Overview
Provides critical insights into how to calibrate the model by calculating the values of key parameters using experimental results
Expands reader understanding of How to construct a mathematical model for the behavior of dental materials by making appropriate guesses of the physical situation
Illustrates in detail how to validate the model by comparing its predictions with other experiments not used in the calibration
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
- Mathematical Models dental materials
- Dental Materials
- Dental materials research
- Bone remodeling dental materials
- Mineral loss dental materials
- Occlusal shrinkage dental materials
- Dental resin modeling materials
- Dental restoration materials modeling
- Biomathematics
- bone remodeling dental
- wolff's law dental materials
- newton's law dental materials
- washburn's equation dental materials
- straight-line equation dental
- dental resin composites math
About this book
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
Authors and Affiliations
About the authors
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.
Bibliographic Information
Book Title: Mathematical Models for Dental Materials Research
Authors: Alex Fok, Hooi Pin Chew
DOI: https://doi.org/10.1007/978-3-030-37849-3
Publisher: Springer Cham
eBook Packages: Biomedical and Life Sciences, Biomedical and Life Sciences (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-37848-6Published: 25 February 2020
Softcover ISBN: 978-3-030-37851-6Published: 25 February 2021
eBook ISBN: 978-3-030-37849-3Published: 24 February 2020
Edition Number: 1
Number of Pages: XIV, 77
Number of Illustrations: 1 b/w illustrations, 40 illustrations in colour
Topics: Biomedical Engineering/Biotechnology, Biomaterials, Mathematical Modeling and Industrial Mathematics, Dentistry, Biomedical Engineering and Bioengineering