A computational model of in vitro angiogenesis based on extracellular matrix fibre orientation

Modeling the extracellular matrix in cell migration and morphogenesis: a guide for the curious biologist

The extracellular matrix (ECM) is a highly complex structure through which biochemical and mechanical signals are transmitted. In processes of cell migration, the ECM also acts as a scaffold, providing structural support to cells as well as points of potential attachment. Although the ECM is a well-studied structure, its role in many biological processes remains difficult to investigate comprehensively due to its complexity and structural variation within an organism. In tandem with experiments, mathematical models are helpful in refining and testing hypotheses, generating predictions, and exploring conditions outside the scope of experiments. Such models can be combined and calibrated with in vivo and in vitro data to identify critical cell-ECM interactions that drive developmental and homeostatic processes, or the progression of diseases. In this review, we focus on mathematical and computational models of the ECM in processes such as cell migration including cancer metastasis, and in tissue structure and morphogenesis. By highlighting the predictive power of these models, we aim to help bridge the gap between experimental and computational approaches to studying the ECM and to provide guidance on selecting an appropriate model framework to complement corresponding experimental studies.

External mechanical loading overrules cell-cell mechanical communication in sprouting angiogenesis during early bone regeneration

Sprouting angiogenesis plays a key role during bone regeneration. For example, insufficient early revascularization of the injured site can lead to delayed or non-healing. During sprouting, endothelial cells are known to be mechano-sensitive and respond to local mechanical stimuli. Endothelial cells interact and communicate mechanically with their surroundings, such as outer-vascular stromal cells, through cell-induced traction forces. In addition, external physiological loads act at the healing site, resulting in tissue deformations and impacting cellular arrangements. How these two distinct mechanical cues (cell-induced and external) impact angiogenesis and sprout patterning in early bone healing remains however largely unknown. Therefore, the aim of this study was to investigate the relative role of externally applied and cell-induced mechanical signals in driving sprout patterning at the onset of bone healing. To investigate cellular self-organisation in early bone healing, an in silico model accounting for the mechano-regulation of sprouting angiogenesis and stromal cell organization was developed. Computer model predictions were compared to in vivo experiments of a mouse osteotomy model stabilized with a rigid or a semirigid fixation system. We found that the magnitude and orientation of principal strains within the healing region can explain experimentally observed sprout patterning, under both fixation conditions. Furthermore, upon simulating the selective inhibition of either cell-induced or externally applied mechanical cues, external mechanical signals appear to overrule the mechanical communication acting on a cell-cell interaction level. Such findings illustrate the relevance of external mechanical signals over the local cell-mediated mechanical cues and could be used in the design of fracture treatment strategies for bone regeneration.

Spatial Configurations of 3D Extracellular Matrix Collagen Density and Anisotropy Simultaneously Guide Angiogenesis

Extracellular matrix (ECM) collagen density and fibril anisotropy are thought to affect the development of new vasculatures during pathologic and homeostatic angiogenesis. Computational simulation is emerging as a tool to investigate the role of matrix structural configurations on cell guidance. However, prior computational models have only considered the orientation of collagen as a model input. Recent experimental evidence indicates that cell guidance is simultaneously influenced by the direction and intensity of alignment (i.e., degree of anisotropy) as well as the local collagen density. The objective of this study was to explore the role of ECM collagen anisotropy and density during sprouting angiogenesis through simulation in the AngioFE and FEBio modeling frameworks. AngioFE is a plugin for FEBio (Finite Elements for Biomechanics) that simulates cell-matrix interactions during sprouting angiogenesis. We extended AngioFE to represent ECM collagen as deformable 3D ellipsoidal fibril distributions (EFDs). The rate and direction of microvessel growth were modified to depend simultaneously on the ECM collagen anisotropy (orientation and degree of anisotropy) and density. The sensitivity of growing neovessels to these stimuli was adjusted so that AngioFE could reproduce the growth and guidance observed in experiments where microvessels were cultured in collagen gels of varying anisotropy and density. We then compared outcomes from simulations using EFDs to simulations that used AngioFE's prior vector field representation of collagen anisotropy. We found that EFD simulations were more accurate than vector field simulations in predicting experimentally observed microvessel guidance. Predictive simulations demonstrated the ability of anisotropy gradients to recruit microvessels across short and long distances relevant to wound healing. Further, simulations predicted that collagen alignment could enable microvessels to overcome dense tissue interfaces such as tumor-associated collagen structures (TACS) found in desmoplasia and tumor-stroma interfaces. This approach can be generalized to other mechanobiological relationships during cell guidance phenomena in computational settings.

