Peri-implant Bone Remodeling Around an Extraction Socket: Predictions of Bone Maintenance by Finite Element Method

Abstract

Purpose:
The aim of this study was to investigate peri-implant bone remodeling as a response to biomechanical factors, including implant size and contour, magnitude of occlusal load, and properties of osteogenic bone grafts through the use of a computational algorithm.

Materials and methods:
A bone-remodeling algorithm was incorporated into the finite element method, where bone remodeling takes place as a result of the biomechanical alteration caused by dental implant placement and continues until the difference between the homeostatic state and the altered state is minimized. The site-specific homeostatic state was based on a model consisting of a natural tooth. Three long (11-mm) implants and two short (5-mm) implants were investigated. A three-dimensional segment of the mandible was constructed from a computed tomographic image of the premolar region, and an extraction socket was filled with bone graft.

Results:
Generally, the extent of bone loss in the cortical region was greater and denser bone developed at both the implant crest and apex with increased occlusal loads. The areas between implant threads were prone to bone resorption. Bone graft materials that were relatively stiff and that had high equilibrium stimulus values appeared to cause increased bone loss.

Conclusions:
Short implants are better for conserving the mechanotransductive signaling environment of the natural tooth than long implants. Also, short implants are predicted to lead to less interfacial bone loss at high loads over the long term, while long implants are associated with a more consistent level of bone loss for different amounts of loading. It is also predicted that in the long term, bone grafts with relatively low elastic modulus lead to lower levels of interfacial bone loss.

Full text

The International Journal of Oral & Maxillofacial Implants e39
The use of dental implants has become an eec-
tive treatment modality to restore partial and/or
complete edentulism.1 The traditional delayed place-
ment protocol requires that an implant remain sub-
merged for a healing period, which may take up to
several months, before the placement of an abutment
and prosthesis for functional loading.2 Advances in
implant technology and continuous clinical research
have resulted in new treatment concepts, such as
early and immediate functional loading, which reduce
treatment time and increase patient comfort during
healing.3 When an implant is placed in an extraction
socket, a gap may occur as a result of the incongruence
of the dental implant with the bony socket walls. Bot-
ticelli et al4,5 demonstrated that such a marginal defect
can be resolved by new bone formation during heal-
ing. Depending on the extent of hard and soft tissue
changes following tooth loss, various site preparation
techniques may be utilized to enhance mechanical sta-
bility of an implant and esthetics of the implant-treat-
ed area. It is often necessary to use grafting material to
ll the peri-implant gap.6
It has been shown that long-term implant stabil-
ity is related to the quality of the peri-implant bone
following remodeling.7 The remodeling process is
carried out by basic multicellular units through the
interplay between osteoclastic and osteoblastic cell
1 Graduate Student, Northeastern University, Depar tment of
Mechanical Engineering, Boston, Massachusetts.
2 Professor, Division of Periodontology, Eastman Institute for
Oral Health, University of Rochester, School of Medicine and
Dentistry, Rochester, New York.
3 Professor, Tufts University, School of Dental Medicine,
Boston, Massachusetts.
4 Professor, Northeastern University, Department of Mechanical
Engineering, Boston, Massachusetts.
Correspondence to: Dr Sinan Müftü, Department of
Mechanical Engineering, Northeastern University, Boston, MA
02115. Fax: +617-373-2921. Email: s.muftu@neu.edu
Peri-Implant Bone Remodeling Around an
Extraction Socket: Predictions of Bone Maintenance
by Finite Element Method
Hsuan-Yu Chou, MSc1/Georgios Romanos, DDS, PhD, Dr Med Dent2/
Ali Müftü, DMD, PhD3/Sinan Müftü, PhD4
Purpose: The aim of this study was to investigate peri-implant bone remodeling as a response to biomechanical
factors, including implant size and contour, magnitude of occlusal load, and properties of osteogenic bone
grafts through the use of a computational algorithm. Materials and Methods: A bone-remodeling algorithm
was incorporated into the nite element method, where bone remodeling takes place as a result of the
biomechanical alteration caused by dental implant placement and continues until the difference between
the homeostatic state and the altered state is minimized. The site-specic homeostatic state was based
on a model consisting of a natural tooth. Three long (11-mm) implants and two short (5-mm) implants were
investigated. A three-dimensional segment of the mandible was constructed from a computed tomographic
image of the premolar region, and an extraction socket was lled with bone graft. Results: Generally, the
extent of bone loss in the cortical region was greater and denser bone developed at both the implant crest
and apex with increased occlusal loads. The areas between implant threads were prone to bone resorption.
Bone graft materials that were relatively stiff and that had high equilibrium stimulus values appeared to
cause increased bone loss. Conclusions: Short implants are better for conserving the mechanotransductive
signaling environment of the natural tooth than long implants. Also, short implants are predicted to lead to
less interfacial bone loss at high loads over the long term, while long implants are associated with a more
consistent level of bone loss for different amounts of loading. It is also predicted that in the long term, bone
grafts with relatively low elastic modulus lead to lower levels of interfacial bone loss. In t J Oral Max IllOfac
IMplan ts 2012;27:e39–e48
Key words: bone graf ts, bone remodeling, dental implants, extraction socket, site- specic stimulus, wide
implants

