Pedro J. Gutiérrez Diez

In Situ Methods for Identifying the Stem Cell of the Normal and Cancerous Breast

Stem cells are unspecialized cells with the ability of self-renewal, a high potential for proliferation, and the ability to become a variety of cell types in the body. There are basically four types of stem cells: Embryonic stem cells, which are isolated from the inner cell mass of blastocysts; adult stem cells, which are found in various tissues including umbilical cord blood, bone marrow, mammary, brain, endothelium, etc.; amniotic stem cells, which are found in amniotic fluid; and inducible pluripotent stem cells—reprogrammed cells (e.g. epithelial cells) given pluripotent capabilities. Mammary stem cells belong to adult stem cells; these cells provide the source of cells for the growth of the mammary gland during puberty and gestation. Single such cells can give rise to both luminal and myoepithelial cell types within the gland, and have the ability to regenerate the entire organ in mice. The practical definition of a stem cell is the functional definition—a cell that has the potential of self-renewal and to regenerate tissue over a lifetime. The stem cell markers used are genes or products used to isolate and identify stem cells.

Inferential Biostatistics (II): Estimating Biomedical Behaviors

With special attention to the study of cancer, this chapter provides a general understanding of the nature and relevance of inferential biostatistical methods in medicine and biology, explains the design behind a biostatistical inferential analysis, and discusses the use in biology and medicine of survival analysis, regression, meta-regression, outlier analysis, and other inferential biostatistical techniques based on functions.

Optimal Control Theory: From Knowledge to Control (I). Basic Concepts

This chapter summarizes the mathematical foundations of optimal control theory and explains its philosophy, main concepts and techniques, making emphasis on the continuity that this theory entails with respect the use of system of equations. First in a static framework and then in a dynamic setting, the construction and use of lagrangian and hamiltonian functions are discussed, Pontryiagin’s maximum principle is demonstrated, and the solution procedures are commented making use of simple illustrative examples.

Inferential Biostatistics (I): Estimating Values of Biomedical Magnitudes

This chapter succinctly describes the main methods and techniques of estimation in inferential biostatistics and their application to the analysis of biomedical questions. With special attention to the study of cancer, this chapter provides a general understanding of the nature and relevance of inferential biostatistical methods of estimation in medicine and biology, and discusses the use in biology and medicine of hypothesis tests, parametric and non parametric estimation, risk ratios, and odds ratios.

Systems of Equations: The Explanation of Biomedical Phenomena (I). Basic Questions

This chapter focuses on the use of systems of equations in biomedical research, and analyzes and discusses basic mathematical issues from the biomedical point of view. The main questions related to equation systems are mathematically analyzed and biomedically interpreted, devoting a particular effort to explaining and elucidating the biological and medical meaning underlying the mathematical concepts of compatibility, determination, steady state and stability, as well as the biological role played by variables and parameters in an equation system.

Equations: Formulating Biomedical Laws and Biomedical Magnitudes

This chapter analyzes and discusses the use of single mathematical equations in medicine and biology. The application in biomedicine of single equations and differential equations, their biomedical meaning, their design process and their exploitation, are explained in detail taking as reference the study of cancer and through examples extracted from the scientific literature. The chapter provides a specific examinati on of the role that single equations play in describing tumor growth, in allowing index numbers to be constructed, in specifying the central tendency of biomedical phenomena that underlies regression analysis, and in explaining paramount biomedical processes such as diffusion and transport processes, enzymatic reactions and spatiotemporal morphogenesis phenomena.

Systems of Equations: The Explanation of Biomedical Phenomena (II). Dynamic Interdependencies

On the basis of the results provided in the previous chapter, this chapter analyzes the dynamic aspects of the interdependencies that, from the mathematical perspective, exist between the involved bio-entities in a biomedical phenomena. Using cancer research as a reference point, the relationships between initial conditions in variables and parameters, dynamics, stability and steady states are explained and discussed in detail, both from the theoretical and empirical points of view. The advantages and disadvantages of the different mathematical models of the dynamic biomedical interdependencies are also analyzed, with emphasis on the importance of the assumed hypotheses on the discrete or continuous nature of time.

Optimal Control Theory: From Knowledge to Control (II). Biomedical Applications

On the basis of the mathematical analysis of optimal control theory carried out in the chapter 8, this chapter presents and discusses the main applications of this theory in biology and medicine. Taking the idea of control inherent to the theory, the design of optimal therapies –understood as externally controlled biomedical phenomena– is analyzed in detail and its applicability in cancer research discussed making use of relevant examples in the literature. In addition, envisaging control as a biological internal ability of bio-entities, biomedical conducts are interpreted as optimal control behaviors, paying special attention to the immunological system response in cancer.