On the role of mechanical signals on sprouting angiogenesis through computer modeling approaches

Sprouting angiogenesis, the formation of new vessels from preexisting vasculature, is an essential process in the regeneration of new tissues as well as in the development of some diseases like cancer. Although early studies identified chemical signaling as the main driver of this process, many recent studies have shown a strong role of mechanical signals in the formation of new capillaries. Different types of mechanical signals (e.g., external forces, cell traction forces, and blood flow-induced shear forces) have been shown to play distinct roles in the process; however, their interplay remains still largely unknown. During the last decades, mathematical and computational modeling approaches have been developed to investigate and better understand the mechanisms behind mechanically driven angiogenesis. In this manuscript, we review computational models of angiogenesis with a focus on models investigating the role of mechanics on the process. Our aim is not to provide a detailed review on model methodology but to describe what we have learnt from these models. We classify models according to the mechanical signals being investigated and describe how models have looked into their role on the angiogenic process. We show that a better understanding of the mechanobiology of the angiogenic process will require the development of computer models that incorporate the interactions between the multiple mechanical signals and their effect on cellular responses, since they all seem to play a key in sprout patterning. In the end, we describe some of the remaining challenges of computational modeling of angiogenesis and discuss potential avenues for future research.

Current Concepts and Future Applications of Non-Invasive Functional and Anatomical Evaluation of Coronary Artery Disease

Over the last decades, significant advances have been achieved in the treatment of coronary artery disease (CAD). Proper non-invasive diagnosis and appropriate management based on functional information and the extension of ischemia or viability remain the cornerstone in the fight against adverse CAD events. Stress echocardiography and single photon emission computed tomography are often used for the evaluation of ischemia. Advancements in non-invasive imaging modalities such as computed tomography (CT) coronary angiography and cardiac magnetic resonance imaging (MRI) have not only allowed non-invasive imaging of coronary artery lumen but also provide additional functional information. Other characteristics regarding the plaque morphology can be further evaluated with the latest modalities achieving a morpho-functional evaluation of CAD. Advances in the utilization of positron emission tomography (PET), as well as software advancements especially regarding cardiac CT, may provide additional prognostic information to a more evidence-based treatment decision. Since the armamentarium on non-invasive imaging modalities has evolved, the knowledge of the capabilities and limitations of each imaging modality should be evaluated in a case-by-case basis to achieve the best diagnosis and treatment decision. In this review article, we present the most recent advances in the noninvasive anatomical and functional evaluation of CAD.

Mechanistic characterization of endothelial sprouting mediated by pro-angiogenic signaling

Objective

We aim to quantitatively characterize the crosstalk between VEGF‐ and FGF‐mediated angiogenic signaling and endothelial sprouting, to gain mechanistic insights and identify novel therapeutic strategies.

Methods

We constructed an experimentally validated hybrid agent‐based mathematical model that characterizes endothelial sprouting driven by FGF‐ and VEGF‐mediated signaling. We predicted the total sprout length, number of sprouts, and average length by the mono‐ and co‐stimulation of FGF and VEGF.

Results

The experimentally fitted and validated model predicts that FGF induces stronger angiogenic responses in the long‐term compared with VEGF stimulation. Also, FGF plays a dominant role in the combination effects in endothelial sprouting. Moreover, the model suggests that ERK and Akt pathways and cellular responses contribute differently to the sprouting process. Last, the model predicts that the strategies to modulate endothelial sprouting are context‐dependent, and our model can identify potential effective pro‐ and anti‐angiogenic targets under different conditions and study their efficacy.

