Multiscale modeling of palisade formation in gliobastoma multiforme

Palisades are characteristic tissue aberrations that arise in glioblastomas. Observation of palisades is considered as a clinical indicator of the transition from a noninvasive to an invasive tumour. In this article we propose a computational model to study the influence of genotypic and phenotypic heterogeneity in palisade formation. For this we produced three dimensional realistic simulations, based on a multiscale hybrid model, coupling the evolution of tumour cells and the oxygen diffusion in tissue, that depict the shape of palisades during its formation. Our results can be summarized as the following: (1) we show that cell heterogeneity is a crucial factor in palisade formation and tumour growth; (2) we present results that can explain the observed fact that recursive tumours are more malignant than primary tumours; and (3) the presented simulations can provide to clinicians and biologists for a better understanding of palisades 3D structure as well as glioblastomas growth dynamics

Multiscale modeling of palisade formation in gliobastoma multiforme

Palisades are characteristic tissue aberrations that arise in glioblastomas. Observation of palisades is considered as a clinical indicator of the transition from a noninvasive to an invasive tumour. In this article we propose a computational model to study the influence of genotypic and phenotypic heterogeneity in palisade formation. For this we produced three dimensional realistic simulations, based on a multiscale hybrid model, coupling the evolution of tumour cells and the oxygen diffusion in tissue, that depict the shape of palisades during its formation. Our results can be summarized as the following: (1) we show that cell heterogeneity is a crucial factor in palisade formation and tumour growth; (2) we present results that can explain the observed fact that recursive tumours are more malignant than primary tumours; and (3) the presented simulations can provide to clinicians and biologists for a better understanding of palisades 3D structure as well as glioblastomas growth dynamic

Multi-scale modelling of the dynamics of cell colonies:insights into cell-adhesion forces and cancer invasion from in silico simulations

Studying the biophysical interactions between cells is crucial to understanding how normal tissue develops, how it is structured and also when malfunctions occur. Traditional experiments try to infer events at the tissue level after observing the behaviour of and interactions between individual cells. This approach assumes that cells behave in the same biophysical manner in isolated experiments as they do within colonies and tissues. In this paper, we develop a multi-scale multi-compartment mathematical model that accounts for the principal biophysical interactions and adhesion pathways not only at a cell-cell level but also at the level of cell colonies (in contrast to the traditional approach). Our results suggest that adhesion/separation forces between cells may be lower in cell colonies than traditional isolated single-cell experiments infer. As a consequence, isolated single-cell experiments may be insufficient to deduce important biological processes such as single-cell invasion after detachment from a solid tumour. The simulations further show that kinetic rates and cell biophysical characteristics such as pressure-related cell-cycle arrest have a major influence on cell colony patterns and can allow for the development of protrusive cellular structures as seen in invasive cancer cell lines independent of expression levels of pro-invasion molecules.Publisher PDFPeer reviewe

La contextualización social en los libros de texto de educación primaria de matemáticas de la India

La India presenta un formato público y universal de libros de texto para todas las escuelas de primaria. En estos, la contextualización de los problemas toma un papel principal en la que factores sociales generan un escenario en el cual la resolución adquiere un sentido real. En este artículo se analiza la contextualización de dos capítulos de los libros de cuarto y quinto curso de primaria de la India; y se muestra cómo la contextualización de los problemas presentados atiende a objetivos específicos del plan de desarrollo del estado Indio

Computational modelling and simulation of cancer growth and migration within a 3D heterogeneous tissue: The effects of fibre and vascular structure

The term cancer covers a multitude of bodily diseases, broadly categorised by having cells which do not behave normally. Since cancer cells can arise from any type of cell in the body, cancers can grow in or around any tissue or organ making the disease highly complex. Our research is focused on understanding the specific mechanisms that occur in the tumour microenvironment via mathematical and computational modeling. We present a 3D individual-based model which allows one to simulate the behaviour of, and spatio-temporal interactions between, cells, extracellular matrix fibres and blood vessels. Each agent (a single cell, for example) is fully realised within the model and interactions are primarily governed by mechanical forces between elements. However, as well as the mechanical interactions we also consider chemical interactions, for example, by coupling the code to a finite element solver to model the diffusion of oxygen from blood vessels to cells. The current state of the art of the model allows us to simulate tumour growth around an arbitrary blood-vessel network or along the striations of fibrous tissue

Computational Modeling of Single-Cell Migration::The Leading Role of Extracellular Matrix Fibers

Cell migration is vitally important in a wide variety of biological contexts ranging from embryonic development and wound healing to malignant diseases such as cancer. It is a very complex process that is controlled by intracellular signaling pathways as well as the cell's microenvironment. Due to its importance and complexity, it has been studied for many years in the biomedical sciences, and in the last 30 years it also received an increasing amount of interest from theoretical scientists and mathematical modelers. Here we propose a force-based, individual-based modeling framework that links single-cell migration with matrix fibers and cell-matrix interactions through contact guidance and matrix remodelling. With this approach, we can highlight the effect of the cell's environment on its migration. We investigate the influence of matrix stiffness, matrix architecture, and cell speed on migration using quantitative measures that allow us to compare the results to experiments

Analysis and applications to the cell interplay and control of low grade gliomas

Tumor-normal cell interplay defines the course of a neoplastic malignancy. The outcome of this dual relation is the ultimate prevailing of one of the cells and the death or retreat of the other. In this paper we study the mathematical principles that underlay one important scenario: that of slow-progressing cancers. For this, we develop, within a stochastic framework, a mathematical model to account for tumor-normal cell interaction in such a clinically relevant situation and derive a number of deterministic approximations from the stochastic model. We consider in detail the existence and uniqueness of the solutions of the deterministic model and study the stability analysis. We then focus our model to the specific case of low grade gliomas, where we introduce an optimal control problem for different objective functionals under the administration of chemotherapy. We derive the conditions for which singular and bang-bang control exist and calculate the optimal control and states

Enabling multiscale modeling in systems medicine

CITATION: Wolkenhauer, O. et al. 2014. Enabling multiscale modeling in systems medicine. Genome Medicine, 6:21, doi:10.1186/gm538.The original publication is available at http://genomemedicine.biomedcentral.com[See article for abstract].Publisher's versio

Enabling multiscale modeling in systems medicine: From reactions in cells to organ physiology

International audienceSystems medicine is an interdisciplinary approach that integrates data from basic research and clinical practice to improve our understanding and treatment of diseases. Systems medicine can be seen as a further development of systems biology and bioinformatics towards applica-tions of clinical relevance. The term 'systems' refers to systems approaches, emphasizing a close integration of data generation with mathematical modeling [1-3]. The (mal)functioning of the human body is a complex process, characterized by multiple interactions between systems that act across multiple levels of structural and functional organization -from molecular reactions to cell-cell interac-tions in tissues to the physiology of organs and organ systems. Over the past decade, we have gained detailed insights into the structure and function of molecular, cellu-lar and organ-level systems, with technologies playing an important role in the generation of data at these different scales