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 \ud 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

Investigating biocomplexity through the agent-based paradigm.

Capturing the dynamism that pervades biological systems requires a computational approach that can accommodate both the continuous features of the system environment as well as the flexible and heterogeneous nature of component interactions. This presents a serious challenge for the more traditional mathematical approaches that assume component homogeneity to relate system observables using mathematical equations. While the homogeneity condition does not lead to loss of accuracy while simulating various continua, it fails to offer detailed solutions when applied to systems with dynamically interacting heterogeneous components. As the functionality and architecture of most biological systems is a product of multi-faceted individual interactions at the sub-system level, continuum models rarely offer much beyond qualitative similarity. Agent-based modelling is a class of algorithmic computational approaches that rely on interactions between Turing-complete finite-state machines--or agents--to simulate, from the bottom-up, macroscopic properties of a system. In recognizing the heterogeneity condition, they offer suitable ontologies to the system components being modelled, thereby succeeding where their continuum counterparts tend to struggle. Furthermore, being inherently hierarchical, they are quite amenable to coupling with other computational paradigms. The integration of any agent-based framework with continuum models is arguably the most elegant and precise way of representing biological systems. Although in its nascence, agent-based modelling has been utilized to model biological complexity across a broad range of biological scales (from cells to societies). In this article, we explore the reasons that make agent-based modelling the most precise approach to model biological systems that tend to be non-linear and complex

Cell-Oriented Modeling of Angiogenesis

Due to its significant involvement in various physiological and pathological conditions, angiogenesis (the development of new blood vessels from an existing vasculature) represents an important area of the actual biological research and a field in which mathematical modeling proved particularly useful in supporting the experimental work. In this paper, we focus on a specific modeling strategy, known as “cell-centered” approach. This type of mathematical models work at a “mesoscopic scale,” assuming the cell as the natural level of abstraction for computational modeling of development. They treat cells phenomenologically, considering their essential behaviors to study how tissue structure and organization emerge from the collective dynamics of multiple cells. The main contributions of the cell-oriented approach to the study of the angiogenic process will be described. From one side, they have generated “basic science understanding” about the process of capillary assembly during development, growth, and pathology. On the other side, models were also developed supporting “applied biomedical research” for the purpose of identifying new therapeutic targets and clinically relevant approaches for either inhibiting or stimulating angiogenesis

Flow dynamics control the effect of sphingosine-1-phosphate on endothelial permeability in a microfluidic vessel bifurcation model

Blood vessels are lined by endothelial cells that form a semipermeable barrier to restrict fluid flow across the vessel wall. The endothelial barrier is known to respond to various molecular mechanisms, but the effects of mechanical signals that arise due to blood flow remain poorly understood. Here, we report a microfluidic model that mimics the flow conditions and endothelial/extracellular matrix (ECM) architecture of a vessel bifurcation to enable systematic investigation of how flow dynamics that arise within bifurcating vessels guides the endothelial response to biochemical signals. Applying the strengths of our system, we further investigate the endothelial response to sphingosine-1-phosphate, a bioactive lipid that has demonstrated flow-dependent regulation of vascular permeability. We demonstrate that bifurcated fluid flow (BFF) that arises at the base of vessel bifurcations and laminar shear stress (LSS) that arises along downstream vessel walls induce a decrease in endothelial permeability. Furthermore, we identify that flow-dynamics and chaperone proteins regulate the endothelial response to S1P. Through pharmacological inhibition of S1P receptors 1 and 2, we report ligand-independent mechanical activation of S1P receptors 1 and 2, providing support for the role of G protein-coupled receptors as mechanosensors. These findings introduce BFF as an important regulator of vascular permeability, and establish flow dynamics as a determinant of the endothelial response to S1P.Pelotonia Fellowship ProgramBarry M. Goldwater Excellence in Education FoundationThe Ohio State University College of EngineeringA one-year embargo was granted for this item.Academic Major: Biomedical Engineerin

Imaging plant germline differentiation within Arabidopsis flowers by light sheet microscopy

In higher plants, germline differentiation occurs during a relatively short period within developing flowers. Understanding of the mechanisms that govern germline differentiation lags behind other plant developmental processes. This is largely because the germline is restricted to relatively few cells buried deep within floral tissues, which makes them difficult to study. To overcome this limitation, we have developed a methodology for live imaging of the germ cell lineage within floral organs of Arabidopsis using light sheet fluorescence microscopy. We have established reporter lines, cultivation conditions, and imaging protocols for high-resolution microscopy of developing flowers continuously for up to several days. We used multiview imagining to reconstruct a three-dimensional model of a flower at subcellular resolution. We demonstrate the power of this approach by capturing male and female meiosis, asymmetric pollen division, movement of meiotic chromosomes, and unusual restitution mitosis in tapetum cells. This method will enable new avenues of research into plant sexual reproduction.Web of Science9art. no. e5254

Module-based multiscale simulation of angiogenesis in skeletal muscle

<p>Abstract</p> <p>Background</p> <p>Mathematical modeling of angiogenesis has been gaining momentum as a means to shed new light on the biological complexity underlying blood vessel growth. A variety of computational models have been developed, each focusing on different aspects of the angiogenesis process and occurring at different biological scales, ranging from the molecular to the tissue levels. Integration of models at different scales is a challenging and currently unsolved problem.</p> <p>Results</p> <p>We present an object-oriented module-based computational integration strategy to build a multiscale model of angiogenesis that links currently available models. As an example case, we use this approach to integrate modules representing microvascular blood flow, oxygen transport, vascular endothelial growth factor transport and endothelial cell behavior (sensing, migration and proliferation). Modeling methodologies in these modules include algebraic equations, partial differential equations and agent-based models with complex logical rules. We apply this integrated model to simulate exercise-induced angiogenesis in skeletal muscle. The simulation results compare capillary growth patterns between different exercise conditions for a single bout of exercise. Results demonstrate how the computational infrastructure can effectively integrate multiple modules by coordinating their connectivity and data exchange. Model parameterization offers simulation flexibility and a platform for performing sensitivity analysis.</p> <p>Conclusions</p> <p>This systems biology strategy can be applied to larger scale integration of computational models of angiogenesis in skeletal muscle, or other complex processes in other tissues under physiological and pathological conditions.</p