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.     

Vascular tumor growth and treatment: Consequences of polyclonality,competition and dynamic vascular support

 A mathematical model is presented to describe the evolution of a vascular tumor in response to traditional chemotherapeutic treatment. Particular attention is paid to the effects of a dynamic vascular support system in a tumor comprised of competing cell populations that differ in proliferation rates and drug susceptibility. The model consists of a system of partial differential equations governing intratumoral drug concentration, cancer cell density, and blood vessel density. The balance between cell proliferation and death along with vessel production and destruction within the tumor generates a velocity field which drives the expansion or regression of the neoplasm. Radially symmetric solutions are obtained for the case when only one cell type is present and when the proportion of the tumor occupied by blood vessels remains constant. The stability of these solutions to asymmetric perturbations and to a small semi-drug resistant cell population is then investigated. The analysis shows that drug concentrations which are sufficient to insure eradication of a spherical tumor may be inadequate for the successful treatment of non-spherical tumors. When the drug is continuously infused, linear analysis predicts that whether or not a cure is possible is crucially dependent on the proliferation rate of the semi-resistant cells and on the competitive effect of the sensitive cells on the resistant population. When the blood vessel density is allowed to change dynamically, the model predicts a dramatic increase in the tumors growth and decrease in its response to therapy. Received: 4 August 2000 / Revised version: 13 July 2001 / Published online: 21 February 2002     

Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis.

The growth of new capillary blood vessels, or angiogenesis, is a prominent component of numerous physiological and pathological conditions. An understanding of the co-ordination of underlying cellular behaviors would be helpful for therapeutic manipulation of the process. A probabilistic mathematical model of angiogenesis is developed based upon specific microvessel endothelial cell (MEC) functions involved in vessel growth. The model focuses on the roles of MEC random motility and chemotaxis, to test the hypothesis that these MEC behaviors are of critical importance in determining capillary growth rate and network structure. Model predictions are computer simulations of microvessel networks, from which questions of interest are examined both qualitatively and quantitatively. Results indicate that a moderate MEC chemotactic response toward an angiogenic stimulus, similar to that measured in vitro in response to acidic fibroblast growth factor, is necessary to provide directed vascular network growth. Persistent random motility alone, with initial budding biased toward the stimulus, does not adequately provide directed network growth. A significant degree of randomness in cell migration direction, however, is required for vessel anastomosis and capillary loop formation, as simulations with an overly strong chemotactic response produce network structures largely absent of these features. The predicted vessel extension rate and network structure in the simulations are quantitatively consistent with experimental observations of angiogenesis in vivo. This suggests that the rate of vessel outgrowth is primarily determined by MEC migration rate, and consequently that quantitative in vitro migration assays might be useful tools for the prescreening of possible angiogenesis activators and inhibitors. Finally, reduction of MEC speed results in substantial inhibition of simulated angiogenesis. Together, these results predict that both random motility and chemotaxis are MEC functions critically involved in determining the rate and morphology of new microvessel network growth.     

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.     

Acheron regulates vascular endothelial proliferation and angiogenesis together with Id1 during wound healing

RNA binding protein acheron has proved to be either the mediator of integrin‐extracellular matrix interactions or the regulatory factor that participates in vertebrate development, cell differentiation and cell death. We report the role of acheron in vascular endothelial proliferation, angiogenesis and wound healing post‐trauma. Co‐immunoprecipitation showed that Acheron forms a ternary complex with β1 integrin and Id1 in human umbilical vein endothelial cells following stimulation with serious trauma serum. Acheron, vascular endothelial growth factor (VEGF), and β1 integrin mRNA expression was apparently inhibited, and capillary density and wound healing rate also were reduced in Id1‐deficient mice trauma model. Acheron together with Id1 significantly induces VEGF, not CD105 level inhibition by serious trauma serum for 24 h. In conclusion, we have demonstrated that acheron may be an effective mediator of promoting endothelial proliferation, angiogenesis and wound healing probably by regulating VEGF together with Id1. Copyright © 2011 John Wiley & Sons, Ltd.     