Chou et al
e40 Volume 27, Number 4, 2012
functions, leading to bone resorption or bone gain.
The hypothesis of bone remodeling induced by me-
chanical stimulation, which was rst suggested by
Wol,8 has been generally accepted and has become
the basis of various mathematical models for predict-
ing bone morphology and density. Bone remodeling
theories distinguish between external remodeling,
where bone is added or removed at the periosteal and
endosteal surfaces to result in changes of shape, and
internal remodeling, which is characterized by changes
in apparent bone density.9,10 Strain, stress, and strain
energy density have been suggested as remodel-
ing stimuli.11–14 Two well known remodeling theories
introduced by Carter et al13 and Huiskes et al14 were
incorporated into nite element models (FEMs) to
mathematically model the bone density distribution
in the proximal femur. These remodeling theories have
also been used to study bone remodeling around or-
thopedic implants14 and the bone structure of other
bone regions, such as the acetabulum, proximal tibia,
metacarpals, and calcaneus.15
Numerous clinical and histologic studies have been
carried out to evaluate osseointegration to improve
dental implant designs, surfaces, and surgical protocols.
Study of mathematical models of dental bone remod-
eling can help clarify the biomechanical factors con-
trolling the short- and long-term survival of implants.
Recently, Lin et al16 suggested that long-bone remod-
eling theories may be applicable to study the bone re-
modeling that takes place in dental implant treatment.
Reina et al17 and Lin et al18 simulated mandibular bone
remodeling with and without a dental implant, respec-
tively, and both groups observed signicant consis-
tency with clinical evaluations. Occlusal overloading is
believed to be a major cause of marginal bone loss; this
was demonstrated by including the condition of over-
load resorption in remodeling theories.19–21 Lian et al22
and Chou et al23 showed long-term peri-implant bone
density patterns that were similar to those observed in
an animal study by Watzek et al.24 A common thread
in these studies is the assumption of a homeostatic re-
modeling stimulus with a constant value, independent
of location. This implies that bone remodels toward a
homogenous biomechanical eld, despite the fact that
the biologic environment (ie, the cells and the nutri-
ents) within bone sites is not homogenous.
The present study hypothesized that bone re-
modeling is regulated by site-specic homeostatic
remodeling (attractor) stimuli, which must be similar
to those induced by a natural tooth in its supporting
structures. The eects of various biomechanical fac-
tors, including implant dimensions, implant designs,
magnitude of occlusal load, and properties of osteo-
genic bone grafts, on peri-implant bone remodeling
are investigated.
MATERIALS AND METHODS
Bone Remodeling Algorithm
Bone remodeling depends on mechanotransduction,
in which the eect of the external loading induces bio-
chemical activity in the basic multicellular units, which
eventually results in bone density adjustments. Various
remodeling stimuli have been suggested to initiate
this response. Huiskes et al14 proposed the remodeling
stimulus (S) to be strain energy per unit mass:
(equation 1)
where u is the strain energy density, ρ is the apparent
bone density, t is time, and r⃑ is the position vector in
the bone.
The bone remodeling rate is expressed in terms of
bone density change, and it is a nonlinear function of
the remodeling stimulus14: (equation 2)
Here, K = K(rˉ) is the attractor stimulus representing the
homeostatic loading conditions of the bone, Af and
Ar are formation and resorption coecients, respec-
tively, and s is a coecient that represents the width of
the dead zone. The thresholds of bone formation and
bone resorption are K(1 + s) and K(1 – s), respectively.
Remodeling stimuli that fall within the dead zone do
not evoke bone remodeling. However, if the bone is
subjected to a mechanical stimulus that is larger than
the threshold value of K(1 + s), its density and elastic
modulus will increase over time. Conversely, if the me-
chanical stimulus is lower than the threshold value of
K(1 – s), the density and elastic modulus are reduced.
Clinical studies show that bone loss takes place at a
faster rate than formation. Thus, the exponents 2 and 3
are used in equation 2 for formation and resorption, re-
spectively.14 Carter and Hayes showed that the elastic
modulus of bone is a function of the bone’s apparent
density, as follows25:
(equation 3)
E = Cρ3
where C = 3.79 and E is the elastic modulus (in GPa, if
ρ is in kg/m3). Equation 2 is solved iteratively by the
forward Euler time integration as follows:
(equation 4)
S(r,t) =⃑u(r,t)⃑
ρ
(r,t)⃑
d
ρ
Af [S – (1 + s) K]2,
Ar [S – (1 – s) K]3,
0,
S ≥ K (1 + s)
S ≤ K (1 – s)
K (1 – s) <S < K (1 + s)=
dt
0,=
ρ
j
m
ρ
j–1
m
ρ
j–1
m+ Ar ∆t [Sj–1 – K (1 – s)]3,
m
+ Af ∆t [Sj–1 – K (1 + s)]2,
mSj-1 ≥ K (1 + s)
m
Sj-1 ≤ K (1 – s)
m
K (1 – s) <Sj-1 < K (1 + s)
m

