数学肿瘤学的研究与应用：微环境的作用

发布时间：2018-05-12 08:45

本文选题：癌症 + 干细胞　；参考：《浙江大学》2011年博士论文

【摘要】：随着医学的不断进步,医疗卫生事业的不断发展,许多疾病都得到了控制甚至完全消灭。但有些疾病的研究却变得更加迫切,尤其是癌症。尽管在很早以前就有癌症的报道,对该疾病的大量研究还是从大约半个世纪前开始的。可以说,最早的癌症研究应该属于医学领域,因为对该病的认识严重不足,所以研究的重点都放在了临床的诊断与治疗上；而如今,随着交叉学科的快速发展,数学和工程的方法也逐步应用于癌症领域,因此,癌症研究也就成为了生物医学工程领域的一个课题。而临床、试验数据的海量化,实验设备和生化试剂的成本级数递增,也迫切需要有一种更高效、更廉价、更易重复的方法出现。于是,数学肿瘤学就应运而生了。虽然在模型建立和验证时,仍然十分依赖于临床实验数据,但是数学肿瘤学极大的推动了该课题的发展,不但节约了人力、物力、财力,而且在海量数据统计分析、发病机理和疾病发展预测方面,都发挥了重大作用。也正因为如此,之前不被看好的数学肿瘤学,才在近年来逐渐被临床医生和实验研究人员接受。对癌症的建模应该是多尺度的,目前大致可以分为三层：分子层次,细胞层次和组织层次。分子层次包括基因转录和蛋白表达、信号通路的信号传递等,对这些过程的建模主要是用一系列的化学反应平衡方程来表示,在给定初始值和测定参数值的情况下,分析各个成分随时间的变化情况。细胞层次描述单个细胞的特性,包括生长、休眠或凋亡,分裂速度、消耗营养的快慢,是否进行分化等,主要通过分子层次的仿真结果来判定。组织层次包括细胞间的相互作用,细胞与细胞周围的生长因子、激素或养分之间的相互作用,建模的方法是用一系列的常微分、偏微分方程组来描述细胞的运动、营养的衰减吸收等过程。根据研究目的的不同,肿瘤模型也可以分为一维、二维和三维等不同的层次：一维模型快速而经济,能方便的给出各种成分随时间的变化情况；二维三维模型能给出各个成分的空间分布情况,有利于更直观和精确的了解发展过程,其缺点是计算量大,对计算机和数值算法的要求较高。哲学上说,任何事物的发展是由内因和外因共同作用的。这句话也适用于癌症。尽管最初的研究倾向于强调癌症发生的内因性,认为基因突变是其发生的原因；近些年来,越来越多的研究表明,外部因素也极重要的影响着癌症的发生。特别的,在本研究中谈及的外部因素主要是肿瘤微环境,也就是肿瘤组织周围的各种细胞成分与非细胞成分的整体。与正常细胞一样,肿瘤细胞也需要有营养物质、生长因子和成纤维细胞等成分,为其存活和增生提供必要的能量、信号和支架等。因此,肿瘤的生长过程可以说与肿瘤微环境之间的相互作用是从不间断的。让我们试想,假如能够通过数学建模的方法来定量描述这些相互作用,并能通过计算机仿真,预测某个特定肿瘤会如何发展,以及该用什么治疗方法去控制甚至是消除,那么,癌症或许就没那么可怕了。事实上,这就是本研究的最终目标。论文完成的主要研究工作包括：一、数学肿瘤学的进展和理论框架研究系统的总结和分析了目前数学肿瘤学的研究进展。首先介绍了癌症研究发展史,给出癌症的定义、分类以及目前的临床统计情况。其次给出数学肿瘤学的定义,并探讨了相关数学模型的发展过程和未来的发展方向。针对癌症的不同发展阶段,我们总结了相应数学模型的建立过程,并给出典型例子来详细说明。然后介绍了目前在癌症研究领域处于领先地位的各个小组,并大致描述并总结了他们所做工作的重点和取得的成果。最后提出了一个实验手段与数学方法紧密结合的多尺度癌症建模的理论框架。二、乳癌的数学建模与仿真研究作为数学肿瘤学的实际应用,我们研究了人体乳癌发生、发展和药物治疗的过程。我们首先描述了乳癌细胞、干细胞微环境、内皮生长因子受体信号通路和药物成分之间的关系,然后用一组微分方程组的区间模型来定量计算乳癌发展过程中各个成分的变化情况。本文首次将肿瘤干细胞微环境的作用考虑到乳癌的仿真模型中来。仿真结果表明,我们的数学模型十分稳定,能很好的考虑干细胞、微环境、信号通路以及药物作用,与临床实验观察的结果十分接近。最后,我们也利用该模型进行了一系列的理论治疗仿真,并提示了干细胞微环境在临床治疗上的重要意义。三、骨髓增生异常综合症的数学建模与仿真研究在分析和总结骨髓增生异常综合症的临床数据后,我们提出了一种简化的区间模型来描述该病症。该模型主要包括骨髓和外周血两个区间,每个区间内又包括正常的和异常的两类细胞,处于骨髓内的干细胞通过分化形成各种血细胞进入到外周血中,而外周血中细胞数量的多少反过来又影响干细胞的增生和分化。在归纳和抽象临床实验知识的基础上,我们首次将干细胞龛的概念引入到该病的数学建模中来。我们用一组常微分方程来描述该病症的发生发展过程,并通过提出一种可能的治疗方法来控制甚至治愈该病。模型仿真结果显示,我们的模型简单、稳定,却能很好的阐释MDS可能的发生机制和并提供可能的治疗方案。
[Abstract]:With the continuous progress of medicine and the continuous development of medical and health services, many diseases have been controlled and even completely eliminated. But the research of some diseases has become more urgent, especially cancer. Despite the reports of cancer early on, a large number of studies on the disease began about half a century ago. Cancer research should be in the field of medicine, because the understanding of the disease is seriously inadequate, so the focus of the research is on clinical diagnosis and treatment. Now, with the rapid development of interdisciplinary, mathematical and engineering methods are gradually applied to the field of cancer. Therefore, cancer research has become the field of biomedical engineering. A subject in which the clinical, experimental data is massive, the cost progression of experimental equipment and biochemical reagents is increasing, and there is an urgent need for a more efficient, cheaper, and more repeatable method. Oncology has greatly promoted the development of the subject. It not only saves manpower, material and financial resources, but also plays a major role in the statistical analysis of massive data, the pathogenesis and the prediction of disease development. Accept.
The modeling of cancer should be multiscale. At present, it can be divided into three layers: molecular level, cell level and organization level. Molecular level, including gene transcription and protein expression, signal transduction, and so on. The modeling of these processes is mainly expressed by a series of chemical reaction equilibrium equations, given initial values and measurements. In the case of the fixed parameter, the changes of each component with time are analyzed. The cell level describes the characteristics of a single cell, including growth, dormancy or apoptosis, the speed of division, the fast and slow consumption of nutrients, or whether the differentiation is carried out, mainly by the simulation results of the molecular level. The organization level includes intercellular interaction, cell and fine. The interaction of growth factors, hormones or nutrients around the cell. The modeling method is to use a series of ordinary differential and partial differential equations to describe the process of cell movement and nutrient attenuation absorption. According to the different purpose of the study, the tumor model can be divided into one dimension, two dimension and three dimensions, and the one dimension model is fast and fast. The economy can easily give the change of various components with time. The two-dimensional three-dimensional model can give the spatial distribution of each component, which is beneficial to the more intuitive and accurate understanding of the development process. Its disadvantage is that the computational complexity is large and the requirements for computer and numerical algorithms are higher.