Conclusions

The model provides detailed mechanistic insight into VEGF and FGF interactions in sprouting angiogenesis. More broadly, this model can be utilized to identify targets that influence angiogenic signaling leading to endothelial sprouting and to study the effects of pro‐ and anti‐angiogenic therapies.

Multiscale computational modeling of cancer growth using features derived from microCT images

Advances in medical imaging technologies now allow noninvasive image acquisition from individual patients at high spatiotemporal resolutions. A relatively new effort of predictive oncology is to develop a paradigm for forecasting the future status of an individual tumor given initial conditions and an appropriate mathematical model. The objective of this study was to introduce a comprehensive multiscale computational method to predict cancer and microvascular network growth patterns. A rectangular lattice-based model was designed so different evolutionary scenarios could be simulated and for predicting the impact of diffusible factors on tumor morphology and size. Further, the model allows prediction-based simulation of cell and microvascular behavior. Like a single cell, each agent is fully realized within the model and interactions are governed in part by machine learning methods. This multiscale computational model was developed and incorporated input information from in vivo microscale computed tomography (microCT) images acquired from breast cancer-bearing mice. It was found that as the difference between expansion of the cancer cell population and microvascular network increases, cells undergo proliferation and migration with a greater probability compared to other phenotypes. Overall, multiscale computational model agreed with both theoretical expectations and experimental findings (microCT images) not used during model training.

Scaffold Architecture and Matrix Strain Modulate Mesenchymal Cell and Microvascular Growth and Development in a Time Dependent Manner

BACKGROUND

Volumetric tissue-engineered constructs are limited in development due to the dependence on well-formed vascular networks. Scaffold pore size and the mechanical properties of the matrix dictates cell attachment, proliferation and successive tissue morphogenesis. We hypothesize scaffold pore architecture also controls stromal-vessel interactions during morphogenesis.

METHODS

The interaction between mesenchymal stem cells (MSCs) seeded on hydroxyapatite scaffolds of 450, 340, and 250 μm pores and microvascular fragments (MVFs) seeded within 20 mg/mL fibrin hydrogels that were cast into the cell-seeded scaffolds, was assessed in vitro over 21 days and compared to the fibrin hydrogels without scaffold but containing both MSCs and MVFs. mRNA sequencing was performed across all groups and a computational mechanics model was developed to validate architecture effects on predicting vascularization driven by stiffer matrix behavior at scaffold surfaces compared to the pore interior.

RESULTS

Lectin staining of decalcified scaffolds showed continued vessel growth, branching and network formation at 14 days. The fibrin gel provides no resistance to spread-out capillary networks formation, with greater vessel loops within the 450 μm pores and vessels bridging across 250 μm pores. Vessel growth in the scaffolds was observed to be stimulated by hypoxia and successive angiogenic signaling. Fibrin gels showed linear fold increase in VEGF expression and no change in BMP2. Within scaffolds, there was multiple fold increase in VEGF between days 7 and 14 and early multiple fold increases in BMP2 between days 3 and 7, relative to fibrin. There was evidence of yap/taz based hippo signaling and mechanotransduction in the scaffold groups. The vessel growth models determined by computational modeling matched the trends observed experimentally.

CONCLUSION

The differing nature of hypoxia signaling between scaffold systems and mechano-transduction sensing matrix mechanics were primarily responsible for differences in osteogenic cell and microvessel growth. The computational model implicated scaffold architecture in dictating branching morphology and strain in the hydrogel within pores in dictating vessel lengths.