Chou et al
The International Journal of Oral & Maxillofacial Implants e41
where j indicates the time iteration level and m indi-
cates the spatial location in the FE representation of
the discretized bone. The remodeling constants, Ar and
Af, can be combined with a time step, ∆t, as a single
time integration parameter, A∆t, the value of which
was chosen as 1 × 10–11 after extensive numeric tests
to ensure convergence. The width of the dead zone (s)
was set to be 0.75 according to the literature.26
To determine the site-specic attractor stimuli (K( r⃑)),
the strain energy per unit mass of bone induced by the
occlusal force acting on a natural tooth was rst com-
puted. The eect of the periodontal ligament was ne-
glected in the present study but should be considered
in future studies. The interstitial space resulting from the
incongruence of the dental implant with the extraction
socket was assumed to be occupied by bone graft in the
computational model. The implant was assumed to be
in full contact with the bone graft. A constant value (Kg)
was assigned to represent the attractor stimulus of the
bone graft. This parameter is treated as the potential of
the bone graft to induce bone remodeling.
The remodeling algorithm used in this work is pre-
sented schematically in Fig 1. Bone remodeling is driven
by the dierence between the remodeling stimulus S
caused by the bone-implant-prosthesis complex and
the site-specic homeostatic stimuli K(rˉ). Bone density
around the dental implant continuously adapts to equal-
ize the remodeling stimuli to the homeostatic stimuli.
Creation of the FEM
A planar computed tomographic (CT) image of the
mandibular premolar region, representative of the
buccolingual plane, was digitized with medical imag-
ing software (Mimics, version 12, Materialise) and then
was extruded to a thickness of 80 mm in the mesio-
distal direction to represent a three-dimensional (3D)
segment of the mandible (Fig 2). A 3D model of the
second premolar was created according to the same
set of CT scan images. The morphology of the extrac-
tion socket was determined by removing the premolar
from the model. This leaves a void in the bone that con-
forms to the root form of the second premolar (Fig 2).
Occlusal
load
Bone implant-
prosthesis FEM
Bone tooth
FEM
Remodeling rules Equilibrium
Attractor stimulus, Kg
Remodeling
stimulus, S(r)
⃑
Attractor stimulus, K(r)⃑
Fig 1 Flow chart of the bone adaptation algorithm.
Fig 2 Schematic FEMs of bone -tooth and bone -
implant-prosthesis complexes.

