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.     

Vascular growth factors in cerebral ischemia

During the past decade, there has been a surge of interest in growth factors (GFs) that act selectively on vascular endothelium and perivascular cells. Studies employing mutant mice or the administration of recombinant proteins have suggested that these factors not only mediate the proliferation of endothelial cells, but also regulate vascular differentiation, regression, and permeability. During and after cerebral ischemia, brain vasculature becomes leaky and unstable, and the normally impermeable blood-brain barrier breaks down. Several days after the ischemic insult, endothelial cells begin to proliferate, and angiogenesis occurs. Expression studies have shown that key vascular GFs are regulated, during these processes, in a complex and coordinated manner. The distinct pattern of regulation exhibited by each vascular GF suggests a unique role for each factor during the initial vascular destabilization and subsequent angiogenesis that occurs after cerebral ischemia. Data from studies in other biological systems support these suggested roles. Thus, manipulation of vascular GFs may prove to be an effective means of stabilizing or enriching brain vasculature after ischemia, and ameliorating the detrimental effects of blood-brain barrier breakdown and vessel regression after stroke.     

On the preservation of vessel bifurcations during flow-mediated angiogenic remodelling

During developmental angiogenesis, endothelial cells respond to shear stress by migrating and remodelling the initially hyperbranched plexus, removing certain vessels whilst maintaining others. In this study, we argue that the key regulator of vessel preservation is cell decision behaviour at bifurcations. At flow-convergent bifurcations where migration paths diverge, cells must finely tune migration along both possible paths if the bifurcation is to persist. Experiments have demonstrated that disrupting the cells’ ability to sense shear or the junction forces transmitted between cells impacts the preservation of bifurcations during the remodelling process. However, how these migratory cues integrate during cell decision making remains poorly understood. Therefore, we present the first agent-based model of endothelial cell flow-mediated migration suitable for interrogating the mechanisms behind bifurcation stability. The model simulates flow in a bifurcated vessel network composed of agents representing endothelial cells arranged into a lumen which migrate against flow. Upon approaching a bifurcation where more than one migration path exists, agents refer to a stochastic bifurcation rule which models the decision cells make as a combination of flow-based and collective-based migratory cues. With this rule, cells favour branches with relatively larger shear stress or cell number. We found that cells must integrate both cues nearly equally to maximise bifurcation stability. In simulations with stable bifurcations, we found competitive oscillations between flow and collective cues, and simulations that lost the bifurcation were unable to maintain these oscillations. The competition between these two cues is haemodynamic in origin, and demonstrates that a natural defence against bifurcation loss during remodelling exists: as vessel lumens narrow due to cell efflux, resistance to flow and shear stress increases, attracting new cells to enter and rescue the vessel from regression. Our work provides theoretical insight into the role of junction force transmission has in stabilising vasculature during remodelling and as an emergent mechanism to avoid functional shunting.     

Anti-tumor activities of the angiogenesis inhibitors interferon-inducible protein-10 and the calreticulin fragment vasostatin

Tumor growth depends upon an adequate supply of oxygen and nutrients achieved through angiogenesis and maintenance of an intact tumor vasculature. Therapy with individual agents that target new vessel formation or existing vessels has suppressed experimental tumor growth, but rarely resulted in the eradication of tumors. We therefore tested the combined anti-tumor activity of vasostatin and interferon-inducible protein-10 (IP-10), agents that differently target the tumor vasculature. Vasostatin, a selective and direct inhibitor of endothelial cell proliferation, significantly reduced Burkitt tumor growth and tumor vessel density. IP-10, an "angiotoxic" chemokine, caused vascular damage and focal necrosis in Burkitt tumors. When combined, vasostatin plus IP-10 reduced tumor growth more effectively than each agent alone, but complete tumor regression was not observed. Microscopically, these tumors displayed focal necrosis and reduction in vessel density. Combination therapy with the inhibitors of angiogenesis vasostatin and IP-10 is effective in reducing the rate of tumor growth but fails to induce tumor regression, suggesting that curative treatment may require supplemental drugs targeting directly the tumor cells.     

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.     

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.     

Antiangiogenic activity of chemopreventive drugs

Tumors growing within the host form dynamic aberrant tissue that consists of host components, including the stroma, an expanding vasculature and often chronic inflammation, in addition to the tumor cells themselves. These host components can contribute to, rather than limit, tumor expansion, whereas deprivation of vessel formation has the potential to confine tumors in small, clinically silent foci. Therapeutic inhibition of vessel formation could be best suited to preventive strategies aimed at the suppression of angiogenesis in primary tumors in subjects at risk, or of micrometastases after surgical removal of a primary tumor. Our analysis of potential cancer chemopreventive molecules including N-acetylcysteine, green tea flavonoids and 4-hydroxyphenyl-retinamide has identified antiangiogenic activities that could account--at least in part--for the tumor prevention effects observed with these compounds. These drugs appear to target common mechanisms of tumor angiogenesis that may permit identification of critical targets for antiangiogenic therapy and antiangiogenic chemoprevention.     

