Mathematical Modelling of a Brain Tumour Initiation and Early Development: A Coupled Model of Glioblastoma Growth,Pre-Existing Vessel Co-Option,Angiogenesis and Blood Perfusion

We propose a coupled mathematical modelling system to investigate glioblastoma growth in response to dynamic changes in chemical and haemodynamic microenvironments caused by pre-existing vessel co-option, remodelling, collapse and angiogenesis. A typical tree-like architecture network with different orders for vessel diameter is designed to model pre-existing vasculature in host tissue. The chemical substances including oxygen, vascular endothelial growth factor, extra-cellular matrix and matrix degradation enzymes are calculated based on the haemodynamic environment which is obtained by coupled modelling of intravascular blood flow with interstitial fluid flow. The haemodynamic changes, including vessel diameter and permeability, are introduced to reflect a series of pathological characteristics of abnormal tumour vessels including vessel dilation, leakage, angiogenesis, regression and collapse. Migrating cells are included as a new phenotype to describe the migration behaviour of malignant tumour cells. The simulation focuses on the avascular phase of tumour development and stops at an early phase of angiogenesis. The model is able to demonstrate the main features of glioblastoma growth in this phase such as the formation of pseudopalisades, cell migration along the host vessels, the pre-existing vasculature co-option, angiogenesis and remodelling. The model also enables us to examine the influence of initial conditions and local environment on the early phase of glioblastoma growth.     

Coupled modelling of tumour angiogenesis, tumour growth and blood perfusion

We propose a mathematical modelling system to investigate the dynamic process of tumour cell proliferation, death and tumour angiogenesis by fully coupling the vessel growth, tumour growth and blood perfusion. Tumour growth and angiogenesis are coupled by the chemical microenvironment and the cell-matrix interaction. The haemodynamic calculation is carried out on the updated vasculature. The domains of intravascular, transcapillary and interstitial fluid flow were coupled in the model to provide a comprehensive solution of blood perfusion variables. An estimation of vessel collapse is made according to the wall shear stress criterion to provide feedback on vasculature remodelling. The simulation can show the process of tumour angiogenesis and the spatial distribution of tumour cells for periods of up to 24 days. It can show the major features of tumour and tumour microvasculature during the period such as the formation of a large necrotic core in the tumour centre with few functional vessels passing through, and a well circulated tumour periphery regions in which the microvascular density is high and associated with more aggressive proliferating cells of the growing tumour which are all consistent with physiological observations. The study also demonstrated that the simulation results are not dependent on the initial tumour and networks, which further confirms the application of the coupled model feedback mechanisms. The model enables us to examine the interactions between angiogenesis and tumour growth, and to study the dynamic response of a solid tumour to the changes in the microenvironment. This simulation framework can be a foundation for further applications such as drug delivery and anti-angiogenic therapies.     

The Vascular Basement Membrane as “Soil” in Brain Metastasis

Brain-specific homing and direct interactions with the neural substance are prominent hypotheses for brain metastasis formation and a modern manifestation of Paget''s “seed and soil” concept. However, there is little direct evidence for this “neurotropic” growth in vivo. In contrast, many experimental studies have anecdotally noted the propensity of metastatic cells to grow along the exterior of pre-existing vessels of the CNS, a process termed vascular cooption. These observations suggest the “soil” for malignant cells in the CNS may well be vascular, rather than neuronal. We used in vivo experimental models of brain metastasis and analysis of human clinical specimens to test this hypothesis. Indeed, over 95% of early micrometastases examined demonstrated vascular cooption with little evidence for isolated neurotropic growth. This vessel interaction was adhesive in nature implicating the vascular basement membrane (VBM) as the active substrate for tumor cell growth in the brain. Accordingly, VBM promoted adhesion and invasion of malignant cells and was sufficient for tumor growth prior to any evidence of angiogenesis. Blockade or loss of the β1 integrin subunit in tumor cells prevented adhesion to VBM and attenuated metastasis establishment and growth in vivo. Our data establishes a new understanding of CNS metastasis formation and identifies the neurovasculature as the critical partner for such growth. Further, we have elucidated the mechanism of vascular cooption for the first time. These findings may help inform the design of effective molecular therapies for patients with fatal CNS malignancies.     