Evaluation of Cell's Passability in the ECM Network

The microstructure of the extracellular matrix (ECM) plays a key role in affecting cell migration, especially nonproteolytic migration. It is difficult, however, to measure some properties of the ECM, such as stiffness and the passability for cell migration. On the basis of a network model of collagen fiber in the ECM, which has been well applied to simulate mechanical behaviors such as the stress-strain relationship, damage, and failure, we proposed a series of methods to study the microstructural properties containing pore size and pore stiffness and to search for the possible migration paths for cells. Finally, with a given criterion, we quantitatively evaluated the passability of the ECM network for cell migration. The fiber network model with a microstructure and the analysis method presented in this study further our understanding of and ability to evaluate the properties of an ECM network.

Stromal Cells Promote Neovascular Invasion Across Tissue Interfaces

Vascular connectivity between adjacent vessel beds within and between tissue compartments is essential to any successful neovascularization process. To establish new connections, growing neovessels must locate other vascular elements during angiogenesis, often crossing matrix and other tissue-associated boundaries and interfaces. How growing neovessels traverse any tissue interface, whether part of the native tissue structure or secondary to a regenerative procedure (e.g., an implant), is not known. In this study, we developed an experimental model of angiogenesis wherein growing neovessels must interact with a 3D interstitial collagen matrix interface that separates two distinct tissue compartments. Using this model, we determined that matrix interfaces act as a barrier to neovessel growth, deflecting growing neovessels parallel to the interface. Computational modeling of the neovessel/matrix biomechanical interactions at the interface demonstrated that differences in collagen fibril density near and at the interface are the likely mechanism of deflection, while fibril alignment guides deflected neovessels along the interface. Interestingly, stromal cells facilitated neovessel interface crossing during angiogenesis via a vascular endothelial growth factor (VEGF)-A dependent process. However, ubiquitous addition of VEGF-A in the absence of stromal cells did not promote interface invasion. Therefore, our findings demonstrate that vascularization of a tissue via angiogenesis involves stromal cells providing positional cues to the growing neovasculature and provides insight into how a microvasculature is organized within a tissue.

A Plugin Framework for Extending the Simulation Capabilities of FEBio

The FEBio software suite is a set of software tools for nonlinear finite element analysis in biomechanics and biophysics. FEBio employs mixture theory to account for the multiconstituent nature of biological materials, integrating the field equations for irreversible thermodynamics, solid mechanics, fluid mechanics, mass transport with reactive species, and electrokinetics. This communication describes the development and application of a new "plugin" framework for FEBio. Plugins are dynamically linked libraries that allow users to add new features and to couple FEBio with other domain-specific software applications without modifying the source code directly. The governing equations and simulation capabilities of FEBio are reviewed. The implementation, structure, use, and application of the plugin framework are detailed. Several example plugins are described in detail to illustrate how plugins enrich, extend, and leverage existing capabilities in FEBio, including applications to deformable image registration, constitutive modeling of biological tissues, coupling to an external software package that simulates angiogenesis using a discrete computational model, and a nonlinear reaction-diffusion solver. The plugin feature facilitates dissemination of new simulation methods, reproduction of published results, and coupling of FEBio with other domain-specific simulation approaches such as compartmental modeling, agent-based modeling, and rigid-body dynamics. We anticipate that the new plugin framework will greatly expand the range of applications for the FEBio software suite and thus its impact.

Hybrid multiscale modeling and prediction of cancer cell behavior

Background

Understanding cancer development crossing several spatial-temporal scales is of great practical significance to better understand and treat cancers. It is difficult to tackle this challenge with pure biological means. Moreover, hybrid modeling techniques have been proposed that combine the advantages of the continuum and the discrete methods to model multiscale problems.

Methods

In light of these problems, we have proposed a new hybrid vascular model to facilitate the multiscale modeling and simulation of cancer development with respect to the agent-based, cellular automata and machine learning methods. The purpose of this simulation is to create a dataset that can be used for prediction of cell phenotypes. By using a proposed Q-learning based on SVR-NSGA-II method, the cells have the capability to predict their phenotypes autonomously that is, to act on its own without external direction in response to situations it encounters.

