The Application Of Mathematical Model In Cancer

Cancer is historically disease that threatens human life.The study on the pathogenesis of cancer is very useful to the therapy of cancer.With the rapid de-velopment of science and technology,the research of cancer has become increasingly rich and colorful.It is widely accepted that cancer is the result of the accumulated mutations by genes.By the early 1980s,epidemiologists had presented many im-portant causes of cancer,such as environment and genetic factors.They had also proposed the mathematical model of cancer.Over the last few decades,the rapid development of cytology and molecular biology has offered the scope and meth-ods for cancer research.Recent research shows that the development of cancer is mainly due to the driver gene mutation.Lung cancer contains two to eight driver gene mutations.However,two-stage model has been considered in the past studies.Therefore,the extension of this model is very necessary to cancer research.The study on the number of gene mutation in the development of cancer is very mean-ingful to cancer diagnosis and treatment.In this paper,we main explore the number of gene mutation in the progression of breast cancer and lung cancer.In addition,the impact of radiation on the development of lung cancer and the mechanism of genomic instability in lung cancer are discussed.These researches can deepen the understanding of cancer,and provide guidance for the prevention,diagnosis and treatment of cancer.There are six chapters in the body of our thesis.In the first chapter,we introduce the background and the research status of cancer,and some preliminaries.Lung cancer is a leading cause of cancer-related death in the world.For lung cancer,mechanistic modeling studies focused almost exclusively on the two-stage model,and no work has been done to explore the gender difference.To explore these issues,chapter 2 discuss the number of gene mutation in the development of all lung cancer patients,male lung cancer patients and female patients.Moreover,the impact of cell mutation and cell clonal expansion on the probability of lung cancer is studied.We set up the multistage model with cell clonal expansion.This model is used to fit the data in the Surveillance,Epidemiology,and End Results(SEER)registry.Then,we can obtain all reasonable models.The optimal model is identified by the statistical test.At last,the analyses of the optimal model parameters in male patients are discussed,which can provide the effective programs for the treatment of lung cancer.By the results of numerical simulation,two to eight driver gene mutations are required for normal lung stem cells to become a malignant cell,and three driver gene mutations is most likely to occur in the development of lung cancer.The interesting result is that,for female patient data is the model with three gene mutations while that for male patients data is the four-stage model.Finally,the analysis of model parameters suggests that the decrease of cell net proliferation rates is more effective than the decrease of mutation rates in reducing the lung cancer risk.Environment factors play an important role in the incidence of lung cancer.Smoking and radiation are two major environmental factors of the development of lung cancer.The relationship between environment and lung cancer is very signifi-cant to the prevention of lung cancer.Although the impact of environment on the development of lung cancer has been studied by a number of works,these research works mainly focused on the impact of environment on the risk of lung cancer and did not give the detailed analysis for parameter changes.To address this issue,chapter 3 discusses the influence of radiation on the mechanism of lung cancer.The three-stage model with cell clonal expansion is used to study this issue.We mainly discuss the impact of radiation on the mutation rates of the mutated cells and the clonal expansion of cells in the model.Using the age-specific lung cancer in the Osaka Cancer Registry(OCR)and Life Span Study(LSS)cohort of atomic bomb survivors in Hiroshima and Nagasaki as the test system,the proposed model is used to fit these data.The results indicate that the major effect of radiation on the de-velopment of lung cancer is to induce gene mutations for male patients and female patients.In particular,radiation for male patients affects the mutation in normal cells and transformation from premalignant cells to malignant ones.However,for female patients,radiation increases the mutation rates of the first two mutations in the model.These conclusions will provide insightful prediction for lung cancer incidence in the radiation exposure.Genomic instability plays a significant role in the development of cancer.Al-though substantial research has been conducted using both clinal and theoretical studies,it is still a hotly debated issue to whether genomic instability precedes oncogenes activation and tumor suppressor genes inactivation.To address this is-sue,in the chapter 4,we set up a model incorporating effects of genetic instability to investigate the genomic instability mechanisms of human lung cancer.The proposed model is used to match the lung cancer data of the Life Span Study cohort of the atomic bomb survivors in Hiroshima and Nagasaki.Our results suggest that ge-nomic instability has no significant effect on the clonal expansion of cells,and there a gender difference in the development of lung cancer.For male patients,genomic instability is an early event in the precess of lung tumorigenesis.However,there is no evidence that genomic instability is necessary in the development of lung cancer for female patients.For female patients,genomic instability is a late event even though it indeed occurs in the tumorigenesis of lung cancer.Statistical analyses suggested that most of gene mutations were harmless and that less than 15 gene mutations were likely to be responsible for driving the initia-tion and progression of breast cancer and colorectal cancer.To study the mutation mechanism of breast cancer,chapter 4 gives the any multistage model with clonal expansion in each compartment of premalignant cells.By fitting the breast cancer incidence in the Surveillance,Epidemiology,and End Results(SEER)registry dur-ing 1990-1999,we find that 2-14 mutations in the genome of breast stem cells are required for normal breast stem cells to become a malignant cell,and three gene mutations are most likely to happen in the progression of female breast cancer.In addition,there is mutator phenotype in the development of female breast cancer.Finally,Chapter 6 concludes the current work and makes a prospect to cancer research.