Numerical modelling of the angiogenesis process in wound contraction

Angiogenesis consists of the growth of new blood vessels from the pre-existing vasculature. This phenomenon takes place in several biological processes, including wound healing. In this work, we present a mathematical model of angiogenesis applied to skin wound healing. The developed model includes biological (capillaries and fibroblasts), chemical (oxygen and angiogenic growth factor concentrations) and mechanical factors (cell traction forces and extracellular matrix deformation) that influence the evolution of the healing process. A novelty from previous works, apart from the coupling of angiogenesis and wound contraction, is the more realistic modelling of skin as a hyperelastic material. Large deformations are addressed using an updated Lagrangian approach. The coupled non-linear model is solved with the finite element method, and the process is studied over two wound geometries (circular and elliptical) of the same area. The results indicate that the elliptical wound vascularizes two days earlier than the circular wound but that they experience a similar contraction level, reducing its size by 25 %.     

Angiogenesis and organ transplantation

Angiogenesis is a vessel development process that maintains the vascular supply for organ function. Regulation of angiogenesis is provided by positive factors, such as vascular endothelial or basic fibroblast growth factors, and negative factors, such as thrombospondin and macrophage-derived inflammatory cytokines. While the role of angiogenesis in the wound healing, embryogenesis, tumor growth and proliferative diseases is clear, in organ transplantation it is not yet well established. Herein we discuss the potential role of angiogenesis in chronic renal disease and in transplant settings.     

A hybrid bioregulatory model of angiogenesis during bone fracture healing

Bone fracture healing is a complex process in which angiogenesis or the development of a blood vessel network plays a crucial role. In this paper, a mathematical model is presented that simulates the biological aspects of fracture healing including the formation of individual blood vessels. The model consists of partial differential equations, several of which describe the evolution in density of the most important cell types, growth factors, tissues and nutrients. The other equations determine the growth of blood vessels as a result of the movement of leading endothelial (tip) cells. Branching and anastomoses are accounted for in the model. The model is applied to a normal fracture healing case and subjected to a sensitivity analysis. The spatiotemporal evolution of soft tissues and bone, as well as the development of a blood vessel network are corroborated by comparison with experimental data. Moreover, this study shows that the proposed mathematical framework can be a useful tool in the research of impaired healing and the design of treatment strategies.     

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.     

Neovascularization and Hematopoietic Stem Cells

Vasculogenesis and angiogenesis are the major forms of blood vessel formation. Angiogenesis is the process where new vessels grow from pre-existing blood vessels, and is very important in the functional recovery of pathological conditions, such as wound healing and ischemic heart diseases. The development of better animal model and imaging technologies in past decades has greatly enriched our understanding on vasculogenesis and angiogenesis processes. Hypoxia turned out to be an important driving force for angiogenesis in various ischemic conditions. It stimulates expression of many growth factors like vascular endothelial growth factor, platelet-derived growth factor, insulin-like growth factor, and fibroblast growth factor, which play critical role in induction of angiogenesis. Other cellular components like monocytes, T cells, neutrophils, and platelets also play significant role in induction and regulation of angiogenesis. Various stem/progenitor cells also being recruited to the ischemic sites play crucial role in the angiogenesis process. Pre-clinical studies showed that stem/progenitor cells with/without combination of growth factors induce neovascularization in the ischemic tissues in various animal models. In this review, we will discuss about the fundamental factors that regulate the angiogenesis process and the use of stem cells as therapeutic regime for the treatment of ischemic diseases.     

Whole Mount Immunofluorescent Staining of the Neonatal Mouse Retina to Investigate Angiogenesis In vivo

Angiogenesis is the complex process of new blood vessel formation defined by the sprouting of new blood vessels from a pre-existing vessel network. Angiogenesis plays a key role not only in normal development of organs and tissues, but also in many diseases in which blood vessel formation is dysregulated, such as cancer, blindness and ischemic diseases. In adult life, blood vessels are generally quiescent so angiogenesis is an important target for novel drug development to try and regulate new vessel formation specifically in disease. In order to better understand angiogenesis and to develop appropriate strategies to regulate it, models are required that accurately reflect the different biological steps that are involved. The mouse neonatal retina provides an excellent model of angiogenesis because arteries, veins and capillaries develop to form a vascular plexus during the first week after birth. This model also has the advantage of having a two-dimensional (2D) structure making analysis straightforward compared with the complex 3D anatomy of other vascular networks. By analyzing the retinal vascular plexus at different times after birth, it is possible to observe the various stages of angiogenesis under the microscope. This article demonstrates a straightforward procedure for analyzing the vasculature of a mouse retina using fluorescent staining with isolectin and vascular specific antibodies.     

