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

Simulation of Soluble and Bound VEGF-stimulated in vitro Capillary-like Network Formation on Deformed Substrate

Capillary plexus cultivation is crucial in tissue engineering and regenerative medicine. Theoretical simulations have been conducted to supplement the expensive experimental works. However, the mechanisms connecting mechanical and chemical stimuli remained undefined, and the functions of the different VEGF forms in the culture environment were still unclear. In this paper, we developed a hybrid model for simulating short-term in vitro capillary incubations. We used the Cellular Potts model to predict individual cell migration, morphology change, and continuum mechanics to quantify biogel deformation and VEGF transport dynamics. By bridging the mechanical regulation and chemical stimulation in the model, the results showed good agreement between the predicted network topology and experiments, in which elongated cells connected, forming the network cords and round cells gathered, creating cobblestone-like aggregates. The results revealed that the capillary-like networks could develop in high integrity only when the mechanical and chemical couplings worked adequately, with the cell morphology and haptotaxis driven by the soluble and bound forms of VEGF, respectively, functioning simultaneously.

Computational Insights into the Interplay of Mechanical Forces in Angiogenesis

This study employs a meshless computational model to investigate the impacts of compression and traction on angiogenesis, exploring their effects on vascular endothelial growth factor (VEGF) diffusion and subsequent capillary network formation. Three distinct initial domain geometries were defined to simulate variations in endothelial cell sprouting and VEGF release. Compression and traction were applied, and the ensuing effects on VEGF diffusion coefficients were analysed. Compression promoted angiogenesis, increasing capillary network density. The reduction in the VEGF diffusion coefficient under compression altered VEGF concentration, impacting endothelial cell migration patterns. The findings were consistent across diverse simulation scenarios, demonstrating the robust influence of compression on angiogenesis. This computational study enhances our understanding of the intricate interplay between mechanical forces and angiogenesis. Compression emerges as an effective mediator of angiogenesis, influencing VEGF diffusion and vascular pattern. These insights may contribute to innovative therapeutic strategies for angiogenesis-related disorders, fostering tissue regeneration and addressing diseases where angiogenesis is crucial.

Isolated Fragments of Intact Microvessels: Tissue Vascularization, Modeling, and Therapeutics

The microvasculature is integral to nearly every tissue in the body, providing not only perfusion to and from the tissue, but also homing sites for immune cells, cellular niches for tissue dynamics, and cooperative interactions with other tissue elements. As a microtissue itself, the microvasculature is a composite of multiple cell types exquisitely organized into structures (individual vessel segments and extensive vessel networks) capable of considerable dynamics and plasticity. Consequently, it has been challenging to include a functional microvasculature in assembled or fabricated tissues. Isolated fragments of intact microvessels, which retain the cellular composition and structures of native microvessels, are proving effective in a variety of vascularization applications including tissue in vitro disease modeling, vascular biology, mechanistic discovery, and tissue prevascularization in regenerative therapeutics and grafting. In this review, we will discuss the importance of recapitulating native tissue biology and the successful vascularization applications of isolated microvessels.

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.

A Comprehensive Look at In Vitro Angiogenesis Image Analysis Software

One of the complex challenges faced presently by tissue engineering (TE) is the development of vascularized constructs that accurately mimic the extracellular matrix (ECM) of native tissue in which they are inserted to promote vessel growth and, consequently, wound healing and tissue regeneration. TE technique is characterized by several stages, starting from the choice of cell culture and the more appropriate scaffold material that can adequately support and supply them with the necessary biological cues for microvessel development. The next step is to analyze the attained microvasculature, which is reliant on the available labeling and microscopy techniques to visualize the network, as well as metrics employed to characterize it. These are usually attained with the use of software, which has been cited in several works, although no clear standard procedure has been observed to promote the reproduction of the cell response analysis. The present review analyzes not only the various steps previously described in terms of the current standards for evaluation, but also surveys some of the available metrics and software used to quantify networks, along with the detection of analysis limitations and future improvements that could lead to considerable progress for angiogenesis evaluation and application in TE research.

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.

Microvascular fragments in microcirculation research and regenerative medicine

Adipose tissue-derived microvascular fragments (MVF) are functional vessel segments, which rapidly reassemble into new microvasculatures under experimental in vitro and in vivo conditions. Accordingly, they have been used for many years in microcirculation research to study basic mechanisms of endothelial cell function, angiogenesis and microvascular network formation in two- and three-dimensional environments. Moreover, they serve as vascularization units for musculoskeletal regeneration and implanted biomaterials as well as for the treatment of myocardial infarction and the generation of prevascularized tissue organoids. Besides, multiple factors determining the vascularization capacity of MVF have been identified, including their tissue origin and cellular composition, the conditions for their short- and long-term storage as well as their implantation site and the general health status and medication of the recipient. The next challenging step is now the successful translation of all these promising experimental findings into clinical practice. If this succeeds, a multitude of future therapeutic applications may significantly benefit from the remarkable properties of MVF.

