The Study And Application Of Mathematical Oncology: The Effect Of Microenvironment

As the medicine and medical care develop quickly, a lot of diseases that are unable to be cured and so show a very high death rate have been well controlled or even eliminated completely. However, some diseases become more emergent nowadays, especially, the cancer. Though the reports of cancer date back to antiquity, it was since half a century ago that much more emphasis was given to cancer research. Honestly, cancer research was originally a medical projett since people knew little about it and clinical diagnosis and treatments is the focus. But now, with the fast development of interdiscipline, mathematics and engineering are gradually used in cancer research and therefore, becomes an important project in biomedical engineering. Besides, clinical and experimental data becomes so huge, and the cost of experimental equipments and biochemical reagents increase exponentially, it is in dire need of methods that are more effective, much cheaper and easier to reproduce. Thus, here comes the mathematical oncology. Although it strongly depends on experimental data to build and validate models, mathematical oncology do drive the fast development of cancer research, not only saving a lot of money and manpower, but also playing an important role in statistic analysis of huge data, discovering underlying mechanism and prediction of cancer progression. Therefore, mathematical oncology is gradually accepted by clinicians and experimental investigators.Modeling of caner should be multiscale, which can usually be bulit at three levels:molecular, cellular and tissue levels. At molecular level, people study gene transcription, protein expression, signaling pathways and so on, by using chemical reaction equations. Given initial condition and measured parameter values, these models can simulate the change of all components across a certain time. At cellular level, with the simulation results at previous level, models are built to describe cellular properties, such as growth, dormancy or apoptosis, proliferation rate, oxygen consumption and differentiation and so on. At tissue level, researchers investigate interactions between cells and growth factors, hormone, and nutrients surrounding them. A group of ordinary (partial) differential equations are commonly used to simulate the motion of cells, absorption and decay of nutrients and so on. Also, according to various purposes, tumor models can be classified with different dimensions. One dimension models are usually simple and show good computing efficiency in simulating temporal changes of model components, while two dimensions and three dimensions models can give spatial distribution as well, thus help to observe the disease more intuitively and accurately. But high dimension models have disvantages of time consuming and need for high quality of computer and numerical algorithms.Philosophically, it says that everything is governed by internal and external factors together. Cancer is not an exception, either. At the beginning of cancer research, most effort was made to study the effect of internal factor on tumorigeneis, that is, gene mutations. Recently, however, more and more research shows that external factor plays an essential role in tumorigenesis as well. In this study, the tumor microenvironment, which is an entity of cellualar and non-cellular components surrounding the tumor tissue, is considered to be the most important external factor. Like normal cells, tumor cells need nutrients, growth factors, fibroblasts and so on, which provide energy, signals and phycial supports for their survival and proliferation. Thus, the interactions between tumor cells and the mircroenvironment never stop. Let us imagine, if we could quantitatively describe these interactions by using mathematical equations and could predict the progression of a certain tumor and even find an optimal treatment, then, the cancer wouldn't be a nightmare anymore. Indeed, this is the ultimate goal of the study.The dissertation has done the following research work:1. Study of progress and theoretical frame of mathematical oncologyThe dissertation summarizes and analyses the main progress in mathematical oncology. Firstly, we introduce the study of cancer, giving the definintion, classification and the clinical situation of this disease. Next, we talk about the definition of mathematical oncology and discuss the history of its development and the future work. Corresponding to a specific stage of caner, we will summarize the general process to build a mathematical model and give an example for explanation. Then, we introduce different research groups all over the world, and briefly summarize their work in this area. Finally, we propose a theoretical frame for multiscal modeling of caner that involves experimental technologies and mathematical methods.2. Modeling and simulation of breast cancerAs an application of mathematical oncology, we study the initiation, progression and therapy strategy of breast cancer in this section. We firstly summarize and describe the interactions between breast cancer cells, niches, EGFR signaling pathway and drugs, then adopt a compartment model that includes a set of differential equations to quantitively simulate the progression of breast cancer. In this work, we integrated the cancer stem cell niches for the first time into modeling and simulation of breast cancer. Simulation results show that our model is of high stability, and is able to consider stem cells, niches, signaling pathway and drugs together and to reproduce phenomena that are clinically observed. At last, we simulate several theoretical treatments with the proposed model and demonstrate the potential significance of stem cell niche to clinical therapy.3. Modeling and simulation of myelodysplastic syndromesAfter analysis and discussion of clinical data of MDS, we propose a simplified compartment model to describe this disease. In this model, two compartments are included:bone marrow and peripheral blood. In each compartment, it contains both normal and abnormal cells, while stem cells in bone marrow differentiate into various blood cells that move to peripheral blood, the cell number in latter compartment in turn affects the proliferation and differentiation of stem cells. On the basis of clinical and experimental data, we introduce the concept of stem cell niches, for the first time, into the mathematical modeling of MDS. We simulate the initiation and development of this disease with a group of ordinary differential equations, propose a new possible strategy to control or even cure MDS. Our simulations show that our model is simple and stable, but could well demonstrate of underlying mechanism and give a possible treatment strategy for MDS.