Finite Element Modeling and Applications to Dental Implants

Dept. Mechanical and Aerospace Engineering

University at Buffalo

Dec 02, 1999

Co-Workers

P. Bock, B. Comella

Prof. M. Meenaghan and Dr. S. Andreana

Sponsors

NSF, GRIT, BUD Inc.

Outline

Introduction

Finite Element Modeling (FEM)
- Why do it ?
- What is it ?

FEM of Dental Implants
- Stress Analysis, 3D/2D, Crestal Bone Loss
- Redesigns
- New Challenges

Introduction

Observation: Dental Implants average 1mm of crestal in the first year and 0.1mm subsequently -Misch 1999, Branemark et. al. 1981

Cumulative Crestal Bone Loss can lead to implant failure.

Introduction

Crestal Bone Loss may be due to
- bacterial infection
  - sterile implants + aseptic placement + oral hygiene
- improper loading of bone
  - functional stress 200-400 psi needed for bone maintenance -- Rieger ‘91
  - complex structure -- analysis needs large computing power and advanced techniques

Engineering Analysis

fender, dental implant

Finite Element Modeling

What is FEM ?
- It is a technique to obtain approximate numerical solutions to the partial differential equations that express the fundamental laws of physics (e.g. equilibrium, balance of mass and energy, material laws etc.)

Finite Element Modeling

Find perimeter of circle.

Finite Element Modeling

Step 2: Construct Local Approximation

Finite Element Modeling

Step 3:Assemble the element equations

Step 4: Solve; n=5, 10, ...(true P=6.28R)

Finite Element Modeling

For mechanical analysis -- similar procedure -- but we construct local approximations of force, energy, mass ...

Elements may be bricks, tetrahedra, plates, rods, beams, etc.

Solution quality can be improved by using smaller elements or better elements

Dental Implants and FEM

Model Geometry of Bone + Implant

Discretize into elements

Assemble and solve equations to compute deformations, stresses etc.

Model Geometry of Bone + Implant

Solid Model of Jaw Bone and Implant

Model Geometry of Bone + Implant

Solid Model of Jaw Bone and Implant

Discretize into elements

Finite Element Modeling

Adding up local approximations of strain energy

(principle of virtual work)

Dental Implants and FEM

Modeling assumptions
- Bone behaves like a homogeneous, linear, elastic material
- Implant and Bone are in perfect contact
- Analysis of static loading is a good predictor of true dynamic behavior

Dental Implants and FEM

Other Modeling assumptions seen in Literature
- 2D representation of geometry
- Use of “hard” constraints
- Static, Axial, symmetric loads

Dental Implants and FEM

Bone - Implant systems do not satisfy these assumptions
- geometry and loading are not axially symmetric
- bone is not homogenous
- resorption and remodeling are time dependent phenomena
- hard constraints do not exist in the system
- there is imperfect bone - implant contact

Dental Implants and FEM

Cortical bone behaves anisotropically

Has both a transverse and longitudinal modulus

Trabecular bone is porous, and has a cellular structure

Stress Analysis

PPT Slide

3D Model Results/Observations

Three Dimensional Models
- From these results it is seen that the cortical layer of the bone carries most of the load
- Stresses were observed to be lower in the adjacent trabecular tissue
- This pattern of local cortical overloading may be the cause of resorption in the apical area

3D Model Results/Observations

Three Dimensional Models
- also, only the first few threads were seen to be carrying the load
- in the case of the BUD implant, the mantle seemed to carry the entire load to the bone tissue
- looking at the different types of constraints used, the use of the spring model seemed more accurately represent the actual system

2D Modeling Problems

Effect of Crestal Bone Loss

Model the effect of the onset of crestal bone loss on residual bone -- using soft elements

Effect of Crestal Bone Loss

Effect of Partial Osseointegration

of osseointegration

easily modeled

Effect of 25% Partial Osseointegration

Effect of 50% Partial Osseointegration

Effect of 100% Partial Osseointegration

Evaluation of Alternate Designs

we should attempt to tailor implants to form an optimal state of stress in the surrounding tissue

Evaluation of Alternate Designs

Alternate Design 1 Stress

Evaluation of Alternate Designs

Alternate Design 2 Stress

Redesigns

redesign 2 shows
- Even stress distribution further down the threads
- decreased stress concentrations
- minimal manufacturing change

Conclusions of Stress Analysis

From these analysis it is seen that the lower half of the implant structure plays little or no role in the load bearing capability of the implant

It may be more cost effective / beneficial to use a shortened implant

However stability concerns due to moment overloading from appliances are also relevant

Error Control in FEM

Motivation

FEM can be powerful tool to
- design new implants for durability and optimal stress distributions

Answers must be reliable !
- must control numerical and modeling errors
- needs very large computer resources

Numerical Error Control

We expect exact stress and strain to be continuous -- but FEM stress is discontinuous

A continuous estimate of stress and strain should be more accurate than the piecewise continuous element strains and stresses

Numerical Error Control

Let us denote such approximations are denoted by e* and s*

Error estimators with good accuracy are

ee = e*(x) - eel(x)

es = s*(x) - sel(x)

Stress averaging is used to yield a continuous solution

Numerical Error Control

Error information can be used to modify the mesh
- use smaller elements where errors are high
- use better (higher order of approximation) elements

Numerical Error Control

Future

High quality FEM is getting cheaper and more available
- better algorithms
- better material models and time dependent simulations
- cheaper and better computers ($30K computer in 1995 = $10 K computer now!)
- can perform simulations for specific patients and custom design implant/prosthesis!

Future

Image data (CT/MRI) can be used to get FEM mesh and bone quality data automatically for each patient

Simulation data can be used to decide
- which implant to use ?
- where to place it ?

PPT Slide