Microenvironmental modulation of the developing tumour: an immune-stromal dialogue

Successful establishment of a tumour relies on a cascade of interactions between cancer cells and stromal cells within an evolving microenvironment. Both immune and nonimmune cellular components are key factors in this process, and the individual players may change their role from tumour elimination to tumour promotion as the microenvironment develops. While the tumour-stroma crosstalk present in an established tumour is well-studied, aspects in the early tumour or premalignant microenvironment have received less attention. This is in part due to the challenges in studying this process in the clinic or in mouse models. Here, we review the key anti- and pro-tumour factors in the early microenvironment and discuss how understanding this process may be exploited in the clinic.

On the preservation of vessel bifurcations during flow-mediated angiogenic remodelling

During developmental angiogenesis, endothelial cells respond to shear stress by migrating and remodelling the initially hyperbranched plexus, removing certain vessels whilst maintaining others. In this study, we argue that the key regulator of vessel preservation is cell decision behaviour at bifurcations. At flow-convergent bifurcations where migration paths diverge, cells must finely tune migration along both possible paths if the bifurcation is to persist. Experiments have demonstrated that disrupting the cells’ ability to sense shear or the junction forces transmitted between cells impacts the preservation of bifurcations during the remodelling process. However, how these migratory cues integrate during cell decision making remains poorly understood. Therefore, we present the first agent-based model of endothelial cell flow-mediated migration suitable for interrogating the mechanisms behind bifurcation stability. The model simulates flow in a bifurcated vessel network composed of agents representing endothelial cells arranged into a lumen which migrate against flow. Upon approaching a bifurcation where more than one migration path exists, agents refer to a stochastic bifurcation rule which models the decision cells make as a combination of flow-based and collective-based migratory cues. With this rule, cells favour branches with relatively larger shear stress or cell number. We found that cells must integrate both cues nearly equally to maximise bifurcation stability. In simulations with stable bifurcations, we found competitive oscillations between flow and collective cues, and simulations that lost the bifurcation were unable to maintain these oscillations. The competition between these two cues is haemodynamic in origin, and demonstrates that a natural defence against bifurcation loss during remodelling exists: as vessel lumens narrow due to cell efflux, resistance to flow and shear stress increases, attracting new cells to enter and rescue the vessel from regression. Our work provides theoretical insight into the role of junction force transmission has in stabilising vasculature during remodelling and as an emergent mechanism to avoid functional shunting.

When new blood vessels are created, the endothelial cells that make up these vessels migrate and rearrange in response to blood flow to remodel and optimise the vessel network. An essential part of this process is maintaining the branched structure of the network; however, it is unclear what cues cells consider at regions where vessels branch (i.e., bifurcations). In this research, we present a computer model of cell migration to interrogate the process of preserving bifurcations during remodelling. In this model, cells at bifurcations are influenced by both flow and force transmitted from neighbouring cells. We found that both cues (flow-based and collective-based) must be considered equally in order to preserve branching in the vessel network. In simulations with stable bifurcations, we demonstrated that these cues oscillate: a strong signal in one was accompanied by a weak signal in the other. Furthermore, we found that these cues naturally compete with each other due to the coupling between blood flow and the size of the blood vessels, i.e. larger vessels with more cells produce less flow signals and vice versa. Our research provides insight into how forces transmitted between neighbouring cells stabilise and preserve branching during remodelling, as well as implicates the disruption of this force transmission as a potential mechanism when remodelling goes wrong as in the case of vascular malformation.

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.

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.

Extracellular matrix compression temporally regulates microvascular angiogenesis

Mechanical cues influence tissue regeneration, and although vasculature is known to be mechanically sensitive, little is known about the effects of bulk extracellular matrix deformation on the nascent vessel networks found in healing tissues. Previously, we found that dynamic matrix compression in vivo potently regulated revascularization during bone tissue regeneration; however, whether matrix deformations directly regulate angiogenesis remained unknown. Here, we demonstrated that load initiation time, magnitude, and mode all regulate microvascular growth, as well as upstream angiogenic and mechanotransduction signaling pathways. Immediate load initiation inhibited angiogenesis and expression of early sprout tip cell selection genes, while delayed loading enhanced microvascular network formation and upstream signaling pathways. This research provides foundational understanding of how extracellular matrix mechanics regulate angiogenesis and has critical implications for clinical translation of new regenerative medicine therapies and physical rehabilitation strategies designed to enhance revascularization during tissue regeneration.

