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.     

Guided migration as a novel mechanism of capillary network remodeling is regulated by basic fibroblast growth factor

 To investigate mechanisms of capillary network remodeling, we developed a serum-free angiogenesis in vitro system in three-dimensional fibrin matrices which allows the study of directional growth of endothelial sprouts, anastomosis, and remodeling (’pruning’) of the primitive plexus toward more elaborated capillary trees. To follow the movements of living endothelial cells by inverse-fluorescence microscopy, we cocultured unlabeled endothelial cells with endothelial cells labeled with the carbocyanine dye 1,1′-dioctadecyl-3,3,3′,3′-tetramethylindocarbocyanine perchlorate (DiI). We show that elongation and retraction of neighboring capillary sprouts occurs simultaneously, resembling a tug-of-war by which endothelial cells are withdrawn from shortening sprouts to become incorporated in other sprouts nearby. For the first time, we directly demonstrate the long-suspected parallel sliding movement of endothelial cells. We show that cell migration persists within immature capillaries even after sprouts have merged to continuous capillary loops, leading to overlapping growth of opposing sprout tips. As a novel concept of capillary remodeling, we distinguish two types of endothelial cell migration: sprouting and guided migration. Sprouting is the de novo invasion of a matrix by endothelial cells, and guided migration is the locomotion of cells along preexistent capillary-like structures. We show that guided migration leads to remodeling of immature capillary networks and to the retraction of sprouts. We describe a method for quantification of sprouting versus guided migration in DiI-mosaic-labeled capillary networks, and we present evidence that endothelial cell-derived basic fibroblast growth factor serves as a chemotactic signal for other cells to migrate along a preestablished capillary-like structure. Accepted: 3 November 1997     

Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: clinical implications and therapeutic targeting strategies

Angiogenesis, the growth of a network of blood vessels, is a crucial component of solid tumour growth, linking the relatively harmless avascular growth phase and the potentially fatal vascular growth phase. As a process, angiogenesis is a well-orchestrated sequence of events involving endothelial cell migration, proliferation; degradation of tissue; new capillary vessel (sprout) formation; loop formation (anastomosis) and, crucially, blood flow through the network. Once there is blood flow associated with the nascent network, the subsequent growth of the network evolves both temporally and spatially in response to the combined effects of angiogenic factors, migratory cues via the extracellular matrix and perfusion-related haemodynamic forces in a manner that may be described as both adaptive and dynamic. In this paper we present a mathematical model which simultaneously couples vessel growth with blood flow through the vessels--dynamic adaptive tumour-induced angiogenesis (DATIA). This new mathematical model presents a theoretical and computational investigation of the process and highlights a number of important new targets for therapeutic intervention. In contrast to earlier flow models, where the effects of perfusion (blood flow) were essentially evaluated a posteriori, i.e. after generating a hollow network, blood flow in the model described in this paper has a direct impact during capillary growth, with radial adaptations and network remodelling occurring as immediate consequences of primary anastomoses. Capillary network architectures resulting from the dynamically adaptive model are found to differ radically from those obtained using earlier models. The DATIA model is used to examine the effects of changing various physical and biological model parameters on the developing vascular architecture and the delivery of chemotherapeutic drugs to the tumour. Subsequent simulations of chemotherapeutic treatments under different parameter regimes lead to the identification of a number of new therapeutic targets for tumour management.     

Cell proliferation along vascular islands during microvascular network growth

ABSTRACT: BACKGROUND: Observations in our laboratory provide evidence of vascular islands, defined as disconnected endothelial cell segments, in the adult microcirculation. The objective of this study was to determine if vascular islands are involved in angiogenesis during microvascular network growth. RESULTS: Mesenteric tissues, which allow visualization of entire microvascular networks at a single cell level, were harvested from unstimulated adult male Wistar rats and Wistar rats 3 and 10 days post angiogenesis stimulation by mast cell degranulation with compound 48/80. Tissues were immunolabeled for PECAM and BRDU. Identification of vessel lumens via injection of FITC-dextran confirmed that endothelial cell segments were disconnected from nearby patent networks. Stimulated networks displayed increases in vascular area, length density, and capillary sprouting. On day 3, the percentage of islands with at least one BRDU-positive cell increased compared to the unstimulated level and was equal to the percentage of capillary sprouts with at least one BRDU-positive cell. At day 10, the number of vascular islands per vascular area dramatically decreased compared to unstimulated and day 3 levels. CONCLUSIONS: These results show that vascular islands have the ability to proliferate and suggest that they are able to incorporate into the microcirculation during the initial stages of microvascular network growth.     

