytochrome P450 2B1, an enzyme that activates the anticancer prodrug ifosfamide. The enclosed cells were shown to express the enzymatic function in the microcapsules in that they suppressed the growth of tumor cells in medium containing ifosfamide. In addition, a more significant regression of preformed tumors was observed in the nude mice implanted with the cell-enclosing microcapsules compared with those implanted with empty capsules after administration of ifosfamide. Preformed tumors shrank by less than 40% in volume in 6 of the 10 recipients implanted with cell-enclosing microcapsules. In contrast, only 1 in 10 of the preformed tumors in the recipient implanted with empty microcapsules shrank by this amount. These results suggest that agarose microcapsules containing cytochrome P450 2B1 enzyme-expressing cells are feasible devices for improving the chemotherapy of tumors. Thus, agarose microcapsule having hollow cores are generally a good candidate as vehicles for cell-encapsulation approaches to cell therapy.

Translating tissue engineering technology platforms into cancer research

Technology platforms originally developed for tissue engineering applications produce valuable models that mimic three-dimensional (3D) tissue organization and function to enhance the understanding of cell/tissue function under normal and pathological situations. These models show that when replicating physiological and pathological conditions as closely as possible investigators are allowed to probe the basic mechanisms of morphogenesis, differentiation and cancer. Significant efforts investigating angiogenetic processes and factors in tumorigenesis are currently undertaken to establish ways of targeting angiogenesis in tumours. Anti-angiogenic agents have been accepted for clinical application as attractive targeted therapeutics for the treatment of cancer. Combining the areas of tumour angiogenesis, combination therapies and drug delivery systems is therefore closely related to the understanding of the basic principles that are applied in tissue engineering models. Studies with 3D model systems have repeatedly identified complex interacting roles of matrix stiffness and composition, integrins, growth factor receptors and signalling in development and cancer. These insights suggest that plasticity, regulation and suppression of these processes can provide strategies and therapeutic targets for future cancer therapies. The historical perspective of the fields of tissue engineering and controlled release of therapeutics, including inhibitors of angiogenesis in tumours is becoming clearly evident as a major future advance in merging these fields. New delivery systems are expected to greatly enhance the ability to deliver drugs locally and in therapeutic concentrations to relevant sites in living organisms. Investigating the phenomena of angiogenesis and anti-angiogenesis in 3D in vivo models such as the Arterio-Venous (AV) loop mode in a separated and isolated chamber within a living organism adds another significant horizon to this perspective and opens new modalities for translational research in this field.

Homeostatic competition drives tumor growth and metastasis nucleation

We propose a mechanism for tumor growth emphasizing the role of homeostatic regulation and tissue stability. We show that competition between surface and bulk effects leads to the existence of a critical size that must be overcome by metastases to reach macroscopic sizes. This property can qualitatively explain the observed size distributions of metastases, while size-independent growth rates cannot account for clinical and experimental data. In addition, it potentially explains the observed preferential growth of metastases on tissue surfaces and membranes such as the pleural and peritoneal layers, suggests a mechanism underlying the seed and soil hypothesis introduced by Stephen Paget in 1889, and yields realistic values for metastatic inefficiency. We propose a number of key experiments to test these concepts. The homeostatic pressure as introduced in this work could constitute a quantitative, experimentally accessible measure for the metastatic potential of early malignant growths.

Biological impact of mechanical stimuli on tumor metastasis

Increasing evidence suggests tumor cell exposure to mechanical stimuli during the perioperative period as well as throughout the normal disease process may have a discernable impact on tumor metastasis and patient outcome. In vitro studies have demonstrated that transient exposure to increased extracellular pressure and shear forces modulates integrin binding affinity and stimulates cancer cell adhesion through a cytoskeleton- and focal adhesion complex-dependent signaling mechanism. More prolonged exposure to elevated pressures stimulates tumor cell proliferation by a distinct signaling pathway. Whether pressure effects on cell adhesion and proliferation pose biological ramifications in vivo remained unknown. We recently reported that pressure activation of malignant cells does indeed have a biological impact on surgical wound implantation, tumor development and tumor-free survival in a murine colon tumor model. Moreover, this effect can be disrupted by preoperative administration of colchicine. Taken together with previous work from our laboratory and others, these findings suggest that further elucidation of the mechanical signaling pathways governing pressure-stimulated tumor cell adhesion and proliferation may identify novel therapeutic targets for the treatment and prevention of tumor metastasis.