Role of copper in tumour angiogenesis--clinical implications.

The formation of new blood vessels is the initial step in progressive tumour development and metastasis. The first stage in tumour angiogenesis is the activation of endothelial cells. Copper ions stimulate proliferation and migration of endothelial cells. It has been shown that serum copper concentration increases as the cancer disease progresses and correlates with tumour incidence and burden. Copper ions also activate several proangiogenic factors, e.g., vascular endothelial growth factor, basic fibroblast growth factor, tumour necrosis factor alpha and interleukin 1. This review concerns a brief introduction into the basics of tumour blood vessel development as well as the regulatory mechanisms of this process. The role of copper ions in tumour angiogenesis is discussed. The new antiangiogenic therapies based on a reduction of copper levels in tumour microenvironment are reviewed.     

A mathematical model of tumour angiogenesis incorporating cellular traction and viscoelastic effects

Angiogenesis is defined as the outgrowth and formation of new vessels from a pre-existing vascular network (Rakusan, In: Cardiac Growth and Regeneration. Annals of the New York Academy of Sciences, 1995), and is of fundamental importance in understanding the processes by which a tumour achieves vascularization. Diffusible substances, collectively called tumour angiogenesis factors are released from the tumour to elicit a variety of responses from the surrounding tissues, most importantly the migration of endothelial cells (lining neighbouring vessels) towards the tumour. To facilitate locomotion, the cells exert appreciable traction forces upon the interstitial extracellular matrix which, in turn, influences the resulting direction of their migration. In this paper, we examine the role played by cellular traction during cell migration and the corresponding viscoelastic effects of the extracellular matrix.     

Vascular remodelling of an arterio-venous blood vessel network during solid tumour growth

We formulate a theoretical model to analyze the vascular remodelling process of an arterio-venous vessel network during solid tumour growth. The model incorporates a hierarchically organized initial vasculature comprising arteries, veins and capillaries, and involves sprouting angiogenesis, vessel cooption, dilation and regression as well as tumour cell proliferation and death. The emerging tumour vasculature is non-hierarchical, compartmentalized into well-characterized zones and transports efficiently an injected drug-bolus. It displays a complex geometry with necrotic zones and “hot spots” of increased vascular density and blood flow of varying size. The corresponding cluster size distribution is algebraic, reminiscent of a self-organized critical state. The intra-tumour vascular-density fluctuations correlate with pressure drops in the initial vasculature suggesting a physical mechanism underlying hot spot formation.     

髓样细胞在肿瘤血管生成过程中的作用

肿瘤血管生成在肿瘤的发展过程中起着关键作用。外周循环血中存在的一些髓样细胞,如巨噬细胞、中性粒细胞、酸性粒细胞、肥大细胞和树突状细胞等具有多方面的能力,被募集到肿瘤组织中,在肿瘤微环境中促进肿瘤的血管生成。这些髓样细胞在肿瘤血管生成过程中起重要的作用。该文对这些不同类型细胞促进肿瘤血管生成的作用进行了论述。     

Regulation of blood vessel sprouting

Blood vessels are essential conduits of nutrients and oxygen throughout the body. The formation of these vessels involves angiogenic sprouting, a complex process entailing highly integrated cell behaviors and signaling pathways. In this review, we discuss how endothelial cells initiate a vessel sprout through interactions with their environment and with one another, particularly through lateral inhibition. We review the composition of the local environment, which contains an initial set of guidance cues to facilitate the proper outward migration of the sprout as it emerges from a parent vessel. The long-range guidance and sprout stability cues provided by soluble molecules, extracellular matrix components, and interactions with other cell types are also discussed. We also examine emerging evidence for mechanisms that govern sprout fusion with its target and lumen formation.     

