Deng et al.

Int Chin J Dent 2008; 8: 1-9.

A new numerical approach for evaluation of dental implantstability using electromagnetic impulse
Bin Deng, BDS, PhD,a,b Keson B. C. Tan, BDS, MSD,b Gui-Rong Liu,a,c Jian-Ping Geng,
BDS, MSD, PhD,d and Wei-Qi Yan, MD, PhDdaCentre for Advanced Computations in Engineering Science (ACES), Department of MechanicalbEngineering, and Department of Restorative Dentistry, Faculty of Dentistry, National University ofcSingapore, and The Singapore-MIT Alliance (SMA), SingaporedClinical Research Center, The Second Affiliated Hospital, Zhejiang University, Hangzhou, P. R. China
Purpose: The aim of this study is to develop and evaluate computationally in detail a new non-contact method
to access noninvasively the dental implant stability under various osseointegration stages and surrounding bonequalities.
Materials and Methods: The finite element analysis is performed with two steps: electromagnetic field analysis
to obtain the electromagnetic forces and resonance frequency analysis subjected to the electromagnetic force.
Osseointegration process is simulated by changing the Young’s modulus and Poisson’s ratio of the implant-boneinterfacial tissue. Four types of surrounding bone quality are modelled by changing the geometry configuration
and bone density.
Results: It is found that a significant increase in resonance frequency is related to the increase in Young’s
modulus (p<0.0001). Varying the Poisson’s ratio has no statistically significant influence on the resonancefrequencies (p>0.99). The bone quality has a significant effect on the resonance frequencies, with lower value insofter bone (p<0.0001).
Conclusion: The results suggest that the use of resonance frequency analysis by an electromagnetic pulse issensitive and hence effective to determine the implant stability during osseointegration process and undervarious surrounding bone conditions. (Int Chin J Dent 2008; 8: 1-9.)
Key Words: bone, electromagnetic impulse, finite element analysis, osseointegration, resonance frequency.

Introduction
Osseointegration of a dental implant is a dynamic process strongly correlating to factors of biology,
biomechanics as well as clinical technique. Both establishment and maintenance of osseointegration require
implant stability.1-5 The clinical measurement of implant stability and osseointegration is important to be able toassess the implant survival and clinical success. The implant stability is determined by the implant boundary
condition.6-8 Osseointegration is characterized by clinical stability of a functionally loaded implant.9 Whenloading is to begin on a given implant, e.g., immediately loading, or loading after first/second-stage surgery, it
would be advantageous if the structure and properties, or biomechanical behaviors of implant-bone interface
could be measured noninvasively and nondestructively using some biomechanical means.

A number of

researchers have used an impulse oscillation method in an attempt to assess the biomechanical state of theimplant-bone interface.10-12 Huang et al.6 proposed a new modal testing method in vitro experiment by applying
a transient force on the tested samples by an impulse hammer. The vibration signal was obtained through a
non-contact acoustic microphone.

Subsequent spectrum analysis enabled the extraction of the resonancefrequency values.
Meanwhile, the use of electronic percussive testing (e.g., Periotest, Siemens AG, Bensheim, Germany) andresonance frequency analysis (RFA, e.g., Osstell, Integration Diagnostics AB, Sweden) provides a possibility toclinically determine implant stability and the ongoing osseointegration process.2,13-16 Many studies have shown
the merit of Periotest device on measurement of implant stability. However, its ability to detect osseointegration
status is still a matter of debate.17,18 A number of in vivo/vitro experiments and numerical simulations haveindicted that the RFA technique could provide relatively more sensitive and precise information compared with1

Deng et al.