Morpho-elastodynamics: the long-time dynamics of elastic growth

As elastic tissues grow and remodel, they generate stresses that influence their mechanical states which influence the way growth proceeds. This complex feedback leads to a dynamic evolution of growth and stresses which can be modelled within the theory of exact nonlinear elasticity. Here, we first review the different theoretical results considering growth laws and then, we present a new approach to look at morphoelasticity as a continuous dynamical process. These evolution laws lead to new dynamical systems that can be studied by the classical methods of dynamical systems theory.

Micro-environmental mechanical stress controls tumor spheroid size and morphology by suppressing proliferation and inducing apoptosis in cancer cells

Background

Compressive mechanical stress produced during growth in a confining matrix limits the size of tumor spheroids, but little is known about the dynamics of stress accumulation, how the stress affects cancer cell phenotype, or the molecular pathways involved.

Methodology/Principal Findings

We co-embedded single cancer cells with fluorescent micro-beads in agarose gels and, using confocal microscopy, recorded the 3D distribution of micro-beads surrounding growing spheroids. The change in micro-bead density was then converted to strain in the gel, from which we estimated the spatial distribution of compressive stress around the spheroids. We found a strong correlation between the peri-spheroid solid stress distribution and spheroid shape, a result of the suppression of cell proliferation and induction of apoptotic cell death in regions of high mechanical stress. By compressing spheroids consisting of cancer cells overexpressing anti-apoptotic genes, we demonstrate that mechanical stress-induced apoptosis occurs via the mitochondrial pathway.

Conclusions/Significance

Our results provide detailed, quantitative insight into the role of micro-environmental mechanical stress in tumor spheroid growth dynamics, and suggest how tumors grow in confined locations where the level of solid stress becomes high. An important implication is that apoptosis via the mitochondrial pathway, induced by compressive stress, may be involved in tumor dormancy, in which tumor growth is held in check by a balance of apoptosis and proliferation.

Biomechanical regulation of cell orientation and fate

Biomechanical regulation of tumor phenotypes have been noted for several decades, yet the function of mechanics in the co-evolution of the tumor epithelium and altered cancer extracellular matrix has not been appreciated until fairly recently. In this review, we examine the dynamic interaction between the developing epithelia and the extracellular matrix, and discuss how similar interactions are exploited by the genetically modified epithelium during tumor progression. We emphasize the process of mechanoreciprocity, which is a phenomenon observed during epithelial transformation, in which tension generated within the extracellular microenvironment induce and cooperate with opposing reactive forces within transformed epithelium to drive tumor progression and metastasis. We highlight the importance of matrix remodeling, and present a new, emerging paradigm that underscores the importance of tissue morphology as a key regulator of epithelial cell invasion and metastasis.

Cell adhesion mechanisms and stress relaxation in the mechanics of tumours

Tumour cells usually live in an environment formed by other host cells, extra-cellular matrix and extra-cellular liquid. Cells duplicate, reorganise and deform while binding each other due to adhesion molecules exerting forces of measurable strength. In this paper, a macroscopic mechanical model of solid tumour is investigated which takes such adhesion mechanisms into account. The extracellular matrix is treated as an elastic compressible material, while, in order to define the relationship between stress and strain for the cellular constituents, the deformation gradient is decomposed in a multiplicative way distinguishing the contribution due to growth, to cell rearrangement and to elastic deformation. On the basis of experimental results at a cellular level, it is proposed that at a macroscopic level there exists a yield condition separating the elastic and dissipative regimes. Previously proposed models are obtained as limit cases, e.g. fluid-like models are obtained in the limit of fast cell reorganisation and negligible yield stress. A numerical test case shows that the model is able to account for several complex interactions: how tumour growth can be influenced by stress, how and where it can generate cell reorganisation to release the stress level, how it can lead to capsule formation and compression of the surrounding tissue.

