Page 15 - Computational Modeling in Biomedical Engineering and Medical Physics

CHAPTER 1

Physical, mathematical, and numerical

modeling

1.1 Experiments and numerical simulation
1
A “thought experiment” is a conceptual experiment that relies on hypotheses, theo-
ries, or principles aiming at thinking through its predictions. Even if it would be possi-
ble there is no need to perform it except for validating its consequences. In this
2
paradigm (concepts or thought patterns, including theories, research methods, postu-
lates) of hypothesis-driven research, thought experiments embodied through physical,
mathematical, numerical modeling is the vehicle used to study a number of models
that are presented throughout this book.
From a converging perspective, there is an underlying concern in complying with
ethical norms and regulations of physical experiments. For example, Art. 7 Line 2 of
the EU Directive 86/609/EEC of November 24, 1986, Bruxelles, and its updates
regarding the protection of the animals subjected to experiments or of other scientific
interests states that “An experiment shall not be conducted if there exists another rea-
sonable and practical method to satisfactorily obtain the pursued result without imply-
ing the usage of animals” (Ruhdel, 2007; Hartung, 2014).
Much has been done to comply with this directive and its subsequent revisions.
Recent progresses in mathematical algorithms, numerical analysis, and the unprece-
dented development of hardware and software tools capable of implementing them
make possible the numerical simulation of complex problems. Thus numerical model-
ing has become a powerful and valuable mean in understanding and predicting medi-
cal applications—underlying physical phenomena, procedures, therapies, and scanning
technologies. The “numerical experiment” based on physical and mathematical
modeling and on numerical simulation may complement the physical experiment that
even when permissible cannot be performed always because, for instance, of ethical
concerns. It may provide also information otherwise inaccessible through physical
experiments; for instance, it may depict the distribution of the electric field inside the
body during the MRI scanning. It is also a design tool aimed, for instance, to optimize

1
German: Gedankenexperiment (Perkowitz, 2010) or Gedankenerfahrung (Brown, 2019)
2
Paradigm comes from Greek παρ αδειγμα (paradeigma), “pattern, example, sample” from the verb
παραδε ικνυμι (paradeiknumi), “exhibit, represent, expose” from παρ α (para), “beside, beyond” from
δε ικνυμι (deiknumi), “to show, to point out” (Paradigm, 2018).

Computational Modeling in Biomedical Engineering and Medical Physics r 2021 Elsevier Inc.
DOI: https://doi.org/10.1016/B978-0-12-817897-3.00001-4 All rights reserved. 1