Numerical Modeling of Interstitial Fluid Flow Coupled with Blood Flow through a Remodeled Solid Tumor Microvascular Network

Modeling of interstitial fluid flow involves processes such as fluid diffusion, convective transport in extracellular matrix, and extravasation from blood vessels. To date, majority of microvascular flow modeling has been done at different levels and scales mostly on simple tumor shapes with their capillaries. However, with our proposed numerical model, more complex and realistic tumor shapes and capillary networks can be studied. Both blood flow through a capillary network, which is induced by a solid tumor, and fluid flow in tumor’s surrounding tissue are formulated. First, governing equations of angiogenesis are implemented to specify the different domains for the network and interstitium. Then, governing equations for flow modeling are introduced for different domains. The conservation laws for mass and momentum (including continuity equation, Darcy’s law for tissue, and simplified Navier–Stokes equation for blood flow through capillaries) are used for simulating interstitial and intravascular flows and Starling’s law is used for closing this system of equations and coupling the intravascular and extravascular flows. This is the first study of flow modeling in solid tumors to naturalistically couple intravascular and extravascular flow through a network. This network is generated by sprouting angiogenesis and consisting of one parent vessel connected to the network while taking into account the non-continuous behavior of blood, adaptability of capillary diameter to hemodynamics and metabolic stimuli, non-Newtonian blood flow, and phase separation of blood flow in capillary bifurcation. The incorporation of the outlined components beyond the previous models provides a more realistic prediction of interstitial fluid flow pattern in solid tumors and surrounding tissues. Results predict higher interstitial pressure, almost two times, for realistic model compared to the simplified model.     

A Cell-Based Model of Extracellular-Matrix-Guided Endothelial Cell Migration During Angiogenesis

Angiogenesis, the formation of new blood vessels sprouting from existing ones, occurs in several situations like wound healing, tissue remodeling, and near growing tumors. Under hypoxic conditions, tumor cells secrete growth factors, including VEGF. VEGF activates endothelial cells (ECs) in nearby vessels, leading to the migration of ECs out of the vessel and the formation of growing sprouts. A key process in angiogenesis is cellular self-organization, and previous modeling studies have identified mechanisms for producing networks and sprouts. Most theoretical studies of cellular self-organization during angiogenesis have ignored the interactions of ECs with the extra-cellular matrix (ECM), the jelly or hard materials that cells live in. Apart from providing structural support to cells, the ECM may play a key role in the coordination of cellular motility during angiogenesis. For example, by modifying the ECM, ECs can affect the motility of other ECs, long after they have left. Here, we present an explorative study of the cellular self-organization resulting from such ECM-coordinated cell migration. We show that a set of biologically-motivated, cell behavioral rules, including chemotaxis, haptotaxis, haptokinesis, and ECM-guided proliferation suffice for forming sprouts and branching vascular trees.     

Contact-dependent inhibition of angiogenesis by cardiac fibroblasts in three-dimensional fibrin gels in vitro: implications for microvascular network remodeling and coronary collateral formation

Angiogenesis and coronary artery collateral formation can improve blood flow and thereby prevent myocardial ischemia. The role of perivascular fibroblasts in neovascularization remains incompletely understood. Here we investigated the effects of epicardial and myocardial fibroblasts on angiogenesis in vitro by using a serum-free microcarrier-based fibrin gel angiogenesis system. To clearly distinguish between different cell types, we either stained endothelial cells or fibroblasts in the living with 1,1′-dioctadecyl-3,3,3′,3′-tetramethyl-indocarbocyanine-perchlorate (DiI). In cocultures, low numbers of heart fibroblasts stimulated endothelial sprouting, and capillary growth was also induced by fibroblast-conditioned media, indicating a paracrine mechanism. Capillary formation was decreased by increasing the density of fibroblasts in the cocultures, indicating contact-dependent inhibition. Using time-lapse studies, it turned out that close contacts between fibroblasts and endothelial cells resulted in rapid retraction of endothelial cells or, rarely, in cell death. Depending on the local ratio of fibroblasts to endothelial cell numbers, fibroblasts determined the location of capillary growth and the size of developing capillaries and thereby contributed to capillary network remodeling. In contrast to primary heart fibroblasts, NIH 3T3 fibroblasts did not display contact-dependent inhibition of endothelial sprouts. NIH fibroblasts were frequently seen in close association with endothelial capillaries, resembling pericytes. Contact-dependent inhibition of angiogenesis by epicardial fibroblasts could not be reversed by addition of neutralizing anti-TGF-β1 antibodies, by addition of serum, of medium conditioned by hypoxic tumor cells or myocardium, by various cytokines or by growing cocultures under hypoxic conditions. Our results implicate a pivotal role of periendothelial mesenchymal cells for the regulation of microvascular network remodeling and collateral formation. Received: 15 September 1997 / Accepted: 6 April 1998     