The extracellular matrix in tumor progression and metastasis

The extracellular matrix (ECM) constitutes the scaffold of tissues and organs. It is a complex network of extracellular proteins, proteoglycans and glycoproteins, which form supramolecular aggregates, such as fibrils and sheet-like networks. In addition to its biochemical composition, including the covalent intermolecular cross-linkages, the ECM is also characterized by its biophysical parameters, such as topography, molecular density, stiffness/rigidity and tension. Taking these biochemical and biophysical parameters into consideration, the ECM is very versatile and undergoes constant remodeling. This review focusses on this remodeling of the ECM under the influence of a primary solid tumor mass. Within this tumor stroma, not only the cancer cells but also the resident fibroblasts, which differentiate into cancer-associated fibroblasts (CAFs), modify the ECM. Growth factors and chemokines, which are tethered to and released from the ECM, as well as metabolic changes of the cells within the tumor bulk, add to the tumor-supporting tumor microenvironment. Metastasizing cancer cells from a primary tumor mass infiltrate into the ECM, which variably may facilitate cancer cell migration or act as barrier, which has to be proteolytically breached by the infiltrating tumor cell. The biochemical and biophysical properties therefore determine the rates and routes of metastatic dissemination. Moreover, primed by soluble factors of the primary tumor, the ECM of distant organs may be remodeled in a way to facilitate the engraftment of metastasizing cancer cells. Such premetastatic niches are responsible for the organotropic preference of certain cancer entities to colonize at certain sites in distant organs and to establish a metastasis. Translational application of our knowledge about the cancer-primed ECM is sparse with respect to therapeutic approaches, whereas tumor-induced ECM alterations such as increased tissue stiffness and desmoplasia, as well as breaching the basement membrane are hallmark of malignancy and diagnostically and histologically harnessed.

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.

Collagen Fiber Orientation Regulates 3D Vascular Network Formation and Alignment

Alignment of collagen type I fibers is a hallmark of both physiological and pathological tissue remodeling. However, the effects of collagen fiber orientation on endothelial cell behavior and vascular network formation are poorly understood because of a lack of model systems that allow studying these potential functional connections. By casting collagen type I into prestrained (0, 10, 25, 50% strain), poly(dimethylsiloxane) (PDMS)-based microwells and releasing the mold strain following polymerization, we have created collagen gels with varying fiber alignment as confirmed by structural analysis. Endothelial cells embedded within the different gels responded to increased collagen fiber orientation by assembling into 3D vascular networks that consisted of thicker, more aligned branches and featured elevated collagen IV deposition and lumen formation relative to control conditions. These substrate-dependent changes in microvascular network formation were associated with altered cell division and migration patterns and related to enhanced mechanosignaling. Our studies indicate that collagen fiber alignment can directly regulate vascular network formation and that culture models with aligned collagen may be used to investigate the underlying mechanisms ultimately advancing our understanding of tissue development, homeostasis, and disease.

FEBio: History and Advances

The principal goal of the FEBio project is to provide an advanced finite element tool for the biomechanics and biophysics communities that allows researchers to model mechanics, transport, and electrokinetic phenomena for biological systems accurately and efficiently. In addition, because FEBio is geared toward the research community, the code is designed such that new features can be added easily, thus making it an ideal tool for testing novel computational methods. Finally, because the success of a code is determined by its user base, integral goals of the FEBio project have been to offer support and outreach to our community; to provide mechanisms for dissemination of results, models, and data; and to encourage interaction between users. This review presents the history of the FEBio project, from its initial developments through its current funding period. We also present a glimpse into the future of FEBio.

Cellular Microbiaxial Stretching to Measure a Single-Cell Strain Energy Density Function

The stress in a cell due to extracellular mechanical stimulus is determined by its mechanical properties, and the structural organization of many adherent cells suggests that their properties are anisotropic. This anisotropy may significantly influence the cells' mechanotransductive response to complex loads, and has important implications for development of accurate models of tissue biomechanics. Standard methods for measuring cellular mechanics report linear moduli that cannot capture large-deformation anisotropic properties, which in a continuum mechanics framework are best described by a strain energy density function (SED). In tissues, the SED is most robustly measured using biaxial testing. Here, we describe a cellular microbiaxial stretching (CμBS) method that modifies this tissue-scale approach to measure the anisotropic elastic behavior of individual vascular smooth muscle cells (VSMCs) with nativelike cytoarchitecture. Using CμBS, we reveal that VSMCs are highly anisotropic under large deformations. We then characterize a Holzapfel-Gasser-Ogden type SED for individual VSMCs and find that architecture-dependent properties of the cells can be robustly described using a formulation solely based on the organization of their actin cytoskeleton. These results suggest that cellular anisotropy should be considered when developing biomechanical models, and could play an important role in cellular mechano-adaptation.

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.

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.