1,784 research outputs found
Multiscale Agent-based Model of Tumor Angiogenesis
AbstractComputational models of cancer complement the biological study of tumor growth. However, existing modeling approaches can be both inefficient and inaccurate due to the difficulties of representing the complex interactions between cells and tissues. We present a three-dimensional multiscale agent-based model of tumor growth with angiogenesis. The model is designed to easily adapt to various cancer types, although we focus on breast cancer. It includes cellular (genetic control), tissue (cells, blood vessels, angiogenesis), and molecular (VEGF, diffusion) levels of representation. Unlike in most cancer models, both normally functioning tissue cells and tumor cells are included in the model. Tumors grow following the expected spheroid cluster pattern, with growth limited by available oxygen. Angiogenesis, the process by which tumors may encourage new vessel growth for nutrient diffusion, is modeled with a new discrete approach that we propose will decrease computational cost. Our results show that despite proposing these new abstractions, we see similar results to previously accepted angiogenesis models. This may indicate that a more discrete approach should be considered by modelers in the future
Multiscale modelling of vascular tumour growth in 3D: the roles of domain size & boundary condition
We investigate a three-dimensional multiscale model of vascular tumour growth, which couples blood flow, angiogenesis, vascular remodelling, nutrient/growth factor transport, movement of, and interactions between, normal and tumour cells, and nutrient-dependent cell cycle dynamics within each cell. In particular, we determine how the domain size, aspect ratio and initial vascular network influence the tumour's growth dynamics and its long-time composition. We establish whether it is possible to extrapolate simulation results obtained for small domains to larger ones, by constructing a large simulation domain from a number of identical subdomains, each subsystem initially comprising two parallel parent vessels, with associated cells and diffusible substances. We find that the subsystem is not representative of the full domain and conclude that, for this initial vessel geometry, interactions between adjacent subsystems contribute to the overall growth dynamics. We then show that extrapolation of results from a small subdomain to a larger domain can only be made if the subdomain is sufficiently large and is initialised with a sufficiently complex vascular network. Motivated by these results, we perform simulations to investigate the tumour's response to therapy and show that the probability of tumour elimination in a larger domain can be extrapolated from simulation results on a smaller domain. Finally, we demonstrate how our model may be combined with experimental data, to predict the spatio-temporal evolution of a vascular tumour
Object-Oriented Paradigms for Modelling Vascular\ud Tumour Growth: a Case Study
Motivated by a family of related hybrid multiscale models, we have built an object-oriented framework for developing and implementing multiscale models of vascular tumour growth. The models are implemented in our framework as a case study to highlight how object-oriented programming techniques and good object-oriented design may be used effectively to develop hybrid multiscale models of vascular tumour growth. The intention is that this paper will serve as a useful reference for researchers modelling complex biological systems and that these researchers will employ some of the techniques presented herein in their own projects
A multiscale hybrid model for pro-angiogenic calcium signals in a vascular endothelial cell
Cytosolic calcium machinery is one of the principal signaling mechanisms by which endothelial cells (ECs) respond to external stimuli during several biological processes, including vascular progression in both physiological and pathological conditions. Low concentrations of angiogenic factors (such as VEGF) activate in fact complex pathways involving, among others, second messengers arachidonic acid (AA) and nitric oxide (NO), which in turn control the activity of plasma membrane calcium channels. The subsequent increase in the intracellular level of the ion regulates fundamental biophysical properties of ECs (such as elasticity, intrinsic motility, and chemical strength), enhancing their migratory capacity. Previously, a number of continuous models have represented cytosolic calcium dynamics, while EC migration in angiogenesis has been separately approached with discrete, lattice-based techniques. These two components are here integrated and interfaced to provide a multiscale and hybrid Cellular Potts Model (CPM), where the phenomenology of a motile EC is realistically mediated by its calcium-dependent subcellular events. The model, based on a realistic 3-D cell morphology with a nuclear and a cytosolic region, is set with known biochemical and electrophysiological data. In particular, the resulting simulations are able to reproduce and describe the polarization process, typical of stimulated vascular cells, in various experimental conditions.Moreover, by analyzing the mutual interactions between multilevel biochemical and biomechanical aspects, our study investigates ways to inhibit cell migration: such strategies have in fact the potential to result in pharmacological interventions useful to disrupt malignant vascular progressio
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
Simulating Brain Tumor Heterogeneity with a Multiscale Agent-Based Model: Linking Molecular Signatures, Phenotypes and Expansion Rate
We have extended our previously developed 3D multi-scale agent-based brain
tumor model to simulate cancer heterogeneity and to analyze its impact across
the scales of interest. While our algorithm continues to employ an epidermal
growth factor receptor (EGFR) gene-protein interaction network to determine the
cells' phenotype, it now adds an explicit treatment of tumor cell adhesion
related to the model's biochemical microenvironment. We simulate a simplified
tumor progression pathway that leads to the emergence of five distinct glioma
cell clones with different EGFR density and cell 'search precisions'. The in
silico results show that microscopic tumor heterogeneity can impact the tumor
system's multicellular growth patterns. Our findings further confirm that EGFR
density results in the more aggressive clonal populations switching earlier
from proliferation-dominated to a more migratory phenotype. Moreover, analyzing
the dynamic molecular profile that triggers the phenotypic switch between
proliferation and migration, our in silico oncogenomics data display spatial
and temporal diversity in documenting the regional impact of tumorigenesis, and
thus support the added value of multi-site and repeated assessments in vitro
and in vivo. Potential implications from this in silico work for experimental
and computational studies are discussed.Comment: 37 pages, 10 figure
On the foundations of cancer modelling: selected topics, speculations, & perspectives
This paper presents a critical review of selected topics related to the modelling of cancer onset, evolution and growth, with the aim of illustrating, to a wide applied mathematical readership, some of the novel mathematical problems in the field. This review attempts to capture, from the appropriate literature, the main issues involved in the modelling of phenomena related to cancer dynamics at all scales which characterise this highly complex system: from the molecular scale up to that of tissue. The last part of the paper discusses the challenge of developing a mathematical biological theory of tumour onset and evolution
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