Immunohistochemical identification of an extracellular matrix scaffold that microguides capillary sprouting in vivo.

To gain insight into how a naturally occurring scaffold composed of extracellular matrix (ECM) proteins provides directional guidance for capillary sprouting, we examined angiogenesis in whole-mount specimens of rat mesentery. Angiogenesis was studied in response to normal maturation, the injection of a mast cell degranulating substance (compound 48/80), and mild wounding. Confocal microscopy of specimens immunolabeled for elastin revealed a network of crosslinked elastic fibers with a density of 140.8 +/- 37 mm of fiber/mm(2) tissue. Fiber diameters ranged from 180 to 1400 nm, with a mean value of 710 +/- 330 nm. Capillary sprouts contained CD31- and OX-43-positive endothelial cells as well as desmin-positive pericytes. During normal maturation, leading endothelial cells and pericytes were in contact and aligned with an elastic fiber in approximately 80-90% of all sprouts. In wounding and compound 48/80-treated specimens, in which angiogenesis was markedly increased, leading endothelial cells remained in contact and aligned with elastic fibers in approximately 60-80% of all sprouts. These observations indicate that elastic fibers are used for endothelial and pericyte migration during capillary sprouting in rat mesentery. The composition of this elastic fiber matrix may provide important clues for the development of tissue-engineered scaffolds that support and directionally guide angiogenesis.     

Distinct signalling pathways regulate sprouting angiogenesis from the dorsal aorta and the axial vein

Angiogenesis, the formation of new blood vessels from pre-existing vessels, is critical to most physiological processes and many pathological conditions. During zebrafish development, angiogenesis expands the axial vessels into a complex vascular network that is necessary for efficient oxygen delivery. Although the dorsal aorta and the axial vein are spatially juxtaposed, the initial angiogenic sprouts from these vessels extend in opposite directions, indicating that distinct cues may regulate angiogenesis of the axial vessels. We found that angiogenic sprouts from the dorsal aorta are dependent on vascular endothelial growth factor A (Vegf-A) signalling, and do not respond to bone morphogenetic protein (Bmp) signals. In contrast, sprouts from the axial vein are regulated by Bmp signalling independently of Vegf-A signals, indicating that Bmp is a vein-specific angiogenic cue during early vascular development. Our results support a paradigm whereby different signals regulate distinct programmes of sprouting angiogenesis from the axial vein and dorsal aorta, and indicate that signalling heterogeneity contributes to the complexity of vascular networks.     

Computational Screening of Tip and Stalk Cell Behavior Proposes a Role for Apelin Signaling in Sprout Progression

Angiogenesis involves the formation of new blood vessels by sprouting or splitting of existing blood vessels. During sprouting, a highly motile type of endothelial cell, called the tip cell, migrates from the blood vessels followed by stalk cells, an endothelial cell type that forms the body of the sprout. To get more insight into how tip cells contribute to angiogenesis, we extended an existing computational model of vascular network formation based on the cellular Potts model with tip and stalk differentiation, without making a priori assumptions about the differences between tip cells and stalk cells. To predict potential differences, we looked for parameter values that make tip cells (a) move to the sprout tip, and (b) change the morphology of the angiogenic networks. The screening predicted that if tip cells respond less effectively to an endothelial chemoattractant than stalk cells, they move to the tips of the sprouts, which impacts the morphology of the networks. A comparison of this model prediction with genes expressed differentially in tip and stalk cells revealed that the endothelial chemoattractant Apelin and its receptor APJ may match the model prediction. To test the model prediction we inhibited Apelin signaling in our model and in an in vitro model of angiogenic sprouting, and found that in both cases inhibition of Apelin or of its receptor APJ reduces sprouting. Based on the prediction of the computational model, we propose that the differential expression of Apelin and APJ yields a “self-generated” gradient mechanisms that accelerates the extension of the sprout.     