Negative regulation of midline vascular development by the notochord

The negative regulation of vascular patterning is one of the least understood processes in vascular biology. In amniotes, blood vessels develop throughout the embryonic disc, except for a midline region surrounding the notochord. Here we show that the notochord is the primary signaling center for the inhibition of vessel formation along the embryonic midline. Notochord ablation in quail embryos results in vascular plexus formation at midline. Implantation of the notochord into paraxial and lateral mesoderm inhibits vessel formation locally. The notochord-expressed BMP antagonists Chordin and Noggin inhibit endothelial cell migration in vitro, and their ectopic expression in vivo results in a local disruption of vessel formation. Conversely, BMP-4 activates endothelial cell migration in vitro, and its ectopic expression along the notochord induces vascular plexus formation at midline. These data indicate an inhibitory role of the notochord in defining an avascular zone at the embryonic midline, in part via BMP antagonism.     

Mesenchymal stem cells promote cell invasion and migration and autophagy‐induced epithelial‐mesenchymal transition in A549 lung adenocarcinoma cells

Mesenchymal stem cells (MSCs) are recruited into the tumour microenvironment and promote tumour growth and metastasis. Tumour microenvironment‐induced autophagy is considered to suppress primary tumour formation by impairing migration and invasion. Whether these recruited MSCs regulate tumour autophagy and whether autophagy affects tumour growth are controversial. Our data showed that MSCs promote autophagy activation, reactive oxygen species production, and epithelial‐mesenchymal transition (EMT) as well as increased migration and invasion in A549 cells. Decreased expression of E‐cadherin and increased expression of vimentin and Snail were observed in A549 cells cocultured with MSCs. Conversely, MSC coculture‐mediated autophagy positively promoted tumour EMT. Autophagy inhibition suppressed MSC coculture‐mediated EMT and reduced A549 cell migration and invasion slightly. Furthermore, the migratory and invasive abilities of A549 cells were additional increased when autophagy was further enhanced by rapamycin treatment. Taken together, this work suggests that microenvironments containing MSCs can promote autophagy activation for enhancing EMT; MSCs also increase the migratory and invasive abilities of A549 lung adenocarcinoma cells. Mesenchymal stem cell‐containing microenvironments and MSC‐induced autophagy signalling may be potential targets for blocking lung cancer cell migration and invasion.     

Postnatal vasculogenesis

It is generally accepted that vasculogenesis is limited to early embryogenesis and is believed not to occur in adult, whereas angiogenesis occurs in both the developing embryo and postnatal life. However, the distinction between them is not absolute, because both require endothelial cell proliferation and migration and three-dimensional reorganization of newly formed blood vessels, nor are they mutually exclusive, inasmuch as angioblasts can be incorporated into expanding pre-existing blood vessels. Recent observations indicate that vasculogenesis may not be restricted to early embryogenesis, but may also have a physiological role or contribute to the pathology of vascular diseases in adults. The major evidence in favor of this new view comes from: (i) demonstration of the presence of circulating endothelial cells and endothelial precursor cells; (ii) newly described mechanisms of blood vessel formation in tumor growth. The potential biomedical applications of endothelial precursor cells and the new opportunities for the development of new forms of tumor-targeted treatments are discussed.     

Signal transduction in vasculogenesis and developmental angiogenesis

The vasculature is a highly specialized organ that functions in a number of key physiological tasks including the transport of oxygen and nutrients to tissues. Formation of the vascular system is an essential and rate-limiting step in development and occurs primarily through two main mechanisms, vasculogenesis and angiogenesis. Both vasculogenesis, the de novo formation of vessels, and angiogenesis, the growth of new vessels from pre-existing vessels by sprouting, are complex processes that are mediated by the precise coordination of multiple cell types to form and remodel the vascular system. A host of signaling molecules and their interaction with specific receptors are central to activating and modulating vessel formation. This review article summarizes the current state of research involving signaling molecules that have been demonstrated to function in the regulation of vasculogenesis and angiogenesis, as well as molecules known to play a role in vessel maturation, hypoxia-driven angiogenesis and arterial-venous specification.     