Chou et al
e42 Volume 27, Number 4, 2012
In addition, ve implant designs, including three long
implants (about 3.5 × 11 mm) and two short implants
(about 5 × 5 mm), were modeled based on commer-
cially available designs (Fig 3).
The remodeling algorithm presented in Fig 1 was
implemented into a commercially available FE analy-
sis software package (ANSYS, version 11) via its script
language. The bone-implant and bone-tooth com-
plexes were imported into this modeling environ-
ment. Ten-node tetrahedral solid elements were used
to discretize the bone, the tooth, and the implants.
For the sake of computational eciency, a symmetric
boundary condition was applied to the mesial side of
the buccolingual plane. The modeled mandibular seg-
ment was constrained in all degrees of freedom on
the distal side of the buccolingual plane. The density
of the FE mesh was increased near the bone-implant
interface, where signicant remodeling activities are
expected. Approximately 95,122 elements and 67,307
nodes were used to mesh the long implant system,
and 89,475 elements and 63,583 nodes were assigned
to the short implant system. These numbers were de-
termined based on numeric experiments and previous
studies.27–29 All materials were assumed to be linearly
elastic, homogenous, and isotropic. The material prop-
erties of the implant,27 the cortical bone, the cancel-
lous bone,30–32 the tooth,32 and the prosthesis32 were
obtained from the literature (Table 1).
Autologous bone harvested from the surgical pa-
tient is considered the ideal grafting material because
of its inherent osteogenic benets.33,34 This mate-
rial forms bone directly as a result of the transplanted
bone cells.6 To study the eect of graft properties on
bone remodeling, the material property of the bone
graft was made variable within a range from cancel-
lous to cortical bone.
The magnitude of occlusal loading generated dur-
ing mastication varies among individuals and is de-
pendent on the chewing scheme, food texture, jaw
movement, and alignment of antagonistic teeth.35,36
An axial load acting on the posterior teeth and on an
implant-supported prosthesis was reported to exert
a force in the range of 390 to 880 N and 42 to 412 N,
respectively.37 The lateral component of the occlusal
load was found to be less than 100 N.38 Considering
the aforementioned physiologic range of force magni-
tudes and the existence of both axial and lateral loads
during occlusion, the loading conditions in this study
were simulated by three levels: 100, 300, and 500 N.
All were applied to the tooth or crown at an 11-degree
angle from the axis.
RESULTS
The iterative changes in the bone modulus induced by
bone remodeling around a short implant are present-
ed in Fig 4. The color contours show that most of the
predicted remodeling process was completed by the
rst 50 iterations, and no signicant remodeling activ-
ity took place between the 50th and 100th iterations.
The average bone stimulus (Save) as a function of itera-
tion number is dened as:
(equation 5)
where Ntotal is the total number of bone elements and
Si is the remodeling stimulus of the ith bone element
(Fig 4). The time dependent change of average bone
Table 1 Properties of the Materials Used in
the Analysis
Material Elastic modulus (GPa) Poisson ratio
Titanium implant 113.8 0.34
Cortical bone 13 .7 0.3
Cancellous bone 20.3
Too th 20 0. 3
Prosthesis 80 0.3
Bone graft 2–1 3.7 0.3
1
=Σ
i=1
Save Si
Ntotal
Ntotal
Fig 3 Various implant designs used in this analysis. Units are
given in millimeters.

Chou et al
The International Journal of Oral & Maxillofacial Implants e43
stimulus (Fig 4) shows that remodeling equilibrium is
represented well by 100 iterations. Therefore, in this
study, the total number of iterations was set to 100.
The distribution of the equilibrium remodeling
stimulus for a natural tooth is presented in Fig 5a. It is
clear that the eect of the occlusal force on remodeling
stimulus was high close to the tooth. This equilibrium
stimulus (S(r⃑)) was then used as a location-dependent
attractor stimulus (K(r⃑)) for the rest of the simulations
that involved implants. The remodeling stimuli of the
bone was then calculated when a short implant was
placed in the osteotomy site (Figs 5b and 5c). Because
of the aforementioned mismatch between the implant
size and the socket diameter and shape, bone grafting
was necessary, as shown in the grey volume (Fig 5b).
Bone eventually replaced the graft, both in vivo and
in the computer implementation. The computational
bone-remodeling algorithm requires assignment of
elastic properties (Eg and, νg) and an attractor stimulus
(Kg) to the graft region. The eects of the initial values
of these variables will be presented later. Nevertheless,
for this short implant, the stimulus (S(r⃑)) distribution
values in the rst step and at remodeling equilibrium
(Figs 5c and 5d) were very similar to those of the natu-
ral tooth (Fig 5a).4
The bone graft around the implant was initially as-
sumed to contain a layer of cortical bone in contact
with the implant crest, and the rest of the implant body
was surrounded by cancellous bone (Fig 6). The attrac-
Fig 4 ( Top) Iterative changes in the distribution of elastic mod-
ulus around a dental implant. No signicant remodeling activi -
ties were predicted after 50 iterations. The histor y of average
bone stimulus (Save) shows that acceptable convergence has
been achieved.
Fig 5 (Right) (Left to right) Attractor stimuli distribution of
a bone-tooth model; the attractor stimulus of the bone graft
(grey); initial remodeling stimuli distribution of a bone-implant-
prosthesis model; remodeling stimuli distribution in a bone-im-
plant-prosthesis model in a state of equilibrium.
Fig 6 Initial elastic modulus distribution of bone shows the
cancellous region surrounded by a layer of cor tical bone. Non -
uniform distributions of the elastic moduli of bone are predicted
at equilibrium state under various conditions.