Vessel abnormalization: another hallmark of cancer? Molecular mechanisms and therapeutic implications

As a result of excessive production of angiogenic molecules, tumor vessels become abnormal in structure and function. By impairing oxygen delivery, abnormal vessels fuel a vicious cycle of non-productive angiogenesis, which creates a hostile microenvironment from where tumor cells escape through leaky vessels and which renders tumors less responsive to chemoradiation. While anti-angiogenic strategies focused on inhibiting new vessel growth and destroying pre-existing vessels, clinical studies showed modest anti-tumor effects. For many solid tumors, anti-VEGF treatment offers greater clinical benefit when combined with chemotherapy. This is partly due to a normalization of the tumor vasculature, which improves cytotoxic drug delivery and efficacy and offers unprecedented opportunities for anti-cancer treatment. Here, we overview key novel molecular players that induce vessel normalization.     

Gamma-secretase inhibitor treatment promotes VEGF-A-driven blood vessel growth and vascular leakage but disrupts neovascular perfusion

The Notch signaling pathway is essential for normal development due to its role in control of cell differentiation, proliferation and survival. It is also critically involved in tumorigenesis and cancer progression. A key enzyme in the activation of Notch signaling is the gamma-secretase protein complex and therefore, gamma-secretase inhibitors (GSIs)--originally developed for Alzheimer's disease--are now being evaluated in clinical trials for human malignancies. It is also clear that Notch plays an important role in angiogenesis driven by Vascular Endothelial Growth Factor A (VEGF-A)--a process instrumental for tumor growth and metastasis. The effect of GSIs on tumor vasculature has not been conclusively determined. Here we report that Compound X (CX), a GSI previously reported to potently inhibit Notch signaling in vitro and in vivo, promotes angiogenic sprouting in vitro and during developmental angiogenesis in mice. Furthermore, CX treatment suppresses tumor growth in a mouse model of renal carcinoma, leads to the formation of abnormal vessels and an increased tumor vascular density. Using a rabbit model of VEGF-A-driven angiogenesis in skeletal muscle, we demonstrate that CX treatment promotes abnormal blood vessel growth characterized by vessel occlusion, disrupted blood flow, and increased vascular leakage. Based on these findings, we propose a model for how GSIs and other Notch inhibitors disrupt tumor blood vessel perfusion, which might be useful for understanding this new class of anti-cancer agents.     

Vasculature in pre-blastema and nerve-dependent blastema stages of regenerating forelimbs of the adult newt, Notophthalmus viridescens

Immunocytochemistry utilizing a monoclonal antibody (BV1; blood vessel 1) highly reactive to the vasculature of the adult newt showed that a developing vasculature was present during early, pre-blastema, and early-bud blastema stages of forelimb regeneration in this species. Infusion of Prussian Blue and DiI into the brachial artery further delineated the intactness of this early vasculature. Finally, macroscopic observations of vascular flow underneath the apical epithelial cap (AEC) and microsurgical removal of the AEC and observation of subsequent bleeding buttressed the conclusion that an intact vasculature exists during early nerve-dependent stages of newt forelimb regeneration. The results suggest that this process of neovascular formation is angiogenesis, i.e., the formation of new vessels from pre-existing vessels in the stump. Furthermore, angiogenesis is an ongoing process initiated early after amputation. Blastema cells and the AEC are likely sourcesof factors that stimulate neovascularization.     

Desmin-positive stellate cells associated with angiogenesis in a tumour and non-tumour system

The angiogenesis induced after implantation of fragments of the Walker 256 carcinoma was compared with the angiogenesis following implantation of different amounts of Indian ink. Morphologically and chronologically the tumour system showed no difference from the Indian ink system, provided sufficient amounts of ink were implanted. Both systems were characterized by significant macrophage infiltration. The vascular development, which was clearly concentrated in a dense rim around the tumour, remained present when the tumour enlarged, suggesting an acquisition of vasculature by the tumour through vessel incorporation and not vessel ingrowth. Initially, scattered desmin-positive cells, in contact or encircled by collagen IV, were found in the developing angiogenic rim. Later many desmin-positive cells were found around vessels and could be identified by electron microscopy as pericytes. They exhibited close local contacts with endothelial cells. After incorporation of the peritumour vascular rim into the tumour the number of pericytes decreased and their shape became flattened and elongated.     

