Multiphysics Modeling with Application to Biomedical Engineering

Z. Yang

• Publisher: CRC Press
• Year: 2020
• Print ISBN: 9780367510831
• eBook ISBN: 9781000088915
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

The aim of this book is to introduce the simulation of various physical fields and their applications for biomedical engineering, which will provide a base for researchers in the biomedical field to conduct further investigation.

The entire book is classified into three levels. It starts with the first level, which presents the single physical fields including structural analysis, fluid simulation, thermal analysis, and acoustic modeling. Then, the second level consists of various couplings between two physical fields covering structural thermal coupling, porous media, fluid structural interaction (FSI), and acoustic FSI. The third level focuses on multi-coupling that coupling with more than two physical fields in the model. Each part in all levels is organized as the physical feature, finite element implementation, modeling procedure in ANSYS, and the specific applications for biomedical engineering like the FSI study of Abdominal Aortic Aneurysm (AAA), acoustic wave transmission in the ear, and heat generation of the breast tumor.

The book should help for the researchers and graduate students conduct numerical simulation of various biomedical coupling problems. It should also provide all readers with a better understanding of various couplings.

1	Introduction

Various physical phenomena exist in the human body: cartilages contacting meniscus in the knee; blood flowing in the vessel; air going in and out of the lung; acoustic wave transiting in the ear; and muscle becoming warm after cyclic tension. Clinical studies have found that some diseases have a close association with physical phenomena. Knee pain is linked with the contact pressures in the knee, and back pain is probably caused by the big mechanical loads on the spine. Abdominal aortic aneurysm is a condition in which the terminal aorta deforms to dangerous proportions under blood pressure. The blasts in a military battle often cause tympanic membrane injuries of the ear. Because these diseases are very common—millions of people are struggling with them—great effort has been taken to study them. One of the keys to ending these diseases is to understand the physical states, including stress and deformation of structure, acoustic pressure in the acoustic problems, temperature in the thermal problems, and velocity and pressure in the fluid field. Many studies have addressed these issues by experimental study and numerical simulation. This book focuses on numerical simulation, covering structural analysis, thermal analysis, fluid analysis, and acoustic analysis, and their couplings, such as fluid structural interaction (FSI), porous media, acoustic FSI, and thermal structural coupling.

Recently, numerical simulation has been extensively applied in the fields of academic research and industry. To meet this rising use of numerical simulation, a great deal of commercial software, including ANSYS, Marc, ABAQUS, and Nastran has been developed in the last 50 years. Among them, ANSYS Fluent is the most widely used computational fluid dynamics software, and mechanical analysis in ANSYS is very powerful in structural/thermal/acoustic analysis. Thus, all examples in this book are implemented in ANSYS, and all input files are attached in the appendixes.

The book is divided into four parts. The first part focuses on single physics phases. After Chapter 1 introduces the subject, Chapter 2 describes the structural analysis. It starts with the nature of solid and the Lagrangian description. This is followed by the equilibrium equation and the corresponding finite element matrix form, as well as the modeling procedure in ANSYS. Chapter 2 ends with a simulation of the deformation of the intervertebral disc under pressure.

Fluid dynamics is briefly discussed in Chapter 3. Because fluid flows freely under loading, the Eulerian description is applied for the fluid field. After describing the governing equations and general modeling procedure in ANSYS Fluent, the blood flow through a stenotic artery is simulated in ANSYS Fluent.

Chapter 4 introduces acoustics, including its wave characteristics, the wave governing equation and corresponding finite element matrix form, and harmonic analysis of a body under a blast in the open area.

Thermal analysis is the focus of Chapter 5. After introducing the governing equation and finite element matrix form, as well as the finite element procedure of the thermal analysis, the heat generation of the breast tumor is modeled and verified by the reference results.

Part I introduces the single physics fields, and Part II turns to the couplings between them. After a short introduction of the general coupling methods and classification in Chapter 6, Chapter 7 presents FSI and its simulation procedure in ANSYS. In the last part of Chapter 7, a FSI study of abdominal aortic aneurysm is performed by two-way coupling and one-way coupling, and then compared against the results of the static analysis.

