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Anmol S Kalha, BSc, BDS,
MDS, Osre2
Viral Ashok Kachiwala,
BDS, MDS, MOrth RCS1
Singatagere Nagaraj
Govardhan, BDS, MDS3
REDEFINING ORTHODONTIC SPACE
CLOSURE: SEQUENTIAL REPETITIVE
LOADING OF THE PERIODONTAL
LIGAMENT—A CLINICAL STUDY
Richard P. McLaughlin,
DDS4
Aims: To assess the rate of tooth movement, anchorage loss, root
resorption, and alkaline phosphatase (ALP) activity in the gingival
crevicular fluid (GCF) as a marker for bone remodeling during orthodontic space closure using two different mechanisms. Methods: Space
closure was completed in 20 patients with extraction of all 4 premolars.
Lateral cephalograms and radio–visiographs taken before (T1) and
after (T2) space closure were assessed for anchorage loss and root
resorption. Alkaline phosphatase levels were measured in 10 patients,
which were divided into two groups of five each. Spaces were closed
with a screw device in the first group and with active tie-backs in the
second. Gingival crevicular fluid samples, collected at intervals, were
assayed for alkaline phosphatase spectrophotometrically in each
patient. Results: The mean rate of tooth movement was 1.32 ± 0.22
mm/month. The mean amount of anchorage loss in the maxilla and
mandible was 1.23 ± 0.60 mm and 1.08 ± 0.65 mm, respectively. Sixty
(25%) roots showed no root resorption, while 180 (75%) roots displayed mild to moderate blunting of their apices. Gingival crevicular
fluid–alkaline phosphatase level increased significantly from day 7 to
day 28 in both groups, but significantly more in the screw retraction
group (P < .05). Conclusion: It is possible to infer that space closure
occurs more rapidly with sequential repetitive loading of the periodontal ligament than with conventional active tie-backs. This observation is
in concurrence with a significant increase in the gingival crevicular
fluid–alkaline phosphatase level. World J Orthod 2010;11:221–229.
Syed Zameer Khurshaid,
BDS, MDS5
1Orthodontist,
Armed Forces Hospital, Al Khoud, Sultanate of Oman.
2Professor and Head, Department of
Orthodontics; Director, Center for
Evidence Based Dentistry, Institute
of Dental Studies and Technologies,
Modinagar, Uttar Pradesh, India.
3Assistant Professor, Department of
Orthodontics, SJM Dental College,
Chitradurga, Karnataka, India.
4Clinical Professor, University of
Southern California, Los Angeles,
California; Associate Professor, St
Louis University, St Louis, Missouri,
USA.
5Lecturer, Department Of Orthodontics, Government Dental College,
Srinagar, J&K State, India.
CORRESPONDENCE
Dr Viral Ashok Kachiwala
PO Box 106, Postal Code-100
Muscat
Sultanate of Oman
Email: [email protected]
Key words: space closure, periodontal ligament, alkaline phosphatase,
root resorption, anchorage loss
rthodontic space closure is time-consuming. There is no consensus as to
how to accomplish it most efficiently.
While the concepts of optimal force
magnitude and duration have received
substantial attention, 1 frequency of
force application has not received due
consideration. Studies on distraction
osteogenesis2 show that repetitive activations result in favorable cellular
O
responses that again lead to more rapid
tooth movements. Each activation
causes an upregulation of the various
markers (interleukins, prostaglandins,
etc) associated with remodeling
processes within the periodontal ligament.3 Research has proven that changing force magnitude produces better
reaction from bone and cartilage cells
than a constant force.4,5
221
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WORLD JOURNAL OF ORTHODONTICS
Kalha et al
Fig 1a Hycon screw as used
in this study for space closure.
Fig 1b Hycon screw set up
on a cast.
b
a
Fig 2 FEM model of canine, premolar, and
molar region after a full turn activation (0.35 mm)
of a Hycon screw and a 0.021 ⫻ 0.025-inch
stainless steel wire; over the periodontal ligament, distributed forces were uniform in the
7 cN/mm2 range on the pressure sites.