Results

Computational simulations of the model were performed in order to analyze its performance. The most striking feature of our results is that each cell can select its phenotype at each time step according to its condition. We provide evidence that the prediction of cell phenotypes is reliable.

Conclusion

Our proposed model, which we term a hybrid multiscale modeling of cancer cell behavior, has the potential to combine the best features of both continuum and discrete models. The in silico results indicate that the 3D model can represent key features of cancer growth, angiogenesis, and its related micro-environment and show that the findings are in good agreement with biological tumor behavior. To the best of our knowledge, this paper is the first hybrid vascular multiscale modeling of cancer cell behavior that has the capability to predict cell phenotypes individually by a self-generated dataset.

A Validated Multiscale In-Silico Model for Mechano-sensitive Tumour Angiogenesis and Growth

Vascularisation is a key feature of cancer growth, invasion and metastasis. To better understand the governing biophysical processes and their relative importance, it is instructive to develop physiologically representative mathematical models with which to compare to experimental data. Previous studies have successfully applied this approach to test the effect of various biochemical factors on tumour growth and angiogenesis. However, these models do not account for the experimentally observed dependency of angiogenic network evolution on growth-induced solid stresses. This work introduces two novel features: the effects of hapto- and mechanotaxis on vessel sprouting, and mechano-sensitive dynamic vascular remodelling. The proposed three-dimensional, multiscale, in-silico model of dynamically coupled angiogenic tumour growth is specified to in-vivo and in-vitro data, chosen, where possible, to provide a physiologically consistent description. The model is then validated against in-vivo data from murine mammary carcinomas, with particular focus placed on identifying the influence of mechanical factors. Crucially, we find that it is necessary to include hapto- and mechanotaxis to recapitulate observed time-varying spatial distributions of angiogenic vasculature.

3D hybrid modelling of vascular network formation

We develop an off-lattice, agent-based model to describe vasculogenesis, the de novo formation of blood vessels from endothelial progenitor cells during development. The endothelial cells that comprise our vessel network are viewed as linearly elastic spheres that move in response to the forces they experience. We distinguish two types of endothelial cells: vessel elements are contained within the network and tip cells are located at the ends of vessels. Tip cells move in response to mechanical forces caused by interactions with neighbouring vessel elements and the local tissue environment, chemotactic forces and a persistence force which accounts for their tendency to continue moving in the same direction. Vessel elements are subject to similar mechanical forces but are insensitive to chemotaxis. An angular persistence force representing interactions with the local tissue is introduced to stabilise buckling instabilities caused by cell proliferation. Only vessel elements proliferate, at rates which depend on their degree of stretch: elongated elements have increased rates of proliferation, and compressed elements have reduced rates. Following division, the fate of the new cell depends on the local mechanical environment: the probability of forming a new sprout is increased if the parent vessel is highly compressed and the probability of being incorporated into the parent vessel increased if the parent is stretched. Simulation results reveal that our hybrid model can reproduce the key qualitative features of vasculogenesis. Extensive parameter sensitivity analyses show that significant changes in network size and morphology are induced by varying the chemotactic sensitivity of tip cells, and the sensitivities of the proliferation rate and the sprouting probability to mechanical stretch. Varying the chemotactic sensitivity directly influences the directionality of the networks. The degree of branching, and thereby the density of the networks, is influenced by the sprouting probability. Glyphs that simultaneously depict several network properties are introduced to show how these and other network quantities change over time and also as model parameters vary. We also show how equivalent glyphs constructed from in vivo data could be used to discriminate between normal and tumour vasculature and, in the longer term, for model validation. We conclude that our biomechanical hybrid model can generate vascular networks that are qualitatively similar to those generated from in vitro and in vivo experiments.