Lipid mediators of angiogenesis and the signalling pathways they initiate

Investigations carried out over the past 3 years have implicated a key role for sphingosine 1-phosphate (SPP) in angiogenesis and blood vessel maturation. SPP is capable of inducing almost every aspect of angiogenesis and vessel maturation in vitro, including endothelial cell chemotaxis, survival, proliferation, capillary morphogenesis and adherence antigen deployment, as well as stabilizing developing endothelial cell monolayers and recruitment of smooth muscle cells to maturing vessels. Acting in conjunction with protein angiogenic factors, SPP induces prolific vascular development in many established models of angiogenesis in vivo. Thus, SPP is a unique, potent and multifaceted angiogenic agent. While SPP induces angiogenic effects by ligating members of the endothelial differentiation gene (EDG) G-protein-coupled family of receptors, recent studies suggest that endogenously produced SPP may also account for the ability of tyrosine kinase receptors to induce cell migration. Thus, SPP provides a clear link between tyrosine kinase and G-protein-coupled receptor agonists involved in the angiogenic response. However, the mechanisms by which SPP exerts its effects on vascular cells remain unclear, conflicting and controversial. Precise definition of the signalling pathways by which SPP induces specific aspects of the angiogenic response promises to lead to new and effective therapeutic approaches to regulate angiogenesis at sites of tissue damage, neoplastic transformation and inflammation. This review will trace the discovery of SPP as a novel angiogenic factor as it outlines present information on the signalling pathways by which SPP induces its effects on cells of the developing vascular bed.     

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.     

Elongation,proliferation & migration differentiate endothelial cell phenotypes and determine capillary sprouting

Background  

Angiogenesis, the growth of capillaries from preexisting blood vessels, has been extensively studied experimentally over the past thirty years. Molecular insights from these studies have lead to therapies for cancer, macular degeneration and ischemia. In parallel, mathematical models of angiogenesis have helped characterize a broader view of capillary network formation and have suggested new directions for experimental pursuit. We developed a computational model that bridges the gap between these two perspectives, and addresses a remaining question in angiogenic sprouting: how do the processes of endothelial cell elongation, migration and proliferation contribute to vessel formation?     

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.     

A possible role of initial cell death due to mechanical stretch in the regulation of subsequent cell proliferation in experimental vein grafts

 The proliferation of vascular cells contributes to the formation of neointima and hypertrophy of the blood vessel wall. Here we show that mechanical stretch possibly regulates the proliferation of vascular cells via the mediation of cell death in a rat vein graft model. The wall of vein grafts is subject to a suddenly increased mechanical stretch due to exposure to arterial blood pressure. Such a stretch induces rapid cell death with a reduction in cell density by ∼60% within the first day after surgery. The initial cell death was followed by an increase in the percentage of proliferating cells, as shown by a BrdU incorporation assay (1.55 ± 1.27%, 8.48 ± 2.27%, 11.93 ± 2.36%, 6.36 ± 1.77%, and 5.60 ± 1.46% at days 1, 5, 10, 20, and 30, respectively). When mechanical stretch was reduced by restraining the vein graft using a polytetrafluoroethylene sheath, the percentage of proliferating cells reduced significantly (0.76 ± 0.76%, 1.70 ± 0.46%, 1.29 ± 0.56%, 0.99 ± 0.83%, and 0.47±0.52% at days 1, 5, 10, 20, and 30, respectively). A further reduction in cell density, induced by local administration of a cell death inducer ceramide to experimental vein grafts (without sheath), enhanced subsequent cell proliferation. In contrast, a prevention of cell death, induced by local administration of a cell death inhibitor tetrapeptide-aldehyde DEVD-CHO to experimental vein grafts (without sheath), significantly reduced subsequent cell proliferation. These results suggest that mechanical stretch induces cell death, which possibly mediates subsequent cell proliferation in the present model. Received: 9 September 2001 / Accepted: 19 November 2001     

Effect of thalidomide affecting VEGF secretion, cell migration, adhesion and capillary tube formation of human endothelial EA.hy 926 cells

Angiogenesis, new blood vessel formation, is a multistep process, precisely regulated by pro-angiogenic cytokines, which stimulate endothelial cells to migrate, proliferate and differentiate to form new capillary microvessels. Excessive vascular development and blood vessel remodeling appears in psoriasis, rheumatoid arthritis, diabetic retinopathy and solid tumors formation. Thalidomide [alpha-(N-phthalimido)-glutarimide] is known to be a potent inhibitor of angiogenesis, but the mechanism of its inhibitory action remains unclear. The aim of the study was to investigate the potential influence of thalidomide on the several steps of angiogenesis, using in vitro models. We have evaluated the effect of thalidomide on VEGF secretion, cell migration, adhesion as well as in capillary formation of human endothelial cell line EA.hy 926. Thalidomide at the concentrations of 0.01 microM and 10 microM inhibited VEGF secretion into supernatants, decreased the number of formed capillary tubes and increased cell adhesion to collagen. Administration of thalidomide at the concentration of 0.01 microM increased cell migration, while at 10 microM, it decreased cell migration. Thalidomide in concentrations from 0.1 microM to 10 microM did not change cell proliferation of 72-h cell cultures. We conclude that anti-angiogenic action of thalidomide is due to direct inhibitory action on VEGF secretion and capillary microvessel formation as well as immunomodulatory influence on EA.hy 926 cells migration and adhesion.     

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.     