Recently, a screw-type appliance, the
Hycon screw5,6 (Adenta) was proposed as
a new method for space closure (Figs 1a
and 1b). It allows precise activation so
that force delivery can be adjusted. The
first part of this study was conducted to
assess the effect of sequential repetitive
loading of the periodontal ligament during space closure using fixed appliances
and the aforementioned screw. The aim
was to assess the rate of tooth movement and the amount of anchorage loss
and root resorption.
A number of gingival crevicular fluid
constituents have been shown to be diagnostic markers of bone remodeling as
indicated by an elevation in alkaline and
acid phosphatase levels.7,8 Therefore, in
the second part of this study, the alkaline
phosphatase level in the GCF during
space closure was evaluated.
METHOD AND MATERIALS
As a precursor to the clinical study, a 2D
finite element model (FEM) of the canine,
premolar, and molar region was constructed using Engineering Mechanical
Research Corporation (EMRC) display;
NISA III software (Cranes); and a peri apical radiograph of the molar, premolar,
and canine region as a reference. The
model consisted of 2,185 nodes and
4,135 elements. To reflect normal
anatomy, the teeth were connected to the
surrounding alveolar bone through a virtual periodontal ligament.
The different structures (alveolar bone,
teeth, and periodontal ligament) were
assigned their respective material constants as determined previously by Tanne
et al9; the experimental archwire received
the mechanical properties of stainless
steel. The load distribution within the periodontal ligament was then studied for
one full turn (0.35 mm) of the Hycon
screw (Fig 2). The model showed minimal
222
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VOLUME 11, NUMBER 3, 2010
Kalha et al
Fig 3a Radiovisiograph image of canine
region before activation; compare width of
the tension side (arrow) with width after
activation.
Fig 3b Radiovisiograph image of canine
region after activation; compare width of the
tension side (arrow) with width before activation. Also note uniform compression of the
distal periodontal ligament.
tipping of the teeth into the extraction
site due to controlled activation and the
presence of guidance by the 0.021-inch
⫻ 0.025-inch wire. The stress on the pressure side was generally low (13 cN/mm2)
and uniformly distributed along the root
surfaces. This was also reflected on the
radiovisiographs (RVGs) before and after
activation (Figs 3a and 3b). Image inversion with Dexis 3.0 software depicted
any changes in the periodontal ligament
more clearly.
For the clinical part of this study,
10 males and 10 females (mean age
19.9 ± 3.8 years) requiring extraction of
all first premolar were randomly selected.
Inclusion criteria were healthy periodontal status, healthy medical status, maximum anchorage requirements, identical
ethnicity, and signed informed consent.
All patients were bonded with 0.022inch slot brackets. Anchorage preparation included banding all second molars
and placing a transpalatal and lingual
arch. Leveling and aligning was initiated
with 0.016-inch and completed with
0.019-inch ⫻ 0.025-inch heat-activated
Ni-Ti wires. Finally, 0.021-inch ⫻ 0.025inch stainless steel wires were placed
with passive tie-backs for 4 weeks. After
leveling and aligning, lateral cephalograms and RVGs of the canine and
molar–premolar regions were taken.
For retraction, the Hycon screw as
described by McLaughlin et al 5 and
Kachiwala et al6 was used. All patients
were advised to activate this screw half a
turn every 3 days until space closure was
complete.
223
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WORLD JOURNAL OF ORTHODONTICS
Kalha et al
a
b
Figs 4a to 4c
Intraoral images showing patient before space closure with a Hycon screw.
a
b
Figs 5a to 5c
c
c
Intraoral images showing patient after space closure with a Hycon screw.
Data collection
Rate of tooth movement. Tooth movement was evaluated by measuring the
distance between the distal wing of the
canine and the mesial wing of the second
premolar bracket with Vernier calipers
(Dentaurum). The readings were noted
every 4 weeks until space closure was
completed. Figs 4 and 5 show a clinical
example before and after space closure.
