This book provides a unified framework for various currently available mathematical models that are used to analyze progression and regression in cancer development, and to predict its dynamics with respect to therapeutic interventions. Accurate and reliable model representations of cancer dynamics are milestones in the field of cancer research. Mathematical modeling approaches are becoming increasingly common in cancer research, as these quantitative approaches can help to validate hypotheses concerning cancer dynamics and thus elucidate the complexly interlaced mechanisms involved. Even though the related conceptual and technical information is growing at an exponential rate, the application of said information and realization of useful healthcare devices are lagging behind.
In order to remedy this discrepancy, more interdisciplinary research works and course curricula need to be introduced in academic, industrial, and clinical organizations alike. To that end, this book reformulates most of the existing mathematical models as special cases of a general model, allowing readers to easily get an overall idea of cancer dynamics and its modeling. Moreover, the book will help bridge the gap between biologists and engineers, as it brings together cancer dynamics, the main steps involved in mathematical modeling, and control strategies developed for cancer management. This also allows readers in both medical and engineering fields to compare and contrast all the therapy-based models developed to date using a single source, and to identify unexplored research directions.
Author(s): Regina Padmanabhan, Nader Meskin, Ala-Eddin Al Moustafa
Series: Series in BioEngineering
Publisher: Springer
Year: 2020
Language: English
Pages: 256
City: Cham
Preface
Contents
Abbreviations
1 Background
1.1 Introduction
1.2 Tumor Dynamics
1.2.1 Basic Mechanisms Involved in Tumor Growth
1.2.2 Various Cell Populations in a Tumor Micro-environment
1.2.3 Tumor-Immune Interaction
1.3 Cancer Therapies
1.4 A General Model of Tumor Dynamics and Effect of Therapy
1.5 Summary
References
2 Time Series Data to Mathematical Model
2.1 Experimental Design
2.2 Data Collection
2.3 Model Fitting
2.3.1 Normalization
2.3.2 Choosing Descriptive Model
2.3.3 Types of Growth Models
2.3.4 Types of Treatment Models
2.3.5 Drug Toxicity Effect
2.3.6 Model Fitting Approaches
2.4 Model Validation
2.4.1 Goodness of Fit
2.4.2 Identifiability
2.4.3 Predictability
2.4.4 Sensitivity Analysis
2.5 Equilibrium Points and Stability Analysis
2.5.1 Non-dimensionalization
2.5.2 Analysis with Drug
2.6 Summary
References
3 Chemotherapy Models
3.1 Three Cell-Based Model of Tumor Dynamics Under Chemotherapy
3.2 Model of Tumor Dynamics That Accounts for the Drug Resistance in Cells
3.3 Model of Tumor Dynamics That Accounts for Cell Transition Delay
3.4 Mathematical Model That Accounts for Tumor Metastasis
3.5 Cell-Cycle-Based Compartmental Model of Tumor Dynamics
3.6 Mathematical Model for Leukemia
3.7 Summary
References
4 Immunotherapy Models
4.1 Immunotherapy Model that Involves Adoptive Cellular Therapy and Cytokine Injection
4.2 Model with DC Vaccination
4.3 Model that Involves Immune Checkpoint Inhibition
4.4 Model with DC Vaccination that Accounts for Time Delay
4.5 An Elaborate Model on Tumor-Immune Interaction
4.6 Summary
References
5 Anti-angiogenic Therapy Models
5.1 Dynamics of Tumor Cells and Endothelial Cells …
5.2 Dynamics of Vasculature in Core and Periphery of Tumor Under Anti-angiogenic Therapy
5.3 Summary
References
6 Radiotherapy Models
6.1 Two Cell-Based Competition Model
6.2 Linear-Quadratic Cell Survival Model
6.3 Summary
References
7 Hormone Therapy Models
7.1 Hormone-Dependent and Hormone-Independent Tumor Dynamics Model
7.2 Tumor Growth Model Under Intermittent Hormone Therapy
7.3 Cell-quota-based Model of Tumor Dynamics for Hormone Therapy
7.4 Androgen Receptor Dynamics-Based Model of Tumor Dynamics …
7.5 Piecewise Linear Tumor Growth Model Under Intermittent Hormone Therapy
7.6 Cell-cycle-based Model of Tumor Dynamics for Hormone Therapy
7.7 Summary
References
8 Miscellaneous Therapy Models
8.1 Gene Therapy
8.1.1 Modified Predator-Prey Model for Gene Therapy
8.1.2 Mathematical Model of siRNA Mediated Cancer Management
8.2 Oncolytic Virotherapy
8.2.1 Model of Cancer Therapy Using Oncolytic Virus with Various Modes of Infection Transmission
8.2.2 Model of Cancer Therapy Using Oncolytic Virus and Dendritic Cells
8.3 Anti-cancer Drug Delivery Using Nanocarriers
8.3.1 Mathematical Model for Anti-cancer Drug Delivery Using Nanocarriers
8.4 Mathematical Models for Stem Cell Therapy
8.4.1 An 8-Compartmental Model for Stem Cell Dynamics
8.4.2 Mathematical Model of Stem Cell Dynamics in the Bone Marrow and Peripheral Blood
8.4.3 Model of Leukemia Stem Cell Dynamics
8.5 Summary
References
9 Combination Therapy Models
9.1 Chemotherapy and Immunotherapy
9.1.1 Chemotherapy, IL-2 Injection, and Vaccine Therapy
9.1.2 Model of Chemotherapy and Immunotherapy that Accounts for Heterogeneous Cell Clones
9.2 Chemotherapy and Oncolytic Virotherapy
9.2.1 Chemotherapy and Oncolytic Virotherapy with Various Drug Inputs
9.2.2 Chemotherapy and Oncolytic Virotherapy for Glioma
9.3 Chemotherapy and HER2 Targeted Therapy
9.4 Immunotherapy Therapy and Anti-angiogenic Therapy
9.5 Summary
References
10 Control Strategies for Cancer Therapy
10.1 Control of Chemotherapy
10.2 Control of Immunotherapy
10.3 Control of Anti-angiogenic Therapy
10.4 Control of Radiotherapy
10.5 Control of Hormone Therapy
10.6 Miscellaneous Therapy
10.7 Control of Combination Therapy
10.8 Summary
References
11 Conclusions
References