Augmenting Surgery via Multi-scale Modeling and Translational Systems Biology in the Era of Precision Medicine: A Multidisciplinary Perspective

In this era of tremendous technological capabilities and increased focus on improving clinical outcomes, decreasing costs, and increasing precision, there is a need for a more quantitative approach to the field of surgery. Multiscale computational modeling has the potential to bridge the gap to the emerging paradigms of Precision Medicine and Translational Systems Biology, in which quantitative metrics and data guide patient care through improved stratification, diagnosis, and therapy. Achievements by multiple groups have demonstrated the potential for (1) multiscale computational modeling, at a biological level, of diseases treated with surgery and the surgical procedure process at the level of the individual and the population; along with (2) patient-specific, computationally-enabled surgical planning, delivery, and guidance and robotically-augmented manipulation. In this perspective article, we discuss these concepts, and cite emerging examples from the fields of trauma, wound healing, and cardiac surgery.

In Silico Investigation of Angiogenesis with Growth and Stress Generation Coupled to Local Extracellular Matrix Density

Mechanical interactions during angiogenesis, i.e., traction applied by neovessels to the extracellular matrix and the corresponding deformation, are important regulators of growth and neovascularization. We have previously designed, implemented, and validated a coupled model of angiogenesis in which a discrete microvessel growth model interacts with a continuous finite element mesh through the application of local remodeling sprout stresses (Edgar et al. in Biomech Model Mechanobiol, 2014). However, the initial implementation of this framework does not take matrix density into account when determined these remodeling stresses and is therefore insufficient for the study of angiogenesis within heterogeneous matrix environments such as those found in vivo. The objective of this study was to implement sensitivity to matrix density in the active stress generation within AngioFE in order to allow the study of angiogenic growth within a heterogeneous density environment. We accomplished this by scaling active sprout stresses relative to local matrix density using a scaling factor previously determined from experimental data. We then exercised the new functionality of the model by simulating angiogenesis within four different scenarios: homogeneous density, a narrow gap model, and matrix density gradient, and a construct subjected to repeated loading/unloading and preconditioning. These numerical experiments predicted heterogeneous matrix density in the initially homogeneous case, the closure and alignment of microvessels along a low-density gap, the formation of a unique cap-like structure during angiogenesis within a density gradient, and the alignment of microvessels in the absence of applied load due to preconditioning. The result of these in silico investigations demonstrate how matrix heterogeneity affects neovascularization and matrix deformation and provides a platform for studying angiogenesis in complicated and multi-faceted mechanical environments that microvessels experience in vivo.

Systems biology of the microvasculature

The vascular network carries blood throughout the body, delivering oxygen to tissues and providing a pathway for communication between distant organs. The network is hierarchical and structured, but also dynamic, especially at the smaller scales. Remodeling of the microvasculature occurs in response to local changes in oxygen, gene expression, cell-cell communication, and chemical and mechanical stimuli from the microenvironment. These local changes occur as a result of physiological processes such as growth and exercise, as well as acute and chronic diseases including stroke, cancer, and diabetes, and pharmacological intervention. While the vasculature is an important therapeutic target in many diseases, drugs designed to inhibit vascular growth have achieved only limited success, and no drug has yet been approved to promote therapeutic vascular remodeling. This highlights the challenges involved in identifying appropriate therapeutic targets in a system as complex as the vasculature. Systems biology approaches provide a means to bridge current understanding of the vascular system, from detailed signaling dynamics measured in vitro and pre-clinical animal models of vascular disease, to a more complete picture of vascular regulation in vivo. This will translate to an improved ability to identify multi-component biomarkers for diagnosis, prognosis, and monitoring of therapy that are easy to measure in vivo, as well as better drug targets for specific disease states. In this review, we summarize systems biology approaches that have advanced our understanding of vascular function and dysfunction in vivo, with a focus on computational modeling.

