3621 words - 14 pages

IB Mathematics HL Internal AssessmentApplication of Mathematics in Modeling Tumor GrowthBy: Trang LeIntroductionThe use of mathematics in biology is useful for modeling the growth of populations. These populations may consist of cells, drug or viral particles, or multicellular organisms. As a result, models of population growth can be applied to many fields, for example, genetics, oncology, immunology, physiology, and epidemiology. In order to develop a model of the population growth, a variety of mathematical calculations can be used such as differential equations, optimization, probability functions and integration. The subject of this study will be focused on the growth of tumors.Cancer happens when abnormal cells grow and reproduce uncontrollably. Since it is one of the main causes of death in the world, it has been the subject of numerous scientific studies. In a normal healthy human, cells grow, divide, die and replace themselves in a controlled fashion. When cancer occurs, the cells grow and multiply and become a lump, which is known as a tumor. There are two kinds of tumors, benign and malignant. A benign tumor is a non-cancerous growth that lacks the ability to metastasize (attack other cells). A malignant tumor is cancerous and consists of cancer cells that are able to invade neighboring tissues, and even spread to other parts of the body (metastasis).The aim of this assignment is to show how mathematics can be applied to scrutinize many biological processes. Modeling tumor growth is one of the most significant mathematical applications since the model can be used to develop effective cancer treatment to the patient. There is a plethora of mathematical approaches and ways that the process of tumor growth can be modeled. In this assignment, I will only focus on some of the most common theoretical tumor growth models and some fundamental mathematical analyses that go along with it. RationaleOne of my aspirations is to pursue the medical career and to become a successful doctor in the future. Ironically, I have never truly experienced the working fashion of a doctor in real life and have never touched the surgical knife, the medical machinery, or even a patient. This internal assessment provides me an opportunity to dig in further into the field, which never fails to make me keep feeling interested. The application of mathematics in biology has always fascinated me with its mathematical calculations that open up many paths and perspectives that lead us to understand the complex system inside us, which even our own selves still have not grabbed entirely despite many great contributions made by many outstanding individuals to this field. I choose modeling tumor growth as the subject for this study simply because the disease is an influential and widespread threat to the whole world and myself is also interested due to the lethal nature of the disease. Using mathematics to understand a biological process is, to me, a perfect learning approach...

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