Optimal Impulsive Control for Cancer Therapy (SpringerBriefs in Electrical and Computer Engineering)

Preface
Contents
Abbreviations
1 Introduction
	1.1 Motivation
	1.2 Problem Formulation
	1.3 Background Literature Review
	1.4 Book Outline
	References
2 Pharmacokinetic and Pharmacodynamical Models
	2.1 Pharmacokinetics
		2.1.1 Types of Models
		2.1.2 Compartmental Models
		2.1.3 Positive Systems
		2.1.4 Example: A 2 Compartment Model
	2.2 Pharmacodynamics
	References
3 Tumor Growth Models
	3.1 Tumor Growth Dynamics
	3.2 Logistic Growth Model
		3.2.1 Solution of the Logistic Equation
	3.3 Gompertz Growth Model
	3.4 Interacting Subsystems
		3.4.1 Immune System
		3.4.2 Angiogenesis
	3.5 Global Model
	References
4 Optimal Impulsive Control
	4.1 Distributions
	4.2 Impulsive Differential Equations
	4.3 Pharmacokinetic Model Response
	4.4 A Maximum Principle for Impulsive Optimal Control
	4.5 A Priori Imposed Impulses
	References
5 Cancer Therapy Optimization
	5.1 Variable Amplitudes and Fixed Time Intervals
		5.1.1 Minimizing the Tumor Volume
		5.1.2 Reducing Side Effects
		5.1.3 Influence of the Parameter ρ
		5.1.4 Influence of the Parameter H
	5.2 Variable Amplitudes and Periodic Time Intervals
		5.2.1 Influence of the Immune System
		5.2.2 Influence of the Angiogenesis Process
	5.3 Variable Amplitudes and Time Intervals
		5.3.1 Minimum Attention Control
		5.3.2 Selection of the Number of Impulses
	5.4 Receding Horizon Control
	References
6 Complementary Aspects
	6.1 Sensitivity Analysis
		6.1.1 Parameter Variation
		6.1.2 Modeling Errors
		6.1.3 Quantization
	6.2 Using the Gompertz Growth Model
	6.3 Pseudospectral Methods
	Reference
7 Conclusions and Research Topics
	7.1 Conclusions
	7.2 Research Topics
	References
Appendix  Series Editor Biographies
Preface
Contents
Abbreviations
1 Introduction
	1.1 Motivation
	1.2 Problem Formulation
	1.3 Background Literature Review
	1.4 Book Outline
	References
2 Pharmacokinetic and Pharmacodynamical Models
	2.1 Pharmacokinetics
		2.1.1 Types of Models
		2.1.2 Compartmental Models
		2.1.3 Positive Systems
		2.1.4 Example: A 2 Compartment Model
	2.2 Pharmacodynamics
	References
3 Tumor Growth Models
	3.1 Tumor Growth Dynamics
	3.2 Logistic Growth Model
		3.2.1 Solution of the Logistic Equation
	3.3 Gompertz Growth Model
	3.4 Interacting Subsystems
		3.4.1 Immune System
		3.4.2 Angiogenesis
	3.5 Global Model
	References
4 Optimal Impulsive Control
	4.1 Distributions
	4.2 Impulsive Differential Equations
	4.3 Pharmacokinetic Model Response
	4.4 A Maximum Principle for Impulsive Optimal Control
	4.5 A Priori Imposed Impulses
	References
5 Cancer Therapy Optimization
	5.1 Variable Amplitudes and Fixed Time Intervals
		5.1.1 Minimizing the Tumor Volume
		5.1.2 Reducing Side Effects
		5.1.3 Influence of the Parameter ρ
		5.1.4 Influence of the Parameter H
	5.2 Variable Amplitudes and Periodic Time Intervals
		5.2.1 Influence of the Immune System
		5.2.2 Influence of the Angiogenesis Process
	5.3 Variable Amplitudes and Time Intervals
		5.3.1 Minimum Attention Control
		5.3.2 Selection of the Number of Impulses
	5.4 Receding Horizon Control
	References
6 Complementary Aspects
	6.1 Sensitivity Analysis
		6.1.1 Parameter Variation
		6.1.2 Modeling Errors
		6.1.3 Quantization
	6.2 Using the Gompertz Growth Model
	6.3 Pseudospectral Methods
	Reference
7 Conclusions and Research Topics
	7.1 Conclusions
	7.2 Research Topics
	References
Appendix  Series Editor Biographies