The purpose of this book is to show how mathematics can be applied to improve cancer chemotherapy. Unfortunately, most drugs used in treating cancer kill both normal and abnormal cells. However, more cancer cells than normal cells can be destroyed by the drug because tumor cells usually exhibit different growth kinetics than normal cells. To capitalize on this last fact, cell kinetics must be studied by formulating mathematical models of normal and abnormal cell growth. These models allow the therapeutic and harmful effects of cancer drugs to be simulated quantitatively. The combined cell and…mehr
The purpose of this book is to show how mathematics can be applied to improve cancer chemotherapy. Unfortunately, most drugs used in treating cancer kill both normal and abnormal cells. However, more cancer cells than normal cells can be destroyed by the drug because tumor cells usually exhibit different growth kinetics than normal cells. To capitalize on this last fact, cell kinetics must be studied by formulating mathematical models of normal and abnormal cell growth. These models allow the therapeutic and harmful effects of cancer drugs to be simulated quantitatively. The combined cell and drug models can be used to study the effects of different methods of administering drugs. The least harmful method of drug administration, according to a given criterion, can be found by applying optimal control theory. The prerequisites for reading this book are an elementary knowledge of ordinary differential equations, probability, statistics, and linear algebra. In order to make this book self-contained, a chapter on cell biology and a chapter on control theory have been included. Those readers who have had some exposure to biology may prefer to omit Chapter I (Cell Biology) and only use it as a reference when required. However, few biologists have been exposed to control theory. Chapter 7 provides a short, coherent and comprehensible presentation of this subject. The concepts of control theory are necessary for a full understanding of Chapters 8 and 9.
References.- I Cells.- 1.1 Introduction.- 1.2 Cell Organization - Protoplasm.- 1.3 Cellular Structures and their Function.- 1.4 The Life Cycle of Cells.- 1.5 Control of Cell Proliferation.- 1.6 Cancer.- 1.7 Metastasis and Invasion.- References.- II Modelling and Cell Growth.- 2.1 Introduction.- 2.2 Modelling Philosophy.- 2.3 Growth Laws.- 2.4 Two Compartment Growth.- References.- III Some Kinetic Cell Models.- 3.1 Introduction.- 3.2 A Discrete Differential Model.- 3.3 Continuous Versions of the Takahashi-Kendall Equations.- 3.4 Solutions of Continuous Models.- 3.5 Another General Approach to Continuous Models.- 3.6 Trucco's Model.- References.- IV Autoradiography.- 4.1 Introduction.- 4.2 Fractional Labelled Mitosis Curve.- 4.3 Mathematical Models for FLM Curves: Pulse Labelling.- 4.4 FLM Curves for Continuous Labelling.- 4.5 The Labelling Index.- 4.6 Discussion.- References.- V Cell Synchrony.- 5.1 Introduction.- 5.2 Definition of Synchrony.- 5.3 Instantaneous Indices of Synchrony.- 5.4 Time-interval Indices of Synchrony.- 5.5 The Decay of Synchronization.- 5.6 Discussion.- References.- VI Flow Microfluorometry.- 6.1 Introduction.- 6.2 DNA Histogram: Steady-state and Constant Phase Length.- 6.3 Generation of DNA Histogram for Random Phase Lengths.- 6.4 Definition of an Asynchronous Population.- 6.5 Graphical Analysis of Asynchronous Populations.- 6.6 Analytic Analysis of Asynchronous Populations.- 6.7 Estimation of Mean Phase Lengths for Asynchronous Populations.- 6.8 Methods of Estimating Mean Cycle and Mitotic Time for Asynchronous Populations.- 6.9 Analysis of Synchronous Populations. Single Histogram.- 6.10 Analysis of Synchronous Populations from Multiple Histograms.- 6.11 Rate of DNA Synthesis.- 6.12 Determination of Percentage of Cells in G0.- 6.13Generalization of the Degree of Synchrony.- 6.14 Discussion.- References.- VII Control Theory.- 7.1 Introduction.- 7.2 External Description of Systems (input output relations).- 7.3 Internal Description of Systems (State Space Description).- 7.4 Optimal Control Theory.- References.- VIII Towards Mathematical Chemotherapy.- 8.1 Introduction.- 8.2 Growth Laws and Cycle Nonspecific Cancer Chemotherapy.- 8.3 Cycle Specific Chemotherapy.- 8.4 Pharmacokinetics.- 8.5 Remarks.- References.- IX Mathematical Models of Leukopoiesis and Leukemia.- 9.1 Introduction.- 9.2 The Hemopoietic System and its Neoplasms.- 9.3 Steady State Models of the Hemopoietic System.- 9.4 Kinetic Model of Neutrophil Production.- 9.5 Acute Myeloblastic Leukemia.- 9.6 A Chemotherapy Model of AML.- 9.7 Models of Chronic Granulocytic Leukemia (CGL).- 9.8 A Discrete Mathematical Model of Acute Lymphoblastic Leukemia.- 9.9 A Comprehensive Computer Model of Granulopoiesis and Cancer Chemotherapy.- 9.10 Discussion.- References.- Appendix A Chemistry of Genes. Protein Synthesis.- 1. Introduction.- 2. The Building Blocks of DNA and RNA.- 3. The Chemical Structure of DNA and RNA.- 4. The Replication of DNA.- 5. The Genetic Code.- 6. Synthesis of RNA.- 7. Formation of Proteins.- 8. Defining the Gene.- References.- Appendix B Viruses.- 1. Introduction.- 2. Structure of Viruses.- 3. Replication of Viruses.- 4. Oncogenic Viruses 402 References.- Appendix C Cellular Energy.- 1. Introduction.- 2. Adenosine Triphosphate (ATP).- 3. Formation of ATP 405 References.- Appendix D Immunology.- 1. The Immune System.- 2. The Immune System and Cancer 409 References.- Appendix E Mathematical Theories of Carcinogenesis.- References.- Appendix F Radiology and Cancer.- References.- Appendix G Applications of Control Theory to Normaland Malignant Cell Growth.- References.