Incisor retraction and anchorage
loss. Pre- (T1) and posttreatment (T2) lateral cephalograms were traced using the
Pancherz method.10 The distance from
the occlusal line perpendicular to the tip
of the maxillary and mandibular incisors
was measured, the difference being the
amount of incisor retraction.
Also, the distance from the occlusal
line perpendicular to the distal aspect of
the maxillary and mandibular molars was
measured; this difference indicated the
amount of anchorage loss.
Root resorption. The RVGs were taken
with an UltraCam (Ultrak Inc.) and projected on a computer screen using Dexis
3.0 software. The canine and molar/premolar regions were scored according to
the criteria given by Sharpe et al11:
0 = No apical root resorption
1 = Slight blunting of the apex
2 = Moderate blunting of the apex up
to one fourth of the root length
3 = Excessive blunting of the apex
beyond one fourth of the root length
By adding the resorption scores for all
the teeth examined, the total resorption
score for each patient was determined.
Alkaline phosphatase activity. For the
alkaline phosphatase study, six females
and four males (mean age 20.6 ± 3.2
years) with the same inclusion criteria
stated previously were enrolled. Leveling
and aligning was performed as described
earlier. In five randomly selected patients,
the anterior teeth were moved with the
Hycon screw; in the remaining five, active
tie-backs were used.
Sampling of gingival crevicular fluid
followed the protocol of Perinetti et al.7
All samples were collected from the distogingival margin of the four canines
using a volumetric micropipette of 1 µl
capacity. The collection took place 1 hour
before and 1 hour after activation and at
7-, 14-, 21-, and 28-day intervals. The
screw was activated by half turn, twice
weekly, while the active tie-backs were
changed every 4 weeks.
224
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VOLUME 11, NUMBER 3, 2010
Kalha et al
Table 1 Total (mm), mean (mm/month) ± SD (standard
deviation) and range of extraction space closure in the
maxilla and mandible, including t and P value
Maxilla
Mandible
Total
Mean ± SD
Range
t*
P
4.50 ± 1.41
4.24 ± 1.32
1.36 ± 0.21
1.27 ± 0.23
0.87–1.77
0.50–1.70
1.85
.07
*Unpaired t test.
Table 2 Mean ± SD (standard deviation) and range (mm)
of retraction and anchorage loss in the maxilla and
mandible, including t and P value
Maxilla
Mean ± SD
Retraction
Anchorage
loss
Mandible
Range
Mean ± SD
Range
t*
P
3.90 ± 0.82 3.0–5.0 3.70 ± 0.86 2.0–5.0 0.75 .46
1.23 ± 0.60 0.0–2.0 1.08 ± 0.65 0.0–2.0 0.76 .45
*Unpaired t test.
STATISTICAL ANALYSIS
For the first part of the study, descriptive
data are presented as means ± SD and
95% confidence limits wherever applicable. One-way ANOVA was used for multiple group and Student t test for
group-wise comparisons. Correlations
between measurements were assessed
by Pearson correlation coefficient. Statistical significance was set at a probability
level of ≤ .05.
For the alkaline phosphatase study,
means ± SD were calculated; categorical
data were presented as absolute values
and percentages. The increase in alkaline phosphatase level for each time
interval was reflected as percentage of
the baseline value (1 hour before activation). ANOVA was performed to statistically compare the measurements at
intervals to the baseline values. The
Mann-Whitney test was then performed
to determine any significant mean differences between the groups at each site.
RESULTS
Space closure
The average space closure was 4.51 ±
1.40 mm in the maxilla and 4.23 ± 1.33 mm
in the mandible. The mean space closure
thus was calculated as 4.37 ± 1.37 mm.
The average time to complete space closure was 3.34 ± 0.94 months.
Rate of tooth movement
The mean rate of tooth movement was
1.36 ± 0.21 mm/month in the maxilla
and 1.27 ± 0.23 mm/month in the
mandible (Table 1). The overall rate of
tooth movement was thus calculated to
be 1.32 ± 0.22 mm/month. Unpaired t
test did not show a significant difference
between tooth movements in both jaws
(P > .05).
