Journal of Dental Biomechanics
© The Author(s) 2012
Reprints and permission: sagepub.
It is well established that tooth extraction is followed by a
reduction of the buccolingual as well as apicocoronal
dimension of the alveolar ridge at the edentulous site.
has been suggested that immediate implant placement into
fresh extraction sockets might counteract this catabolic pro-
cess and preserve the dimensions of the alveolar ridge.
However, studies in humans
and experiments in dogs
have belied this hypothesis. In another dog study, it was
found that the resorption of the buccal/lingual walls
occurred in two overlapping phases. In a first phase, the
bundle bone was resorbed and replaced with woven bone.
The second phase included resorption from the outer sur-
face of both bone walls.
It was stated that the reason for
this additional bone loss was not understood. In a dog study,
extraction sockets were found to be filled by woven bone
after 1 month and after 3 months a cortical ridge including
woven and lamellar bone had been formed.
months, woven bone was being replaced with lamellar bone
and bone marrow. The application of freeze-dried bone
allograft in combination with a membrane was found to
improve the ridge dimensions in patients after 6 months
compared to a control, both vertically and horizontally.
studies in dogs, grafting with Bio-Oss™ collagen in extrac-
tion sockets improved the ridge dimensions after 6 months
compared to a control,
while grafting with autologous
bone did not.
The above literature gives the impression that the reason
for bone loss after tooth extraction is unknown. In the year
suggested that the loss of alveolar bone
occurring after tooth loss in the old age is an example of
disuse atrophy. His reasoning was that after tooth loss, the
forces on the bone are reduced, which means that less bone
is needed and that the body gets rid of bone that is not suf-
ficiently used. Our knowledge of bone physiology has
expanded greatly since 1881.
law suggests that bone tissue adapts its mass
and structure to the mechanical demands. A more detailed
discussion on this subject requires some insights in the dis-
cipline mechanics of materials. When a structure, for exam-
ple, the mandible, is loaded, it is deformed. There are
stresses and strains in the structure. An infinitesimal cubic
element in the structure is considered (Figure 1(a)). The
stresses on the surfaces of this cube are expressed: tensile/
compressive stresses perpendicularly to the surfaces and
shear stresses parallel to the surfaces. The cube can be
rotated, so that the shear stresses disappear and we only
have stresses perpendicularly to the surfaces (Figure 1(b)).
These latter stresses are called principal stresses. The cor-
responding strains are called principal strains (Figure 1(c)).
With knowledge of the geometry of a structure, the material
properties and the loads upon the structure the stresses and
Alveolar ridge resorption after tooth
extraction: A consequence of a fundamental
principle of bone physiology
and Anders Halldin
It is well established that tooth extraction is followed by a reduction of the buccolingual as well as the apicocoronal
dimension of the alveolar ridge. Different measures have been taken to avoid this bone modelling process, such as
immediate implant placement and bone grafting, but in most cases with disappointing results. One fundamental principle
of bone physiology is the adaptation of bone mass and bone structure to the levels and frequencies of strain. In the
present article, it is shown that the reduction of the alveolar ridge dimensions after tooth extraction is a natural
consequence of this physiological principle.
bone resorption, tooth extraction, implant
Astra Tech AB, Mölndal, Sweden
Department of Prosthodontics, Faculty of Odontology, Malmö
University, Malmö, Sweden
Stig Hansson, Astra Tech AB, P.O. Box 14, SE-431 21 Mölndal, Sweden.
DBM0010.1177/1758736012456543Journal of Dental BiomechanicsHansson and Halldin
2 Journal of Dental Biomechanics
strains can be calculated.
Figure 2 illustrates the concept
of strain. Figure 2(a) shows a piece of material that is
unloaded. In Figure 2(b), it is subjected to a tensile force.
The piece is elongated. The elongation (ΔL) divided by the
original length (L) gives the strain (ΔL/L). In this case, the
strain is positive. With a compressive load, the piece of
material becomes shorter. The strain is negative. Strains in,
for example, cortical bone are small. For this reason, the unit
microstrain is often used. If the elongation is 1% of the orig-
inal length, the strain is 10,000 microstrain.
