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RISS 인기검색어
- 검색키워드
- 저자 : Othmer, Hans G. (검색결과 4 건)
- 무료
- 기관 내 무료
- 유료
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The Role of the Tumor Microenvironment in Glioblastoma: A Mathematical Model
Kim, Yangjin,Jeon, Hyejin,Othmer, Hans IEEE 2017 IEEE Transactions on Biomedical Engineering Vol.64 No.3
<P>Glioblastoma multiforme is one of the deadliest human cancers and is characterized by tumor cells that hijack immune system cells in a deadly symbiotic relationship. Microglia and glioma infiltrating macrophages, which in principle should mount an immune response to the tumor, are subverted by tumor cells to facilitate growth in several ways. In this study, we seek to understand the interactions between the tumor cells and the microglia that enhance tumor growth, and for this purpose, we develop a mathematical and computational model that involves reaction-diffusion equations for the important components in the interaction. These include the densities of tumor and microglial cells, and the concentrations of growth factors and other signaling molecules. We apply this model to a transwell assay used in the laboratory to demonstrate that microglia can stimulate tumor cell invasion by secreting the growth factor TGF-β. We show that the model can both replicate the major components of the experimental findings and make new predictions to guide future experiments aimed at the development of new therapeutic approaches. Sensitivity analysis is used to identify the most important parameters as an aid to future experimental work. This study is the first step in a program that involves development of detailed 3-D models of the mechanical and biochemical interactions between a glioblastoma and the tumor microenvironment.</P>
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The role of stromal cells in cancer cell invasion
Yangjin Kim,Hans G Othmer,Sookkyung Lim 한국산업응용수학회 2012 한국산업응용수학회 학술대회 논문집 Vol.7 No.1
Ductal carcinoma in situ (DCIS) is an early stage non-invasive breast cancer that originates in the epithelial lining of the milk ducts. These cells actively proliferate and stay in the duct. However, DCIS can evolve into comedo DCIS and ultimately the most common type of breast cancer, invasive ductal carcinoma, which can induce metastasis. Understanding the progression and how to effectively intervene in it presents a major scientific challenge. Stromal tissue surrounding a duct contains the extracellular matrix (ECM), several types of cells and several types of growth factors that are known to individually affect tumor growth and invasion, but at present the complex mechanical and biochemical interactions of these stromal cells with cancer cells is poorly understood. Among those stromal cells, fibroblasts and their aggressive types, myofibroblasts, were shown to play an important role in tumor growth and invasion. Here we illustrate how hybrid models can reproduce experimental results and generate predictions that need to be verified in followup experiments. The mathematical model incorporates the cross-talk between stromal and tumor cells via growth factors and several types of proteases. The model predict how perturbations of the local biochemical and mechanical state influence tumor evolution and invasion. Epithelial cells (ECs) and stromal cells are modeled individually and their interactions are mediated by a set of partial differential equations for growth factors and proteases. Our results shed light on the biochemical and mechanical interactions between growth factors, mechanical properties of the ECM, and feedback signaling loops between stromal and tumor cells, and suggest how epigenetic changes in transformed cells affect tumor progression.
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A multi-time-scale analysis of chemical reaction networks: II. Stochastic systems
Kan, Xingye,Lee, Chang Hyeong,Othmer, Hans G. Springer-Verlag 2016 Journal of mathematical biology Vol.73 No.5
<P>We consider stochastic descriptions of chemical reaction networks in which there are both fast and slow reactions, and for which the time scales are widely separated. We develop a computational algorithm that produces the generator of the full chemical master equation for arbitrary systems, and show how to obtain a reduced equation that governs the evolution on the slow time scale. This is done by applying a state space decomposition to the full equation that leads to the reduced dynamics in terms of certain projections and the invariant distributions of the fast system. The rates or propensities of the reduced system are shown to be the rates of the slow reactions conditioned on the expectations of fast steps. We also show that the generator of the reduced system is a Markov generator, and we present an efficient stochastic simulation algorithm for the slow time scale dynamics. We illustrate the numerical accuracy of the approximation by simulating several examples. Graph-theoretic techniques are used throughout to describe the structure of the reaction network and the state-space transitions accessible under the dynamics.</P>
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