Int Chin J Dent 2008; 8: 1-9.

the Periotest device.2,7,19,20 Recently, a new non-contact RFA device (Osstell mentor) has been developed todetect implant stability. This methodology uses a magnetic pulse from a wireless probe to excite the transducer(a metal rod with a permanent magnet on top) that is screwed to an implant or abutment. The hand-heldresonance frequency analyzer is not directly contacted with the transducer.
It has been reported that this magnetic technique can detect changes in stability during early healing process,21
but effect of several factors (e.g., the changes of the implant-bone interface and bone type) on the resonancefrequency measured by means of this technique is not yet fully know. Therefore, the aim of this study is todevelop and evaluate a new non-contact model to determine the resonance frequencies of the dental
implant-bone structure under various osseointegration stages and quality types of surrounding cancellous andcortical bone by applying an electromagnetic (EM) impulse. A sequential coupled method is used for thissimulation by a two-dimensional (2-D) finite element analysis (FEA). The interaction between the EM field andimplant-bone structural field is accomplished via the EM force.

Materials and Methods
Sequential coupled physics analysis
The ANSYS 6.1 FEA software (ANSYS Inc., Canonsburg, PA, USA) is used to perform sequentially coupledphysics analyses in our system, in which the input of one physics analysis depends on the results from theanalysis of another physics. In this study, the EM field analysis and structural analysis are coupled in asequential manner via the EM force. An EM field analysis is performed first to obtain the EM force field. The
EM force is then applied on the dental implant-bone system to perform an analysis of structural dynamics. Since
the electric excitation is harmonic, the resultant EM force will be harmonic. Therefore, harmonic response of thedental implant-bone system is computed in the form of frequency response. Fig. 1 illustrates the procedure usedin this study.

Create a model encompass ing all physics
requirements : electromagnetics & mechanics
Assign attributes to the model
Create physics environment s for both EM anddental implant -bone structur e

Read in EM physics environment

BuccalPalatalSolve for the EM physics environment

Read in dental implant -bone structural physics
environment

Read in coupled -field load from EM physics
environment

Rod

Coil
Air gap
Backiron

Solve for the structural physics environment withthe coupled -field load

Output of frequency response for the dental
implant-bone s tructure

Fig. 1.

Procedure for a sequentially coupledphysics analysis.

X
Z
Y

Fig. 2.

2Overall 2-D FEA model of a dental implant-bonestructure with an EM pulse generator.

Deng et al.

Int Chin J Dent 2008; 8: 1-9.

FEA modelling of implant-bone structure
A 2-D FEA model is created using ANSYS 6.1 (Fig. 2). This model presents a non-threaded titanium implant
encased in a portion of the maxillary bone at the first left premolar region. The implant is modelled with 15 mm
in length and 4 mm in diameter. The configuration of this maxillary cancellous and cortical bone is modelledusing the computed tomography (CT) data of a patient of 68 years old. A layer of cortical bone (with a thicknessof 0.3-2.5 mm) surrounds a core of dense cancellous bone. The material properties of the implant, maxillarycancellous bone and cortical bone are listed in Table 1.22-24
Table1. Material properties of bone, implant, and rod.
Material
Cancellous bone
Cortical bone
Implant
Rod

Young’s modulus (GPa)
0.48
14.4
117
193

Poisson’s ratio
0.3
0.3
0.3
0.3

Density (g/cm3)
0.55
1.77
4.5
7.8

In the FEA model (Fig. 2), a 15 mm in length stainless steel rod is attached into the implant. This rod is
excited by an EM force generated by a modified solenoid actuator with an alternating voltage-fed coil. A thinlayer of air gap is modelled between the coil, the rod and the pole faces of the back iron. The details of theactuator geometry and material properties are listed in Table 2. The material properties of the rod are presented
in Table 1. Both element types of the magnet and implant-bone structure and material properties of eachcomponent are stored in this FEA model.
As presently defined, the mechanism of osseointegration is a very high rate of living bone modelling andremodelling within about 1 mm of the implant surface.25,26 Within this FEA model, a layer of 0.2-mm-thick
implant-bone interfacial tissue is created to simulate its biologic change during osseointegration process. The
implant is assumed to be inserted into the center of the alveolar ridge. The quadrilateral solid elements are used
to mesh the implant-bone model. The interfaces between the cortical and cancellous bone, cancellous bone andinterfacial tissue, implant and interfacial tissue are assumed to be perfectly connected.
Table 2. Parameters of the actuator geometry and material properties.
Coil
Turns
Across area
Permeability
1*
650
8×10-6 m2
Rod
LengthWidthPermeability
1.5×10-2 m
1.4×10-3 m
2,000*
Back ironThickness
Permeability
1.5×10-3 m
1,000*Air
Gap
Permeability
5×10-4 m
1**from ANSYS release 6.1 documentation. ANSYS Inc., Canonsburg, PA, USA.