Vascular network remodeling via vessel cooption, regression and growth in tumors

The transformation of the regular vasculature in normal tissue into a highly inhomogeneous tumor specific capillary network is described by a theoretical model incorporating tumor growth, vessel cooption, neo-vascularization, vessel collapse and cell death. Compartmentalization of the tumor into several regions differing in vessel density, diameter and in necrosis is observed for a wide range of parameters in agreement with the vessel morphology found in human melanoma. In accord with data for human melanoma the model predicts that microvascular density (MVD), regarded as an important diagnostic tool in cancer treatment, does not necessarily determine the tempo of tumor progression. Instead it is suggested that the MVD of the original tissue as well as the metabolic demand of the individual tumor cell plays the major role in the initial stages of tumor growth.     

Transforming growth factor beta 1-induced changes in cell migration, proliferation, and angiogenesis in the chicken chorioallantoic membrane

Application of TGF beta 1 (10-100 ng) to the chicken chorioallantoic membrane (CAM) for 72 h resulted in a dose-dependent, gross angiogenic response. The vascular effects induced by TGF beta 1 were qualitatively different than those induced by maximal doses of basic FGF (bFGF) (500 ng). While TGF beta 1 induced the formation of large blood vessels by 72 h, bFGF induced primarily small blood vessels. Histologic analysis revealed that TGF beta 1 stimulated pleiotropic cellular responses in the CAM. Increases in fibroblast and epithelial cell density in the area of TGF beta 1 delivery were observed as early as 4 h after TGF beta 1 treatment. By 8 h, these cell types also demonstrated altered morphology and marked inhibition of proliferation as evidenced by 3H-thymidine labeling. Thus, the TGF beta 1-stimulated accumulation of these cell types was the result of cellular chemotaxis from peripheral areas into the area of TGF beta 1 delivery. Microscopic angiogenesis in the form of capillary sprouts and increased endothelial cell density first became evident at 16 h. By 24 h, capillary cords appeared within the mesenchyme of the CAM, extending towards the point of TGF beta 1 delivery. 3H-thymidine labeling revealed that the growth of these capillary cords was due to endothelial cell proliferation. Finally, perivascular mononuclear inflammation did not become evident until 48 h of treatment, and its presence correlated spatially and temporally with the gross and histological remodelling of newly formed capillary cords into larger blood vessels. In summary, these data suggest that, in the chicken CAM, TGF beta 1 initiates a sequence of cellular responses that results in growth inhibition, cellular accumulation through migration, and microvascular angiogenesis.     

Tumor necrosis factor inhibits the proliferation of cultured capillary endothelial cells

We have examined the effect of tumor necrosis factor (TNF) on the proliferation of capillary endothelial cells derived from brain or adrenal cortex. In both cell types, TNF inhibits basal as well as basic fibroblast growth factor (bFGF)-stimulated cell proliferation. TNF induces an additional cytotoxic effect in bFGF-stimulated, but not in unstimulated, capillary endothelial cells. These results suggest that TNF could act as a negative regulator of angiogenesis in vivo and further, that TNF might induce selective cytotoxicity of capillary endothelial cells stimulated by tumor-derived bFGF. These results could explain why TNF induces hemorrhagic necrosis of certain, solid tumors.     

A multiphase model describing vascular tumour growth

In this paper we present a new model framework for studying vascular tumour growth, in which the blood vessel density is explicitly considered. Our continuum model comprises conservation of mass and momentum equations for the volume fractions of tumour cells, extracellular material and blood vessels. We include the physical mechanisms that we believe to be dominant, namely birth and death of tumour cells, supply and removal of extracellular fluid via the blood and lymph drainage vessels, angiogenesis and blood vessel occlusion. We suppose that the tumour cells move in order to relieve the increase in mechanical stress caused by their proliferation. We show how to reduce the model to a system of coupled partial differential equations for the volume fraction of tumour cells and blood vessels and the phase averaged velocity of the mixture. We consider possible parameter regimes of the resulting model. We solve the equations numerically in these cases, and discuss the resulting behaviour. The model is able to reproduce tumour structure that is found in vivo in certain cases. Our framework can be easily modified to incorporate the effect of other phases, or to include the effect of drugs.     

