Dental implantation is one of the most common dental restorative techniques to replace a missing tooth. The longevity and the stability of the dental implant can be directly impacted by two factors: 1) The degree of integration between the implant and its surrounding bones; and 2) The quality of the surrounding bones. The former factor can be identified as osseointegration, while the later can be affected by bone remodelling. The magnitude of bone remodelling can be predicted mathematically where remodelling is be triggered by the mechanical strain. The objective of this study is to quantify the magnitude of bone remodelling in the bones surrounding a dental implant. A 2D finite element model was constructed in ABAQUS 6.6.1. The results revealed the bone density change due to remodelling, and can be used as the preliminary step towards future study on similar topic by using a more accurate, 3D finite element model

Ichim, Ionut

Li, Qing

Lic, Wei

Lin, Daniel

Swain, Michael

University of Queensland eSpace

5th Australasian Congress on Applied Mechanics, ACAM 2007  
10-12 December 2007, Brisbane, Australia 
Evaluation of dental implant induced bone remodelling by using a 2D Finite 
Element model 
 
Daniel Lin1,a, Qing Li1,b, Wei Lic, Ionut Ichim2d and Michael Swain2,3e 
 
1 School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, 
NSW 2006, Australia 
2 Department of Oral Science, Faculty of Dentistry, University of Otago, New Zealand 
3Faculty of Dentistry, The University of Sydney, NSW 2006, Australia 
 
amaster.yoda99@yahoo.com, bQing.Li@aeromech.usyd.edu.au, wei@aeromech.usyd.edu.au, 
dionut.ichim@stonebow.otago.ac.nz, emswain@mail.usyd.edu.au 
Abstract: Dental implantation is one of the most common dental restorative techniques to replace a 
missing tooth. The longevity and the stability of the dental implant can be directly impacted by two 
factors: 1) The degree of integration between the implant and its surrounding bones; and 2) The 
quality of the surrounding bones.  The former factor can be identified as osseointegration, while the 
later can be affected by bone remodelling. The magnitude of bone remodelling can be predicted 
mathematically where remodelling is be triggered by the mechanical strain.  The objective of this study 
is to quantify the magnitude of bone remodelling in the bones surrounding a dental implant.  A 2D 
finite element model was constructed in ABAQUS 6.6.1.  The results revealed the bone density 
change due to remodelling, and can be used as the preliminary step towards future study on similar 
topic by using a more accurate, 3D finite  element model.       
Keywords: 2D finite element, bone remodelling, dental implant, mechanostat. 
1 Introduction 
In the past two decades, dental implants are made out of bio-compatible materials to enhance its 
ability to be integrated into the living bone structure [1]. The longevity of the dental implant is 
dependant on the quality  of its surrounding bones [2].  The osseointegration process takes place after 
implantation, and can impact  the resulting success of the implantation [3]. Branemark [4] suggested 
that the healing time for dental implantation should be between 4 and 6 months in the maxilla, and 
between 3 and 4 months for implants in the mandible. Fini et al [2] reported the mechanism of 
osseointegratin can be treated as a fracture-repair process. The sequence of osseointegration can be 
summarized as follows: The healing process at the peri-implant interface can be considered as a 
scenario of tissue repair, where the gap between the implant and the host bone is rapidly filled by the 
blood clots at the early stage of implantation. The blood clot is then substituted by trabecular bone, 
which remodels into the lamellar bone [5].  At the end of the healing process, the mature bone can be 
found in direct contact with the implant surface, therefore completing the process of osseointegration 
and better implant stability can be achieved [6].   
 
Bone remodelling is a process where the density of bone changes in response to the mechanical 
loading, and as a result leading to the alteration of its material property.  In general, the magnitude of 
bone density is directly related to bones Youngs modulus value. This type of relationship has been 
established by Carter and Hayes [7].  Therefore bone remodelling can affect  the mechanical stress 
and strain in the bony tissues.  From literature, the Youngs modulus value is usually 14GPa for the 
cortical bone and 1.4GPa for the cancellous bone. The density for the cortical bone and the cancellous 
bone are 1.8g/cm3 and 0.8g/cm3 respectively [7].  
 
Rho et al [8] associated the Youngs modulus of cortical bone to its density as: 
 
  r2493.23 +-=E                                                                                                                       (1)  
where E is the Youngs modulus in GPa, and  is the bone density in g/cm3.   
 
Aisling et al [9] related the cancellous bone density to its Youngs modulus by: 
  
  15.2349.2 r=E                                                                                                                            (2)  
 
where E is the Youngs modulus in GPa and  is the bone density in g/cm3.   
 