Chou et al
e44 Volume 27, Number 4, 2012
tor stimulus of the graft was chosen as a constant: Kg =
0.5 J/kg. For the rest of the bone, the attractor stimulus
was the site-dependent value K( r⃑), computed for the
natural tooth under the oblique occlusal force, as de-
scribed earlier. Three load levels, 100, 300, and 500 N,
were evaluated for the eect of occlusion on bone re-
modeling. For each load, the K(r⃑) value was computed
separately using the natural tooth model. The predicted
bone elastic modulus (E) distributions in the equilibri-
um state (100 iterations) induced by various load mag-
nitudes for the dierent implants are presented in Fig 6.
For the case in which the implant was subject to
a 100-N occlusal load, elastic modulus distribution in
the subcortical region remained intact for both of the
modeled short implants, except near the implant body.
It was apparent that the bone density, and hence its
elastic modulus, increased around the threads of the
short implants and connected the implants to the
cortical region, resulting in increased stability. How-
ever, stress shielding caused a reduction in bone den-
sity within the implant threads. The thread design also
made a dierence, as can be seen in the comparison
of short 1 and short 2 implants (Fig 6). All three long
implants stimulated the bone in their apical region and
caused a substantial volume of bone to attain cortical
properties. In contrast, the crestal and subcrestal re-
gions of the bone around the long implants expe-
rienced bone density reduction and bone loss. The
extent of this reduction and loss also was dependent
on the implant contour and the thread shape for all
long implants (Fig 6).
Several characteristics were observed when the oc-
clusal load was increased. Generally, the extent of bone
loss in the cortical region increased and a larger area of
dense bone developed at both the implant crest and
apex. In particular, the region of total bone loss (grey
region) enlarged in the cases of long 1 and long 3 im-
plants, but the long 2 and short implants did not in-
duce the same phenomenon. Short implants did not
alter the biomechanical environment as much as the
long implants, which required a substantial amount of
bone densication to reach a homeostatic equilibrium.
The eect of external loading was represented in
terms of the relative amount of interfacial bone loss
(IBL) with respect to a fully osseointegrated scenario
for each implant type (Fig 7). The IBL indicates the
relative surface area of the implant in which the bone
density was reduced to 0 as a consequence of remod-
eling. Figure 7 reveals the distinct dierence between
the short and long implant groups; the short implants
were better at preventing IBL at higher loads, and
the long implants displayed a more consistent IBL re-
sponse at dierent load levels.
The eects of the initial value of the attractor stimu-
lus (Kg) of the graft region on the outcome of bone re-
modeling were also investigated. It was observed that
the remodeling stimulus of the bone around a natural
tooth varied between 0.1 and 0.5 J/kg (Fig 4a). Based
on this observation, three dierent Kg values—0.1,
0.2, and 0.5 J/kg— were assigned to the graft region
(Fig 5b). The results at remodeling equilibrium were
presented in terms of the IBL as a function of Kg for oc-
clusal loads (Fo) of 100, 300, and 500 N. Figures 8a to
8c show, in general, that high IBL at remodeling equi-
librium correlated with high initial Kg values and that
less IBL was predicted with increasing levels of loads
on the implant. The implant length was observed to
add to this behavior in a nonlinear manner; the short
implants appeared to lose considerably less interfacial
bone at high levels of loading, whereas the long im-
plants appeared to be relatively less sensitive to the
load level in terms of the amount of IBL.
To determine the eects of the elastic modulus of
the bone graft on remodeling, three dierent elastic
modulus values (Eg = 2, 7.5, and 13 GPa) were consid-
ered, while the attractor stimulus of the graft and the
occlusal load were set at Kg = 0.5 J/kg and Fo = 100 N,
respectively. The results are presented in terms of IBL
in Fig 8d, where it is apparent that the IBL increased
when the graft stiness was high.
Fig 7 Effect of occlusal load (Fo) on the p ercent IBL for the ve
implant designs can be rendered as Kg = 0.5 J/kg.