References.- I Cells.- 1.1 Introduction.- 1.2 Cell Organization - Protoplasm.- 1.3 Cellular Structures and their Function.- 1.4 The Life Cycle of Cells.- 1.5 Control of Cell Proliferation.- 1.6 Cancer.- 1.7 Metastasis and Invasion.- References.- II Modelling and Cell Growth.- 2.1 Introduction.- 2.2 Modelling Philosophy.- 2.3 Growth Laws.- 2.4 Two Compartment Growth.- References.- III Some Kinetic Cell Models.- 3.1 Introduction.- 3.2 A Discrete Differential Model.- 3.3 Continuous Versions of the Takahashi-Kendall Equations.- 3.4 Solutions of Continuous Models.- 3.5 Another General Approach to Continuous Models.- 3.6 Trucco's Model.- References.- IV Autoradiography.- 4.1 Introduction.- 4.2 Fractional Labelled Mitosis Curve.- 4.3 Mathematical Models for FLM Curves: Pulse Labelling.- 4.4 FLM Curves for Continuous Labelling.- 4.5 The Labelling Index.- 4.6 Discussion.- References.- V Cell Synchrony.- 5.1 Introduction.- 5.2 Definition of Synchrony.- 5.3 Instantaneous Indices of Synchrony.- 5.4 Time-interval Indices of Synchrony.- 5.5 The Decay of Synchronization.- 5.6 Discussion.- References.- VI Flow Microfluorometry.- 6.1 Introduction.- 6.2 DNA Histogram: Steady-state and Constant Phase Length.- 6.3 Generation of DNA Histogram for Random Phase Lengths.- 6.4 Definition of an Asynchronous Population.- 6.5 Graphical Analysis of Asynchronous Populations.- 6.6 Analytic Analysis of Asynchronous Populations.- 6.7 Estimation of Mean Phase Lengths for Asynchronous Populations.- 6.8 Methods of Estimating Mean Cycle and Mitotic Time for Asynchronous Populations.- 6.9 Analysis of Synchronous Populations. Single Histogram.- 6.10 Analysis of Synchronous Populations from Multiple Histograms.- 6.11 Rate of DNA Synthesis.- 6.12 Determination of Percentage of Cells in G0.- 6.13Generalization of the Degree of Synchrony.- 6.14 Discussion.- References.- VII Control Theory.- 7.1 Introduction.- 7.2 External Description of Systems (input output relations).- 7.3 Internal Description of Systems (State Space Description).- 7.4 Optimal Control Theory.- References.- VIII Towards Mathematical Chemotherapy.- 8.1 Introduction.- 8.2 Growth Laws and Cycle Nonspecific Cancer Chemotherapy.- 8.3 Cycle Specific Chemotherapy.- 8.4 Pharmacokinetics.- 8.5 Remarks.- References.- IX Mathematical Models of Leukopoiesis and Leukemia.- 9.1 Introduction.- 9.2 The Hemopoietic System and its Neoplasms.- 9.3 Steady State Models of the Hemopoietic System.- 9.4 Kinetic Model of Neutrophil Production.- 9.5 Acute Myeloblastic Leukemia.- 9.6 A Chemotherapy Model of AML.- 9.7 Models of Chronic Granulocytic Leukemia (CGL).- 9.8 A Discrete Mathematical Model of Acute Lymphoblastic Leukemia.- 9.9 A Comprehensive Computer Model of Granulopoiesis and Cancer Chemotherapy.- 9.10 Discussion.- References.- Appendix A Chemistry of Genes. Protein Synthesis.- 1. Introduction.- 2. The Building Blocks of DNA and RNA.- 3. The Chemical Structure of DNA and RNA.- 4. The Replication of DNA.- 5. The Genetic Code.- 6. Synthesis of RNA.- 7. Formation of Proteins.- 8. Defining the Gene.- References.- Appendix B Viruses.- 1. Introduction.- 2. Structure of Viruses.- 3. Replication of Viruses.- 4. Oncogenic Viruses 402 References.- Appendix C Cellular Energy.- 1. Introduction.- 2. Adenosine Triphosphate (ATP).- 3. Formation of ATP 405 References.- Appendix D Immunology.- 1. The Immune System.- 2. The Immune System and Cancer 409 References.- Appendix E Mathematical Theories of Carcinogenesis.- References.- Appendix F Radiology and Cancer.- References.- Appendix G Applications of Control Theory to Normaland Malignant Cell Growth.- References.
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