Human adipose tissue stromal vascular fraction cells differentiate depending on distinct types of media

Abstract.  Objectives : Angiogenesis, the process of formation of blood vessels, is essential for many physiological as well as pathological processes. It has been shown that human adipose tissue contains a population of non-characterized cells, called stromal-vascular fraction (SVF) cells, which are able to differentiate into several lineages. The aim of this study was to determine conditions for promoting differentiation of human adipose tissue progenitors towards endothelial cells, as well as to show that SVF cells cooperate with differentiated endothelium in capillary network formation. Materials and methods : Stromal vascular fraction cells were isolated according to modified Hauner's method and after adaptation they were cultured in pro-angiogenic or pro-adipogenic medium. Cells were characterized by presence of surface antigens by flow cytometry, and by expression of genes characteristic for endothelial cells or for adipocytes, quantitative real-time polymerase chain reaction. A number of tests were performed to verify their differentiation. Results : Differentiation of human SVF cells towards endothelium was stimulated by the presence of serum and absence of adipogenic factors, documented by the pattern of gene expression as well as different functional in vitro assays. SVF cells were found to work together with human umbilical vein endothelial cells to form capillary networks. Conclusions : Here, we show that differentiation of SVF cells to endothelial cells or adipocyte-like cells depended on the medium used. Our work provides a clear model for analysing the differentiation capacity of SVF cells.     

Absence of OX-43 antigen expression in invasive capillary sprouts: identification of a capillary sprout-specific endothelial phenotype

Endothelial cells exhibit a number of unique phenotypes, some of which are angiogenesis dependent. To identify a capillary sprout-specific endothelial phenotype, we labeled angiogenic rat mesentery tissue using a microvessel and capillary sprout marker (laminin), selected endothelial cell markers (CD31, tie-2, and BS-I lectin), and the OX-43 monoclonal antibody, which recognizes a 90-kDa membrane glycoprotein of unknown function. In tissues that were stimulated through wound healing and compound 48/80 application, double-immunolabeling experiments with an anti-laminin antibody revealed that the OX-43 antigen was expressed strongly in all microvessels. However, the OX-43 antigen was completely absent from a large percentage (>85%) of the capillary sprouts that were invading the avascular tissue space. In contrast, sprouts that were introverting back into the previously vascularized tissue retained high levels of OX-43 antigen expression. Double-labeling experiments with endothelial markers indicated that the OX-43 antigen was expressed by microvessel endothelium but was absent from virtually all invasive capillary sprout endothelial cells. We conclude that the absence of OX-43 antigen expression marks a novel, capillary sprout-specific, endothelial cell phenotype. Endothelial cells of this phenotype are particularly abundant in capillary sprouts that invade avascular tissue during angiogenesis.     

A heterogeneous in vitro three dimensional model of tumour-stroma interactions regulating sprouting angiogenesis

Angiogenesis, the formation of new blood vessels, is an essential process for tumour progression and is an area of significant therapeutic interest. Different in vitro systems and more complex in vivo systems have been described for the study of tumour angiogenesis. However, there are few human 3D in vitro systems described to date which mimic the cellular heterogeneity and complexity of angiogenesis within the tumour microenvironment. In this study we describe the Minitumour model--a 3 dimensional human spheroid-based system consisting of endothelial cells and fibroblasts in co-culture with the breast cancer cell line MDA-MB-231, for the study of tumour angiogenesis in vitro. After implantation in collagen-I gels, Minitumour spheroids form quantifiable endothelial capillary-like structures. The endothelial cell pre-capillary sprouts are supported by the fibroblasts, which act as mural cells, and their growth is increased by the presence of cancer cells. Characterisation of the Minitumour model using small molecule inhibitors and inhibitory antibodies show that endothelial sprout formation is dependent on growth factors and cytokines known to be important for tumour angiogenesis. The model also shows a response to anti-angiogenic agents similar to previously described in vivo data. We demonstrate that independent manipulation of the different cell types is possible, using common molecular techniques, before incorporation into the model. This aspect of Minitumour spheroid analysis makes this model ideal for high content studies of gene function in individual cell types, allowing for the dissection of their roles in cell-cell interactions. Finally, using this technique, we were able to show the requirement of the metalloproteinase MT1-MMP in endothelial cells and fibroblasts, but not cancer cells, for sprouting angiogenesis.     

