Book description
Introduction to Mathematical Oncology presents biologically well-motivated and mathematically tractable models that facilitate both a deep understanding of cancer biology and better cancer treatment designs. It covers the medical and biological background of the diseases, modeling issues, and existing methods and their limitations. The authors introduce mathematical and programming tools, along with analytical and numerical studies of the models. They also develop new mathematical tools and look to future improvements on dynamical models.
After introducing the general theory of medicine and exploring how mathematics can be essential in its understanding, the text describes well-known, practical, and insightful mathematical models of avascular tumor growth and mathematically tractable treatment models based on ordinary differential equations. It continues the topic of avascular tumor growth in the context of partial differential equation models by incorporating the spatial structure and physiological structure, such as cell size. The book then focuses on the recent active multi-scale modeling efforts on prostate cancer growth and treatment dynamics. It also examines more mechanistically formulated models, including cell quota-based population growth models, with applications to real tumors and validation using clinical data. The remainder of the text presents abundant additional historical, biological, and medical background materials for advanced and specific treatment modeling efforts.
Extensively classroom-tested in undergraduate and graduate courses, this self-contained book allows instructors to emphasize specific topics relevant to clinical cancer biology and treatment. It can be used in a variety of ways, including a single-semester undergraduate course, a more ambitious graduate course, or a full-year sequence on mathematical oncology.
Table of contents
- Preliminaries
- Preface
- Chapter 1 Introduction to Theory in Medicine
-
Chapter 2 Introduction to Cancer Modeling
- 2.1 Introduction to cancer dynamics
- 2.2 Historical roots
- 2.3 Applications of Gompertz and von Bertalanffy models
- 2.4 Amore general approach
- 2.5 Mechanistic insights from simple tumor models
- 2.6 Sequencing of chemotherapeutic and surgical treatments
- 2.7 Stability of steady states for ODEs
- 2.8 Exercises
- 2.9 Projects and open questions
- References
-
Chapter 3 Spatially Structured Tumor Growth
- 3.1 Introduction
- 3.2 The simplest spatially structured tumor model
- 3.3 Spheroid dynamics and equilibrium size
- 3.4 Greenspan’s seminal model
- 3.5 Testing Greenspan’s model
- 3.6 Sherratt-Chaplain model for avascular tumor growth
- 3.7 A model of in vitro glioblastoma growth
- 3.8 Derivation of one-dimensional conservation equation
- 3.9 Exercises
- 3.10 Projects
- References
- Chapter 4 Physiologically Structured Tumor Growth
-
Chapter 5 Prostate Cancer: PSA, AR, and ADT Dynamics
- 5.1 Introduction
- 5.2 Models of PSA kinetics
- 5.3 Dynamical models
- 5.4 Androgens and the evolution of prostate cancer
- 5.5 Prostate growth mediated by androgens
- 5.6 Evolution and selection for elevated AR expression
- 5.7 Jackson ADT model
- 5.8 The Ideta et al. ADT model
- 5.9 Predictions and limitations of current ADT models
- 5.10 An immunotherapy model for advanced prostate cancer
- 5.11 Other prostate models
- 5.12 Exercises
- 5.13 Projects
- References
-
Chapter 6 Resource Competition and Cell Quota in Cancer Models
- 6.1 Introduction
- 6.2 A cell-quota based population growth model
- 6.3 From Droop cell-quota model to logistic equation
- 6.4 Cell-quota models for prostate cancer hormone treatment
- 6.5 Other cell-quota models for prostate cancer hormonetreatment
- 6.6 Stoichiometry and competition in cancer
- 6.7 Mathematical analysis of a simplified KNE model
- 6.8 Exercises
- 6.9 Projects
- References
-
Chapter 7 Natural History of Clinical Cancer
- 7.1 Introduction
- 7.2 Conceptual models for the natural history of breast cancer: Halsted vs. Fisher
- 7.3 A simple model for breast cancer growth kinetics
- 7.4 Metastatic spread and distant recurrence
- 7.5 Tumor dormancy hypothesis
- 7.6 The hormonal environment and cancer progression
- 7.7 The natural history of breast cancer and screening protocols
- 7.8 Cancer progression and incidence curves
- 7.9 Exercises
- References
-
Chapter 8 Evolutionary Ecology of Cancer
- 8.1 Introduction
- 8.2 Necrosis: What causes the tumor ecosystem to collapse?
- 8.3 What causes cell diversity within malignant neopla-sia?
- 8.4 Synthesis: Competition, natural selection and necrosis
- 8.5 Necrosis and the evolutionary dynamics of metastatic disease
- 8.6 Conclusion
- 8.7 Exercises
- References
-
Chapter 9 Models of Chemotherapy
- 9.1 Dose-response curves in chemotherapy
- 9.2 Models for in vitro drug uptake and cytotoxicity
- 9.3 Pharmacokinetics
- 9.4 The Norton-Simon hypothesis and the Gompertz model
- 9.5 Modeling the development of drug resistance
- 9.6 Heterogeneous populations: The cell cycle
- 9.7 Drug transport and the spatial tumor environment
- 9.8 Exercises
- References
- Chapter 10 Major Anticancer Chemotherapies
- Chapter 11 Radiation Therapy
- Chapter 12 Chemical Kinetics
- Chapter 13 Epilogue: Toward a Quantitative Theory of Oncology
Product information
- Title: Introduction to Mathematical Oncology
- Author(s):
- Release date: April 2016
- Publisher(s): Chapman and Hall/CRC
- ISBN: 9781584889915
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