Page 24 - Control Theory in Biomedical Engineering

12 Control theory in biomedical engineering

many aspects of identifiability are studied, like the role of initial conditions
(Pia Saccomani et al., 2003) and optimal design of clinical tests (Bezzo and
Galvanin, 2018). Different application papers of structural identifiability
have been published (Xia and Moog, 2003; Raue et al., 2009; Miao
et al., 2011; Eberle and Ament, 2012; Tuncer et al., 2016; Pironet et al.,
2019). A software tool to test global identifiability of biological and physi-
ological system is described in Bellu et al. (2007).

2.5 Practical identifiability

Practical identifiability concerns parameter and state estimation processes via
online or offline techniques. Since the 1970s, great efforts have been made to
describe physiological systems in explicit mathematical models for which
several online or offline techniques for parameter estimation are developed
and the entire procedure of estimation, from model formulation to
computer selection, is re-examined (Rideout and Beneken, 1975). Nowa-
days, parameter estimation techniques are of ever-increasing interest in
the fields of medicine and biology for which few books and book
chapters (Marmarelis and Marmarelis, 1978; Khoo, 1999; Westwick and
Kearney, 2003; Heldt et al., 2013; Ho, 2019), survey papers (De Nicolao
et al., 1997; Giannakis and Serpedin, 2001), and application papers
(Tong, 1976; Misgeld et al., 2016) are available. A software package is also
available that solves structural/practical identifiability problems (Galvanin
et al., 2013), as described in Fig. 6. This framework first conducts a thorough
analysis to identify and classify the nonidentifiable parameters and provides a
guideline for solving them. If no feasible solution can be found, the frame-
work instead initializes the filtering technique prior to yield a unique
solution.

2.6 Application examples
There are several well-known examples of mathematical models in physio-
logical systems, such as the endocrine system, immune system and cardio-
vascular system. In this subsection, we describe the simplest models of
these renowned systems and give an extensive bibliography.

2.6.1 The endocrine system models
The endocrine system is the set of glands in the body that produce hormones
directly into the circulatory system in order to regulate physiological and
behavioral activities (Neave, 2008). Hormones are used to communicate
between organs and tissues. The endocrine process is primordial for the