Regulation of angiogenesis: wound healing as a model

Normal tissue function requires adequate supply of oxygen through blood vessels. Understanding how blood vessels form is a challenging objective because angiogenesis is vital to many physiological and pathological processes. Unraveling mechanisms of angiogenesis would offer therapeutic options to ameliorate disorders that are currently leading causes of mortality and morbidity, including cardiovascular diseases, cancer, chronic inflammatory disorders, diabetic retinopathy, excessive tissue defects, and chronic non-healing wounds. Restoring blood flow to the site of injured tissue is a prerequisite for mounting a successful repair response, and wound angiogenesis represents a paradigmatic model to study molecular mechanisms involved in the formation and remodeling of vascular structures. In particular, repair of skin defects offers an ideal model to analyze angiogenesis due to its easy accessibility to control and manipulate this process. Most of those growth factors, extracellular matrix molecules, and cell types, recently discovered and considered as crucial factors in blood vessel formation, have been identified and analyzed during skin repair and the process of wound angiogenesis. This article will review cellular and molecular mechanisms controlling angiogenesis in cutaneous tissue repair in light of recent reports and data from our laboratories. In this article we will discuss the contribution of growth factors, basement membrane molecules, and mural cells in wound angiogenesis. The article provides a rationale for targeting the angiogenic response in order to modulate the outcome of the healing response.     

Continuous and discrete mathematical models of tumor-induced angiogenesis

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 dendritic 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 tumors. In this paper we present both continuous and discrete mathematical models which describe the formation of the capillary sprout network in response to chemical stimuli (tumor angiogenic factors, TAF) supplied by a solid tumor. The models also take into account essential endothelial cell-extracellular matrix interactions via the inclusion of the matrix macromolecule fibronectin. The continuous model consists of a system of nonlinear partial differential equations describing the initial migratory response of endothelial cells to the TAF and the fibronectin. Numerical simulations of the system, using parameter values based on experimental data, are presented and compared qualitatively with in vivo experiments. We then use a discretized form of the partial differential equations to develop a biased random-walk model which enables us to track individual endothelial cells at the sprout tips and incorporate anastomosis, mitosis and branching explicitly into the model. The theoretical capillary networks generated by computer simulations of the discrete model are compared with the morphology of capillary networks observed in in vivo experiments.     

Carbon inhibits vascular endothelial growth factor- and fibroblast growth factor-promoted angiogenesis

Angiogenesis is important for normal growth and wound healing processes. An imbalance of the growth factors involved in this process, however, causes the acceleration of several diseases including malignant, ocular, and inflammatory diseases. Inhibiting angiogenesis through interfering with its pathway is a promising methodology to hinder the progression of these diseases. Herein, we studied the anti-angiogenic effects of various carbon materials such as graphite, multiwalled carbon nanotubes and fullerenes in vascular endothelial growth factor (VEGF) and basic fibroblast growth factor (FGF2)-induced angiogenesis evaluated in the chick chorioallantoic membrane (CAM) model. All the carbon materials tested showed substantial anti-angiogenic activity against either FGF2- or VEGF-induced angiogenesis in the CAM model. Those carbon materials did not have any significant effects on basal angiogenesis in the absence of the added growth factors.     

Vascular endothelial growth factor (VEGF) - part 1: in physiology and pathophysiology

Angiogenesis is an important component of many physiological processes, such as the female sexual cycle, placenta formation, the processes of growth and differentiation of tissues, and reparative processes including wound healing, fracture repair, and liver regeneration. The formation of new blood vessels during angiogenesis and vasculogenesis allows the growth and functioning of multicellular organisms. Pathological angiogenesis most commonly occurs in ischaemic, inflammatory and neoplastic diseases. Conditions in the pathogenesis of which angiogenesis plays an important role are sometimes labelled angiogenic diseases. To date, a number of pro-and anti-angiogenic factors have been defined. VEGF is the only specific mitogen for endothelial cells. It stimulates their growth and inhibits apoptosis, increases vascular permeability in many tissues, promotes vasculogenesis and angiogenesis. VEGF signalling activity in relation to the cell is dependent on having its specific membrane receptors (Flt-1, KDR, Flt-4). Angiogenesis plays a protective role in ischaemic heart disease and myocardial infarction. Angiogenesis extends life for patients after a stroke. Most of the facts about physiological angiogenesis are derived from studies into liver regeneration as a result of an acute injury or partial hepatectomy. Pathological hepatic angiogenesis occurs in the course of inflammation, fibrosis, hypoxia, and during tumourogenesis. There is interesting data relating to liver steatosis and obesity.     