Incisor retraction and anchorage
loss
The amount of incisor retraction was
3.90 ± 0.82 mm for maxillary incisors
and 3.7 ± 0.86 mm for mandibular
incisors, the difference not being significant (P > .05) (Table 2).
The average anchorage loss
amounted to 1.23 ± 0.60 mm for the
maxillary molars and 1.08 ± 0.65 mm for
the mandibular molars; the difference
was not significant (P > .05). The Pearson
correlation test showed a positive, but not
significant, correlation between the
amount of anchorage loss and incisor
retraction in the maxilla (r = 0.32, P > .05)
and the mandible (r = 0.18, P > .05).
Approximately 3.2 mm of maxillary and
3.4 mm of mandibular incisor retraction
resulted in 1.0 mm of anchorage loss.
Root resorption
Of the 240 roots assessed, 60 (25%)
exhibited no root resorption, 132 (55%)
showed slight root resorption, and 48
(20%) had a moderate blunting of their
apices. The resorption scores did not differ significantly for the individual teeth in
the maxilla and mandible (P > .05) (Table
3). The ANOVA test showed that the combined resorption scores for the canines,
225
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Kalha et al
Table 3 Mean ± SD (standard deviation) and total
resorption score in the maxilla and mandible for canines,
premolars, and molars
Canines
Premolars
Molars
Maxilla
Mandible
t*
P
Total
resorption
score
1.4 ± 0.9
1.5 ± 0.8
2.5 ± 1.1
1.6 ± 0.9
1.9 ± 1.0
2.4 ± 1.1
0.50
1.18
0.29
.62
.25
.77
3.0 ± 1.6
3.4 ± 1.6
4.9 ± 1.9
Table 4 Statistical comparison of the resorption scores
among canines, premolars, and molars
Canines vs premolars
Canines vs molars
Premolasr vs molars
t*
P
0.81
3.52
2.80
.43
.01
.01
*Unpaired t test.
*Student t test.
premolars, and molars were significantly
different from one another (P < .01). The
unpaired t test again revealed that the
molars were characterized by significantly greater root resorption than the
canines (P < .01) and premolars (P < .01)
(Table 4).
Alkaline phosphatase activity
Compared with the baseline measurement, the mean concentrations of alkaline phosphatase levels were significantly
increased in both groups at the various
time intervals (Tables 5 and 6). The oneway ANOVA showed that the values differed significantly between groups. There
was an increase of about 200% in the
alkaline phosphatase level between days
21 and 28 in the active tie-back group at
all sites, while that in the retraction screw
group was more than 260%. Also,
between day 14 and 28, the difference in
the alkaline phosphatase level between
the two groups was significant for all four
sites.
DISCUSSION
Despite their varying force magnitude,
traditional tooth-moving devices (closing
loops, elastic chains/modules, and
springs) produce consistently hyalinization12 because their activation length is
beyond the width of the periodontal
space (0.25 mm).13 Thus, the blood supply is reduced, leading to cell-free zones.
The impact of force-application frequency with a controlled minimum activation length on a biologic system has not
yet received due attention. In this study,
besides classical tie-backs, the Hycon
retraction screw was used for space
closure. If it is activated one full turn
(360 degrees), it contracts 0.350 mm.5,6
Because force distribution occurs reciprocally, one full turn would produce approximately 0.175 mm activation on both
sides of the extraction site. This is less
than the width of the periodontal ligament
so blood supply can be maintained. In
this study, the screw was turned only one
half turn (180 degrees) twice a week. The
ef ficient and rapid space closure
observed here is an indication that the
activation sequence used ensured adequate tissue response while not impeding
blood supply to the periodontium. This is
optimal for metabolism and subsequent
osteoclast and osteoblast activity.12
The force generated by a full turn activation was determined to be 410 cN5; it
is in the 200 cN range for a 180-degree
activation. This force is sufficient to overcome the friction generated between the
0.021- ⫻ 0.025-inch stainless steel wire
and the 0.022-inch bracket slot. A fullsized wire used for en masse retraction
of the anterior teeth will minimally deflect
and thus allow a better inclination control
as clinical observation also signified.
