book

Introduction to Mathematical Oncology

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

April 2016

Intermediate to advanced

470 pages

13h 2m

English

Chapman and Hall/CRC

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Preliminaries
Preface
Chapter 1 Introduction to Theory in Medicine
1.1 Introduction1.2 Disease1.3 A brief survey of trends in health and disease1.4 The scientific basis of medicine1.5 Aspects of the medical art1.6 Key scientific concepts in mathematical medicine1.6.1 Genetics1.6.2 Evolution1.7 Pathology—where science and art meetReferencesFigure 1.1Figure 1.2Figure 1.3Figure 1.4Figure 1.5
Chapter 2 Introduction to Cancer Modeling
2.1 Introduction to cancer dynamics2.2 Historical roots2.2.1 The von Bertalanffy growth model2.2.2 Gompertzian growth2.3 Applications of Gompertz and von Bertalanffy models2.4 Amore general approach2.5 Mechanistic insights from simple tumor models2.6 Sequencing of chemotherapeutic and surgical treatments2.7 Stability of steady states for ODEs2.8 Exercises2.9 Projects and open questions2.9.1 Mathematical open questions2.9.2 Tumor growth with a time delay2.9.3 Tumor growth with cell diffusionReferencesFigure 2.1Figure 2.2Figure 2.3Figure 2.4Figure 2.5Table 2.1
Chapter 3 Spatially Structured Tumor Growth
3.1 Introduction3.2 The simplest spatially structured tumor model3.2.1 Model formulation3.2.2 Equilibrium nutrient profile with no necrosis3.2.3 Size of the necrotic core3.3 Spheroid dynamics and equilibrium size3.4 Greenspan’s seminal model3.4.1 The Greenspan model3.4.2 Threshold for quiescence3.4.3 Growth dynamics of the Greenspan model3.5 Testing Greenspan’s model3.6 Sherratt-Chaplain model for avascular tumor growth3.6.1 MATLAB® file for Figure 3.63.6.2 Minimum wave speed3.7 A model of in vitro glioblastoma growth3.7.1 Model formulation3.7.2 Traveling wave system properties3.7.3 Existence of traveling wave solutions3.8 Derivation of one-dimensional conservation equation3.9 Exercises3.10 Projects3.10.1 Nutrient limitation induced quiescence3.10.2 Inhibitor generated by living cells3.10.3 Glioblastoma growth in a Petri dish or in vivo3.10.4 A simple model of tumor-host interfaceReferencesFigure 3.1Figure 3.2Figure 3.3Figure 3.4Figure 3.5Figure 3.6Figure 3.7Figure 3.8Figure 3.9
Chapter 4 Physiologically Structured Tumor Growth
4.1 Introduction4.2 Construction of the cell-size structured model4.3 No quiescence, some intuition4.4 Basic behavior of the model4.5 ExercisesReferencesFigure 4.1Figure 4.2Figure 4.3
Chapter 5 Prostate Cancer: PSA, AR, and ADT Dynamics
5.1 Introduction5.2 Models of PSA kinetics5.2.1 Vollmer et al. model5.2.2 Prostate cancer volume5.3 Dynamical models5.3.1 Swanson et al. model5.3.2 Vollmer and Humphrey model5.3.3 PSA kinetic parameters: Conclusions from dynamical models5.4 Androgens and the evolution of prostate cancer5.4.1 Evolutionary role5.4.2 Intracellular AR kinetics model5.4.3 Basic dynamics of the AR kinetics model5.5 Prostate growth mediated by androgens5.6 Evolution and selection for elevated AR expression5.6.1 Model5.6.2 Results5.7 Jackson ADT model5.8 The Ideta et al. ADT model5.9 Predictions and limitations of current ADT models5.10 An immunotherapy model for advanced prostate cancer5.11 Other prostate models5.12 Exercises5.13 Projects5.13.1 The epithelial-vascular interface and serum PSA5.13.2 A clinical algorithm based on a dynamical model5.13.3 An extension of Vollmer and Humphrey’s model5.13.4 Androgens positively regulating AI cell proliferation5.13.5 Combining androgen ablation with other therapiesReferencesFigure 5.1Figure 5.2Figure 5.3Figure 5.4Figure 5.5Table 5.1Table 5.2Table 5.3Table 5.4Table 5.5Table 5.6Table 5.7