Large-scale time series microscopy of neovessel growth during angiogenesis

During angiogenesis, growing neovessels must effectively navigate through the tissue space as they elongate and subsequently integrate into a microvascular network. While time series microscopy has provided insight into the cell activities within single growing neovessel sprouts, less is known concerning neovascular dynamics within a large angiogenic tissue bed. Here, we developed a time-lapse imaging technique that allowed visualization and quantification of sprouting neovessels as they form and grow away from adult parent microvessels in three dimensions over cubic millimeters of matrix volume during the course of up to 5 days on the microscope. Using a new image acquisition procedure and novel morphometric analysis tools, we quantified the elongation dynamics of growing neovessels and found an episodic growth pattern accompanied by fluctuations in neovessel diameter. Average elongation rate was 5 μm/h for individual vessels, but we also observed considerable dynamic variability in growth character including retraction and complete regression of entire neovessels. We observed neovessel-to-neovessel directed growth over tens to hundreds of microns preceding tip-to-tip inosculation. As we have previously described via static 3D imaging at discrete time points, we identified different collagen fibril structures associated with the growing neovessel tip and stalk, and observed the coordinated alignment of growing neovessels in a deforming matrix. Overall analysis of the entire image volumes demonstrated that although individual neovessels exhibited episodic growth and regression, there was a monotonic increase in parameters associated with the entire vascular bed such as total network length and number of branch points. This new time-lapse imaging approach corroborated morphometric changes in individual neovessels described by us and others, as well as captured dynamic neovessel behaviors unique to days-long angiogenesis within the forming neovascular network.

Mechanical interaction of angiogenic microvessels with the extracellular matrix

Angiogenesis is the process by which new blood vessels sprout from existing blood vessels, enabling new vascular elements to be added to an existing vasculature. This review discusses our investigations into the role of cell-matrix mechanics in the mechanical regulation of angiogenesis. The experimental aspects of the research are based on in vitro experiments using an organ culture model of sprouting angiogenesis with the goal of developing new treatments and techniques to either promote or inhibit angiogenic outgrowth, depending on the application. Computational simulations were performed to simulate angiogenic growth coupled to matrix deformation, and live two-photon microscopy was used to obtain insight into the dynamic mechanical interaction between angiogenic neovessels and the extracellular matrix. In these studies, we characterized how angiogenic neovessels remodel the extracellular matrix (ECM) and how properties of the matrix such as density and boundary conditions influence vascular growth and alignment. Angiogenic neovessels extensively deform and remodel the matrix through a combination of applied traction, proteolytic activity, and generation of new cell-matrix adhesions. The angiogenic phenotype within endothelial cells is promoted by ECM deformation and remodeling. Sensitivity analysis using our finite element model of angiogenesis suggests that cell-generated traction during growth is the most important parameter controlling the deformation of the matrix and, therefore, angiogenic growth and remodeling. Live two-photon imaging has also revealed numerous neovessel behaviors during angiogenesis that are poorly understood such as episodic growth/regression, neovessel colocation, and anastomosis. Our research demonstrates that the topology of a resulting vascular network can be manipulated directly by modifying the mechanical interaction between angiogenic neovessels and the matrix.

A coupled model of neovessel growth and matrix mechanics describes and predicts angiogenesis in vitro

During angiogenesis, sprouting microvessels interact with the extracellular matrix (ECM) by degrading and reorganizing the matrix, applying traction forces, and producing deformation. Morphometric features of the resulting microvascular network are affected by the interaction between the matrix and angiogenic microvessels. The objective of this study was to develop a continuous-discrete modeling approach to simulate mechanical interactions between growing neovessels and the deformation of the matrix in vitro. This was accomplished by coupling an existing angiogenesis growth model which uses properties of the ECM to regulate angiogenic growth with the nonlinear finite element software FEBio (www.febio.org). FEBio solves for the deformation and remodeling of the matrix caused by active stress generated by neovessel sprouts, and this deformation was used to update the ECM into the current configuration. After mesh resolution and parameter sensitivity studies, the model was used to accurately predict vascular alignment for various matrix boundary conditions. Alignment primarily arises passively as microvessels convect with the deformation of the matrix, but active alignment along collagen fibrils plays a role as well. Predictions of alignment were most sensitive to the range over which active stresses were applied and the viscoelastic time constant in the material model. The computational framework provides a flexible platform for interpreting in vitro investigations of vessel-matrix interactions, predicting new experiments, and simulating conditions that are outside current experimental capabilities.