Theoretical models of wound healing: past successes and future challenges

The complex biology of wound healing is an area in which theoretical modelling has already made a significant impact. In this review article, the authors describe the key features of wound healing biology, divided into four components: epidermal wound healing, remodelling of the dermal extracellular matrix, wound contraction, and angiogenesis. Within each of these categories, previous modelling work is described, and the authors identify what they regard as the main challenges for future theoretical work.     

血管生成抑制素作用机理的研究进展

血管生成抑制素(angiostatin)是纤溶酶原(plasminogen)在体内的天然水解产物,能够有效抑制血管内皮细胞的增殖、迁移和管状结构的形成而参与对血管生成过程(angiogenesis)的调节。血管生成是指从已经存在的血管生长出新的分枝血管的过程。该过程在成体组织并不活跃,然而在某些病理条件下如伤口愈合、炎症、肿瘤的生长和恶性转移时却常常伴随活跃的血管生成过程。血管生成抑制素对血管生成的抑制作用,提示其作为一种特异性的针对血管内皮细胞的药物治疗与血管生成有关的一些疾病,如肿瘤的可能性。本文主要介绍近年来关于Angiostatin作用机理的研究进展以及其作为治疗药物的应用前景。     

PAKing up to the endothelium

Angiogenesis recapitulates the growth of blood vessels that progressively expand and remodel into a highly organized and stereotyped vascular network. During adulthood, endothelial cells that formed the vascular wall retain their plasticity and can be engaged in neo-vascularization in response to physiological stimuli, such as hypoxia, wound healing and tissue repair, ovarian cycle and pregnancy. In addition, numerous human diseases and pathological conditions are characterized by an excessive, uncontrolled and aberrant angiogenesis. The signalling pathways involving the small Rho GTPase, Rac and its downstream effector the p21-activated serine/threonine kinase (PAK) had recently emerged as pleiotropic modulators in these processes. Indeed, Rac and PAK were found to modulate endothelial cell biology, such as sprouting, migration, polarity, proliferation, lumen formation, and maturation. Elucidating the Rac/PAK molecular circuitry will provide essential information for the development of new therapeutic agents designed to normalize the blood vasculature in human diseases.     

An IP-10 (CXCL10)-derived peptide inhibits angiogenesis

Angiogenesis plays a critical role in processes such as organ development, wound healing, and tumor growth. It requires well-orchestrated integration of soluble and matrix factors and timely recognition of such signals to regulate this process. Previous work has shown that newly forming vessels express the chemokine receptor CXC receptor 3 (CXCR3) and, activation by its ligand IP-10 (CXCL10), both inhibits development of new vasculature and causes regression of newly formed vessels. To identify and develop new therapeutic agents to limit or reverse pathological angiogenesis, we identified a 21 amino acid fragment of IP-10, spanning the α-helical domain residues 77-98, that mimic the actions of the whole IP-10 molecule on endothelial cells. Treatment of the endothelial cells with the 22 amino acid fragment referred to as IP-10p significantly inhibited VEGF-induced endothelial motility and tube formation in vitro, properties critical for angiogenesis. Using a Matrigel plug assay in vivo, we demonstrate that IP-10p both prevented vessel formation and induced involution of nascent vessels. CXCR3 neutralizing antibody was able to block the inhibitory effects of the IP-10p, demonstrating specificity of the peptide. Inhibition of endothelial function by IP-10p was similar to that described for IP-10, secondary to CXCR3-mediated increase in cAMP production, activation of PKA inhibiting cell migration, and inhibition of VEGF-mediated m-calpain activation. IP-10p provides a novel therapeutic agent that inhibits endothelial cell function thus, allowing for the modulation of angiogenesis.     

Copper-induced vascular endothelial growth factor expression and wound healing

Angiogenesis plays a central role in wound healing. Among many known growth factors, vascular endothelial growth factor (VEGF) is believed to be the most prevalent, efficacious, and long-term signal that is known to stimulate angiogenesis in wounds. Whereas a direct role of copper to facilitate angiogenesis has been evident two decades ago, the specific targets of copper action remained unclear. This report presents first evidence showing that inducible VEGF expression is sensitive to copper and that the angiogenic potential of copper may be harnessed to accelerate dermal wound contraction and closure. At physiologically relevant concentrations, copper sulfate induced VEGF expression in primary as well as transformed human keratinocytes. Copper shared some of the pathways utilized by hypoxia to regulate VEGF expression. Topical copper sulfate accelerated closure of excisional murine dermal wound allowed to heal by secondary intention. Copper-sensitive pathways regulate key mediators of wound healing such as angiogenesis and extracellular matrix remodeling. Copper-based therapeutics represents a feasible approach to promote dermal wound healing.     

