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Optimal Impulsive Control for Cancer Therapy

Part of the SpringerBriefs in Electrical and Computer Engineering Book Series

DOI: 10.1007/978-3-030-50488-5

ISBN: 978-3-030-50487-8

Publisher: Springer International Publishing - Springer Journals

Jun 20, 2020

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Introduction

Belfo, João P.; Lemos, João M.

Pages: 1 –9

[This chapter motivates the study of Optimal Impulsive Control (OIC) applied to cancer therapy. The OIC problem is formulated and divided in three control sub-problems that are treated in detail in Chap. 5. The model structure used, that comprises pharmacokinetics, pharmacodynamics, and tumor...
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Pharmacokinetic and Pharmacodynamical Models

Belfo, João P.; Lemos, João M.

Pages: 11 –18

[This chapter presents the Pharmacokinetic (PK) and Pharmacodynamical (PD) models. Concerning PK models, empirical and mechanistic models are explained, including their advantages and disadvantages. Compartmental models are described, including a discussion on their properties: positivity, mass...
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Tumor Growth Models

Belfo, João P.; Lemos, João M.

Pages: 19 –26

[In this chapter, two of the most widely used tumor growth models (TGM) are studied: the logistic and Gompertz models. The chapter begins with a study of the logistic model and the generalized logistic model. A study of the immune system (IS) and the angiogenesis process is also presented, since...
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Optimal Impulsive Control

Belfo, João P.; Lemos, João M.

Pages: 27 –41

[This chapter describes methods for optimizing cancer therapies that consist of a sequence of impulsive actions. Since the manipulated variable is not an “ordinary” time function but a distribution (generalized function), some background on this topic is included, together with the basic facts...
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Cancer Therapy Optimization

Belfo, João P.; Lemos, João M.

Pages: 43 –78

[In this chapter, the method proposed to obtain suboptimal impulsive control strategies is applied to design tumor suppression therapies. First, it is assumed that the impulses are applied at a priori decided time instants. In a latter stage, the concept of minimum attention control is used to...
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Complementary Aspects

Belfo, João P.; Lemos, João M.

Pages: 79 –93

[This chapter discusses a number of issues that complement the design of the optimized impulsive therapy presented, namely the sensitivity of the control action with respect to parameter uncertainty and quantization, the use of the Gompertz growth model instead of the logistic model, and model...
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Conclusions and Research Topics

Belfo, João P.; Lemos, João M.

Pages: 95 –99

[In this final chapter, the main points previously addressed are summarized, namely the optimization of impulsive therapy by its reduction to a finite-dimensional optimization problem, the use of a receding horizon strategy to combine impulsive optimal control with feedback, and minimum attention...

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