Extracellular matrix modulates angiogenesis in physiological and pathological conditions

Angiogenesis is a multistep process driven by a wide range of positive and negative regulatory factors. Extracellular matrix (ECM) plays a crucial role in the regulation of this process. The degradation of ECM, occurring in response to an angiogenic stimulus, leads to degradation or partial modification of matrix molecules, release of soluble factors, and exposure of cryptic sites with pro- and/or antiangiogenic activity. ECM molecules and fragments, resulting from proteolysis, can also act directly as inflammatory stimuli, and this can explain the exacerbated angiogenesis that drives and maintains several inflammatory diseases. In this review we have summarized some of the more recent literature data concerning the molecular control of ECM in angiogenesis in both physiological and pathological conditions.

Extracellular matrix density regulates the rate of neovessel growth and branching in sprouting angiogenesis

Angiogenesis is regulated by the local microenvironment, including the mechanical interactions between neovessel sprouts and the extracellular matrix (ECM). However, the mechanisms controlling the relationship of mechanical and biophysical properties of the ECM to neovessel growth during sprouting angiogenesis are just beginning to be understood. In this research, we characterized the relationship between matrix density and microvascular topology in an in vitro 3D organ culture model of sprouting angiogenesis. We used these results to design and calibrate a computational growth model to demonstrate how changes in individual neovessel behavior produce the changes in vascular topology that were observed experimentally. Vascularized gels with higher collagen densities produced neovasculatures with shorter vessel lengths, less branch points, and reduced network interconnectivity. The computational model was able to predict these experimental results by scaling the rates of neovessel growth and branching according to local matrix density. As a final demonstration of utility of the modeling framework, we used our growth model to predict several scenarios of practical interest that could not be investigated experimentally using the organ culture model. Increasing the density of the ECM significantly reduced angiogenesis and network formation within a 3D organ culture model of angiogenesis. Increasing the density of the matrix increases the stiffness of the ECM, changing how neovessels are able to deform and remodel their surroundings. The computational framework outlined in this study was capable of predicting this observed experimental behavior by adjusting neovessel growth rate and branching probability according to local ECM density, demonstrating that altering the stiffness of the ECM via increasing matrix density affects neovessel behavior, thereby regulated vascular topology during angiogenesis.

A systems biology view of blood vessel growth and remodelling

Blood travels throughout the body in an extensive network of vessels – arteries, veins and capillaries. This vascular network is not static, but instead dynamically remodels in response to stimuli from cells in the nearby tissue. In particular, the smallest vessels – arterioles, venules and capillaries – can be extended, expanded or pruned, in response to exercise, ischaemic events, pharmacological interventions, or other physiological and pathophysiological events. In this review, we describe the multi-step morphogenic process of angiogenesis – the sprouting of new blood vessels – and the stability of vascular networks in vivo. In particular, we review the known interactions between endothelial cells and the various blood cells and plasma components they convey. We describe progress that has been made in applying computational modelling, quantitative biology and high-throughput experimentation to the angiogenesis process.

Manipulating the microvasculature and its microenvironment

The microvasculature is a dynamic cellular system necessary for tissue health and function. Therapeutic strategies that target the microvasculature are expanding and evolving, including those promoting angiogenesis and microvascular expansion. When considering how to manipulate angiogenesis, either as part of a tissue construction approach or a therapy to improve tissue blood flow, it is important to know the microenvironmental factors that regulate and direct neovessel sprouting and growth. Much is known concerning both diffusible and matrix-bound angiogenic factors, which stimulate and guide angiogenic activity. How the other aspects of the extravascular microenvironment, including tissue biomechanics and structure, influence new vessel formation is less well known. Recent research, however, is providing new insights into these mechanisms and demonstrating that the extent and character of angiogenesis (and the resulting new microcirculation) is significantly affected. These observations and the resulting implications with respect to tissue construction and microvascular therapy are addressed.