Lowell T. Edgar

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.

Determinants of Microvascular Network Topologies in Implanted Neovasculatures

Objective— During neovascularization, the end result is a new functional microcirculation composed of a network of mature microvessels with specific topologies. Although much is known concerning the mechanisms underlying the initiation of angiogenesis, it remains unclear how the final architecture of microcirculatory beds is regulated. To begin to address this, we determined the impact of angiogenic neovessel prepatterning on the final microvascular network topology using a model of implant neovascularization. Methods and Results— We used 3D direct-write bioprinting or physical constraints in a manner permitting postangiogenesis vascular remodeling and adaptation to pattern angiogenic microvascular precursors (neovessels formed from isolated microvessel segments) in 3D collagen gels before implantation and subsequent network formation. Neovasculatures prepatterned into parallel arrays formed functional networks after 4 weeks postimplantation but lost the prepatterned architecture. However, maintenance of uniaxial physical constraints during postangiogenesis remodeling of the implanted neovasculatures produced networks with aligned microvessels, as well as an altered proportional distribution of arterioles, capillaries, and venules. Conclusion— Here we show that network topology resulting from implanted microvessel precursors is independent from prepatterning of precursors but can be influenced by a patterning stimulus involving tissue deformation during postangiogenesis remodeling and maturation.

Cell-generated traction forces and the resulting matrix deformation modulate microvascular alignment and growth during angiogenesis

The details of the mechanical factors that modulate angiogenesis remain poorly understood. Previous in vitro studies of angiogenesis using microvessel fragments cultured within collagen constructs demonstrated that neovessel alignment can be induced via mechanical constraint of the boundaries (i.e., boundary conditions). The objective of this study was to investigate the role of mechanical boundary conditions in the regulation of angiogenic alignment and growth in an in vitro model of angiogenesis. Angiogenic microvessels within three-dimensional constructs were subjected to different boundary conditions, thus producing different stress and strain fields during growth. Neovessel outgrowth and orientation were quantified from confocal image data after 6 days. Vascularity and branching decreased as the amount of constraint imposed on the culture increased. In long-axis constrained hexahedral constructs, microvessels aligned parallel to the constrained axis. In contrast, constructs that were constrained along the short axis had random microvessel orientation. Finite element models were used to simulate the contraction of gels under the various boundary conditions and to predict the local strain field experienced by microvessels. Results from the experiments and simulations demonstrated that microvessels aligned perpendicular to directions of compressive strain. Alignment was due to anisotropic deformation of the matrix from cell-generated traction forces interacting with the mechanical boundary conditions. These findings demonstrate that boundary conditions and thus the effective stiffness of the matrix regulate angiogenesis. This study offers a potential explanation for the oriented vascular beds that occur in native tissues and provides the basis for improved control of tissue vascularization in both native tissues and tissue-engineered constructs.

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

Recent interest in the process of vascularisation within the biomedical community has motivated numerous new research efforts focusing on the process of angiogenesis. Although the role of chemical factors during angiogenesis has been well documented, the role of mechanical factors, such as the interaction between angiogenic vessels and the extracellular matrix, remains poorly understood. In vitro methods for studying angiogenesis exist; however, measurements available using such techniques often suffer from limited spatial and temporal resolutions. For this reason, computational models have been extensively employed to investigate various aspects of angiogenesis. This paper outlines the formulation and validation of a simple and robust computational model developed to accurately simulate angiogenesis based on length, branching and orientation morphometrics collected from vascularised tissue constructs. Microvessels were represented as a series of connected line segments. The morphology of the vessels was determined by a linear combination of the collagen fibre orientation, the vessel density gradient and a random walk component. Excellent agreement was observed between computational and experimental morphometric data over time. Computational predictions of microvessel orientation within an anisotropic matrix correlated well with experimental data. The accuracy of this modelling approach makes it a valuable platform for investigating the role of mechanical interactions during angiogenesis.

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.

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.

The effects of geometry and static boundary conditions on microvessel outgrowth in a 3D model of angiogenesis

We reported previously that, in addition to mechanical strain, a constrained boundary condition alone can alter the organization of microvessel outgrowth during in vitro angiogenesis [1]. After 6 days of culture in vitro, microvessels aligned parallel to the long axis of rectangular 3D collagen gels that had constrained edges on the ends. However, unconstrained cultures did not show any alignment of microvessels. The ability to direct microvessel outgrowth during angiogenesis has significant implications for engineering prevascularized grafts and tissues in vitro, therefore an understanding of this process is important. Since there is direct relationship between the ability of endothelial cells to contract 3D gels and matrix stiffness [2], we hypothesize that some constrained boundary conditions will increase the apparent matrix stiffness and in turn will limit gel contraction, prevent microvessel alignment, and reduce microvessel outgrowth. The objective of this study was to compare microvessel growth and alignment under several different static boundary conditions.Copyright

A Continuous-Discrete Finite Element Model of Angiogenesis That Couples Vessel Growth With Matrix Deformation

Recent developments in tissue engineering have created demand for the ability to create microvascular networks with specific topologies in vitro. During angiogenesis, sprouting endothelial cells apply traction forces and migrate along components of the extracellular matrix (ECM), resulting in neovessel elongation [1]. The fibrillar structure of the ECM serves as the major pathway for mechanotransduction between contact-dependent cells. Using a three-dimensional (3D) organ culture model of microvessel fragments within a type-I collagen gel, we have shown that subjecting the culture to different boundary conditions during angiogenesis can lead to drastically different vascular topologies [2]. Fragments cultured in a rectangular gel that were free to contract grew into a randomly oriented network [3, 4]. When the long-axis of the gel was constrained as to prevent contraction, microvessels and collagen fibers were found aligned along the constrained axis (Fig. 1) [4].Copyright

Three-Dimensional Simulation of In Vitro Angiogenesis: Effects of Extracellular Matrix Structure and Density

The process of angiogenesis is regulated by both chemical and mechanical signaling. While the role of chemical factors such as vascular endothelial growth factor (VEGF) during angiogenesis has been extensively studied, the influence of the mechanostructural environment on new vessel generation has received significantly less attention. During angiogenesis, endothelial cells in the existing vasculature detach and migrate out into the surrounding extracellular matrix (ECM), forming tubular structures that eventually mature into new blood vessels. This process is modulated by the structure and composition of the ECM [1]. The ECM is then remodeled by endothelial cells in the elongating neovessel tip, resulting in matrix condensation and changes in fiber orientation [2]. The mechanism as to how angiogenic vasculature and the ECM influence each other is poorly understood.© 2010 ASME