Ilea M, Turnea M, Rotariu M
Faculty of Medical Bioengineering, University of Medicine and Pharmacy "Grigore T. Popa" - Iasi.
Rev Med Chir Soc Med Nat Iasi. 2013 Apr-Jun;117(2):572-7.
Mathematical modeling is a process by which a real world problem is described by a mathematical formulation. The cancer modeling is a highly challenging problem at the frontier of applied mathematics. A variety of modeling strategies have been developed, each focusing on one or more aspects of cancer.
The vast majority of mathematical models in cancer diseases biology are formulated in terms of differential equations. We propose an original mathematical model with small parameter for the interactions between these two cancer cell sub-populations and the mathematical model of a vascular tumor. We work on the assumption that, the quiescent cells' nutrient consumption is long. One the equations system includes small parameter epsilon. The smallness of epsilon is relative to the size of the solution domain.
MATLAB simulations obtained for transition rate from the quiescent cells' nutrient consumption is long, we show a similar asymptotic behavior for two solutions of the perturbed problem. In this system, the small parameter is an asymptotic variable, different from the independent variable. The graphical output for a mathematical model of a vascular tumor shows the differences in the evolution of the tumor populations of proliferating, quiescent and necrotic cells. The nutrient concentration decreases sharply through the viable rim and tends to a constant level in the core due to the nearly complete necrosis in this region.
Many mathematical models can be quantitatively characterized by ordinary differential equations or partial differential equations. The use of MATLAB in this article illustrates the important role of informatics in research in mathematical modeling. The study of avascular tumor growth cells is an exciting and important topic in cancer research and will profit considerably from theoretical input. Interpret these results to be a permanent collaboration between math's and medical oncologists.
数学建模是一个通过数学公式描述现实世界问题的过程。癌症建模是应用数学前沿的一个极具挑战性的问题。已经开发了多种建模策略，每种策略都聚焦于癌症的一个或多个方面。
癌症疾病生物学中的绝大多数数学模型都是用微分方程来表述的。我们针对这两个癌细胞亚群之间的相互作用以及血管肿瘤提出了一个带有小参数的原创数学模型。我们基于静止细胞营养消耗时间长这一假设进行研究。方程组中包含小参数ε。ε的小是相对于解域的大小而言的。
针对静止细胞营养消耗时间长的转移率进行MATLAB模拟，我们展示了受扰问题的两个解具有相似的渐近行为。在这个系统中，小参数是一个渐近变量，不同于自变量。血管肿瘤数学模型的图形输出显示了增殖、静止和坏死细胞的肿瘤群体演变的差异。由于该区域几乎完全坏死，营养浓度在存活边缘急剧下降，并在核心区域趋于恒定水平。
许多数学模型可以用常微分方程或偏微分方程进行定量表征。本文中MATLAB的使用说明了信息学在数学建模研究中的重要作用。无血管肿瘤生长细胞的研究是癌症研究中一个令人兴奋且重要的课题，将从理论输入中受益匪浅。将这些结果解释为数学和医学肿瘤学家之间的长期合作。