Resistivity
3×10-8*
Resistivity
7×10-7*The literature data for the mechanical properties of the dental implant-bone interfacial tissues are veryscare.27-29 In this study, the same value for Young’s modulus of the interfacial tissue (Eit) is set both for the
implant-cortical bone interface and the implant-cancellous interface at each healing stage. The Eit is given
different values in a series of calculations, ranging from 10% of Young’s modulus of cancellous bone (Eca=480
MPa) up to 100% of Eca, in steps of 10 % of Eca, in order to simulate the healing process. The very low values of3

Deng et al.

Int Chin J Dent 2008; 8: 1-9.

Eit correspond to the very early stages of healing where provisional connective tissue (e.g., newly formed vessels,
fibroblasts, mesenchymal cells, osteoid) bridges the interface, while the higher values of Eit correspond to laterstages where formation of bony callus and mature bone (e.g., newly formed lamellar, woven bone) occurs. It is
assumed that the value of Eit is equal to Eca at the final stage of osseointegration. Although the real density of
the interface tissue may be changing during the osseointegration process due to collagen reorganization andmineralization, the density of the interface tissue is held constant at 0.1 g/cm3 since our main interest is on theinfluence of Eit on the vibrating behaviors of the implant-bone structure. For each of these FEA models, thePoisson’s ratio of the interface tissue is varied: 0.1, 0.2, 0.3, and 0.4, to analyze its influence on the resonancefrequencies.
According to the Lekholm and Zarb classification,30 four types of surrounding bone quality (Q1, Q2, Q3, and
Q4) are simulated to evaluate their effects on the resonance frequencies. The created bone model, as shown in
Fig. 2, can be classified as Q3 in which a thin layer of cortical bone (with a thickness of 0.3-2.5 mm) surrounds acore of dense cancellous bone (with a density of 0.55 g/cm3). The Q1, Q2 and Q4 bone are then created based on
Q3 model. In Q1 model, the mechanical properties of the entire bone block are set as cortical bone (Fig. 3a). In
Q2 model, the material properties is equal to Q3, but with a thick layer of cortical bone (0.8-3.0 mm, Fig. 3b).
The Q4 model has the same geometric configuration as Q3 (Figs. 2 and 3c), but the density of cancellous bone isdecreased to 0.275 g/cm3. The correlation between the Young’s modulus and density of bone can be expressed
as follows: E=Cρ3 (1), where E is the Young’s modulus of bone, C is a constant, and ρ is the bone density. This
formula is used to determine the Young’s modulus of cancellous bone (E´ca) in Q4 model. According to thematerial properties of cancellous bone listed in Table 2, the constant C can be calculated as 2,885. E´ca is thencalculated as 60 MPa. In each of the four types of models, the Eit is altered form 48 to 480 MPa in increments of
48 MPa. The Poisson’s ratio and density values for the interface are defined as 0.3 and 0.1 g/cm3, respectively.

X

X

Z
Y

Y

(a)

X
Z

Z

Y

(b)

(c)

Fig. 3. 2-D FEA models of (a) Q1 model: almost entire jaw is comprised of cortical bone; (b) Q2 model: athick layer of cortical bone surrounds a core of dense cancellous bone; (c) Q4 model: a thin layer ofcortical bone surrounds a core of low-density cancellous bone.

EM and structural physics environments
The EM physics environment is created by assigning the 2-D magnetic element and material properties to theactuator components. The implant and its surrounding tissues are specified as a null element type. A 2-D
harmonic magnetic analysis is performed to calculate the EM force excited by a 12 V alternating voltage fed into4

Deng et al.