There is a wealth of literature testifying of profound
effects of strain on bone mass and bone structure. The
lamellae of cancellous bone are preferentially aligned with
the principal strains caused by the dominating loads.
This enables the most economical use of the bone material.
Changes in loading direction result in changes in the direc-
tions of the principal strains, and the lamellae of the cancel-
lous bone realign with the new principal strain directions.
Petrtýl et al.
found that the Haversian systems of cortical
bone preferentially are aligned with the first principal strain
caused by the dominating loads. This also means an eco-
nomical use of the bone material. The bone mass primarily
depends on the magnitude of the strains
and the number
of strain cycles per time unit.
Based on a compilation of
animal experimental data, Qin et al.
proposed the follow-
ing formula for a daily stress stimulus,
is the daily number of cycles of loading type i, σ
is the stress associated with loading type i and the exponent
m is a constant, the value of which depends on the daily
number of loading cycles. By substituting σ
in equation (1)
/E, where ε
is the strain associated with loading type
i and E is the modulus of elasticity of the bone, a formula
for a daily strain stimulus is obtained (equation (2))
Qin et al.
found that the strain stimulus needed per day
to maintain bone mass could be expressed by the following
y = 10
(5.6 – log
where x is the number of loading cycles per day and y is the
strain magnitude. Rubin et al.
observed that the maximum
bone strains measured in the metacarpal bone of a galloping
horse, the tibia of a running human, the femur of a running
sheep, the humerus of a flying goose and the mandible of a
chewing macaque are remarkably similar, ranging between
2000 and 3500 microstrain. These strains are about 50% of
the yield strain of cortical bone, indicating that nature
applies a safety factor of approximately 2 when designing
bones. The aim of the present study was to investigate
whether the observed changes in alveolar ridge dimensions,
after tooth extraction, can be understood within the frame-
work of established principles of bone physiology.
Methods and results
Bending of a beam
Consider the beam in Figure 3 that is subjected to pure
bending. The beam is assumed to have a symmetrical cross
section. The bending moment (M) gives rise to stresses and
strains in the beam. At the longitudinal axis of the beam, the
stresses and strains are zero. When the strains are below the
yield strain of the material (6000 microstrain for cortical
Figure 1. (a) Tensile/compressive stresses and shear stresses on the surfaces of an infinitesimal cubic element, (b) principal stresses
and (c) principal strains.
Hansson and Halldin 3
bone), there is a linear relationship between stress and
strain. The stresses create an internal bending moment that
exactly counterbalances the external bending moment (M).
The mandible as a beam subjected to
Consider a mandibular tooth. When the tooth is loaded, it
will induce a mechanical stimulation, strains, in the bone
immediately adjacent to the tooth. The loading of more dis-
tant teeth, the action of the masticatory muscles and the
reaction forces at the temporomandibular joints will give
rise to bending moments in the mandible. These bending
moments will also give rise to strains in the bone adjacent
to the tooth in question. A steady-state condition is assumed
to prevail, which means that the sum of these strains will
represent the strain stimulus needed to maintain bone mass
as proposed by Qin et al.
Consider a section of the mandible containing one tooth
(Figure 4). The mandible section is assumed to be subjected
to a bending moment (M
), which gives rise to deformations
in the horizontal plane (vertical moment vector). Consider a
bending moment of such a magnitude that an average strain
of ±2000 microstrain arises in the buccal and lingual extrem-
ities of the mandible section. This is an unusually high strain
for cortical bone.
As the length of the mandible section is
assumed to be 7 mm, these bending moments will give rise
to a maximum elongation or reduction in the length of the
section, which amounts to 0.002 × 7 = 0.014 mm. The length
changes of the part of the mandible section that contains the
periodontal ligament are smaller (Figure 4). Theoretically,
these latter length changes will be absorbed by the bone, by
the periodontal ligament and by the tooth. Subtracting the
part that is absorbed by the bone, the maximum length
changes that are absorbed by the periodontal ligament and
the tooth will be well below 0.014 mm.
In Figure 5, the mandible section is assumed to be sub-
jected to bending in vertical direction, which results in an
average strain in the uppermost part of ±2000 microstrain.
