Spatio-temporal Models of Lymphangiogenesis in Wound Healing

Several studies suggest that one possible cause of impaired wound healing is failed or insufficient lymphangiogenesis, that is the formation of new lymphatic capillaries. Although many mathematical models have been developed to describe the formation of blood capillaries (angiogenesis), very few have been proposed for the regeneration of the lymphatic network. Lymphangiogenesis is a markedly different process from angiogenesis, occurring at different times and in response to different chemical stimuli. Two main hypotheses have been proposed: 1) lymphatic capillaries sprout from existing interrupted ones at the edge of the wound in analogy to the blood angiogenesis case; 2) lymphatic endothelial cells first pool in the wound region following the lymph flow and then, once sufficiently populated, start to form a network. Here we present two PDE models describing lymphangiogenesis according to these two different hypotheses. Further, we include the effect of advection due to interstitial flow and lymph flow coming from open capillaries. The variables represent different cell densities and growth factor concentrations, and where possible the parameters are estimated from biological data. The models are then solved numerically and the results are compared with the available biological literature.Comment: 29 pages, 9 Figures, 6 Tables (39 figure files in total

The VI-Suite: a set of environmental analysis tools with geospatial data applications

Background: The VI-Suite is a free and open-source addon for the 3D content creation application Blender, developed primarily as a tool for the contextual and performative analysis of buildings. Its functionality has grown from simple, static lighting analysis to fully parametric lighting, shadowing, and building energy analyses. It adopts a flexible, mesh geometry based approach to the specification of calculation points and this has made it suitable for certain types of 3D geospatial analyses and data visualisation.Results: As this is the first academic paper to discuss the VI-Suite, a history of its development is presented along with a review of its capabilities of relevance to geospatial analysis. As the VI-Suite combines the functionality of 3D design software with performance simulation, some of the benefits of this combination are discussed including aspects that make it suitable for the processing and analysis of potentially large geospatial datasets. Example use cases with a 3D city model of the Hague are used to demonstrate some of the geospatial workflows possible and some of the result visualisation options.Conclusions: The free and open-source nature of the VI-Suite, combined with the use of Blender mesh geometry to define calculation points, has encouraged usage scenarios not originally intended by the authors, for example large scale urban shadow and radiation analyses. The flexibility inherent in this mesh based approach enables the analysis of large geospatial datasets by giving the user refined control over the distribution of calculation points within the model. The integration of GIS analysis into a digital design package such as Blender offers advanced geometry/material editing and specification, provides tools such as ray casting and BVH tree generation to speed up the simulation of large datasets, and enhanced visualisation of GIS simulation data including animated city fly-throughs and high quality image production. The VI-Suite is part of a completely open-source tool chain and contributions from the community are welcome to further enhance its current geospatial data capabilities.3D Geo-Informatio

Hybrid cellular Potts model for solid tumor growth

We present a hybrid computational framework whose aim is to reproduce and analyze the early growth of a solid tumor. The model couples an extended version of the discrete Cellular Potts Model, used to represent the phenomenological behavior of malignant cells, with a continuous approach of reaction-diffusion equations, employed to describe the evolution of microscopic variables, as the growth factors and the matrix proteins present in the host tissue and the proteolytic enzymes secreted by the tumor. The behavior of each cancer cell is determined by a balance of interaction forces, such as homotypic (cell-cell) and heterotypic (cell-matrix) adhesions and haptotaxis, and is mediated by its molecular state, which regulates the motility and proliferation rate. The resulting model captures the different phases of the development of the tumor mass, i.e. its exponential growth and the subsequent stabilization in a steady-state due to limitations in vital molecules. The proposed approach also predicts the influence on the cancer morphology of changes in specific intercellular adhesive mechanisms

Spheroid Formation of Hepatocarcinoma Cells in Microwells: Experiments and Monte Carlo Simulations

The formation of spherical aggregates during the growth of cell population has long been observed under various conditions. We observed the formation of such aggregates during proliferation of Huh-7.5 cells, a human hepatocarcinoma cell line, in a microfabricated low-adhesion microwell system (SpheroFilm; formed of mass-producible silicone elastomer) on the length scales up to 500 μm. The cell proliferation was also tracked with immunofluorescence staining of F-actin and cell proliferation marker Ki-67. Meanwhile, our complementary 3D Monte Carlo simulations, taking cell diffusion and division, cell-cell and cell-scaffold adhesion, and gravity into account, illustrate the role of these factors in the formation of spheroids. Taken together, our experimental and simulation results provide an integrative view of the process of spheroid formation for Huh-7.5 cells