Tooth movements as high as 1.98 mm/
month could be achieved, although the
mean was 1.32 ± 0.22 mm/month
(95% CI = 0.88 mm to 1.98 mm/month).
Ninety-five percent showed a movement of
1.5 mm/month or more, and 40% showed
even more than 1.9 mm/month. Smaller
movements may be attributed to the variability in bone density and trabeculation
pattern. At the end of 4 months, space
closure was completed in 91% of the
80 quadrants studied. In comparing the
present data with those of Dixon et al,14
226
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P
60.6 ± 2.6
–
–
81.8 ± 1.9
21.2 ± 2.8 < .01
169.4 ± 14.5 108.8 ± 13.7 < .01
177.8 ± 41.3 137.2 ± 12.5 < .01
229.2 ± 5.4
168.6 ± 6.5 < .01
232.2 ± 4.4
171.6 ± 5.4 < .01
F = 380.2, P < .001, LSD = 8.5
Mean ± SD
Difference
to BL
Hycon screw
–
NS
S
S
S
S
Difference
to BL
Tie-back
P
59.6 ± 8.6
–
–
79.2 ± 7.2
19.6 ± 2.6 < .01
150.0 ± 7.0
90.4 ± 8.4 < .01
165.6 ± 3.8 106.0 ± 5.6 < .01
175.8 ± 6.5 116.2 ± 11.1 < .01
174.8 ± 5.6 115.2 ± 9.8 < .01
F = 301.6, P < .001, LSD = 12.9
Difference
between
groups** Mean ± SD
P
63.8 ± 5.9
–
–
85.2 ± 5.3
21.4 ± 3.0
< .01
173.8 ± 10.8 110.0 ± 13.9 < .01
201.4 ± 13.7 137.6 ± 17.0 < .01
233.6 ± 6.6 169.8 ± 6.1
< .01
234.6 ± 6.1 170.8 ± 5.1
< .01
F = 370.8, P < .001, LSD = 16.8
Mean ± SD
Difference
to BL
Hycon screw
Maxillary left canine
–
NS
NS
S
S
S
Difference
between
groups**
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P
Difference
to BL
Tie-back
P
Mean ± SD
Difference
to BL
Hycon screw
P
64.8 ± 4.8
–
–
67.2 ± 4.5
–
–
85.0 ± 3.1
20.2 ± 4.5
–
90.0 ± 4.9
22.8 ± 3.3 < .01
150.0 ± 6.4
85.2 ± 8.6 < .01
178.2 ± 14.2 111.0 ± 11.4 < .01
168.4 ± 3.8 103.6 ± 5.8 < .01
208.0 ± 12.7 140.8 ± 10.8 < .01
175.6 ± 8.5 110.8 ± 11.1 < .01
232.4 ± 5.6 165.2 ± 6.8 < .01
171.6 ± 5.5 106.8 ± 9.7 < .01
235.2 ± 4.2 235.2 ± 4.1 < .01
F = 366, P < .001, LSD =11.1 F = 350.6, P < .001, LSD = 16.5
Difference
between
groups** Mean ± SD
65.4 ± 8.0
–
–
–
89.2 ± 4.9
25.4 ± 4.2 < .01
NS
154.0 ± 36.5
90.2 ± 33.4 < .01
NS
204.6 ± 11.3 140.8 ± 15.6 < .01
S
234.8 ± 6.6
169.4 ± 14.2 < .01
S
235.2 ± 2.9
169.8 ± 10.6 < .01
S
F = 380.2, P < .001, LSD = 16.6 Mean ± SD
Difference
to BL
Hycon screw
Mandibular left canine
*One-way ANOVA, ** Mann- Whitney test, NS = not significant, S = significant, F = ratio of model mean square to error of mean square, LSD = least significant difference.
