Page 96 - Control Theory in Biomedical Engineering

CHAPTER 4

Modeling and optimal control

of cancer-immune system

a
Fathalla A. Rihan , Nouran F. Rihan b
a
Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al Ain,
United Arab Emirates
b
Faculty of Pharmacy, Clinical Program, Cairo University, Cairo, Egypt
1 Introduction

Cancer is a generic term for a large group of diseases that can affect any part
of the body, and is considered the second-leading cause of death worldwide.
Globally, it was responsible for an estimated 9.6 million deaths in 2018,
according to the International Agency for Research on Cancer (IARC)
(WHO, 2018). Other terms used are malignant tumors and neoplasms.
One defining feature of cancer is the rapid creation of abnormal cells that
grow beyond their usual boundaries, and that can then invade adjoining
parts of the body and spread to other organs. The latter process is referred
to as metastasizing. Metastases are a major cause of death from cancer
(Bray et al., 2018).
The interactions between cancer cells and the immune system (IS) are
very complex and need sophisticated models to describe them. The IS is
responsible for monitoring substances that are normally present in the body
(Rihan et al., 2016). Once foreign substances exist in the body that the IS is
unable to identify, it raises an alarm to initiate an attack. The substances that
cause the IS response are called antigens. The IS attack includes destruction
of any cells containing foreign antigens, such as pathogens or cancer cells.
Pathogens are identified by certain proteins that are found on their outer
surfaces that are not normally found in the human body. Immunity has
two categories: innate (natural or nonspecific) immunity and adaptive
(acquired or specific) immunity, which work synergically to eliminate path-
ogens. The innate IS is responsible for recognizing the molecules emitted by
foreign substances. However, adaptive immunity is very specific; it controls
responses caused by repeated exposures to the same antigens. Exposure to a
particular antigen will lead to a quick and effective response to that particular
antigen in the future, but not to any other antigens. Certain memory

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