Mathematical Models for Dental Materials Research (eBook)

Alex Fok, Hooi Pin Chew (Autoren)

eBook Download: PDF

2020 | 1st ed. 2020
XIV, 77 Seiten
Springer International Publishing (Verlag)
978-3-030-37849-3 (ISBN)

Infos

This book presents a mechanistic approach-mathematical modeling-for carrying out dental materials research. This approach allows researchers to go beyond the null hypothesis and obtain a solution that is more general and therefore predictive for conditions other than those considered in a study. Hence it can be used either on its own or to complement the commonly used statistical approach. 

Through a series of practical problems with wide-ranging application, the reader will be guided on:

• How to construct a mathematical model for the behavior of dental materials by making informed assumptions of the physical, chemical, or mechanical situation
• How to simplify the model by making suitable simplifications
• How to calibrate the model by calculating the values of key parameters using experimental results
• How to refine the model when there are discrepancies between predictions and experiments

Only elementary calculus is required to follow the examples and all the problems can be solved by using MS Excel© spreadsheets.

This is an ideal book for dental materials researchers without a strong mathematical background who are interested in applying a more mechanistic approach to their research to give deeper insight into the problem at hand. 

Advance praise for Mathematical Models for Dental Materials Research:

'This is a nice addition for research students on how to conduct their work and how to manage data analysis. It brings together a number of important aspects of dental materials investigations which has been missing in the literature. The practical examples make it much easier to understand.' - Michael F. Burrow, Clinical Professor in Prosthodontics, The University of Hong Kong

'The great strengths of this volume are the real world examples of dental materials research in the successive chapters. In turn, this is an outcome of the outstanding expertise of both authors. I warmly recommend this book to the dental biomaterials community worldwide.' - David C. Watts, Professor of Biomaterials Science, University of Manchester, UK

Dr. Alex Fok is a Professor in the Department of Restorative Sciences and Director of the Minnesota Dental Research Center for Biomaterials and Biomechanics (MDRCBB)? at the University of Minnesota. He has expertise in stress and structural analysis. His research activities cover a range of topics in the biomechanics of dental restorations. These include probabilistic failure analysis, shrinkage stress and strain, design of mechanical tests, nondestructive examination and shape optimization. A principal aim of his research is to instill more rigorous engineering principles into the design and assessment of dental restorations and treatments so as to improve their reliability.

Dr. Hooi Pin Chew is an Associate Professor in the Biomaterials Division of the Department of Restorative Sciences, University of Minnesota. She received her specialist training in Restorative Dentistry from the Royal College of Surgeon England. Her research interests are mainly driven by clinical practice and teaching and most of her research are translational in nature. Her research activities include development of optical techniques such as optical coherence tomography as objective clinical tools to detect and quantify dental erosion and dental caries, the study of erosive wear and its associated risk factors and the conduct of clinical trials for dental restorative materials.

Inhalt

Foreword: Enjoying and Applying Mathematics in Dental Materials Research 5
References 8
Preface 10
Contents 12
Chapter 1: Systematic Errors in Longitudinal Measurements 14
1.1 Introduction 14
1.2 Effect of Systematic Errors 15
1.3 Corrections for Fractional Changes 16
1.4 Corrections for Absolute Changes 17
1.5 Concluding Remarks 20
References 21
Chapter 2: Endodontic Treatment and Vertical Root Fracture 22
2.1 Introduction 22
2.2 Theory 23
2.3 Validation 26
2.4 Concluding Remarks 27
References 28
Chapter 3: Debonding of Resin Composite Restorations 29
3.1 Introduction 29
3.2 Theory 30
3.3 Application 32
3.4 Nonuniform Shrinkage 33
3.5 Numerical Solution 34
References 36
Chapter 4: Attenuation of Curing Light Through Resin Composite Restorations 37
4.1 Introduction 37
4.2 Theory 38
4.3 Numerical Solution 39
4.4 Analytical Solution 40
4.5 Specular Reflection 41
4.6 Concluding Remarks 43
References 43
Chapter 5: Release of Ions or Molecules from Dental Restorations 44
5.1 Introduction 44
5.2 Model and Numerical Computation 45
5.3 Analytical Solution 47
5.4 Refinement of Model 49
5.5 Concluding Remarks 49
References 50
Chapter 6: Heat Generated from Dental Resin Composites During Curing 52
6.1 Introduction 52
6.2 Model and Numerical Computation 53
6.3 Analytical Solutions 54
6.4 Concluding Remarks 57
References 57
Chapter 7: Mechanical Failure of Dental Restorations: The Weakest-Link Theory 58
7.1 Introduction 58
7.2 The Weakest-Link Theory 59
7.3 Estimating Survival Probability 60
7.4 Application 61
7.5 Fatigue Failure 62
References 64
Chapter 8: Stability of Dental Implants 65
8.1 Introduction 65
8.2 Mass-Spring System 66
8.3 Analytical Solution 67
8.4 Model for a Vibrating Implant 69
8.5 Effect of Bone Density 70
8.6 Concluding Remarks 73
References 74
Chapter 9: Kinetics of Photo-Polymerization 75
9.1 Introduction 75
9.2 The Chemical Reaction 76
9.3 The Rate Equations 77
9.4 Photo-Initiators and Free Radicals 77
9.5 Monomers 78
9.6 Polymer Chain Radicals 78
9.7 Computation 79
9.8 Effect of Light Intensity 82
9.9 Concluding Remarks 84
References 84
Index 85

Produkt-Details

• Erscheint lt. Verlag: 24.2.2020
• Zusatzinfo: XIV, 77 p. 41 illus., 40 illus. in color.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Medizin / Pharmazie ► Allgemeines / Lexika
• Themenwelt: Medizin / Pharmazie ► Zahnmedizin
• Themenwelt: Naturwissenschaften ► Biologie ► Genetik / Molekularbiologie
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Biomathematics • bone remodeling dental • Bone remodeling dental materials • Dental materials • dental materials Research • dental resin composites math • Dental resin modeling materials • Dental restoration materials modeling • Mathematical Models dental materials • Mineral loss dental materials • newton's law dental materials • Occlusal shrinkage dental materials • straight-line equation dental • washburn's equation dental materials • wolff's law dental materials
• ISBN-10: 3-030-37849-7 / 3030378497
• ISBN-13: 978-3-030-37849-3 / 9783030378493