Philosophically, the development of everything is combined with internal and external factors. This sentence also applies to cancer. Although the initial research tends to emphasize the internal causes of cancer, it is considered the cause of the mutation; in recent years, more and more studies have shown that the external factors are also very important to the occurrence of cancer. In addition, the external factors involved in this study are mainly the tumor microenvironment, that is, the various cellular components and non cellular components around the tumor tissue. Like the normal cells, the tumor cells also need nutrients, growth factors and fibroblasts to provide the necessary energy, signals and branches for their survival and proliferation. Therefore, the interaction between the tumor growth process and the tumor microenvironment is uninterrupted. Let us try to imagine how these interactions can be described quantitatively by mathematical modeling and can be simulated by computer to predict how a particular tumor will develop and what treatment should be used to control it. Even if it is eliminated, then cancer may not be so terrible. In fact, this is the ultimate goal of this study.
The main research work completed in this paper includes:
First, research on the progress and theoretical framework of mathematical oncology
The research progress of mathematical oncology at present is summarized and analyzed. First, the history of cancer research and development, definition, classification and clinical statistics of cancer are given. Secondly, the definition of oncology is given, and the development and future direction of the mathematical models are also discussed. In this stage, we summarize the process of establishing the corresponding mathematical model and give a typical example. Then we introduce the groups that are in the leading position in the field of cancer research, and describe and summarize the focus and achievements of their work. Finally, we put forward an experimental method and a mathematical method. A theoretical framework for multi-scale cancer modeling.
Two, mathematical modeling and Simulation of breast cancer
As a practical application of mathematical oncology, we studied the process of human breast cancer, development and drug treatment. We first described the relationship between breast cancer cells, stem cell microenvironment, endothelial growth factor receptor signaling pathway and drug components, and then used a group of differential equations to quantify the development of breast cancer. In this paper, the role of the tumor stem cell microenvironment is considered in the simulation model of breast cancer for the first time. The simulation results show that our mathematical model is very stable and can consider the stem cells, microenvironment, signal pathways and drug effects very well. Finally, we are in close proximity to the results of clinical observation. A series of theoretical treatment simulations are also carried out using this model. It also indicates the importance of stem cell microenvironment in clinical treatment.
Three, mathematical modeling and Simulation of myelodysplastic syndrome.
After analyzing and summarizing the clinical data of myelodysplastic syndrome, we present a simplified interval model to describe the disease. This model mainly includes two intervals of bone marrow and peripheral blood, each of which includes two types of normal and abnormal cells, and the stem cells in the bone marrow form various blood cells through the differentiation. In the peripheral blood, the number of cells in the peripheral blood in turn affects the proliferation and differentiation of stem cells. On the basis of induction and abstract clinical knowledge, we introduce the concept of stem cell niche to the mathematical modeling of the disease for the first time. We use a group of ordinary differential Cheng Lai to describe the occurrence and development of the disease. A possible treatment to control or even cure the disease has been proposed. The model simulation results show that our model is simple and stable, but it can explain the possible mechanisms of MDS and provide possible treatment options.

【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2011
【分类号】：R311

【参考文献】