Mechanotransduction in embryonic vascular development

A plethora of biochemical signals provides spatial and temporal cues that carefully orchestrate the complex process of vertebrate embryonic development. The embryonic vasculature develops not only in the context of these biochemical cues, but also in the context of the biomechanical forces imparted by blood flow. In the mature vasculature, different blood flow regimes induce distinct genetic programs, and significant progress has been made toward understanding how these forces are perceived by endothelial cells and transduced into biochemical signals. However, it cannot be assumed that paradigms that govern the mature vasculature are pertinent to the developing embryonic vasculature. The embryonic vasculature can respond to the mechanical forces of blood flow, and these responses are critical in vascular remodeling, certain aspects of sprouting angiogenesis, and maintenance of arterial–venous identity. Here, we review data regarding mechanistic aspects of endothelial cell mechanotransduction, with a focus on the response to shear stress, and elaborate upon the multifarious effects of shear stress on the embryonic vasculature. In addition, we discuss emerging predictive vascular growth models and highlight the prospect of combining signaling pathway information with computational modeling. We assert that correlation of precise measurements of hemodynamic parameters with effects on endothelial cell gene expression and cell behavior is required for fully understanding how blood flow-induced loading governs normal vascular development and shapes congenital cardiovascular abnormalities.     

Proteome analysis of the rat cornea during angiogenesis

Angiogenesis is the formation of new blood vessels from the pre-existing vasculature. However, the study of this complex process is often hampered by the lack of a suitable cell-based model and the tools to study the biochemical events that lead to new blood vessel growth. The most widely accepted model for angiogenesis is the in vivo rat corneal model. In this model, the cornea, which is normally an avascular tissue, is stimulated to undergo angiogenesis in response to silver nitrate cauterization or to the implantation of an exogenous angiogenic agent. The physical changes associated with the new vessel growth can be readily monitored visually, but the regulated biochemical events that result in the growth and remodeling of the new vessels are much more challenging to decipher. In this report, a proteomics approach is evaluated for its utility in deciphering the biochemical events during a time course of angiogenic stimulation. At various time points post-silver nitrate cautery, corneas were harvested, solubilized, and analyzed by two-dimensional gel electrophoresis. Protein expression profiles at the various stages of angiogenesis were compared to those of control corneas. One hundred and eleven differentially-expressed proteins were identified by either matrix-assisted laser desorption/ionization-time of flight mass spectrometry or liquid chromatography-coupled electrospray ionization tandem mass spectrometry. Many of the proteins up-regulated during the angiogenesis process were identified as blood-related proteins, thus validating the development of functional blood vessels in the normally avascular tissue of the cornea. Furthermore, detection of differentially-regulated proteins in cauterized versus control tissue clearly validated the utility of a proteomics approach to study this model of angiogenesis. However, in order to get at the key regulatory proteins in the angiogenesis process, it is clear that additional scale-up and enrichment approaches will be required.     

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.     

A central function for perlecan in skeletal muscle and cardiovascular development

Perlecan's developmental functions are difficult to dissect in placental animals because perlecan disruption is embryonic lethal. In contrast to mammals, cardiovascular function is not essential for early zebrafish development because the embryos obtain adequate oxygen by diffusion. In this study, we use targeted protein depletion coupled with protein-based rescue experiments to investigate the involvement of perlecan and its C-terminal domain V/endorepellin in zebrafish development. The perlecan morphants show a severe myopathy characterized by abnormal actin filament orientation and disorganized sarcomeres, suggesting an involvement of perlecan in myopathies. In the perlecan morphants, primary intersegmental vessel sprouts, which develop through angiogenesis, fail to extend and show reduced protrusive activity. Live videomicroscopy confirms the abnormal swimming pattern caused by the myopathy and anomalous head and trunk vessel circulation. The phenotype is partially rescued by microinjection of human perlecan or endorepellin. These findings indicate that perlecan is essential for the integrity of somitic muscle and developmental angiogenesis and that endorepellin mediates most of these biological activities.     

A Continuum Mathematical Model of the Developing Murine Retinal Vasculature

Angiogenesis, the process of new vessel growth from pre-existing vasculature, is crucial in many biological situations such as wound healing and embryogenesis. Angiogenesis is also a key regulator of pathogenesis in many clinically important disease processes, for instance, solid tumour progression and ocular diseases. Over the past 10–20 years, tumour-induced angiogenesis has received a lot of attention in the mathematical modelling community and there have also been some attempts to model angiogenesis during wound healing. However, there has been little modelling work of vascular growth during normal development. In this paper, we describe an in silico representation of the developing retinal vasculature in the mouse, using continuum mathematical models consisting of systems of partial differential equations. The equations describe the migratory response of cells to growth factor gradients, the evolution of the capillary blood vessel density, and of the growth factor concentration. Our approach is closely coupled to an associated experimental programme to parameterise our model effectively and the simulations provide an excellent correlation with in vivo experimental data. Future work and development of this model will enable us to elucidate the impact of molecular cues upon vasculature development and the implications for eye diseases such as diabetic retinopathy and neonatal retinopathy of prematurity.     