The role of extracellular matrix in glioma invasion: a cellular Potts model approach

In this work, a cellular Potts model based on the differential adhesion hypothesis is employed to analyze the relative importance of select cell-cell and cell-extracellular matrix (ECM) contacts in glioma invasion. To perform these simulations, three types of cells and two ECM components are included. The inclusion of explicit ECM with an inhomogeneous fibrous component and a homogeneously dispersed afibrous component allows exploration of the importance of relative energies of cell-cell and cell-ECM contacts in a variety of environments relevant to in vitro and in vivo experimental investigations of glioma invasion. Simulations performed here focus chiefly on reproducing findings of in vitro experiments on glioma spheroids embedded in collagen I gels. For a given range and set ordering of energies associated with key cell-cell and cell-ECM interactions, our model qualitatively reproduces the dispersed glioma invasion patterns found for most glioma cell lines embedded as spheroids in collagen I gels of moderate concentration. In our model, we find that invasion is maximized at intermediate collagen concentrations, as occurs experimentally. This effect is seen more strongly in model gels composed of short collagen fibers than in those composed of long fibers, which retain significant connectivity even at low density. Additional simulations in aligned model matrices further elucidate how matrix structure dictates invasive patterns. Finally, simulations that allow invading cells to both dissolve and deposit ECM components demonstrate how Q-Potts models may be elaborated to allow active cell alteration of their surroundings. The model employed here provides a quantitative framework with which to bound the relative values of cell-cell and cell-ECM interactions and investigate how varying the magnitude and type of these interactions, as well as ECM structure, could potentially curtail glioma invasion.

Simulating tumor growth in confined heterogeneous environments

The holy grail of computational tumor modeling is to develop a simulation tool that can be utilized in the clinic to predict neoplastic progression and propose individualized optimal treatment strategies. In order to develop such a predictive model, one must account for many of the complex processes involved in tumor growth. One interaction that has not been incorporated into computational models of neoplastic progression is the impact that organ-imposed physical confinement and heterogeneity have on tumor growth. For this reason, we have taken a cellular automaton algorithm that was originally designed to simulate spherically symmetric tumor growth and generalized the algorithm to incorporate the effects of tissue shape and structure. We show that models that do not account for organ/tissue geometry and topology lead to false conclusions about tumor spread, shape and size. The impact that confinement has on tumor growth is more pronounced when a neoplasm is growing close to, versus far from, the confining boundary. Thus, any clinical simulation tool of cancer progression must not only consider the shape and structure of the organ in which a tumor is growing, but must also consider the location of the tumor within the organ if it is to accurately predict neoplastic growth dynamics.

Angiogenesis in salivary carcinomas with and without myoepithelial differentiation

To investigate whether salivary carcinomas with and without myoepithelial differentiation could present differences regarding degree of angiogenesis, we compared tumor vascularization between adenoid cystic (31 cases) and epithelial-myoepithelial carcinomas (14) versus mucoepidermoid (37) carcinoma. The expression of peroxiredoxin I was also studied to verify the potential relationship between cellular metabolism and microvascular density. Microvascular density for CD34 and CD105 were significantly lower in carcinomas with myoepithelial differentiation. However, no correlation was found between degree of angiogenesis and amounts of myoepithelial cells. High-grade peroxiredoxin I expression was found in 73.7% of mucoepidermoid carcinomas, whereas 85.1% of carcinomas with myoepithelial differentiation presented low-grade expression. In conclusion, carcinomas with myoepithelial differentiation, regardless of the amounts of myoepithelial cells, are associated to a significantly lower vascular density. The reasons for this lower angiogenic activity remain to be determined but could be related to metabolic characteristics of the cancer cells.