An integrated approach to quantitative modelling in angiogenesis research

Connor, Anthony J.; Nowak, Radosław P.; Lorenzon, Erica; Thomas, Markus; Herting, Frank; Hoert, Stefan; Quaiser, Tom; Shochat, Eliezer; Pitt-Francis, Joe; Cooper, Jonathan; Maini, Philip K.; Byrne, Helen M.

doi:10.1098/rsif.2015.0546

Cited by 24 publications

(69 citation statements)

References 27 publications

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“…Schematics of the corneal micropocket assay and typical in silico and in vitro geometries. A) An image of the micropocket assay from Connor et al [5]. B) The placement of a pellet of radius r p into the cornea at height h from the limbus, where h is the distance along the shown y or z axis.…”

Section: Introductionmentioning

confidence: 99%

“…The authors performed qualitative 41 comparisons of vascular patterning and front velocity with the previous studies of Tong 42 and Yuan [3,7]. In terms of continuum models, Connor et al [5] used a classical 1D 43 modeling approach to perform detailed quantitative comparisons of predicted vessel 44 densities with their own experimental measurements.…”

Section: Introductionmentioning

confidence: 99%

“…As shown schematically in Fig 1C, new vessel 13 formation is often focused in the region where the distance between the pellet and 14 limbus is smallest, with vessels tending to grow toward the pellet. 15 19process [5,[7][8][9][10][11][12][13][14]. To date, these models have exclusively adopted either one-dimensional 20 (1D) or two-dimensional (2D) representations of the cornea-pellet system, with the 21 former allowing efficient, continuum modeling of the developing vessel network by the 22 solution of systems of partial differential equations (PDEs) [5,10,11].…”

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confidence: 99%

“…80 It is assumed that the pellet contains a single pro-angiogenic compound, Vascular 81 Endothelial Growth Factor 165 (denoted VEGF in the present study). Two situations 82 are considered, one where the concentration of VEGF in the tissue domain is described 83 by a time-independent, spatially varying field where VEGF levels decrease linearly from 84 the pellet, and the other where VEGF dynamics are explicitly modeled, following 85 approaches in Tong and Yuan [7] and Connor et al [5]. 86 Overviews of the simulated tissue domains, angiogenesis model and VEGF dynamics 87 model are provided in this section.…”

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confidence: 99%

“…binding to the nylon pellet constituents is assumed. Under this assumption it is possible 215 to derive the following relationship between the total c p and free c f amounts of VEGF 216 in the pellet [5]:…”

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confidence: 99%

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The importance of geometry in the corneal micropocket angiogenesis assay

Grogan

Connor

Pitt-Francis

et al. 2017

Preprint

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The corneal micropocket assay is an experimental protocol for studying vessel network formation, or neovascularization, in vivo. The assay is attractive due to the ease with which the developing vessel network can be observed in the same animal over time. However, it is difficult to relate observations of neovascularization in the hemispherical geometry of the cornea to predictions from mathematical (in silico) models and observations from in vitro models, which mostly adopt planar geometries. Here, we develop a three-dimensional, off-lattice mathematical model of neovascularization in the cornea, with a new repulsion model for the interaction of vessels with tissue boundaries. The model allows us to: i) investigate how the hemispherical geometry of the cornea influences vessel network formation and ii) identify the metrics of neovascularization that are most robust to geometrical differences between typical in silico, in vitro and in vivo tissue domains. We predict that two-dimensional geometries lead to increased vessel 'merging', or anastomosis, relative to three-dimensional versions, with differences being most pronounced when circular geometries are adopted. Cuboidal geometries lead to patterns of neovascularization that most closely mimic the in vivo case. The 'distance of the vascular front to the limbus' is found to be a robust metric of neovascularization across the studied tissue domains, while densities of tip cells and vessels and 'vascularized fraction' are more sensitive to domain choice. Given the widespread adoption and attractive simplicity of planar tissue domains, the differences identified in the present study should prove useful in relating the results of previous and future in silico and in vitro studies of neovascularization to in vivo observations in the cornea. Author summaryNeovascularization, or the formation of new blood vessels, is an important process in development, wound healing and cancer. The corneal micropocket assay is used to better understand the process and, in the case of cancer, how it can be controlled with drug therapies for improved patient outcomes. In the assay, the hemispherical shape of the cornea can influence the way the vessel network forms. This makes it difficult to directly compare results from experiments with the predictions of mathematical models or cell culture experiments, which are

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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confidence: 99%

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The importance of geometry in the corneal micropocket angiogenesis assay

Grogan

Connor

Pitt-Francis

et al. 2017

Preprint

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Computational models for generating microvascular structures: Investigations beyond medical imaging resolution

Apeldoorn

Safaei

Paton

et al. 2022

WIREs Mechanisms of Disease

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Angiogenesis, arteriogenesis, and pruning are revascularization processes essential to our natural vascular development and adaptation, as well as central players in the onset and development of pathologies such as tumoral growth and stroke recovery. Computational modeling allows for repeatable experimentation and exploration of these complex biological processes. In this review, we provide an introduction to the biological understanding of the vascular adaptation processes of sprouting angiogenesis, intussusceptive angiogenesis, anastomosis, pruning, and arteriogenesis, discussing some of the more significant contributions made to the computational modeling of these processes. Each computational model represents a theoretical framework for how biology functions, and with rises in computing power and study of the problem these frameworks become more accurate and complete. We highlight physiological, pathological, and technological applications that can be benefit from the advances performed by these models, and we also identify which elements of the biology are underexplored in the current state‐of‐the‐art computational models. This article is categorized under: Cancer > Computational Models Cardiovascular Diseases > Computational Models

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Computational modeling of angiogenesis: The importance of cell rearrangements during vascular growth

Stepanova,

Byrne,

Maini

et al. 2023

WIREs Mechanisms of Disease

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Angiogenesis is the process wherein endothelial cells (ECs) form sprouts that elongate from the pre‐existing vasculature to create new vascular networks. In addition to its essential role in normal development, angiogenesis plays a vital role in pathologies such as cancer, diabetes and atherosclerosis. Mathematical and computational modeling has contributed to unraveling its complexity. Many existing theoretical models of angiogenic sprouting are based on the “snail‐trail” hypothesis. This framework assumes that leading ECs positioned at sprout tips migrate toward low‐oxygen regions while other ECs in the sprout passively follow the leaders' trails and proliferate to maintain sprout integrity. However, experimental results indicate that, contrary to the snail‐trail assumption, ECs exchange positions within developing vessels, and the elongation of sprouts is primarily driven by directed migration of ECs. The functional role of cell rearrangements remains unclear. This review of the theoretical modeling of angiogenesis is the first to focus on the phenomenon of cell mixing during early sprouting. We start by describing the biological processes that occur during early angiogenesis, such as phenotype specification, cell rearrangements and cell interactions with the microenvironment. Next, we provide an overview of various theoretical approaches that have been employed to model angiogenesis, with particular emphasis on recent in silico models that account for the phenomenon of cell mixing. Finally, we discuss when cell mixing should be incorporated into theoretical models and what essential modeling components such models should include in order to investigate its functional role.This article is categorized under: Cardiovascular Diseases > Computational Models Cancer > Computational Models

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An integrated approach to quantitative modelling in angiogenesis research

Cited by 24 publications

References 27 publications

The importance of geometry in the corneal micropocket angiogenesis assay

The importance of geometry in the corneal micropocket angiogenesis assay

Computational models for generating microvascular structures: Investigations beyond medical imaging resolution

Computational modeling of angiogenesis: The importance of cell rearrangements during vascular growth

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