Introduction to Mathematical Oncology / Edition 1

Introduction to Mathematical Oncology / Edition 1

by Yang Kuang, John D. Nagy, Steffen E. Eikenberry
     
 

ISBN-10: 158488990X

ISBN-13: 9781584889908

Pub. Date: 03/02/2016

Publisher: Taylor & Francis

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

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Overview

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.

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Product Details

ISBN-13:
9781584889908
Publisher:
Taylor & Francis
Publication date:
03/02/2016
Series:
Chapman & Hall/CRC Mathematical and Computational Biology Series, #59
Pages:
503

Table of Contents

Introduction to Theory in Medicine
Introduction
Disease
A brief survey of trends in health and disease
The scientific basis of medicine
Aspects of the medical art
Key scientific concepts in mathematical medicine
Pathology—where science and art meet

Introduction to Cancer Modeling
Introduction to cancer dynamics
Historical roots
Applications of Gompertz and von Bertalanffy models
A more general approach
Mechanistic insights from simple tumor models
Sequencing of chemotherapeutic and surgical treatments
Stability of steady states for ODEs
Exercises
Projects and open questions

Spatially Structured Tumor Growth
Introduction
The simplest spatially structured tumor model
Spheroid dynamics and equilibrium size
Greenspan's seminal model
Testing Greenspan's model
Sharratt–Chaplain model for avascular tumor growth
A model of in vitro glioblastoma growth
Derivation of one dimensional balance equation
Exercises
Projects

Physiologically Structured Tumor Growth
Introduction
Construction of the cell-size structured model
No quiescence, some intuition
Basic behavior of the model
Exercises

Prostate Cancer: PSA, AR, and ADT Dynamics
Introduction
Models of PSA kinetics
Dynamical models
Androgens and the evolution of prostate cancer
Prostate growth mediated by androgens
Evolution and selection for elevated AR expression
Jackson ADT model
The Ideta et al. ADT model
Predictions and limitations of current ADT models
An immunotherapy model for advanced prostate cancer
Other prostate models
Exercises
Projects

Resource Competition and Cell Quota in Cancer Models
Introduction
A cell-quota based population growth model
From Droop cell-quota model to logistic equation
Cell-quota models for prostate cancer hormone treatment
Other cell-quota models for prostate cancer hormone treatment
Stoichiometry and competition in cancer
Mathematical analysis of a simplified KNE model
Exercises
Projects

Natural History of Clinical Cancer
Introduction
Conceptual models for the natural history of breast cancer: Halsted vs. Fisher
A simple model for breast cancer growth kinetics
Metastatic spread and distant recurrence
Tumor dormancy hypothesis
The hormonal environment and cancer progression
The natural history of breast cancer and screening protocols
Cancer progression and incidence curves
Exercises

Evolutionary Ecology of Cancer
Introduction
Necrosis: What causes the tumor ecosystem to collapse?
What causes cell diversity within malignant neoplasia?
Synthesis: Competition, natural selection and necrosis
Necrosis and the evolutionary dynamics of metastatic disease
Conclusion
Exercises

Models of Chemotherapy
Dose-response curves in chemotherapy
Models for in vitro drug uptake and cytotoxicity
Pharmacokinetics
The Norton-Simon hypothesis and the Gompertz model
Modeling the development of drug resistance
Heterogeneous populations: the cell cycle
Drug transport and the spatial tumor environment
Exercises

Major Anti-Cancer Chemotherapies
Introduction
Alkylating and alkalating-like agents
Anti-tumor antibiotics
Anti-metabolites
Mitotic inhibitors
Non-cytotoxic and targeted therapies

Radiation Therapy
Introduction
Molecular mechanisms
Classical target-hit theory
Lethal DNA misrepair
Saturable and enzymatic repair
Kinetics of damage repair
The LQ model and dose fractionation
Applications

Chemical Kinetics
Introduction and the law of mass action
Enzyme kinetics
Quasi-steady-state approximation
Enzyme inhibition
Hemoglobin and the Hill equation
Monod–Wyman–Changeux model

Epilogue: Toward a Quantitative Theory of Oncology

References appear at the end of each chapter.

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