Int Chin J Dent 2008; 8: 1-9.

the coil. The frequency of the alternating voltage is 20 kHz. The magnetic flux produced by the coil current isassumed to be so small that no saturation of the iron occurred. The flux leakage out of the iron at the perimeterof the model is assumed to be negligible. The structural solution is also a harmonic analysis. Before creating thestructural physics environment, the boundary conditions and loads of the EM physics environment arecompletely removed. The 2-D solid structural element type and materials are reset to the rod, implant and its
surrounding bones. The null element type is specified in the air, coil and iron regions. This model is restrained
from motion in any direction at all nodes on the buccal and palatal sides of the cortical bone.
EM and structural solution
The EM analysis is performed by reading the created EM physics environment file. The resulting magnetic
force will be used as input in the structural analysis. Then it reads the structural physics environment file andreads the magnetic force from the previous EM analysis for the solution of the harmonic response analysis of
implant-bone structure. Finally, the resonance frequencies of the implant-bone structure can be obtained by
identifying the frequency at which the peak response quantity of displacements is obtained. In this work wefocus on only the fundamental resonance frequency.

Results
EM analysis
Fig. 4 shows the flux lines distribution in the components of the actuator. It can be observed that no flux
leakage occurred out of the back-iron. As shown in Fig. 5, the maximum magnetic flux density can be found in
the interface between the air and rod. The summarized magnetic forces on the rod by Maxwell stress tensor
approach were 7.96E-5 N/m for Force-X, and 1.67E-2 for Force-Y. The forces along the Y-axis and X-axis
present an attractive force and a drive force, respectively.

(Unit: Tesla)ironFig. 4.

Fig. 5.

Contour of 2-D flux distribution in the EM field.

Magnitude of the flux density distribution in the EM
field.

Structural analysis
Before applying the harmonic force generated from the EM filed, modal analysis is carried out to determine
the first natural frequency of each FEA model. These frequencies are used as a reference data to verify theefficiency and accuracy of EM-structural sequential simulations. The computed resonance frequencies are very
close to the nature frequencies of the dental implant-bone structure (p>0.99). The Young’s modulus, Poisson’s

5

Deng et al.

Int Chin J Dent 2008; 8: 1-9.

ratio of the implant-bone interfacial tissue and the surrounding bone quality affect the resonance frequencies. It
is found that the Young’s modulus of the interfacial tissue affects resonance frequency most significantly. The
resonance frequency increases with the increase in the Young’s modulus (p<0.0001; Fig. 6). An increase in
Poisson’s ratio results in small increase in resonance frequency, however, this influence is not staticallysignificant (p>0.99; Fig. 6). The bone quality has a significant effect on resonance frequency, with lower

Resonance frequency (Hz)Resonance frequency (Hz)resonance frequency in the implant’s surrounding softer bone (p<0.0001; Fig. 7).

9000
8500
8000

v=0.1

7500

v=0.2
v=0.3

7000

v=0.4

9500
9000
8500
8000
7500
7000
6500
6000
5500

6500
48

96

5000

144 192 240 288 336 384 432 480

Q1Young's modulus (MPa)

Q2

Q3

Q4

Bone typeFig. 6.
Influence of Young’s modulus and Poisson’s ratio (v) of theimplant-bone interfacial tissue on the resonance frequency.

Fig. 7.
Influence of type of bone quality according to the
Lekholm-Zarb index on the resonance frequency.