Bone marrow stromal cells stimulate an angiogenic program that requires endothelial MT1-MMP

Bone marrow-derived stromal/stem cells (BMSCs) have recently been characterized as mediators of tissue regeneration after injury. In addition to preventing fibrosis at the wound site, BMSCs elicit an angiogenic response within the fibrin matrix. The mechanistic interactions between BMSCs and invading endothelial cells (ECs) during this process are not fully understood. Using a three-dimensional, fibrin-based angiogenesis model, we sought to investigate the proteolytic mechanisms by which BMSCs promote vessel morphogenesis. We find that BMSC-mediated vessel formation depends on the proteolytic ability of membrane type 1-matrix metalloproteinase (MT1-MMP). Knockdown of the protease results in a small network of vessels with enlarged lumens. Contrastingly, vessel morphogenesis is unaffected by the knockdown of MMP-2 and MMP-9. Furthermore, we find that BMSC-mediated vessel morphogenesis in vivo follows mechanisms similar to what we observe in vitro. Subcutaneous, cellular fibrin implants in C.B-17/SCID mice form aberrant vasculature when MMPs are inhibited with a broad-spectrum chemical inhibitor, and a very minimal amount of vessels when MT1-MMP proteolytic activity is interrupted in ECs. Other studies have debated the necessity of MT1-MMP in the context of vessel invasion in fibrin, but this study clearly demonstrates its requirement in BMSC-mediated angiogenesis.     

Mechanisms of normal and tumor-derived angiogenesis

Often those diseases most evasive totherapeutic intervention usurp the human body's own cellular machineryor deregulate normal physiological processes for propagation.Tumor-induced angiogenesis is a pathological condition that resultsfrom aberrant deployment of normal angiogenesis, an essential processin which the vascular tree is remodeled by the growth of newcapillaries from preexisting vessels. Normal angiogenesis ensures thatdeveloping or healing tissues receive an adequate supply of nutrients.Within the confines of a tumor, the availability of nutrients islimited by competition among actively proliferating cells, anddiffusion of metabolites is impeded by high interstitial pressure (Jain RK. Cancer Res 47: 3039-3051, 1987). As a result, tumorcells induce the formation of a new blood supply from the preexisting vasculature, and this affords tumor cells the ability to survive andpropagate in a hostile environment. Because both normal and tumor-induced neovascularization fulfill the essential role of satisfying the metabolic demands of a tissue, the mechanisms by whichcancer cells stimulate pathological neovascularization mimic thoseutilized by normal cells to foster physiological angiogenesis. Thisreview investigates mechanisms of tumor-induced angiogenesis. Thestrategies used by cancer cells to develop their own blood supply arediscussed in relation to those employed by normal cells duringphysiological angiogenesis. With an understanding of blood vesselgrowth in both normal and abnormal settings, we are better suited todesign effective therapeutics for cancer.

     

Haemodynamics-driven developmental pruning of brain vasculature in zebrafish

The brain blood vasculature consists of a highly ramified vessel network that is tailored to meet its physiological functions. How the brain vasculature is formed has long been fascinating biologists. Here we report that the developing vasculature in the zebrafish midbrain undergoes not only angiogenesis but also extensive vessel pruning, which is driven by changes in blood flow. This pruning process shapes the initial exuberant interconnected meshwork into a simplified architecture. Using in vivo long-term serial confocal imaging of the same zebrafish larvae during 1.5-7.5 d post-fertilization, we found that the early formed midbrain vasculature consisted of many vessel loops and higher order segments. Vessel pruning occurred preferentially at loop-forming segments via a process mainly involving lateral migration of endothelial cells (ECs) from pruned to unpruned segments rather than EC apoptosis, leading to gradual reduction in the vasculature complexity with development. Compared to unpruned ones, pruned segments exhibited a low and variable blood flow, which further decreased irreversibly prior to the onset of pruning. Local blockade of blood flow with micro-bead obstruction led to vessel pruning, whereas increasing blood flow by noradrenergic elevation of heartbeat impeded the pruning process. Furthermore, the occurrence of vessel pruning could be largely predicted by haemodynamics-based numerical simulation of vasculature refinement. Thus, changes of blood flow drive vessel pruning via lateral migration of ECs, leading to the simplification of the vasculature and possibly efficient routing of blood flow in the developing brain.