Chapter 6 Resource Competition and Cell Quota in Cancer Models
6.1 Introduction6.2 A cell-quota based population growth model6.3 From Droop cell-quota model to logistic equation6.4 Cell-quota models for prostate cancer hormone treatment6.4.1 Preliminary model6.4.2 Final model6.4.3 Simulation6.4.4 Predictions6.5 Other cell-quota models for prostate cancer hormonetreatment6.5.1 Basic model6.5.2 Long-term competition in the basic model6.5.3 Intermittent androgen deprivation6.5.4 Cell quota with chemical kinetics6.6 Stoichiometry and competition in cancer6.6.1 KNE model6.6.2 Predictions6.7 Mathematical analysis of a simplified KNE model6.8 Exercises6.9 Projects6.9.1 Beyond the KNE model6.9.1.1 Phosphate homeostasis6.9.1.2 Intracellular phosphate: A Droop approach?6.9.1.3 Tumor lysis syndrome6.9.2 Iodine and thyroid cancer6.9.3 Iron and microbes6.9.3.1 Salmonella infection6.9.3.2 MalariaReferencesFigure 6.1Figure 6.2Figure 6.3Figure 6.4Figure 6.5Figure 6.6Figure 6.7Figure 6.8Figure 6.9Table 6.1Table 6.2
Chapter 7 Natural History of Clinical Cancer
7.1 Introduction7.2 Conceptual models for the natural history of breast cancer: Halsted vs. Fisher7.2.1 Surgery and the Halsted model7.2.2 Systemic chemotherapy and the Fisher model7.2.3 Integration of Halsted and Fisher concepts: Surgery with adjuvant chemotherapy7.3 A simple model for breast cancer growth kinetics7.3.1 Speer model: Irregular Gompertzian growth7.3.2 Calibration and predictions of the Speer model7.3.3 Limitations of the Speer approach7.4 Metastatic spread and distant recurrence7.4.1 The Yorke et al. model7.4.2 Parametrization and predictions of the Yorke model7.4.3 Limitations of the Yorke approach7.4.4 Iwata model7.4.5 Thames model7.4.6 Other models7.5 Tumor dormancy hypothesis7.6 The hormonal environment and cancer progression7.7 The natural history of breast cancer and screening protocols7.7.1 Pre-clinical breast cancer and DCIS7.7.2 CISNET program7.7.3 Continuous growth models7.7.4 Conclusions and optimal screening strategies7.8 Cancer progression and incidence curves7.8.1 Basic multi-hit model7.8.2 Two-hit models7.8.3 The case of colorectal cancer7.8.4 Multiple clonal expansions7.8.5 Smoking and lung cancer incidence7.8.6 Summary7.9 ExercisesReferencesFigure 7.1Figure 7.2Figure 7.3Figure 7.4Figure 7.5Figure 7.6Figure 7.7Figure 7.8
Chapter 8 Evolutionary Ecology of Cancer
8.1 Introduction8.2 Necrosis: What causes the tumor ecosystem to collapse?8.2.1 Necrosis in multicell spheroids8.2.2 Necrosis in tumor cords8.2.3 Diffusion limitation in ductal carcinoma in situ8.2.4 Necrosis caused by mechanical disruption of cells8.2.5 Necrosis from local acidosis8.2.6 Necrosis due to local ischemia8.3 What causes cell diversity within malignant neopla-sia?8.3.1 Causes of Type I diversity8.3.1.1 Incomplete competitive exclusion8.3.1.2 Fungiform invasion8.3.1.3 Turing instabilities8.3.2 Causes of Type II diversity8.3.2.1 Natural selection favoring proliferation rate and efficient nutrient use8.3.2.2 Natural selection favoring insensitivity to hypoxia8.3.2.3 Natural selection favoring fungiform invasion8.4 Synthesis: Competition, natural selection and necrosis8.5 Necrosis and the evolutionary dynamics of metastatic disease8.5.1 Pre-metastatic selection hypothesis8.5.2 Reproductive fitness and export probability8.5.3 Tumor self-seeding8.6 Conclusion8.7 ExercisesReferencesFigure 8.1Figure 8.2Figure 8.3Table 8.1