Cheiradone: a vascular endothelial cell growth factor receptor antagonist

Background  

Angiogenesis, the growth of new blood vessels from the pre-existing vasculature is associated with physiological (for example wound healing) and pathological conditions (tumour development). Vascular endothelial growth factor (VEGF), fibroblast growth factor-2 (FGF-2) and epidermal growth factor (EGF) are the major angiogenic regulators. We have identified a natural product (cheiradone) isolated from a Euphorbia species which inhibited in vivo and in vitro VEGF- stimulated angiogenesis but had no effect on FGF-2 or EGF activity. Two primary cultures, bovine aortic and human dermal endothelial cells were used in in vitro (proliferation, wound healing, invasion in Matrigel and tube formation) and in vivo (the chick chorioallantoic membrane) models of angiogenesis in the presence of growth factors and cheiradone. In all cases, the concentration of cheiradone which caused 50% inhibition (IC₅₀) was determined. The effect of cheiradone on the binding of growth factors to their receptors was also investigated.     

A Hybrid Discrete-Continuum Mathematical Model of Pattern Prediction in the Developing Retinal Vasculature

Pathological angiogenesis has been extensively explored by the mathematical modelling community over the past few decades, specifically in the contexts of tumour-induced vascularisation and wound healing. However, there have been relatively few attempts to model angiogenesis associated with normal development, despite the availability of animal models with experimentally accessible and highly ordered vascular topologies: for example, growth and development of the vascular plexus layers in the murine retina. The current study aims to address this issue through the development of a hybrid discrete-continuum mathematical model of the developing retinal vasculature in neonatal mice that is closely coupled with an ongoing experimental programme. The model of the functional vasculature is informed by a range of morphological and molecular data obtained over a period of several days, from 6?days prior to birth to approximately 8?days after birth.The spatio-temporal formation of the superficial retinal vascular plexus (RVP) in wild-type mice occurs in a well-defined sequence. Prior to birth, astrocytes migrate from the optic nerve over the surface of the inner retina in response to a chemotactic gradient of PDGF-A, formed at an earlier stage by migrating retinal ganglion cells (RGCs). Astrocytes express a variety of chemotactic and haptotactic proteins, including VEGF and fibronectin (respectively), which subsequently induce endothelial cell sprouting and modulate growth of the RVP. The developing RVP is not an inert structure; however, the vascular bed adapts and remodels in response to a wide variety of metabolic and biomolecular stimuli. The main focus of this investigation is to understand how these interacting cellular, molecular, and metabolic cues regulate RVP growth and formation.In an earlier one-dimensional continuum model of astrocyte and endothelial migration, we showed that the measured frontal velocities of the two cell types could be accurately reproduced by means of a system of five coupled partial differential equations (Aubert et?al. in Bull. Math. Biol. 73:2430-2451, 2011). However, this approach was unable to generate spatial information and structural detail for the entire retinal surface. Building upon this earlier work, a more realistic two-dimensional hybrid PDE-discrete model is derived here that tracks the migration of individual astrocytes and endothelial tip cells towards the outer retinal boundary. Blood perfusion is included throughout plexus development and the emergent retinal architectures adapt and remodel in response to various biological factors. The resulting in?silico RVP structures are compared with whole-mounted retinal vasculatures at various stages of development, and the agreement is found to be excellent. Having successfully benchmarked the model against wild-type data, the effect of transgenic over-expression of various genes is predicted, based on the ocular-specific expression of VEGF-A during murine development. These results can be used to help inform future experimental investigations of signalling pathways in ocular conditions characterised by aberrant angiogenesis.     

A DNA vaccine against VEGF receptor 2 prevents effective angiogenesis and inhibits tumor growth

Tumor cells are elusive targets for immunotherapy due to their heterogeneity and genetic instability. Here we describe a novel, oral DNA vaccine that targets stable, proliferating endothelial cells in the tumor vasculature rather than tumor cells. Targeting occurs through upregulated vascular-endothelial growth factor receptor 2 (FLK-1) of proliferating endothelial cells in the tumor vasculature. This vaccine effectively protected mice from lethal challenges with melanoma, colon carcinoma and lung carcinoma cells and reduced growth of established metastases in a therapeutic setting. CTL-mediated killing of endothelial cells indicated breaking of peripheral immune tolerance against this self antigen, resulting in markedly reduced dissemination of spontaneous and experimental pulmonary metastases. Angiogenesis in the tumor vasculature was suppressed without impairment of fertility, neuromuscular performance or hematopoiesis, albeit with a slight delay in wound healing. Our strategy circumvents problems in targeting of genetically unstable tumor cells. This approach may provide a new strategy for the rational design of cancer therapies.