A Functional Requirement for Astroglia in Promoting Blood Vessel Development in the Early Postnatal Brain

Astroglia are a major cell type in the brain and play a key role in many aspects of brain development and function. In the adult brain, astrocytes are known to intimately ensheath blood vessels and actively coordinate local neural activity and blood flow. During development of the neural retina, blood vessel growth follows a meshwork of astrocytic processes. Several genes have also been implicated in retinal astrocytes for regulating vessel development. This suggests a role of astrocytes in promoting angiogenesis throughout the central nervous system. To determine the roles that astrocytes may play during brain angiogenesis, we employ genetic approaches to inhibit astrogliogenesis during perinatal corticogenesis and examine its effects on brain vessel development. We find that conditional deletion from glial progenitors of orc3, a gene required for DNA replication, dramatically reduces glial progenitor cell number in the subventricular zone and astrocytes in the early postnatal cerebral cortex. This, in turn, results in severe reductions in both the density and branching frequency of cortical blood vessels. Consistent with a delayed growth but not regression of vessels, we find neither significant net decreases in vessel density between different stages after normalizing for cortical expansion nor obvious apoptosis of endothelial cells in these mutants. Furthermore, concomitant with loss of astroglial interactions, we find increased endothelial cell proliferation, enlarged vessel luminal size as well as enhanced cytoskeletal gene expression in pericytes, which suggests compensatory changes in vascular cells. Lastly, we find that blood vessel morphology in mutant cortices recovers substantially at later stages, following astrogliosis. These results thus implicate a functional requirement for astroglia in promoting blood vessel growth during brain development.     

Rat mesentery exteriorization: a model for investigating the cellular dynamics involved in angiogenesis

Microvacular network growth and remodeling are critical aspects of wound healing, inflammation, diabetic retinopathy, tumor growth and other disease conditions. Network growth is commonly attributed to angiogenesis, defined as the growth of new vessels from pre-existing vessels. The angiogenic process is also directly linked to arteriogenesis, defined as the capillary acquisition of a perivascular cell coating and vessel enlargement. Needless to say, angiogenesis is complex and involves multiple players at the cellular and molecular level. Understanding how a microvascular network grows requires identifying the spatial and temporal dynamics along the hierarchy of a network over the time course of angiogenesis. This information is critical for the development of therapies aimed at manipulating vessel growth. The exteriorization model described in this article represents a simple, reproducible model for stimulating angiogenesis in the rat mesentery. It was adapted from wound-healing models in the rat mesentery, and is an alternative to stimulate angiogenesis in the mesentery via i.p. injections of pro-angiogenic agents. The exteriorization model is attractive because it requires minimal surgical intervention and produces dramatic, reproducible increases in capillary sprouts, vascular area and vascular density over a relatively short time course in a tissue that allows for the two-dimensional visualization of entire microvascular networks down to single cell level. The stimulated growth reflects natural angiogenic responses in a physiological environment without interference of foreign angiogenic molecules. Using immunohistochemical labeling methods, this model has been proven extremely useful in identifying novel cellular events involved in angiogenesis. Investigators can readily correlate the angiogenic metrics during the time course of remodeling with time specific dynamics, such as cellular phenotypic changes or cellular interactions.     

Enhancement of neovascularization with mobilized blood cells transplantaion: supply of angioblasts and angiogenic cytokines

We have recently provided evidence that transplantation of G-CSF mobilized peripheral blood mononuclear cells (M-PBMNCs) improves limb ischemia in diabetic patients. This method represents a simple, safe, effective, and novel therapeutic approach for diabetic ischemia. Here we investigated the mechanisms by which mobilized blood cells transplantation improves limb ischemia. Unilateral hindlimb ischemia was surgically induced in streptozotocin-induced diabetic nude mice, and they were intramuscularly injected 10(6) M-PBMNCs, or human umbilical vein endothelial cells (HUVECs), PBS controls. We compared their blood-flow restoration via laser Doppler perfusion image (LDPI), angiogenesis via histological determination of capillary density. Physiological and histological assessment revealed an acceleration of ischemia recovery and increase in capillary density with less apoptosis in M-PBMNCs group, compared with those in HUVECs and PBS groups. In vivo noninvasive imaging and immunofluorescence revealed the survival, migration, proliferation, differentiation, and incorporation of M-PBMNCs into foci of vessel networks. More angioblasts were from blood cells after mobilization, and they also produced a number of antiapoptotic and proagniogenic factors that promoted angiogenesis in vivo. M-PBMNCs and its conditioned medium augmented the vessel formation in matrigel plugs in vivo. Thus, transplantation of M-PBMNCs achieved therapeutic neovascularization via supply of abundant angioblasts and angiogenic factors.     

Diffusion model of tumor vascularization and growth

A diffusion model of tumor growth, vascularization and necrosis is used to analyze experimental data describing the temporal changes in tumor cell and blood vessel radial distributions in a host-tissue field transplanted with a fibrosarcoma. The experimental results showed a peak density of vessels occurring at the advancing migration front of the tumor and a decline in the vessel surface area at the tumor center with time. The peak density of tumor cells shifts away from the tumor center with time. These dynamic changes can be explained by a mathematical model which views the process as one of diffusion and proliferation in time and space. Coupled diffusion equations with nonlinear source and sink terms describe the proliferation, death, and migration of tumor cells and vascular surface area. The concept of an angiogenic factor elaborated by tumor cells is incorporated.