Page 11 - Computational Modeling in Biomedical Engineering and Medical Physics

xii Preface

Solvable physical mathematical models
The solvable formulations of the “thought” experiments are the trait of a union of the
examples offered in this book and ensure consistency with the physical experiment
counterpart. Even if it would be possible to verify experimentally the numerical results
of the thought experiments, there is no need to perform it except for confirming their
consequences. They may complete the physical experiments that, even when
indulged, cannot be performed because, for instance, of ethical concerns. Not in the
least, numerical modeling is also a design tool that may contribute to optimize the
equipment’s development, reduce the design cycle and costs, and augment the safety
margins. Numerical experiments in simulacra to real-life conditions provide a wealth of
knowledge and qualify as an exceptionally useful tool. In the paradigm of hypothesis-
driven research, the thought experiments expressed through physical, mathematical,
numerical modeling are the means used to study the models presented throughout this
book. This perspective strengthens and confers predictability to medical procedures
and techniques, complementary to diagnosis.

Shape, structure, and rhythm
The fundamental question that arises when attempting to describe the animate and
inanimate systems may be seen as an evolutionary design, which is governed by the
laws of physics, free to morph and to evolve toward greater access. A compact and
robust phrasing of what is observed in nature is propositioned by the Constructal law
of physics, which perceives the living systems in motion, driven by power, subjected
finite-size constraints, endowed with the freedom to change, and abiding the time
arrow for evolution. The Constructal law does not rely on the time arrow of empiricism,
which starts with nature and the unsolved observation, for example, the allometric
laws, nor does it rely on abstract constructs emptied of physics, for example, the fractal
geometry. Life has to be maintained, and the constructal theory explains that this is a
predictable result of evolutionary design: the growth and the evolution refer to archi-
tectures that change and flow. They apply to organs and vascularized tissues that have
the same objectives and perform under the same constraints.

From the drawing to the numerical modeling—computational
domains

The starting point in numerical modeling is a good sketch of the thought experi-
ment—the drawing. It has to bear the main features of the physical experiment coun-
terpart. To this end, the physical systems are conceptualized into “solid models” that