Mathematical models for tumour angiogenesis: Numerical simulations and nonlinear wave solutions

To ensure its sustained growth, a tumour may secrete chemical compounds which cause neighbouring capillaries to form sprouts which then migrate towards it, furnishing the tumour with an increased supply of nutrients. In this paper a mathematical model is presented which describes the migration of capillary sprouts in response to a chemoattractant field set up by a tumour-released angiogenic factor, sometimes termed a tumour angiogenesis factor (TAF). The resulting model admits travelling wave solutions which correspond either to successful neovascularization of the tumour or failure of the tumour to secure a vascular network, and which exhibit many of the characteristic features of angiogenesis. For example, the increasing speed of the vascular front, and the evolution of an increasingly developed vascular network behind the leading capillary tip front (the brush-border effect) are both discernible from the numerical simulations. Through the development and analysis of a simplified caricature model, valuable insight is gained into how the balance between chemotaxis, tip proliferation and tip death affects the tumour's ability to induce a vascular response from neighbouring blood vessels. In particular, it is possible to define the success of angiogenesis in terms of known parameters, thereby providing a potential framework for assessing the viability of tumour neovascularization in terms of measurable quantities.     

Tumour metabolites regulate tissue kallikrein in human umbilical vein endothelial cells

Angiogenesis, the sprouting of new blood vessels, is tightly mediated via a myriad of endogenous factors. A pro-angiogenic alteration facilitates the formation of neovascular tumour networks, thereby providing mechanisms for uncontrolled growth. The kallikrein-kinin system is postulated to be pro-angiogenic since its components have been detected in both endothelial cells and tumour tissue. No studies have, however, focussed on the role of tissue kallikrein (TK) in human angiogenic endothelial cell-tumour interactions. This study has optimised a challenge model whereby endothelial cells are presented with neuroblastoma metabolites, and vice versa. Image analysis of immunoreactive TK revealed a dose-dependant, significant reduction of TK localisation within endothelial cells, while gene expression remained unchanged, the latter determined by in situ RT-PCR. Neuroblastoma cells, when challenged with endothelial cell metabolites, displayed no change in TK synthesis or localisation. Alterations in TK synthesis and/or storage by angiogenic endothelial cells may be mediated by tumour-released signals and possibly indicate a shift from a proteolytic to a mitogenic function of TK. The challenge model provides a relatively simple experimental system to study angiogenic factors in tumour-endothelial cell interaction, and is the first to localise both TK and its mRNA within angiogenic endothelial and tumour cells.     

Self-sustained Oscillations in Blood Flow Through a Honeycomb Capillary Network

Numerical simulations of unsteady blood flow through a honeycomb network originating at multiple inlets and terminating at multiple outlets are presented and discussed under the assumption that blood behaves as a continuum with variable constitution. Unlike a tree network, the honeycomb network exhibits both diverging and converging bifurcations between branching capillary segments. Numerical results based on a finite difference method demonstrate that as in the case of tree networks considered in previous studies, the cell partitioning law at diverging bifurcations is an important parameter in both steady and unsteady flow. Specifically, a steady flow may spontaneously develop self-sustained oscillations at critical conditions by way of a Hopf bifurcation. Contrary to tree-like networks comprised entirely of diverging bifurcations, the critical parameters for instability in honeycomb networks depend weakly on the system size. The blockage of one or more network segments due to the presence of large cells or the occurrence of capillary constriction may cause flow reversal or trigger a transition to unsteady flow.     

Pericyte involvement in capillary sprouting during angiogenesis in situ

Summary To investigate the participation of microvascular pericytes in the process of capillary sprouting, we examined whole-mount preparations of the rat mesentery by use of a double immunofluorescence approach. Angiogenesis was induced by intraperitoneal injections of either the mast cell-degranulating substance compound 48/80 or tumor cell-conditioned medium. Capillary sprouts were visualized by staining with rhodaminconjugated phalloidin and pericytes were simultaneosly stained by an antibody to the intermediate filament protein desmin. Developing pericytes were negative for the smooth-muscle isoform of -actin, bbut were clearly reactive for desmin. Pericytes appear to be involved in the carliest stages of capillary sprouting. Pericytes were regularly found lying at and in front of the advancing tips of endothelial sprouts. At many sites pericytes were seen to bridge the gap between the leading edges of opposing endothelial sprouts, which were apparently preparing to merge, suggesting that pericytic processes may serve as guiding structures aiding outgrowth of endothelial cells.     