Chou et al
The International Journal of Oral & Maxillofacial Implants e45
DISCUSSION
Osseointegration begins with rapid bone healing, and
the initial bony structure is maintained by bone remod-
eling and bone adaptation. Bone healing is a process
of skeletal tissue regeneration that is triggered by trau-
ma, such as fracture or surgical osteotomy, that causes
physical disruption of the mineralized tissue matrix, the
death of cells, and interruption of the blood supply.39
During bone healing, skeletal tissue is originated by the
proliferation and dierentiation of the common pool of
pluripotent mesenchymal stem cells, and the dieren-
tiation pathway that results in the nal phenotype is
at least partially inuenced by mechanical loading.39,40
While mathematical models of tissue dierentiation
have been developed,41 this phase of bone healing was
not modeled in the present work. The work present-
ed here considered the maintenance phase of bone
Fig 8a Effect of attractor stimulus of graft Kg as Fo = 100 N. Fig 8b Effect of at tractor stimulus of graft Kg as Fo = 300 N.
Fig 8c Effect of at tractor stimulus of graft Kg as Fo = 500 N. Fig 8d Effect of elastic modulus of graf t, Eg, on the percent IBL
for the ve implant designs.

Chou et al
e46 Volume 27, Number 4, 2012
remodeling, which is mathematically represented by
the remodeling theory of Huiskes et al.14 This and other
bone remodeling theories have been used to predict
changes in bone density around dental implants and
in remodeling of the mandible in response to other
prosthodontic treatments.16–23 Field et al showed a
correlation between the observed (radiographic) and
computed changes in mandibular bone density in a
combined longitudinal clinical and numeric study of
mandibular bone remodeling induced by a xed par-
tial denture.42 Lin et al18 observed similar correlations
between computed and actual bone density changes
for remodeling around dental implant systems.
Bone remodels around osseointegrated implants.
In a histomorphometric study in dogs, Coelho et al43
found high levels of osteoactivity near the implant
surface. Peri-implant bone remodeling is triggered
by the geometric and material dierences between
a natural tooth and a dental implant. Bone density
gradually adapts to the new conditions by minimizing
the dierence between the current and the reference
remodeling stimuli. It was assumed in this work that
the homeostatic reference stimulus is site-specic and
that its value should be similar to that caused by the
natural tooth. This hypothesis has been used to simu-
late the stress shielding and bone resorption that take
place around hip prostheses.26,44 The present work
showed that, for short implants, remodeling was local-
ized around the implant and decreased with increas-
ing distance from the implant. Short implants were
predicted to keep the bone density distribution closer
to that of the natural tooth.
This work also showed that an increased load on
the implant resulted in decreased levels of IBL, and this
was accompanied by an increase of bone density near
the implant apex. This eect was strongly dependent
on implant length and type and is the result of a few
factors working together. Most important of these is
the fact that bone remodeling redistributes the bone
density to provide better anchorage to counteract the
increased load, resulting in lower IBL.
Increased bone densication was predicted around
the apices of implants. The extent of bone remodeling
around a short implant diered considerably from that
around a long implant. For the long implants modeled
in this work, the load was directly transferred to the
deeper regions of the cancellous bone; this caused rela-
tively high remodeling stimulus S to develop, resulting
in increased bone density near the implant apex. On
the other hand, for the short implants, the dierence
between the homeostatic stimulus K and the remodel-
ing stimulus S was conned to a more localized region
near the apex of the implant, resulting in a more mod-
erate increase in bone density. These eects are clearly
the result of implant dimensions and morphology.
The current predictions, especially for the short im-
plants, showed a degree of resemblance to observa-
tions reported in histologic studies. Watzek et al24
investigated the eects of designs and surface modi-
cations of dental implants on peri-implant bone and
observed a layer of peri-implant cortical bone, with
dense bone regions oriented toward the preexisting
bone. Schenk and Buser7 suggested that the implant
thread tips promote bone growth as a result of their
role in transferring load from the implant to the sur-