Discussion
It is well known that the resonance frequency can be used as an important parameter to determine theboundary conditions of a mechanical structure.6,19,33 In implant dentistry, the RFA technique has been adopted
as an effective means to evaluate the relationship between implant stability and implant surrounding conditions
such as osseointegration degree. This study applies a sequential coupled physics analysis to compute theresonance frequencies of the dental implant-bone structure subjected to an excitation of an alternating
voltage-fed actuator.
In the EM analysis, the coil is fed with an alternating voltage and produced a local alternating magnetic field(Figs. 4 and 5). There is no flux leakage occurring out of the back-iron. The maximum flux density can be seenin the interface between the air and rod. The magnetic forces acting on the rod obtained using Maxwell stressapproach are very low and the resulted amplitude of the vibration is very small, hence stresses generated to theimplant-bone interfacial tissue are also so small, so as to avoid any damage to the dental implant-bone system.
The induced heating effect on the implant-bone interface tissue can also be negligible due to this pulse withintermediate frequency applied in a very short time and very low energy level.34
In the implant-bone structural analysis, the results confirm the fact that the resonance frequency issignificantly influenced by the implant surrounding conditions2,7,19,35,36 and suggest that this sequential coupled
method is effective to obtain the resonance frequency that reflect the property of the implant surrounding tissues
and hence the osseointegration status. Previous studies have indicated that the clinical success of an implantdepends largely on the biomechanical state of the implant-bone interface.25,27,30
Recently, RFA combined with other destructive or nondestructive techniques, such as removal torquemeasurement, histological evaluation, radiography and CT have been applied to determine the dental implantbiomechanical behaviors in vivo or in vitro tests. A number of observations have shown that the resonancefrequency corresponds well to the measurements obtained by the techniques mentioned above because the bony

6

Deng et al.

Int Chin J Dent 2008; 8: 1-9.

modelling and remodelling on the implant-bone interfacial layer during healing process resulted in an increase instability.37-41 From a biomechanical point of view, the effects of material properties of this layer can be assessedby considering an increase in its stiffness during the process of osseointegration.25,28,29,42
In the present study, increasing resonance frequencies can be seen with increasing Young’s modulus (Fig. 6),
which suggests that the increase in implant stability observed are attributed to an increase in the interface
stiffness of implant-bone structure duo to new bone formation there.43 It is also interesting to observe in Fig. 6that resonance frequencies increase a little with the increase in Poisson’s ratio. These findings can also beinterpreted based on the theory of vibration:2,7,33,44 f=(2π)-1(k/m)0.5 (2), where k stands for the stiffness of the
support of the surrounding tissue to the implant, m is the mass of the implant, and f is the fundamental resonancefrequency.

In the step of simulation of osseointegration process, the configuration of implant and thesurrounding tissues and their density are the same. Therefore, the resonance frequency of the structure would
only be associated with its mechanical properties. According to the relations between the elasticity constants of
an isotropic material45,46 and Equation (2), an increase in Young’s modulus or Poisson’s ratio would result inincrease in the resonance frequency values, which is also in line with the previous findings and with thevibration theory. However, the Poisson’s ratio has no significant effect on the resonance frequency (p>0.99)
because the increment of Poisson’s ratio is limited.
According to the degree of bone density and drilling resistance experienced by the surgeon, the bone quality isranked from type 1 to 4.30 It is evident that decrease in bone quality results in decrease in implant stability(p<0.0001; Fig. 7), which can be explained by the Equation (2). With Q4 bone, for example, the overall stiffnessof the bone is less because of the thin cortical layer and large cancellous bone core of low density. The dataobtained also agree with the findings of previous studies.38,47-49 They found a correlation between the bonequality, as assessed by using the installation/cutting torque measurement, CT evaluation, and RFA. In this study,
the highest resonance frequency is found in Q1 model. In contrast, the implant inserted in Q4 bone has the lowest
value, which suggests that lower interface restriction would result in lower initial stability of a dental implant at
the time of placement. The results can be explained in part by the fact that implant replacement in Q4 bone typehas a higher failure rate than the other three types50-52 and the fact that lower implant stability level are obtainedfor implant in the maxilla than in the mandible.53,54
In order to completely understand the healing process adjacent to the implant, a more realistic situation of theimplant-bone-EM pulse system is needed in the future research. A detailed three-dimensional (3-D) nonlinear
dental implant-bone model is needed for further determination of the implant stability in an EM field. A 3-D
EM physics field, which is more difficult to generate than a 2-D modelling and requires much more computerresource, is demanded. The influence of the flux leakage out of the iron at the perimeter of the model and thesaturation of the iron should be evaluated. The EM actuator model should be created with a layer of air
surrounding the iron equal to or greater than the maximum radius of the iron or put in an open (infinite) domain.
The changes of distance and angle between the actuator and the rod have to be modelled to study their effect on
response of the implant-bone structure.

