Finite Element Analysis and its Application in Dental Implant Research

Finite Element Analysis and its Application in Dental Implant Research

Antonios Zampelis (School of Applied Mathematics and Physical Sciences, Greece) and George Tsamasphyros (School of Applied Mathematics and Physical Sciences, Greece)
DOI: 10.4018/978-1-60566-292-3.ch012
OnDemand PDF Download:


Biomechanical research has gained recognition in medical sciences. Osseointegrated dental implants, being medical devices functioning under constant load, are one of the focal points of such research. One of the most powerful tools for biomechanical research on dental implants is finite element analysis (FEA). This chapter will cope with basic elements of FEA research, the mechanical properties of bone and the various parts of dental implants, as well as delve into published literature on the subject.
Chapter Preview


Finite element analysis (FEA) is a computer simulation technique used in engineering analysis. It uses a numerical technique called the finite element method (FEM). There are many finite element software packages available, both free and proprietary. The sophistication of this technique has rendered it an invaluable tool in biomechanical research.

The finite element analysis was first developed in 1943 by Richard Courant, who used the Ritz method of numerical analysis and minimization of variational calculus to obtain approximate solutions to vibration systems. Shortly thereafter, the work of M.J.Turner, R.W.Clough, H.C.Martin and L.J.Topp in 1956 established a broader definition of numerical analysis. The researchers centered on the “stiffness and deflection of complex structures”. Development of the finite element method in structural mechanics is usually based on an energy principle such as the virtual work principle or the minimum total potential energy principle.

In its applications, the object or system is represented by a geometrically similar model consisting of multiple, linked, simplified representations of discrete regions-i.e. finite elements on an unstructured grid. Equations of equilibrium, in conjunction with applicable physical considerations, such as compatibility and constitutive relations, are applied to each element and a system of simultaneous equations is constructed. The system of partial differential equations is solved for unknown values using the techniques of linear algebra or nonlinear numerical schemes, as appropriate.

In lay terms, the mathematical model is represented by a mesh geometrically identical to the object being studied. The mesh is broken down to elements. There is a set number of elements for a distinct mesh, hence the term finite element analysis. Each element is defined by points called nodes. Depending on the type of analysis, a wide variety of elements can be used, such as one-dimensional (straight or curved), two-dimensional (triangles or quadrilaterals), torus-shaped and three-dimensional (such as tetrahedrals and hexahedrals). As a force is applied, these interconnected elements start to move. Movement is defined by means of displacement of their nodes. This displacement is transformed, through the calculations, to stress and strain values (Figure 1). While being an approximate method, the accuracy of the FEA method can be improved by refining the mesh in the model using more elements and nodes.

Figure 1.

Close up of an implant cervix (right) and bone (left). The finite elements are depicted as the ares marked by white lines. Each quadrilateral element consists of four nodes. The different colors depict iso-stress areas

A common use of FEA is for the determination of stresses and displacements in mechanical objects and systems. However, it is also routinely used in the analysis of many other types of problems, including those in heat transfer, fluid dynamics and electromagnetism. FEA is able to handle complex systems that defy closed-form analytical solutions.

Finite element analysis is also frequently used in biological systems, for example in orthopedics, but also for dental implants. In fact, realization of the importance of biomechanical aspects in implant dentistry have rendered FEA an essential tool in dental implant research.

Among the subjects investigated in dental implantology are both material properties and biomechanical performance of implants and their components. The behavior of titanium parts, such as abutments and screws, has been put under scrutiny to determine their function under load and the possibility of failure due to fatigue. From a mechanical point of view, such studies are trivial.

On the other hand, the biological behavior of implants integrated in bone is a more complicated matter. A number of studies have investigated the effect of implant length, diameter, shape, as well as different placement configurations and the resulting stresses transmitted to the bone. Often, the effect of prosthetic material and shape of construction, such as the inclusion of cantilevers, is taken into consideration.

The main concern with the application of FEA in implant research is to which extent a mathematical model can represent a biological system. Published studies show a notable trend towards optimization of mathematical models. Improved software and a dramatic increase in easily available computational power have assisted in this trend.