Chapter 9 Models of Chemotherapy
9.1 Dose-response curves in chemotherapy9.1.1 Simple models9.1.2 Concentration, time, and cyotoxicity plateaus9.1.3 Shoulder region9.1.4 Pharmacodynamics for antimicrobials9.2 Models for in vitro drug uptake and cytotoxicity9.2.1 Models for cistplatin uptake and intracellular pharma-cokinetics9.2.2 Paclitaxel uptake and intracellular pharmacokinetics9.3 Pharmacokinetics9.4 The Norton-Simon hypothesis and the Gompertz model9.4.1 Gompertzian model for human breast cancer growth9.4.2 The Norton-Simon hypothesis and dose-density9.4.3 Formal Norton-Simon model9.4.4 Intensification and maintenance regimens9.4.5 Clinical implications and results9.4.6 Depletion of the growth fraction9.5 Modeling the development of drug resistance9.5.1 Luria-Delbrück fluctuation analysis9.5.1.1 Step 1: Expected number of mutations and resistant cells9.5.1.2 Step 2: Test the mutation-selection hypothesis9.5.1.3 Later work9.5.2 The Goldie-Coldman model9.5.3 Extensions of Goldie-Coldman and alternating therapy9.5.3.1 Two-drug Goldie-Coldman model9.5.3.2 Stochastic two-drug Goldie-Coldman model9.5.3.3 Relaxation of the “symmetry assumption”9.5.3.4 Goldie-Coldman contra Norton-Simon9.5.4 The Monro-Gaffney model and palliative therapy9.5.4.1 The model9.5.4.2 Predictions of the Monro-Gaffney model9.5.4.3 Summary9.5.5 The role of host physiology9.6 Heterogeneous populations: The cell cycle9.6.1 The Smith-Martin conceptual model9.6.2 A delay differential model of the cell cycle9.6.3 Age-structured models for the cell cycle9.6.4 More general sensitivity and resistance9.7 Drug transport and the spatial tumor environment9.7.1 Solute transport across tumor capillaries9.7.2 Fluid flow in tumors9.7.3 Tumor spheroid9.7.4 Tumor cord framework9.8 ExercisesReferencesFigure 9.1Figure 9.2Figure 9.3Figure 9.4Figure 9.5Figure 9.6Figure 9.7Figure 9.8Figure 9.9Figure 9.10Figure 9.11Figure 9.12Figure 9.13Figure 9.14Figure 9.15Figure 9.16
Chapter 10 Major Anticancer Chemotherapies
10.1 Introduction10.2 Alkylating and alkalating-like agents10.2.1 Nitrogen mustards10.2.2 Platinum-based drugs10.2.3 Nitrosoureas10.2.4 Methylating agents10.3 Antitumor antibiotics10.3.1 Anthracyclines10.3.2 Mitomycin-C10.3.3 Bleomycins10.4 Antimetabolites10.5 Mitotic inhibitors10.5.1 Taxanes10.5.2 Vinca alkaloids10.6 Non-cytotoxic and targeted therapiesReferencesFigure 10.1Figure 10.2
Chapter 11 Radiation Therapy
11.1 Introduction11.2 Molecular mechanisms11.2.1 Ions and radical reactions11.2.1.1 DSB repair mechanisms11.2.1.2 Radical detoxification mechanisms11.2.2 Oxygen status11.2.3 The four R’s11.3 Classical target-hit theory11.4 Lethal DNA misrepair11.4.1 Repair-misrepair model11.4.2 Lethal-potentially lethal model11.4.3 Parametrization11.5 Saturable and enzymatic repair11.5.1 Haynes model11.5.2 Goodhead model11.5.3 General saturable-repair model11.6 Kinetics of damage repair11.7 The LQ model and dose fractionation11.8 Applications11.8.1 Tumor cure probability11.8.2 Regrowth11.8.3 Hypoxia11.8.4 Radiation with chemotherapyReferencesFigure 11.1Figure 11.2Figure 11.3Figure 11.4Figure 11.5Figure 11.6Figure 11.7Figure 11.8Figure 11.9
Chapter 12 Chemical Kinetics
12.1 Introduction and the law of mass action12.1.1 Dissociation constant12.2 Enzyme kinetics12.2.1 Equilibrium approximation12.3 Quasi-steady-state approximation12.3.1 Turnover number12.3.2 Specificity constant12.3.3 Lineweaver-Burk equation12.4 Enzyme inhibition12.4.1 Competitive inhibition12.4.2 Allosteric inhibition12.5 Hemoglobin and the Hill equation12.6 Monod-Wyman-Changeux modelReferencesFigure 12.1Figure 12.2Figure 12.3
Chapter 13 Epilogue: Toward a Quantitative Theory of Oncology
References

Content preview from Introduction to Mathematical Oncology

Chapter 7

Natural History of Clinical Cancer

7.1 Introduction

The natural history of a disease refers to its uninterrupted course in the absence of intervention, from initiation through its end stage—resolution, chronic illness or death. Any model for natural history of clinical cancer, either conceptual or formal, must address at least two central dynamics: (1) the growth kinetics of the primary tumor, and (2) the dynamics of metastatic spread to both regional (e.g., lymph nodes) and distant sites. Ultimately, our motivation to study cancer natural history is not purely intellectual interest. After all, cancer is very rarely left to follow its unperturbed natural history, so at first glance this might be considered an irrelevant problem. However, ...

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Introduction to Mathematical Oncology

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

Natural History of Clinical Cancer

7.1 Introduction

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