rounding bone. Although the present work predicted
several similarities, dierences with respect to clinical
observations exist as a result of the biologic aspects.
Bone grafting is an acceptable and necessary tech-
nique for socket preservation and sinus and ridge aug-
mentation.45 Biomechanical studies have shown that
initial implant stability is improved when the implant
is secured by a greater quantity and better quality of
graft materials.46–48 On the other hand, long-term im-
plant stability is dependent on overall bone remod-
eling and remodeling within the bone graft.49,50 The
results presented in this work show that peri-implant
bone remodeling is inuenced by the initial quality of
the graft material. Lowering the elastic modulus of the
grafted region to the level of cancellous bone (2 GPa)
resulted in relatively less resorption, whereas increas-
ing it to the level of cortical bone (13.7 GPa) induced
relatively more resorption. This observation is attribut-
ed to the nature of bone remodeling, in which a stier
grafting material causes a lower level of strain, which
results in a lower level of remodeling stimulus, thus
shielding the bone into the resorption region of equa-
tion 2. This work thus shows that relatively low graft
stiness encourages the interfacial bone to experi-
ence an adequate remodeling stimulus. This nding is
in agreement with Inglam et al,46 who investigated the
eect of graft stiness on load sharing and suggested
that bone grafting material with a stiness of 2 GPa
demonstrated the optimal load-sharing characteristics
versus a bone graft with a stiness of 11 GPa.
In addition to the mechanical properties of graft
material, the attractor stimulus assigned to the graft
region (Kg), which is assumed to represent the os-
teogenic potential, was also seen to be inuential in
peri-implant bone remodeling. The bone graft in the
present model could only represent osteogenic graft
materials, as the attractor stimulus is related to a me-
chanical signal that can be sensed by osteoblasts. This
work showed that lower values of Kg led to a higher
level of bone formation and thus lower IBL.
In general, the outcome of bone grafting is dicult
to predict because of a variety of factors involved in the
mechanism of healing, including absence of infection,
soft tissue closure, defect morphology, space mainte-
nance, healing time, graft immobilization, blood supply,

Chou et al
The International Journal of Oral & Maxillofacial Implants e 47
growth factors, collagen, and calcium phosphate.6 It
should also be mentioned that the assumption of full
contact between the implant surface and the graft
made in the present study simplied the situation with
respect to clinical reality. The amount of initial contact
between the implant and the grafting material is an-
other variable that could be investigated and that may
potentially inuence the outcome of osseointegration.
Apparently, a non–site-specic constant, Kg, similar to
the attractor stimulus dened in the aforementioned
literature16–23 is insucient and needs to be further
explored. Nevertheless, the choice of Kg based on the
observation of overall stimuli around a natural tooth
that was used in this preliminary work seems to be a
fair approximation. The computational predictions
presented here are also limited by the other simplica-
tions made in this study. In particular, the application
of occlusal loading in an FEM was greatly simplied in
comparison to regular mastication. Determination of
the loading conditions of the jaw during mastication
involves the activity level of each muscle and the con-
straints of the temporomandibular joint.
CONCLUSIONS
The computational bone remodeling work presented
here showed distinct dierences in the bone main-
tenance characteristics around short and long im-
plants. Short implants were predicted to conserve the
mechanotransductive signaling environment of the
natural tooth, whereas the long implants were not. It
was also observed that the short implants were bet-
ter in preventing interfacial bone loss at high loads,
whereas the long implants showed a consistent level
of bone loss at dierent load levels. In this work, the
eects of bone graft properties on long-term bone
maintenance were also studied. It was predicted that,
in the long term, bone grafts with relatively low elastic
modulus in combination with high loads will lead to
lower levels of interfacial bone loss.
ACKNOWLEDGMENT
This work was suppor ted in par t by Bicon Dental Implants (Bos-
ton, Massachusetts) through a research grant to Nor theastern
Uni ve rs it y.
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