Computational Modeling in Biomedical Engineering and Medical Physics

Alexandru Morega, Mihaela Morega, Alin Dobre

• Publisher: Academic Press
• Year: 2020
• Print ISBN: 9780128178973
• eBook ISBN: 9780128178980
• Topic: Biological Sciences
• Subtopic: Biotechnology
• Index: Biological Sciences

Mathematical and numerical modelling of engineering problems in medicine is aimed at unveiling and understanding multidisciplinary interactions and processes and providing insights useful to clinical care and technology advances for better medical equipment and systems. When modelling medical problems, the engineer is confronted with multidisciplinary problems of electromagnetism, heat and mass transfer, and structural mechanics with, possibly, different time and space scales, which may raise concerns in formulating consistent, solvable mathematical models.Computational Medical Engineering presents a number of engineering for medicine problems that may be encountered in medical physics, procedures, diagnosis and monitoring techniques, including electrical activity of the heart, hemodynamic activity monitoring, magnetic drug targeting, bioheat models and thermography, RF and microwave hyperthermia, ablation, EMF dosimetry, and bioimpedance methods. The authors discuss the core approach methodology to pose and solve different problems of medical engineering, including essentials of mathematical modelling (e.g., criteria for well-posed problems); physics scaling (homogenization techniques); Constructal Law criteria in morphing shape and structure of systems with internal flows; computational domain construction (CAD and, or reconstruction techniques based on medical images); numerical modelling issues, and validation techniques used to ascertain numerical simulation results. In addition, new ideas and venues to investigate and understand finer scale models and merge them into continuous media medical physics are provided as case studies.- Presents the fundamentals of mathematical and numerical modeling of engineering problems in medicine- Discusses many of the most common modelling scenarios for Biomedical Engineering, including, electrical activity of the heart hemodynamic activity monitoring, magnetic drug targeting, bioheat models and thermography, RF and microwave hyperthermia, ablation, EMF dosimetry, and bioimpedance methods- Includes discussion of the core approach methodology to pose and solve different problems of medical engineering, including essentials of mathematical modelling, physics scaling, Constructal Law criteria in morphing shape and structure of systems with internal flows, computational domain construction, numerical modelling issues, and validation techniques used to ascertain numerical simulation results

Chapter 1

Physical, mathematical, and numerical modeling

Abstract

This chapter presents several modeling, unifying grounds: concepts, hypotheses, homogenization techniques, mathematical models, and numerical methods that are used throughout the book. The underlying mathematical models are formulated as consistent boundary and initial value problems. They assume the scales where continuum media equivalent properties for the anatomic media may be hypothesized, and the biomedical processes of concern are predictable. All models here are “multiphysics,” in the sense that two or more coupled phenomena may occur. Therefore several concerns regarding the time and space scales, transfer mechanisms, and couplings are discussed, and strategies to solve them efficiently are proposed.

The pending computational domains need not replicate exactly the human anatomy; however, they have to be designed such as to provide realistic, physical perspectives on the processes that are investigated. Allometric laws, fractal geometry, and constructal law are introduced then with this aim. Finally the general framework of the solution strategy is presented.

Keywords

Bioengineering problems; multiphysics; mathematical modeling; numerical simulation; continuum medium; electromagnetic fields; heat and mass transfer; allometric laws; fractal geometry; constructal law

1.1 Experiments and numerical simulation

A “thought experiment”¹ is a conceptual experiment that relies on hypotheses, theories, or principles aiming at thinking through its predictions. Even if it would be possible there is no need to perform it except for validating its consequences. In this paradigm² (concepts or thought patterns, including theories, research methods, postulates) 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 reasonable and practical method to satisfactorily obtain the pursued result without implying 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 unprecedented development of hardware and software tools capable of implementing them make possible the numerical simulation of complex problems. Thus numerical modeling has become a powerful and valuable mean in understanding and predicting medical 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 the scanner development, reduce the design costs, and enhance its safety margins. Numerical experiments in simulacra to real-life circumstances provide a wealth of knowledge, and numerical simulation qualifies as an extremely useful tool.

1.2 The system and its boundary

The starting point in any experimental or theoretical analysis has to be the precise definition of the system, which is—for a simple, comprehensive definition—a collection of matter in a region of interest (ROI) in space, to be observed, investigated, and measured. In particular in numerical modeling, the system substantiates and hosts the thought experiment. With the system comes its environment, or surroundings, with which the system interacts through work, heat, and mass transfer. The entity that separates the system and its environment is thus the boundary, which belongs in the same time to the system and to its surroundings. In fact the state of the system (i.e., the collection of values that the state quantities have at a specific time moment) depends on the interactions with its environment, which are perceived or stated at the boundar...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Preface
• Acknowledgments
• Chapter 1. Physical, mathematical, and numerical modeling
• Chapter 2. Shape and structure morphing of systems with internal flows
• Chapter 3. Computational domains
• Chapter 4. Electrical activity of the heart
• Chapter 5. Bioimpedance methods
• Chapter 6. Magnetic drug targeting
• Chapter 7. Magnetic stimulation and therapy
• Chapter 8. Hyperthermia and ablation
• Index