References
1. Friberg B, Jemt T, Lekholm U. Early failures in 4641 consecutively placed Branemark dental implants: a study from stage 1
surgery to the connection of completed prostheses. Int J Oral Maxillofac Implants 1991; 6: 142-6.
2. Meredith N, Alleyne D, Cawley P. Quantitative determination of the stability of the implant-tissue interface using resonancefrequency analysis. Clin Oral Implants Res 1996; 7: 261-7.

7

Deng et al.

Int Chin J Dent 2008; 8: 1-9.

3. Nedir R, Bischof M, Szmukler-Moncler S, Bernard JP, Samson J. Predicting osseointegration by means of implant primarystability. Clin Oral Implants Res 2004; 15: 520-8.
4. Gedrange T, Hietschold V, Mai R, Wolf P, Nicklisch M, Harzer W. An evaluation of resonance frequency analysis for thedetermination of the primary stability of orthodontic palatal implants. A study in human cadavers. Clin Oral Implants Res
2005; 16: 425-31.
5. Ostman PO, Hellman M, Wendelhag I, Sennerby L. Resonance frequency analysis measurements of implants at placement
surgery. Int J Prosthodont 2006; 19: 77-83.
6. Huang HM, Pan LC, Lee SY, Chiu CL, Fan KH, Ho KN. Assessing the implant/bone interface by using natural frequency
analysis. Oral Surg Oral Med Oral Pathol Oral Radiol Endod 2000; 90: 285-91.
7. Pattijn V, Van Lierde C, Van der Perre G, Naert I, Vander Sloten J. The resonance frequencies and mode shapes of dental
implants: Rigid body behaviour versus bending behaviour. A numerical approach. J Biomech 2006; 39: 939-47.
8. Lachmann S, Laval JY, Jager B, et al. Resonance frequency analysis and damping capacity assessment. Part 2: peri-implantbone loss follow-up. An in vitro study with the Periotest and Osstell instruments. Clin Oral Implants Res 2006; 17: 80-4.
9. Albrektsson T, Zarb G. Current interpretations of the osseointegrated response: clinical significance. Int J Prosthodont 1993;
6: 95-105.
10. Kaneko T. Pulsed oscillation technique for assessing the mechanical state of the dental implant-bone interface. Biomaterials
1991; 12: 555-60.
11. Elias JJ, Carollo JS, Brunski JB, Scarton HA. Noninvasive method for measuring the Integrity of implant-tissue Interfaces.
Bioengineering Conference, BED-Vol. 24. ASME, NY, 1993: 327-30.
12. Elias JJ, Brunski JB, Scarton HA. A dynamic modal testing technique for noninvasive assessment of bone-dental implantinterfaces. Int J Oral Maxillofac Implants 1996; 11: 728-34.
13. Olive J, Aparicio C. The Periotest method as a measure of osseointegrated oral implant stability. Int J Oral Maxillofac
Implants 1990; 5: 390-400.
14. Meredith N, Book K, Friberg B, Jemt T, Sennerby L. Resonance frequency measurements of implant stability in vivo. A
cross-sectional and longitudinal study of resonance frequency measurements on implants in the edentulous and partiallydentate maxilla. Clin Oral Implants Res 1997; 8: 226-33.
15. Meredith N, Shagaldi F, Alleyne D, Sennerby L, Cawley P. The application of resonance frequency measurements to study
the stability of titanium implants during healing in the rabbit tibia. Clin Oral Implants Res 1997; 8: 234-43.
16. Simunek A, Vokurkova J, Kopecka D, et al. Evaluation of stability of titanium and hydroxyapatite-coated osseointegrated
dental implants: a pilot study. Clin Oral Implants Res 2002; 13: 75-9.
17. Derhami K, Wolfaardt JF, Faulkner G, Grace M. Assessment of the periotest device in baseline mobility measurements of
craniofacial implants. Int J Oral Maxillofac Implants 1995; 10: 221-9.
18. Caulier H, Naert I, Kalk W, Jansen JA. The relationship of some histologic parameters, radiographic evaluations, andPeriotest measurements of oral implants: an experimental animal study. Int J Oral Maxillofac Implants 1997; 12: 380-6.