Excessive loading of the implant during the healing stage may cause high mechanical strain to be 
induced at the interface.  This will in tern cause premature implant failure. However, several studies 
have reported positive response to the healing process by applying loads at low magnitude to the 
implant; this can lead to positive response to bone remodelling [10]. Insight into the interface 
parameter variation during the healing process can be achieved by animal removal torque tests.  
Wilke et al [11] reported that, the magnitudes of removal torque increases throughout the healing 
process.  Furthermore, a non-linear relationship exists between the removal torque and the angle of 
rotation [11].  Therefore, osseointegration affects the elastic property, as well as the outcome of bone 
remodelling at the interface  and its surrounding structures. The magnitude of bone remodelling can be 
identified mathematically.  Up to date, there are several algorithms available to predict bone 
remodelling. Some common theories include: 1.) the theory of Mechanostat, where the induced 
mechanical strain is treated as the key factor that triggers bone remodelling [12]. 2.) The continual 
damage-based algorithm (CDM), where remodelling is driven by the rate of micro-damage/fracture in 
the bone. CDM can be easily related to osseointegration due to its  fracture-repair nature [13].   
 
The theory of mechanostat proposed by Frost can be used to predict the result of bone remodelling, 
where the sequence of bone remodelling is triggered by the minimum effective strain (MES) [14]. 
Consequently, mechanical strains greater than the upper limit of MES will lead to bone growth. In 
contrast, mechanical strain below the lower bound of MES wi ll cause bone resorption as illustrated in 
Fig.1. 
Bone resorption
Lazy zone
(No remodeling)
Bone formation
Minimum
Effective
Strain 
R
em
od
el
in
g
bo
ne
 d
en
si
ty
MES1
MES2
R
em
od
el
in
g
bo
ne
 d
en
si
ty
 
Figure 1: Bone growth and MES distribution 
 
The two threshold values were identified by Frost [17] to be 0.015and 0.15% respectively, the region 
between the two threshold values can be referred to as the lazy zone where the remodelling process 
is non-active. 
 
Mathematically, mechanostat algorithm can be expressed as a differential equation: 
  
  )( 2 MESa
k
dt
d
-=
r
sr
                                                                                                                 (3 ) 
where  is the density of bone, k is the remodelling constant,  is the mechanical stress and a is a 
material constant equal to E/ 2.  Eq. (3) is used to calculate the incremental change of bone density.  
By adding this incremental change to the original density, the new density of bone after remodelling 
can be obtained.  Combining Eqs.(1)-(3), the full material property due to bone remodelling can be 
calculated. 
  
2 Method 
2.1 2D finite element model 
The 2D finite element model consists of four parts: a ceramic crown, dental implant, a layer of cortical 
bone with thickness of 2mm, and the cancellous bone.  There are in total 95670 triangular elements, 
and the bone tissues were partitioned into 708 sections.  Boundary conditions were applied to the side 
edges of the model so all forms of translational movements are constrained.  An occlusal load of 200N 
was applied to the top of the crown.   
 
 
The material property used for the crown and the dental implant are 90GPa and 110GPa respectively 
[ref].  The properties of all the bones were assumed to be isotropic and linear elastic.  The initial 
Youngs moduli employed in the model were 14GPa for the cortical bone and 1.4GPa for the 
cancellous bone. Bone densities are 1800kg/m³ for the cortical bone and 1200kg/m³ for the cancellous 
bone [13].   
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2: 2D finite element model 
 
2.2 Finite element analysis and bone remodelling calculations 
In this study, the system of protocol employed for bone remodelling calculation involves the execution 
of ABAQUS software and an external coded program simultaneously.  ABAQUS was used for finite 
element calculation where the mechanical stress and strain were analyzed based on the 2D model.  
The external program was coded using Python scripting language and contains all the remodelling 
algorithms.  The system can be summarized by a flow chart as follows: 
Eqn.3
Eqn.1
Eqn.2
Initial condition
Updating of material
Property in the FE
model
Finite element 
analysis
New bone 
density
 
Figure 3: Flow chart of bone remodelling protocol 
ImplantCancellous
bone
Cortical
bone
Crown
Load
  
From Fig.3, the initial conditions of the bone, such as bone density will be input into the remodelling 
equation where the incremental change of bone density is calculated.  The new density of bone after 
remodelling is then substituted into both eqn.1 and 2 where the Youngs modulus values of bones are 
obtained.  Followed by the updating of material property in the FE model, thereafter finite element 
calculation is performed.  The stress and strain values are then fed into Eq. (3) where the entire 
protocol is looped continuously.  Seven iterations are performed per analysis to resemble the 7 days in 
a weekly cycle. 
2.3 Interface parameters 
As mentioned before, the interface strength can be measured by animal removal torque test.  The 
values for the interface parameters were gathered from literature [14], and are listed in the table 
below. The interface parameters are changed in the FE model at various healing phase to simulate 
interface strength variation during osseointegration. 
        Table 1: Parameters used for FE model [11] 
Week Coefficient of friction Shear modulus (MPa) 
2 0.1 24 
4 0.2 43 
8 0.35 62.5 
10 0.425 79.17 
12 0.5 90 
14 0.55 93.33 
16 0.58 97.5 
20 0.692 105 
24  0.8 113 
28 0.825 114.17 
32 0.864 116.67 
36 0.893 117.5 
44 0.964 118.17 
48 1 120 
 