Complete Chapter List

Search this Book:
Editorial Advisory Board
Table of Contents
Petros Koidis
Andriani Daskalaki
Andriani Daskalaki
Chapter 1
Demetrios J. Halazonetis
Cephalometric analysis has been a routine diagnostic procedure in Orthodontics for more than 60 years, traditionally employing the measurement of... Sample PDF
Software Support for Advanced Cephalometric Analysis in Orthodontics
Chapter 2
Jorg Hendricks, Gert Wollny, Alexander Hemprich, Thomas Hierl
This chapter presents a toolchain including image segmentation, rigid registration and a voxel based non-rigid registration as well as 3D... Sample PDF
A New Software Environment for 3D-Time Series Analysis
Chapter 3
Antheunis Versluis, Daranee Tantbirojn
Residual stress due to polymerization shrinkage of restorative dental materials has been associated with a number of clinical symptoms, ranging from... Sample PDF
Relationship Between Shrinkage and Stress
Chapter 4
Andreas Vogel
This chapter introduces a computer-controlled method for mandible alignment. The exact positioning of the mandible in relation to the maxilla is... Sample PDF
An Objective Registration Method for Mandible Alignment
Chapter 5
Thomas Hierl, Heike Huempfner-Hierl, Daniel Kruber, Thomas Gaebler, Alexander Hemprich, Gert Wollny
This chapter discusses the requirements of an image analysis tool designed for dentistry and oral and maxillofacial surgery focussing on 3D-image... Sample PDF
Requirements for a Universal Image Analysis Tool in Dentistry and Oral and Maxillofacial Surgery
Chapter 6
N.A. Borghese, I. Frosio
This chapter shows how large improvement in image quality can be obtained when radiographs are filtered using adequate statistical models. In... Sample PDF
Denoising and Contrast Enhancement in Dental Radiography
Chapter 7
Ralf K.W. Schulze
Established techniques for three-dimensional radiographic reconstruction such as computed tomography (CT) or, more recently cone beam computed... Sample PDF
3D Reconstructions from Few Projections in Oral Radiology
Chapter 8
Shital Patel, Yos Morsi
Tooth loss due to several reasons affects most people adversely at some time in their lives. A biological tooth substitute, which could not only... Sample PDF
Advances and Trends in Tissue Engineering of Teeth
Chapter 9
Wei-Bang Chen, Chengcui Zhang
Bacterial colony enumeration is an essential tool for many widely used biomedical assays. This chapter introduces a cost-effective and fully... Sample PDF
Automated Bacterial Colony Counting for Clonogenic Assay
Chapter 10
Michele Jacotti, Domenico Ciambrone
In this chapter the authors describe a new system for guided surgery in implantology. The aim of this system is to have a “user friendly”... Sample PDF
A New System in Guided Surgery: The Flatguide(TM) System
Chapter 11
Ferenc Pongracz
Intraoperative transfer of the implant and prosthesis planning in dentistry is facilitated by drilling templates or active, image-guided navigation.... Sample PDF
Visualization and Modelling in Dental Implantology
Chapter 12
Antonios Zampelis, George Tsamasphyros
Biomechanical research has gained recognition in medical sciences. Osseointegrated dental implants, being medical devices functioning under constant... Sample PDF
Finite Element Analysis and its Application in Dental Implant Research
Chapter 13
Amit Chattopadhyay, Tiago Coelho de Souza, Oscar Arevalo
Electronic Oral Health Records (EOHRs) contains all personal health information belonging to an individual and is entered and accessed... Sample PDF
Electronic Oral Health Records in Practice and Research
Chapter 14
Maxim Kolesnikov, Arnold D. Steinberg, Milos Zefran
This chapter describes the haptic dental simulator developed at the University of Illinois at Chicago. It explores its use and advantages as an... Sample PDF
Haptic-Based Virtual Reality Dental Simulator as an Educational Tool
Chapter 15
Anka Letic-Gavrilovic
In this chapter, the author will demonstrate and describe a project to develop a unique database with multilingual information and knowledge... Sample PDF
Digital Library for Dental Biomaterials
Chapter 16
Petros Koidis, Marianthi Manda
The present chapter deals with the introduction and implementation of rapid prototyping technologies in medical and dental field. Its purpose is to... Sample PDF
Rapid Prototyping and Dental Applications
Chapter 17
Hiroo Tamagawa, Hideaki Amano, Naoji Hayashi, Yasuyuki Hirose
In this chapter, the authors report the minimal set of characters from the Unicode Standard that is sufficient for the notation of human dentition... Sample PDF
Unicode Characters for Human Dentition: New Foundation for Standardized Data Exchange and Notation in Countries Employing Double-Byte Character Sets
Chapter 18
Nikos Nikolaidis, Ioannis Marras, Georgios Mikrogeorgis, Kleoniki Lyroudia, Ioannis Pitas
The availability of datasets comprising of digitized images of human body cross sections (as well as images acquired with other modalities such as... Sample PDF
Virtual Dental Patient: A 3D Oral Cavity Model and its Use in Haptics-Based Virtual Reality Cavity Preparation in Endodontics
About the Contributors