19. Huang HM, Lee SY, Yeh CY, Lin CT. Resonance frequency assessment of dental implant stability with various bone qualities:
a numerical approach. Clin Oral Implants Res 2002; 13: 65-74.
20. Lachmann S, Jager B, Axmann D, Gomez-Roman G, Groten M, Weber H. Resonance frequency analysis and damping
capacity assessment. Part I: an in vitro study on measurement reliability and a method of comparison in the determination ofprimary dental implant stability. Clin Oral Implants Res 2006; 17: 75-9.
21. Valderrama P, Oates TW, Jones AA, Simpson J, Schoolfield JD, Cochran DL. Evaluation of two different resonancefrequency devices to detect implant stability: a clinical trial. J Periodontol 2007; 78: 262-72.
22. O’Mahony AM, Williams JL, Spencer P. Anisotropic elasticity of cortical and cancellous bone in the posterior mandible
increases peri-implant stress and strain under oblique loading. Clin Oral Impl Res 2001; 12: 648-57.
23. Lang LA, Kang B, Wang RF, Lang BR. Finite element analysis to determine implant preload. J Prosthet Dent 2003; 90:539-46.
24. Zhang QH, Tan SH, Chou SM. Investigation of fixation screw pull-out strength on human spine. J Biomech 2004; 37: 479-85.
25. Lindhe J, Karring T, Lang NP. Clinical periodontology and implant dentistry. 4th ed. Oxford: Blackwell Science; 2003. p.
809-20.
26. Huja SS, Roberts WE. Mechanism of osseointegration: Characterization of supporting bone with indentation testing andbackscattered imaging. Seminars in Orthodontics 2004; 10: 162-73.
27. Brunski JB, Puleo DA, Nanci A. Biomaterials and biomechanics of oral and maxillofacial implants: current status and future
developments. Int J Oral Maxillofac Implants 2000; 15: 15-46.
28. Natali AN, Pavan PG, Ruggero AL. Analysis of bone-implant interaction phenomena by using a numerical approach. Clin Oral
Implants Res 2006; 17: 67-74.
29. Natali AN, Pavan PG, Schileo E, Williams KR. A numerical approach to resonance frequency analysis for the investigation oforal implant osseointegration. J Oral Rehabil 2006; 33: 674-81.
30. Lekholm U, Zarb GA. Patient selection and preparation. In: Branemark PI, Zarb GA, Albrektsson T. Eds. Tissue-integrated
prostheses: osseointegration in clinical dentistry. Chicago: Quintessence Publishing; 1985. p. 199-209.
31. Carter DR, Hayes WC. The compressive behavior of bone as a two-phase porous structure. J Bone Jt Surg 1977; 59A:
954-62.
32. Weinans H, Huiskes R, Grootenboer HJ. Effects of material properties of femoral hip components on bone remodeling. J
Orthop Res 1992; 10: 845-53.
33. Thomson WT, Dahleh MD. Theory of vibration with applications. New York: Prentice-Hall; 1998. p. 16-48.
34. Litvak E, Foster KR, Repacholi MH. Health and safety implications of exposure to electromagnetic fields in the frequency
range 300Hz-10MHz. Bioelectromagnetics 2002; 23: 68-82.
35. Bischof M, Nedir R, Szmukler-Moncler S, Bernard JP, Samson J. Implant stability measurement of delayed and immediately
loaded implants during healing. Clin Oral Implants Res 2004; 15: 529-39.
36. Ostman PO, Hellman M, Wendelhag I, Sennerby L. Resonance frequency analysis measurements of implants at placement
surgery. Int J Prosthodont 2006; 19: 77-83.
37. Sul YT, Johansson CB, Jeong Y, Wennerberg A, Albrektsson T. Resonance frequency and removal torque analysis of
implants with turned and anodized surface oxides. Clin Oral Implants Res. 2002; 13: 252-9.
38. Nkenke E, Hahn M, Weinzierl K, Radespiel-Troger M, Neukam FW, Engelke K. Implant stability and histomorphometry: acorrelation study in human cadavers using stepped cylinder implants. Clin Oral Implants Res 2003; 14: 601-9.
39. Buchter A, Kleinheinz J, Wiesmann HP, et al. Biological and biomechanical evaluation of bone remodelling and implantstability after using an osteotome technique. Clin Oral Implants Res 2005; 16: 1-8.

