2,648 research outputs found
A Review of Mathematical Models for the Formation of\ud Vascular Networks
Mainly two mechanisms are involved in the formation of blood vasculature: vasculogenesis and angiogenesis. The former consists of the formation of a capillary-like network from either a dispersed or a monolayered population of endothelial cells, reproducible also in vitro by specific experimental assays. The latter consists of the sprouting of new vessels from an existing capillary or post-capillary venule. Similar phenomena are also involved in the formation of the lymphatic system through a process generally called lymphangiogenesis.\ud
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A number of mathematical approaches have analysed these phenomena. This paper reviews the different modelling procedures, with a special emphasis on their ability to reproduce the biological system and to predict measured quantities which describe the overall processes. A comparison between the different methods is also made, highlighting their specific features
Mechanical cell-matrix feedback explains pairwise and collective endothelial cell behavior in vitro
In vitro cultures of endothelial cells are a widely used model system of the
collective behavior of endothelial cells during vasculogenesis and
angiogenesis. When seeded in an extracellular matrix, endothelial cells can
form blood vessel-like structures, including vascular networks and sprouts.
Endothelial morphogenesis depends on a large number of chemical and mechanical
factors, including the compliancy of the extracellular matrix, the available
growth factors, the adhesion of cells to the extracellular matrix, cell-cell
signaling, etc. Although various computational models have been proposed to
explain the role of each of these biochemical and biomechanical effects, the
understanding of the mechanisms underlying in vitro angiogenesis is still
incomplete. Most explanations focus on predicting the whole vascular network or
sprout from the underlying cell behavior, and do not check if the same model
also correctly captures the intermediate scale: the pairwise cell-cell
interactions or single cell responses to ECM mechanics. Here we show, using a
hybrid cellular Potts and finite element computational model, that a single set
of biologically plausible rules describing (a) the contractile forces that
endothelial cells exert on the ECM, (b) the resulting strains in the
extracellular matrix, and (c) the cellular response to the strains, suffices
for reproducing the behavior of individual endothelial cells and the
interactions of endothelial cell pairs in compliant matrices. With the same set
of rules, the model also reproduces network formation from scattered cells, and
sprouting from endothelial spheroids. Combining the present mechanical model
with aspects of previously proposed mechanical and chemical models may lead to
a more complete understanding of in vitro angiogenesis.Comment: 25 pages, 6 figures, accepted for publication in PLoS Computational
Biolog
Computational Screening of Tip and Stalk Cell Behavior Proposes a Role for Apelin Signaling in Sprout Progression
Angiogenesis involves the formation of new blood vessels by sprouting or
splitting of existing blood vessels. During sprouting, a highly motile type of
endothelial cell, called the tip cell, migrates from the blood vessels followed
by stalk cells, an endothelial cell type that forms the body of the sprout. To
get more insight into how tip cells contribute to angiogenesis, we extended an
existing computational model of vascular network formation based on the
cellular Potts model with tip and stalk differentiation, without making a
priori assumptions about the differences between tip cells and stalk cells. To
predict potential differences, we looked for parameter values that make tip
cells (a) move to the sprout tip, and (b) change the morphology of the
angiogenic networks. The screening predicted that if tip cells respond less
effectively to an endothelial chemoattractant than stalk cells, they move to
the tips of the sprouts, which impacts the morphology of the networks. A
comparison of this model prediction with genes expressed differentially in tip
and stalk cells revealed that the endothelial chemoattractant Apelin and its
receptor APJ may match the model prediction. To test the model prediction we
inhibited Apelin signaling in our model and in an \emph{in vitro} model of
angiogenic sprouting, and found that in both cases inhibition of Apelin or of
its receptor APJ reduces sprouting. Based on the prediction of the
computational model, we propose that the differential expression of Apelin and
APJ yields a "self-generated" gradient mechanisms that accelerates the
extension of the sprout.Comment: 48 pages, 10 figures, 8 supplementary figures. Accepted for
publication in PLoS ON
Mesoscopic and continuum modelling of angiogenesis
Angiogenesis is the formation of new blood vessels from pre-existing ones in
response to chemical signals secreted by, for example, a wound or a tumour. In
this paper, we propose a mesoscopic lattice-based model of angiogenesis, in
which processes that include proliferation and cell movement are considered as
stochastic events. By studying the dependence of the model on the lattice
spacing and the number of cells involved, we are able to derive the
deterministic continuum limit of our equations and compare it to similar
existing models of angiogenesis. We further identify conditions under which the
use of continuum models is justified, and others for which stochastic or
discrete effects dominate. We also compare different stochastic models for the
movement of endothelial tip cells which have the same macroscopic,
deterministic behaviour, but lead to markedly different behaviour in terms of
production of new vessel cells.Comment: 48 pages, 13 figure
Modelling of chemotactic sprouting endothelial cells through an extracellular matrix
Sprouting angiogenesis is a core biological process critical to vascular development. Its accurate simulation, relevant to multiple facets of human health, is of broad, interdisciplinary appeal. This study presents an in-silico model replicating a microfluidic assay where endothelial cells sprout into a biomimetic extracellular matrix, specifically, a large-pore, low-concentration fibrin-based porous hydrogel, influenced by chemotactic factors. We introduce a novel approach by incorporating the extracellular matrix and chemotactic factor effects into a unified term using a single parameter, primarily focusing on modelling sprouting dynamics and morphology. This continuous model naturally describes chemotactic-induced sprouting with no need for additional rules. In addition, we extended our base model to account for matrix sensing and degradation, crucial aspects of angiogenesis. We validate our model via a hybrid in-silico experimental method, comparing the model predictions with experimental results derived from the microfluidic setup. Our results underscore the intricate relationship between the extracellular matrix structure and angiogenic sprouting, proposing a promising method for predicting the influence of the extracellular matrix on angiogenesis
The complex TIE between macrophages and angiogenesis
Macrophages are primarily known as phagocytic immune cells, but they also play a role in diverse processes, such as morphogenesis, homeostasis and regeneration. In this review, we discuss the influence of macrophages on angiogenesis, the process of new blood vessel formation from the pre-existing vasculature. Macrophages play crucial roles at each step of the angiogenic cascade, starting from new blood vessel sprouting to the remodelling of the vascular plexus and vessel maturation. Macrophages form promising targets for both pro- and anti-angiogenic treatments. However, to target macrophages, we will first need to understand the mechanisms that control the functional plasticity of macrophages during each of the steps of the angiogenic cascade. Here, we review recent insights in this topic. Special attention will be given to the TIE2-expressing macrophage (TEM), which is a subtype of highly angiogenic macrophages that is able to influence angiogenesis via the angiopoietin-TIE pathway
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