This implies that length changes amount to ±0.014 mm,
which will be absorbed by the bone, the periodontal liga-
ment and the tooth together. The maximum length changes
that will be absorbed by the periodontal ligament and the
tooth together will be below 0.014 mm.
Figure 2. (a) A piece of a material that is unloaded and (b) a distributed tensile force (F) elongates the piece of material.
Figure 3. A beam, with a symmetric cross section, subjected to pure bending. The bending moment (M) induces tensile stresses and
strains in the lower half of the beam and compressive stresses and strains in the upper half.
4 Journal of Dental Biomechanics
From a mechanical point of view, the mandible
behaves as if the space occupied by the
periodontal ligament and the tooth was empty
The thickness of the human periodontal ligament is about
0.1–0.3 mm. Assume an average thickness of 0.2 mm.
Pini et al.
derived stress–strain curves in compression and
tension for bovine periodontal ligaments. With strains
below ±10%, the stresses were close to 0. This finding was
confirmed by Sanctuary et al.
who investigated the
mechanical properties of the bovine periodontal ligament.
The stress–strain curves exhibited a central ‘zero zone’ in
which the periodontal ligament behaved like a fluid. In this
zone, straining of the periodontal ligament sample did not
result in any significant stress response. Independently of
strain rate, no significant stresses appeared below a strain
of ±20%. The above discussed length change of less than
0.014 mm distributed over two periodontal ligament pas-
sages (2 × 0.2 = 0.4 mm) implies a strain that is less than
0.014/0.4 = 0.035. It can be concluded that the stresses in
the periodontal ligament with this strain are negligible. This
means that no stresses are transmitted from the bone to the
tooth. The tooth does not participate in resisting the bend-
ing moments. From a mechanical point of view, the mandi-
ble behaves as if the space occupied by the periodontal
ligament and the tooth was empty.
Figure 4. Schematic picture of a section of a mandible seen from above. The section contains a tooth, the periodontal ligament and
the surrounding bone. The mandible section is subjected to bending in the horizontal plane. The tensile and compressive strains and
the length changes are the highest buccally and lingually.
Figure 5. (a) A section of a mandible containing one tooth. The mandible section is subjected to bending in a vertical plane, which
creates strains. The strains are highest in the upper and lower extremities of the section. (b) The mandible section seen from above.
The length changes in the uppermost part are shown.
Hansson and Halldin 5
When the extraction socked is filled with
bone the mandible becomes stiffer and the
strains are reduced
After resorption of the bundle bone, the extraction socket
will gradually be filled with lamellar and cancellous bone
(Figure 6), which will make the mandible section stiffer
both with respect to horizontal bending and vertical bend-
ing. A consequence of this is that with unchanged bending
moments, the bone strains will be reduced. The absence of
the extracted tooth represents a further strain reduction.
Reduced bone strains result in bone loss.
In a study in
dogs, the right forelimb was functionally isolated, by encas-
ing in plaster, while the left forelimb served as control.
Functional isolation results in reduction of the bone strains.
After 40 weeks, approximately 50% of the bone mass was
lost on the third metacarpal, 42% on the radius, 35% on the
ulna and 28% on the humerus of the experimental limb. In
total, 80%–90% of the bone loss occurred at the periosteal
surface. Thus, bone resorption, mainly at the external bone
envelope, resulting in reduced vertical and horizontal
dimensions of the mandible, appears to be a natural conse-
quence of tooth extraction. The bone resorption can be
expected to continue until the bone strains have reached the
levels of the pre-extraction time with healed conditions in
the extraction socket.
An implant will further increase the stiffness
of the mandible
Consider the mandible section, now containing an implant,
that is subjected to a bending moment (M
), which gives
rise to deformations in the horizontal plane (Figure 7(a)).
About half of the implant will be subjected to compressive
stresses, and the other half will be subjected to tensile
stresses. On the compression side, the implant will contrib-
ute to the stiffening of the mandible. The magnitude of this
stiffening effect depends on the implant design and the
implant material. The modulus of elasticity of titanium,
cortical bone and cancellous bone are about 107, 19 and 0.8
Since titanium is much stiffer than cor-
tical and cancellous bone, the implant will, compared to the
situation with bone completely filling the previous extrac-
tion socket, further increase the stiffness of the mandible on
the compression side. On the tension side, the situation is
more complicated. The tensile strength between implant
and bone is limited.