Tumor necrosis factor and vascular endothelial growth factor induce endothelial integrin repertories, regulating endovascular differentiation and apoptosis in a human extravillous trophoblast cell line

Angiogenesis is crucial in human development. Extravillous trophoblast (EVT) cells mimic endothelial cells in angiogenesis during endovascular differentiation, inducing a remodeling of spiral arteries that increases blood flow toward the intravillous space. We have previously shown that tumor necrosis factor (TNF) alpha regulates expression of ITGA6 and ITGA1, which are involved in cell survival, in the human EVT cell line TCL1. To further investigate endovascular differentiation, we examined the effects of vascular endothelial growth factor (VEGF), TNF, and extracellular matrix (ECM) on TCL1 cells. Seeded on Matrigel, TCL1 cells show tube-like formation that specifically recalls morphological changes in endothelial cells. Anti-ITGAV/ITGB3 antibodies significantly reduced the size of the capillary network (P < 0.05) on Matrigel and also suppressed TNF-induced apoptosis (P < 0.05) in TCL1 cells. VEGF induced expression of ITGAV/ITGB3 subunits and protein aggregation, as in the case of TNF, which in turn, induces synthesis of VEGF in TCL1 cells. Soluble FLT1 suppressed these activities in TCL1 cells, indicating that signals involving VEGF axis are essential for endovascular differentiation. These results suggest that TNF, VEGF, and ECM collaboratively regulate EVT behavior, including cell survival and endovascular differentiation, through integrin signaling during establishment and maintenance of successful human pregnancies.     

Flow-Regulated Endothelial S1P Receptor-1 Signaling Sustains Vascular Development

During angiogenesis, nascent vascular sprouts fuse to form vascular networks, enabling efficient circulation. Mechanisms that stabilize the vascular plexus are not well understood. Sphingosine 1-phosphate (S1P) is a blood-borne lipid mediator implicated in the regulation of vascular and immune systems. Here we describe a mechanism by which the G protein-coupled S1P receptor-1 (S1P(1)) stabilizes the primary vascular network. A gradient of S1P(1) expression from the mature regions of the vascular network to the growing vascular front was observed. In the absence of endothelial S1P(1), adherens junctions are destabilized, barrier function is breached, and flow is perturbed, resulting in abnormal vascular hypersprouting. Interestingly, S1P(1) responds to S1P?as well as laminar shear stress to transduce flow-mediated signaling in endothelial cells both in?vitro and in?vivo. These data demonstrate that blood flow and circulating S1P activate endothelial S1P(1) to stabilize blood vessels in development and homeostasis.     

Mapping 3-D functional capillary geometry in rat skeletal muscle in vivo

We have developed a novel mapping software package to reconstruct microvascular networks in three dimensions (3-D) from in vivo video images for use in blood flow and O2 transport modeling. An intravital optical imaging system was used to collect video sequences of blood flow in microvessels at different depths in the tissue. Functional images of vessels were produced from the video sequences and were processed using automated edge tracking software to yield location and geometry data for construction of the 3-D network. The same video sequences were analyzed for hemodynamic and O2 saturation data from individual capillaries in the network. Simple user-driven commands allowed the connection of vessel segments at bifurcations, and semiautomated registration enabled the tracking of vessels across multiple focal planes and fields of view. The reconstructed networks can be rotated and manipulated in 3-D to verify vessel connections and continuity. Hemodynamic and O2 saturation measurements made in vivo can be indexed to corresponding vessels and visualized using colorized maps of the vascular geometry. Vessels in each reconstruction are saved as text-based files that can be easily imported into flow or O2 transport models with complete geometry, hemodynamic, and O2 transport conditions. The results of digital morphometric analysis of seven microvascular networks showed mean capillary diameters and overall capillary density consistent with previous findings using histology and corrosion cast techniques. The described mapping software is a valuable tool for the quantification of in vivo microvascular geometry, hemodynamics, and oxygenation, thus providing rich data sets for experiment-based computational models.