Biological soft tissues are biphasic with the coupling of the solid and fluid phases, which can be modeled by coupled pore-pressure thermal (CPT) elements in ANSYS. Chapter 8 introduces the governing equations and general modeling procedure of CPT elements. Then, it shows a simulation of biological tissues in the confined compression test.

Compared with FSI, acoustic FSI is relatively simple due to the linear acoustic governing equations. After listing the governing equations and simulation procedure in ANSYS in the first two parts of Chapter 9, the acoustic wave transmission in the ear is studied using acoustic FSI.

Chapter 10 presents the thermal structural analysis, which starts with thermal-structural coupling equations and modeling procedures in ANSYS, and it follows the study of temperature change of biological tissues under cycle loadings.

Part III discusses models with more than two physical fields. With more physical fields, the coupling problems become more complicated, and it is more difficult to reach convergence. Two cases are presented in Chapters 11 and 12, respectively. Chapter 11 focuses on the thermal problem of soft tissues, in which the thermal analysis works with CPT elements. The thermal analysis of porous media is implemented in ANSYS using CPT elements with keyopt(11) = 1 and applied for modeling the tissue fusion in the last part of Chapter 11. Another case in Chapter 12 studies the murmur detected in the skin surface due to blocking in the blood vessel. This case is solved with two couplings: (1) one coupling between the blood flow and wall of the vessel and (2) another acoustic FSI between the vessel (solid) and the soft tissues (fluid).

The last part is retrospective. Based on the above three parts, Chapter 13 describes the influence of physics natures on physical modeling, problem-dependent coupling methods, special meshing requirements for various physical models, and units for coupling problems.

Multiphysics is a big field. Besides the couplings mentioned in the book, it also includes piezoelectric analysis, electrostatic-structure coupling, magneto-structure coupling, magneto-fluid coupling, electrothermal coupling, and magnetic-thermal coupling. These couplings are not covered in the book because they occur rarely in biomedical engineering. If the readers are interested in these couplings, they may read the relevant part of the ANSYS theory manual and other reference books, such as Chapter 22 in Material Modeling in Finite Element Analysis (CRC Press, 2019), Chapter 2 in Multiphysics Modeling: Numerical Methods and Engineering Applications (Elsevier, 2015), and Multiphysics Modeling with Finite Element Methods (World Scientific Publishing, 2006).

Most examples in the book have been implemented using ANSYS Parametric Design Language. Reading this book requires knowledge of the ANSYS Parametric Design Language. I suggest the readers to study the ANSYS help documentation, and then practice some problems in Finite Element Analysis for Biomedical Engineering Applications (CRC Press, 2019).

Section I

Single Physics Phases

The first section focuses on single physics phases, including structural analysis, fluid analysis, thermal analysis, and acoustic analysis. These single physics phases have their unique features and corresponding modeling procedure in ANSYS, which Chapter 2, Chapter 3, Chapter 4, Chapter 5 discuss.

Chapter 2 presents structural analysis. After briefly introducing the finite deformation of the solid and the corresponding balance equations, as well as the ANSYS modeling procedure, the intervertebral disc under pressure is simulated in ANSYS.

Fluid analysis is the topic of Chapter 3. Unlike a solid, fluid is easily deformed. The governing equation of the fluid and modeling procedure in ANSYS Fluent are presented along with one example of blood flowing through a stenotic artery.

Sound is a wave controlled by the wave equation. Chapter 4 introduces the governing equation of acoustic, finite element procedure, and its ap...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Preface
• Author
• Chapter 1 Introduction
• SECTION I Single Physics Phases
• SECTION II Coupling Between Two Physics Phases
• SECTION III Coupling among More Than Two Physics Phases
• SECTION IV Retrospective
• Appendix 1
• Appendix 2
• Appendix 3
• Appendix 4
• Appendix 5
• Appendix 6
• Appendix 7
• Appendix 8
• Appendix 9
• Index