Theoretically, this tensile strength can
locally be exceeded, and a small gap arise between implant
and bone. This will have a reducing effect on the mandible
stiffness. However, the net effect of the implant should be a
further stiffening of the mandible as compared to the situa-
tion with bone filling the previous extraction socket. The
same line of argument applies to the situation when the
mandible section is subjected to vertical bending (Figure
7(b)). Thus, on theoretical grounds, immediate implant
placement into fresh extraction sockets should not be
expected to prevent the reduction of the buccolingual or
apicocoronal dimensions of the alveolar ridge.
Retention elements at the endosseous neck
portion of the implant should preserve the
apicocoronal dimension of the alveolar ridge
An increased resistance to bending of the mandible, both in
horizontal and vertical directions, seems to be an inevitable
consequence of the replacement of the tooth and periodontal
Figure 6. (a) A mandible section containing one tooth (bottom) or one extraction socket (top), as seen from above. The mandible
section is subjected to bending in a horizontal plane with a specific bending moment (M
). The stiffness of the mandible section is
the same in these two cases. Consequently, the strains are the same. (b) When the extraction socket is filled with bone, it becomes
stiffer and the strains are reduced. (c) A mandible section containing one tooth (bottom) or one extraction socket (top). The mandible
section is subjected to bending in a vertical plane with a specific bending moment (M
). The stiffness of the mandible section is the
same in these two cases. Consequently, the strains are the same. (d) When the extraction socket is filled with bone, it becomes stiffer
and the strains are reduced.
6 Journal of Dental Biomechanics
ligament by an implant and bone. An increased resistance to
bending implies reduced strains provided that the magnitude
of the bending moments remains unchanged. Nature’s nor-
mal response to reduced bone strains is to reduce the bone
mass and architecture in such a way that the daily stress/
strain stimulus needed to maintain bone mass is reached
This is normally done by resorption at the external
The resistance to bending of the mandible in horizontal
and vertical directions can be reduced by reducing the
buccal-lingual dimensions, by reducing the apicocoronal
dimensions or by doing both. Theoretical
have demonstrated that the reduction of the api-
cocoronal dimensions can be reduced to a minimum if the
endosseous neck portion is equipped with retention ele-
ments of suitable design. With such retention elements of a
dental implant, the daily stress/strain stimulus needed to
maintain bone mass seems to be reached for the coronal-
most bone. Thus, with an implant that maintains the mar-
ginal bone level, nature achieves the required reduction in
resistance to bending of the mandible primarily by reduc-
tion of the buccal-lingual dimensions.
A theoretical possibility to also maintain the
buccal-lingual dimensions of the mandible
The bending moment required to produce a certain strain
on the surface of the beam in Figure 3 is proportional to the
product of a geometric entity called section modulus and
the modulus of elasticity of the material. For a beam with a
circular cross section, the section modulus equals πD
where D is the diameter of the cross section. The fact that
the diameter, D, is raised to the power of three means that
the section modulus is very sensitive to the size of the cross
section. In the mandible containing one implant, there are
three different materials: cortical bone, cancellous bone
and the implant material. The modulus of elasticity of corti-
cal bone is about 20–50 times as high as that of cancellous
If cortical bone is replaced by cancellous bone, the
resistance to bending is decreased, and the bending moment
required to produce a certain strain is decreased. This
should imply that if there exists a means to reduce the
thickness of the cortical bone and to replace this by cancel-
lous bone, this should be instrumental in maintaining
the buccal-lingual dimensions of the mandible ridge.
Furthermore, the modulus of elasticity of cancellous bone
varies widely, which means that if there exists a means to
get cancellous bone of a low modulus of elasticity, this
should also be instrumental in maintaining the buccolin-
gual dimensions of the mandible ridge.
Physiology is the science about the physical and chemical
functions of a living body. This article deals with the physi-
cal aspect of bone physiology. The language of physics is
mathematics. It would have been natural to express the line
of arguments of this study in a strictly mathematical lan-
guage. However, in the interest of readability, the message
has been worded in a qualitative manner.