Modelling the Role of Angiogenesis and Vasculogenesis in Solid Tumour Growth

Recent experimental evidence suggests that vasculogenesis may play an important role in tumour vascularisation. While angiogenesis involves the proliferation and migration of endothelial cells (ECs) in pre-existing vessels, vasculogenesis involves the mobilisation of bone-marrow-derived endothelial progenitor cells (EPCs) into the bloodstream. Once blood-borne, EPCs home in on the tumour site, where subsequently they may differentiate into ECs and form vascular structures. In this paper, we develop a mathematical model, formulated as a system of nonlinear ordinary differential equations (ODEs), which describes vascular tumour growth with both angiogenesis and vasculogenesis contributing to vessel formation. Submodels describing exclusively angiogenic and exclusively vasculogenic tumours are shown to exhibit similar growth dynamics. In each case, there are three possible scenarios: the tumour remains in an avascular steady state, the tumour evolves to a vascular equilibrium, or unbounded vascular growth occurs. Analysis of the full model reveals that these three behaviours persist when angiogenesis and vasculogenesis act simultaneously. However, when both vascularisation mechanisms are active, the tumour growth rate may increase, causing the tumour to evolve to a larger equilibrium size or to expand uncontrollably. Alternatively, the growth rate may be left unaffected, which occurs if either vascularisation process alone is able to keep pace with the demands of the growing tumour. To clarify further the effects of vasculogenesis, the full model is also used to compare possible treatment strategies, including chemotherapy and antiangiogenic therapies aimed at suppressing vascularisation. This investigation highlights how, dependent on model parameter values, targeting both ECs and EPCs may be necessary in order to effectively reduce tumour vasculature and inhibit tumour growth.     

Extracellular matrix density regulates the formation of tumour spheroids through cell migration

In this work, we show how the mechanical properties of the cellular microenvironment modulate the growth of tumour spheroids. Based on the composition of the extracellular matrix, its stiffness and architecture can significantly vary, subsequently influencing cell movement and tumour growth. However, it is still unclear exactly how both of these processes are regulated by the matrix composition. Here, we present a centre-based computational model that describes how collagen density, which modulates the steric hindrance properties of the matrix, governs individual cell migration and, consequently, leads to the formation of multicellular clusters of varying size. The model was calibrated using previously published experimental data, replicating a set of experiments in which cells were seeded in collagen matrices of different collagen densities, hence producing distinct mechanical properties. At an initial stage, we tracked individual cell trajectories and speeds. Subsequently, the formation of multicellular clusters was also analysed by quantifying their size. Overall, the results showed that our model could accurately replicate what was previously seen experimentally. Specifically, we showed that cells seeded in matrices with low collagen density tended to migrate more. Accordingly, cells strayed away from their original cluster and thus promoted the formation of small structures. In contrast, we also showed that high collagen densities hindered cell migration and produced multicellular clusters with increased volume. In conclusion, this model not only establishes a relation between matrix density and individual cell migration but also showcases how migration, or its inhibition, modulates tumour growth.     