3 Results and discussions 
Since there are 708 sections in the 2D model, it will be difficult to present all the bone density and 
Youngs modulus values.  Therefore the results are presented using the average values of these 708 
sections, representing the overall response due to bone remodelling in the bone tissues.  
3.1 Cortical bone remodelling 
The cortical bone is much stiffer than the cancellous bone, therefore their results are presented 
separately in Fig.4 and 5. 
Cortical bone density distribution
1.760
1.780
1.800
1.820
1.840
1.860
1.880
1.900
1 3 5 7 9 11 13
Week
D
en
si
ty
 o
f b
on
e 
(g
/c
m
^3
)
Cortical bone Young's modulus distribution
13
13.5
14
14.5
15
15.5
16
16.5
1 3 5 7 9 11 13
Week
Yo
un
g'
s 
m
od
ul
us
 (G
Pa
)
 
          Figure 4: Cortical bone density distribution              Figure 5: Cortical bone Youngs modulus  
  
Fig.4 is the result for the cortical bone density due to remodelling. From Fig.4 it can be seen that, in 
general the average density of bone increases continuously. The increase is observed as a smooth 
and rapid growth, greater gain of bone density was found in the period between week 4 and week 10, 
as well as between week 28 and week 32.  In addition, the rate of increase in the magnitude of bone 
seems to accelerate from week 10, this is evident from the steep increase in the slope of the graph in 
Fig.4. This phenomenon could be explained by the osseointegration effect, because the interface 
strength is improved at week 10, therefore speeding up the progress of bone remodelling  drastically. 
At week 48, the bone density approaches the value of 1.88g/cm3. 
Fig.5 gives the Youngs modulus values due to bone remodelling, and the Youngs modulus 
distribution coincide with that of the bone density progression due to bone remodeling because both 
results displayed rapid, continuous growth.  However, this growth seems to accelerate after week 10, 
followed by the slower rate of growth between week 12 and week 20.  The rate of increase in Youngs 
modulus is accelerated after week 24 and starts to approach a steady state by week 44.  The 
magnitude of Youngs modulus is 16GPa by the end of week 48. 
 
3.2 Cancellous bone remodeling 
The remodeling results for the cancellous bone are presented in this section.  Fig.6 gives the density 
change over the healing period. The results for cancellous bone remodelling shows great difference 
when compared to the results from cortical bone remodelling.  The density of the cancellous bone 
seems to decrease from week 2 to week 4.  After week 4, the density of bone appears to increase at a 
very fast rate of growth until week 10.  Once again, this steep increase in bone density at week 10 is 
possibly due to the strengthening effect of osseointegration. The density of bone remains constant 
from week 12 to week 14, and followed by the second rapid growth in bone density from week 16 to 
week 28.  Most importantly, the density of bone decreases between week 28 and week 36 and finally 
appears to be approaching a constant value of 0.8035g/cm3 at week 48.  This type of behaviour could 
be seen as the bones attempt to change itself and adjust its density to adapt to its surrounding 
environment, i.e. adjusting its density to a value that is best suited for its  mechanical loading 
environment.  Therefore, the result suggests the mechanical strain in the bone falls within the upper 
and lower limit of MES, consequently the remodelling phenomenon slowly ceases. 
 
Cancellous bone distribution
0.796
0.798
0.8
0.802
0.804
0.806
2 8 12 16 24 32 44
Week
D
en
si
ty
 o
f b
on
e 
(g
/c
m
^3
)
Cancellous bone Young's modulus 
distribution
1.430
1.440
1.450
1.460
1.470
1.480
1 3 5 7 9 11 13
Week
Yo
un
g'
s 
m
od
ul
us
 (G
Pa
)
 
     Figure 6: Cancellous bone density distribution       Figure 7: Cancellous bone Youngs modulus 
 
The Youngs modulus distribution of the cancellous bone is presented in Fig.7. It is seen that the 
Youngs modulus progression repeats the pattern of bone density progression in the cancellous bone.  
A rapid growth in Youngs modulus value occurs between week 4 and week 10 can be contributed to 
the effect of osseointegration.  The Youngs modulus value starts to reach the steady state at week 36 
and finally approach a constant value of 1.467GPa at week 48. 
 
