Page 56 - Control Theory in Biomedical Engineering

CHAPTER 2

Mathematical modeling of

cholesterol homeostasis

a
Krystian Kubica , Joanna Balbus b
a
Faculty of Fundamental Problems of Technology, Department of Biomedical Engineering, Wroclaw
University of Science and Technology, Wroclaw, Poland
b
Department of Pure and Applied Mathematics, Wroclaw University of Science and Technology,
Wroclaw, Poland

1 Introduction
Cholesterol is an important component of the membranes of eukaryotic
cells, which determines their physical properties (Reinitzer, 1989; Alberts
et al., 2010; Maxfield and van Meer, 2010; Mukherjee et al., 1998). Among
the other functions, it stabilizes the so-called lipid rafts and membrane
proteins (Simons and Ikonen, 1997; Edidin, 2003), while its derivatives
participate in hormonal signaling (Steck and Lange, 2010; Burger et al.,
2000). Cholesterol also acts as a precursor in the synthesis of adrenal steroid
hormones, which include aldosterone and cortisol and about 50 steroids that
are intermediates (Berg et al., 2006) as well as sex metabolites (estrogen, pro-
gesterone, testosterone) (Falkenstein et al., 2000). In addition, cholesterol
acts as a substrate in the synthesis pathways of hepatic acid (Berg et al.,
2006) and vitamin D3 (Zhu and Okamura, 1995), which plays an essential
role in controlling the metabolism of calcium and phosphorus (Berg et al.,
2006; Papadakis and McPhee, 2014). The total amount of cholesterol in the
human body is approximately 0.2% of body weight (Sabine, 1977).
High blood cholesterol has been recognized as a risk factor for ischemic
diseases. It is believed that an abnormal level of cholesterol is the cause of
approximately 30% of ischemic heart diseases (according to the World
Health Organization, https://www.who.int/gho/ncd/risk_factors/
cholesterol_text/en/). For this reason, preventive measures must be fol-
lowed to maintain cholesterol level within the normal physiological range,
that is, 180mg/dL of blood plasma (total cholesterol). These measures
include maintaining a low-cholesterol diet in combination with an active
and healthy lifestyle and/or administration of cholesterol-lowering drugs.
Despite extensive research over the last 100 years, the links between

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