Glioblastoma: A Pathogenic Crosstalk between Tumor Cells and Pericytes

Cancers likely originate in progenitor zones containing stem cells and perivascular stromal cells. Much evidence suggests stromal cells play a central role in tumor initiation and progression. Brain perivascular cells (pericytes) are contractile and function normally to regulate vessel tone and morphology, have stem cell properties, are interconvertible with macrophages and are involved in new vessel formation during angiogenesis. Nevertheless, how pericytes contribute to brain tumor infiltration is not known. In this study we have investigated the underlying mechanism by which the most lethal brain cancer, Glioblastoma Multiforme (GBM) interacts with pre-existing blood vessels (co-option) to promote tumor initiation and progression. Here, using mouse xenografts and laminin-coated silicone substrates, we show that GBM malignancy proceeds via specific and previously unknown interactions of tumor cells with brain pericytes. Two-photon and confocal live imaging revealed that GBM cells employ novel, Cdc42-dependent and actin-based cytoplasmic extensions, that we call flectopodia, to modify the normal contractile activity of pericytes. This results in the co-option of modified pre-existing blood vessels that support the expansion of the tumor margin. Furthermore, our data provide evidence for GBM cell/pericyte fusion-hybrids, some of which are located on abnormally constricted vessels ahead of the tumor and linked to tumor-promoting hypoxia. Remarkably, inhibiting Cdc42 function impairs vessel co-option and converts pericytes to a phagocytic/macrophage-like phenotype, thus favoring an innate immune response against the tumor. Our work, therefore, identifies for the first time a key GBM contact-dependent interaction that switches pericyte function from tumor-suppressor to tumor-promoter, indicating that GBM may harbor the seeds of its own destruction. These data support the development of therapeutic strategies directed against co-option (preventing incorporation and modification of pre-existing blood vessels), possibly in combination with anti-angiogenesis (blocking new vessel formation), which could lead to improved vascular targeting not only in Glioblastoma but also for other cancers.     

鸡胚原肠胚期原条细胞命运决定于其所处的局部微环境

在果蝇、斑马鱼、鸡等三胚层动物胚胎早期发育的原肠胚期,原条两侧的上胚层细胞进入原条经历上皮-间充质转化(EMT),迁移进入囊胚腔,形成松散的中胚层细胞,位于原条不同部位的细胞其迁移路线和分化命运不同,如前部原条细胞贡献于体节和心脏等,而后部原条细胞则迁移至胚外形成血岛。为了研究细胞的迁移途径及分化命运是否会随着细胞所处不同部位微环境的改变而改变,利用传统的移植技术,将宿主鸡胚原条前部的一部分细胞用GFP阳性的相同时期鸡胚原条组织替换,培养一段时间后,用荧光体视显微镜追踪GFP阳性细胞的迁移途径。结果发现,从供体原条后部移植到宿主原条前部的细胞遵循原条前部细胞迁移的路线,反之亦然;原位杂交结果显示移植后的GFP阳性细胞分化为所处部位的细胞类型。上述结果表明:鸡胚原肠胚期原条细胞迁移和分化的命运决定于细胞所处的微环境或者说局部基因表达的时空性。     

Long-term Intravital Immunofluorescence Imaging of Tissue Matrix Components with Epifluorescence and Two-photon Microscopy

Besides being a physical scaffold to maintain tissue morphology, the extracellular matrix (ECM) is actively involved in regulating cell and tissue function during development and organ homeostasis. It does so by acting via biochemical, biomechanical, and biophysical signaling pathways, such as through the release of bioactive ECM protein fragments, regulating tissue tension, and providing pathways for cell migration. The extracellular matrix of the tumor microenvironment undergoes substantial remodeling, characterized by the degradation, deposition and organization of fibrillar and non-fibrillar matrix proteins. Stromal stiffening of the tumor microenvironment can promote tumor growth and invasion, and cause remodeling of blood and lymphatic vessels. Live imaging of matrix proteins, however, to this point is limited to fibrillar collagens that can be detected by second harmonic generation using multi-photon microscopy, leaving the majority of matrix components largely invisible. Here we describe procedures for tumor inoculation in the thin dorsal ear skin, immunolabeling of extracellular matrix proteins and intravital imaging of the exposed tissue in live mice using epifluorescence and two-photon microscopy. Our intravital imaging method allows for the direct detection of both fibrillar and non-fibrillar matrix proteins in the context of a growing dermal tumor. We show examples of vessel remodeling caused by local matrix contraction. We also found that fibrillar matrix of the tumor detected with the second harmonic generation is spatially distinct from newly deposited matrix components such as tenascin C. We also showed long-term (12 hours) imaging of T-cell interaction with tumor cells and tumor cells migration along the collagen IV of basement membrane. Taken together, this method uniquely allows for the simultaneous detection of tumor cells, their physical microenvironment and the endogenous tissue immune response over time, which may provide important insights into the mechanisms underlying tumor progression and ultimate success or resistance to therapy.     