8

Deng et al.

Int Chin J Dent 2008; 8: 1-9.

40. Sennerby L, Persson LG, Berglundh T, Wennerberg A, Lindhe J. Implant stability during initiation and resolution ofexperimental periimplantitis: an experimental study in the dog. Clin Implant Dent Relat Res 2005; 7: 136-40.
41. Buchter A, Joos U, Wiesmann HP, Seper L, Meyer U. Biological and biomechanical evaluation of interface reaction at conicalscrew-type implants. Head Face Med 2006; 2: 5.
42. Brunski JB. Biomechanical factors affecting the bone-dental implant interface. Clin Mater 1992; 10: 153-201.
43. Johansson CB, Albrektsson T. A removal torque and histomorphometric study of commercially pure niobium and titanium
implants in rabbit bone. Clin Oral Implants Res 1991; 2: 24-9.
44. Fertis DG. Mechanical and structural vibrations. New York: Wiley; 1995. p. 41-196.
45. Bertholet JM. Composite materials: mechanical behavior and structural analysis. New York: Springer; 1998. p. 121-30.
46. Hosford WF. Mechanical behavior of materials. New York: Cambridge University Press; 2005. p. 21-38.
47. Friberg B, Sennerby L, Roos J, Lekholm U. Identification of bone quality in conjunction with insertion of titanium implants. A
pilot study in jaw autopsy specimens. Clin Oral Implants Res 1995; 6: 213-9.
48. Friberg B, Sennerby L, Linden B, Grondahl K, Lekholm U. Stability measurements of one-stage Branemark implants during
healing in mandibles. A clinical resonance frequency analysis study. Int J Oral Maxillofac Surg 1999; 28: 266-72.
49. Friberg B, Sennerby L, Meredith N, Lekholm U. A comparison between cutting torque and resonance frequency
measurements of maxillary implants. A 20-month clinical study. Int J Oral Maxillofac Surg 1999; 28: 297-303.
50. van Steenberghe D, Lekholm U, Bolender C, et al. Applicability of osseointegrated oral implants in the rehabilitation of partial
edentulism: a prospective multicenter study on 558 fixtures. Int J Oral Maxillofac Implants 1990; 5: 272-81.
51. Jaffin RA, Berman CL. The excessive loss of Branemark fixtures in type IV bone: a 5-year analysis. J Periodontol 1991; 62:
2-4.
52. Fugazzotto PA, Gulbransen HJ, Wheeler SL, Lindsay JA. The use of IMZ osseointegrated implants in partially and completely
edentulous patients: success and failure rates of 2,023 implant cylinders up to 60+ months in function. Int J Oral Maxillofac
Implants 1993; 8: 617-21.
53. Sennerby L, Meredith N. Resonance frequency analysis: measuring implant stability and osseointegration. Compend Contin
Educ Dent 1998; 19: 493-8.
54. Barewal RM, Oates TW, Meredith N, Cochran DL. Resonance frequency measurement of implant stability in vivo on implants
with a sandblasted and acid-etched surface. Int J Oral Maxillofac Implants 2003; 18: 641-51.

Correspondence to:
Dr. Deng Bin
Centre for Advanced Computations in Engineering Science (ACES)
Department of Mechanical Engineering, National University of Singapore
10 Kent Ridge Crescent, Singapore, 119260
Fax: +65-6516-4795 E-mail: mpedb@nus.edu.sg
Received September 29, 2007. Accepted January 30, 2008.
Copyright ©2008 by the International Chinese Journal of Dentistry.

9