The above analysis shows that the changes in the dimen-
sions of the alveolar ridge observed after tooth extractions
and after placement of implants in fresh extraction sockets
appear to be a natural consequence of the biologic laws
according to which the body is designed. In the evolution,
in the struggle for life, it has been important not to be too
Figure 7. (a) A mandible section, containing an implant, as seen from above. The mandible section is subjected to bending in the
horizontal plane. The implant makes the mandible section stiffer, and the strains are reduced. (b) A mandible section containing an
implant. The mandible section is subjected to bending in a vertical plane. The implant makes the mandible section stiffer, and the strains
Hansson and Halldin 7
heavy. For this reason, nature economizes with bone; it gets
rid of bone that is not sufficiently used by which the daily
stress/strain stimulus seems to be the measure of use
The above analysis was made on the mandible since the
mandible exhibits many similarities with a common engi-
neering structure – a curved beam. It is however suggested
that the same line of arguments can be applied on the max-
illa with its more complicated anatomy. Like the mandible,
the maxilla, in a mechanical sense, behaves as if the space
occupied by the periodontal ligament and the tooth was
empty. When, after tooth extraction, this space is occupied
by bone or by an implant and bone, the stiffness of the max-
illa will be increased. With unchanged loads, increased
stiffness implies reduced strains. The strain stimulus needed
to maintain bone mass is no longer reached. The biologic
response to this is to remove bone, which is preferentially
performed at the external bone envelope. The dimensions
of the alveolar ridge will be reduced.
Freeze-dried bone allograft in combination with a mem-
brane was found to improve the ridge dimensions in patients
after 6 months,
and in dogs grafting with Bio-Oss colla-
gen in extraction sockets was found to improve the ridge
dimensions, also after 6 months.
It was suggested above
that a theoretical possibility to maintain the ridge dimen-
sions after tooth extraction is to have the extraction socket
filled with bone of a low modulus of elasticity. It can be
speculated that the freeze-dried allograft and the Bio-Oss
collagen achieved that. A question that immediately pre-
sents itself is ‘what will happen in the long run?’ Will the
modulus of elasticity of the bone filling the extraction
socket increase with time? Grafting with autologous bone
did not improve the ridge dimensions after 6 months.
A consequence of tooth extraction is alveolar ridge
The placement of implants in fresh extraction
sockets has failed to prevent this bone modelling process.
The present analysis shows that this reduction of the dimen-
sions of the alveolar ridge after tooth extraction seems to be
a natural consequence of well-known physiological laws.
After healing of the extraction socket, the strain stimulus
needed to maintain bone mass is no longer reached. The
bone resorption is normally larger at the buccal aspect of
the ridge than at the lingual aspect.
In animal and clini-
cal studies, the vertical component of the bone loss has
been more pronounced at the buccal aspect.
quence of a greater vertical bone loss buccally than lin-
gually is a ridge that is sloped in the lingual-buccal
direction. In cases with such a sloped alveolar ridge anat-
omy, the placement of a standard implant might not be opti-
mal. The placement of the implant in level with the lingual
bone margin may result in compromised aesthetics. If the
implant instead is placed in level with the buccal bone mar-
gin, the lingual marginal bone is at risk to be resorbed due
to insufficient strain stimulus. In a clinical study, Fiorellini
used an implant with a sloped marginal contour in
cases where the patient presented with an alveolar crest that
was sloped in the lingual to buccal direction. Both the mean
buccal marginal bone level change and the mean lingual
marginal bone level change after 16 weeks amounted to
−0.2 mm. Thus, the installation of an implant with a sloped
marginal contour may be a treatment option in cases where
the alveolar ridge is sloped in lingual to buccal direction.
The reduction of the buccolingual as well as the apicocoro-
nal dimension of the alveolar ridge, commonly observed
after tooth extraction, can be explained by the physiologi-
cal law, according to which the maintenance of the bone
anatomy requires a certain daily stress/strain stimulus.
This research received no specific grant from any funding agency
in the public, commercial, or not-for-profit sectors.
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