Lymphocyte recirculation and homing: roles of adhesion molecules and chemoattractants

Lymphocyte migration from high endothelial venules into lymphoid organs is mediated by a sequence of interactions between cell adhesion molecules on lymphocytes and those on the vascular endothelial cells that line the vessels. recent studies suggest that the so-called lymphocyte homing receptors and vascular addressins regulate the first stages of this process, that of binding of lymphocytes from flowing blood. The subsequent crawling of lymphocytes over the endothelial cell surface and migration across the vessel wall (diapedesis) are regulated independently of initial binding. These latter stages are thought to be mediated by functional activation of integrins on the lymphocyte by chemoattractants located in the vessel wall.     

Mathematical modelling of flow through vascular networks: implications for tumour-induced angiogenesis and chemotherapy strategies

Angiogenesis, the formation of blood vessels from a pre-existing vasculature, is a process whereby capillary sprouts are formed in response to externally supplied chemical stimuli. The sprouts then grow and develop, driven initially by endothelial cell migration, and organize themselves into a branched, connected network structure. Subsequent cell proliferation near the sprout-tip permits further extension of the capillary and ultimately completes the process. Angiogenesis occurs during embryogenesis, wound healing, arthritis and during the growth of solid tumours. In this paper we initially generate theoretical capillary networks (which are morphologically similar to those networks observed in vivo) using the discrete mathematical model of Anderson and Chaplain. This discrete model describes the formation of a capillary sprout network via endothelial cell migratory and proliferative responses to external chemical stimuli (tumour angiogenic factors, TAF) supplied by a nearby solid tumour, and also the endothelial cell interactions with the extracellular matrix. The main aim of this paper is to extend this work to examine fluid flow through these theoretical network structures. In order to achieve this we make use of flow modelling tools and techniques (specifically, flow through interconnected networks) from the field of petroleum engineering. Having modelled the flow of a basic fluid through our network, we then examine the effects of fluid viscosity, blood vessel size (i.e., diameter of the capillaries), and network structure/geometry, upon: (i) the rate of flow through the network; (ii) the amount of fluid present in the complete network at any one time; and (iii) the amount of fluid reaching the tumour. The incorporation of fluid flow through the generated vascular networks has highlighted issues that may have major implications for the study of nutrient supply to the tumour (blood/oxygen supply) and, more importantly, for the delivery of chemotherapeutic drugs to the tumour. Indeed, there are also implications for the delivery of anti-angiogenesis drugs to the network itself. Results clearly highlight the important roles played by the structure and morphology of the network, which is, in turn, linked to the size and geometry of the nearby tumour. The connectedness of the network, as measured by the number of loops formed in the network (the anastomosis density), is also found to be of primary significance. Moreover, under certain conditions, the results of our flow simulations show that an injected chemotherapy drug may bypass the tumour altogether.     

Effects of soluble factors and extracellular matrix components on vascular cell behavior in vitro and in vivo: models of de-endothelialization and repair.

Vessel walls are comprised of several different cell populations residing in and on complex extracellular matrices. Each of the vascular cell types has diverse and sometimes unique functions and morphologies, and each has roles in repair processes following injury. Large vessel endothelial cells are known to respond to denudation injury by sheet migration and proliferation. This is in contrast to the migration through soft tissues with tube formation and subsequent lumen formation exhibited by microvascular endothelial cells in response to injury. Vascular smooth muscle cells of larger vessels respond to injury by migration from the arterial media into the intima, proliferation, and matrix biosynthesis, ultimately causing intimal thickening. Both these cell types exhibit "dysfunctional" phenotypes during their responses to injury. Microvascular cell responses to injury, while extremely variable, are less well documented. Specifically, responses to injury by microvascular endothelial vascular cells appear to be modulated, in part, by the composition and organization of the surrounding matrix as well as by the various soluble factors and cytokines found at sites of injury, suggesting that the extracellular matrix and soluble factors modulate each other's effects on local vascular cell populations following injury.