4. Conclusion 
In general, the study led to satisfactory results and the objective of the study was achieved.  The 
results indicated that initial healing period of 20 weeks after implantation is of vital importance to the 
overall recovering and strengthening process after surgery. Furthermore this observation confirms the 
recommended healing period of 3 to 6 months from literature study.  Furthermore, the cancellous bone 
  
appears to reach the steady state of bone remodeling at an earlier stage than the cortical bone, i.e. 
approaching steady state by week 36.  The density and Youngs modulus of cortical bone are 
1.88g/cm3 and 16GPa at week 48, where the density and Youngs modulus of cancellous bone are 
0.8035g/cm3 and 1.467GPa at 48.  The osseointegration effect can enhance the rate of bone 
remodeling, since all results indicated that by week 10, the rate of bone remodeling increases rapidly, 
this also confirms the suggested initial healing time of 3months after the dental surgery.   
 
Finally, although this study achieved reasonable results, the finite element analysis was performed 
using a 2D model, obviously this cannot simulate the real life case.  Therefore in the future a 3D finite 
element model should be used.  Further, at the current status no clinical data is available for 
comparison against FE results.  Future study should attempt to obtain clinical data for validation of FE 
results. 
Acknowledgements 
This study was supported by Australian Research Council Discovery Project (DP0666446). The first 
author is grateful for University of Sydney postgraduate student conference travel grant.  
References 
[1]  Jae-Hoon Lee, DDS, MS, Val Frais, DDS, MS, Keun-Woo Lee, DDS, MSc, PHD, and Robert F. Wright, 
DDS. (2005) Effect of implant size and shape on implant success rates: A literature review. The Journal of 
Prosthetic Dentistry 94:377-381. 
[2]  Branemark PI.  (1985). An introduction to osseointegraion.  In: Branemark, Albrektsson T, eds.  Tissue-
integrated Prostheses: Osseointegration in Clinical dentistry. Chicago Quintessence. 11-53. 
[3] Franchi Marco, Fini Milena, Giavaresi Gianluca, Ottani Vittoria. (2005). Peri-implant osteogenesis in health 
and osteoporosis Micron 36:630-644. 
[4] Branemark PI. (1983). Osseointegration and its experimental background. J Prosthet Dent. 50:399-410.  
[5] Franchi, M., Orsini, E., Trire, A., Quaranta, M., Martini, D., Guiliani Piccari, G., Ruggeri, A., Ottani, V 
(2004b). Osteogenesis and morphology of the peri-implant bone facing dental implants.  The Scientific 
World Journal 4:1093-1095. 
[6] Chappard, D., Aguado, E., Hure, G., Grizon, F., Basle, M.F. (1999). The early remodeling phases around 
titanium implants: a histomorphometric assessment of bone quality in a 3 and 6 months study in 
sheep.International Journal of Oral and Maxillofacial Implants 14:189-196. 
[7] Carter, D.R. & Hayes, W.C (1997). The compressive behavior of bone as a two-phase porous structure. 
Journal of Bone and Joint Surgery (59):954-962. 
[8] Rho, J.Y., Hobatho, M.C., Ashman, R.B. (1995). Relations of mechanical properties to density and CT 
numbers in human bone.  Medical Engineering Physics (17):347-355 
[9] Aisling M. OMahony, John L. Williams, Paulette Spencer (2001). Anisotropic elasticity of cortical and  
cancellous bone in the posterior mandible increases peri-implant stress and strain under oblique loading. 
Clin. Oral Impl. Res. (12):648-657. 
[10] Piattelli, A., Ruggeri, A., Franchi, M., Romasco, N., Trisi, P. (1993). A histologic and histomorphometric 
study of  bone reactions to unloaded and loaded non-submerged single implants in monkeys: A pilot study. 
Journal of Oral Implantology 19:314-320. 
[11] Wilke, H.J., Claes, L., Steinemann, S. (1990). The influences of various titanium surfaces on the interface 
shear  strength between implants and bone. In: Heimke, G., Soltesz, U., Lee, A.J.C. (Eds), Clinical Implants  
Materials,Advances in Biomaterials, Vol. 8. Elsevier Science Publisher B.V., Amsterdam, Printed in The 
Netherlands,pp.309-314. 
[12] Frost HM. (1983). A determinant of bone architecture: the minimum effective strain. Clin. Orthop. 175:286-
292. 
[13] Brian P. McNamara, David Taylor and Patrick J. Prendergast (1997) Computer prediction of adaptive bone 
modeling around noncemented femoral prostheses: the relationship between damage-based and strain-
based algorithms Med.Eng. Phys. 19(5): 454-463.  
[14] Frost HM. (2003) Bones mechanostat: A 2003 Update. The anatomical record part A (275A): 1081 -1101 
 


Evaluation of dental implant induced bone remodelling by using a 2D Finite Element model

http://espace.library.uq.edu.au/view/UQ:132169/P1.8.pdf

Evaluation of dental implant induced bone remodelling by using a 2D Finite Element model

Abstract

Similar works

Full text

Available Versions

University of Queensland eSpace