63.6 ± 4.2
–
–
83.2 ± 6.5
19.6 ± 4.4 < .01
151.2 ± 7.9
87.6 ± 7.8 < .01
165.8 ± 4.8 102.2 ± 4.0 < .01
179.0 ± 5.7 115.4 ± 8.6 < .01
177.6 ± 4.4 114.0 ± 7.4 < .01
F = 388.2, P < .001, LSD = 11.6 Before activation
After activation
Day 7
Day 14
Day 21
Day 28
ANOVA* P
Mean ± SD
Time
Difference
to BL
Tie-back
Mandibular right canine
–
NS
S
S
S
S
Difference
between
groups**
Table 6 Mean alkaline phosphatase values ± SD (standard deviation) (in IU/l) in the gingival crevicular fluid, difference to baseline value (BL), and P value
for mandibular left and right canines in the tie-back and Hycon groups at the various time points and differences between groups
*One-way ANOVA, ** Mann- Whitney test, NS = not significant, S = significant, F = ratio of model mean square to error of mean square, LSD = least significant difference.
58.4 ± 11.5
–
–
79.0 ± 11.5
20.6 ± 2.4 < .05
150.6 ± 9.4
92.2 ± 7.3
< .01
164.0 ± 5.7
105.6 ± 6.3 < .01
172.0 ± 11.6 113.6 ± 5.1 < .01
171.6 ± 12.1 113.2 ± 4.4 < .01
F = 115.0, P < .001, LSD = 20.6
Before activation
After activation
Day 7
Day 14
Day 21
Day 28
ANOVA* P
Mean ± SD
Time
Difference
to BL
Tie-back
Maxillary right canine
Table 5 Mean alkaline phosphatase values ± SD (standard deviation) (IU/l) in the gingival crevicular fluid, difference to baseline value (BL), and P value
for the maxillary right and left canines in the tie-back and Hycon groups at the various time points and differences between groups
VOLUME 11, NUMBER 3, 2010
Kalha et al
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WORLD JOURNAL OF ORTHODONTICS
Kalha et al
Nightingale and Jones,15 and Barlow,16 it
can be inferred that the mean space closure with the Hycon screw is much faster
and more efficient than traditional spaceclosing mechanisms. As mentioned, this
may be attributed to the repetitive loading
of the periodontal ligament. The upregulation of the various markers involved in the
anabolic and catabolic modeling activities
during tooth movement was demonstrated
by Lee et al3 and Carano and Siciliani.4
As an exudate, gingival crevicular fluid
reflects metabolic changes in the periodontal tissues. The increase in alkaline
phosphatase activity in the gingival
crevicular fluid seems to be related to
orthodontic force application because
alkaline phosphatase is considered to be
a marker for bone remodeling.8,9,17 Several studies have reported changes in
alkaline phosphatase activity in
osteoblasts during experimental tooth
movements in both animals and
humans.18–20
In this study, gingival crevicular
fluid–alkaline phosphatase activity was
assayed longitudinally during tooth movement in relation to the type of force system used. Significant increases in the
gingival crevicular fluid–alkaline phosphatase activity level were found over a
1-month period. The particularly significant alkaline phosphatase increase in
the Hycon retraction group between days
14 and 28 as compared to the tie-back
group can be explained by the fact that
the elastomeric modules used in the latter sample generally lose 50% to 70% of
their initial force during the first day of
loading; at 3 weeks, they retain only 30%
to 40% of their original force. In contrast,
retraction screws do not wear out.
The mean amount of incisor retraction
achieved was 3.90 ± 0.81 mm for the
maxillary and 3.70 ± 0.86 mm for the
mandibular incisors, and the mean
anchorage loss was 1.23 ± 0.60 mm and
1.08 ± 0.65 mm for the maxillary and
mandibular arches, respectively. Thus, the
anchorage loss accounted for 24% to 27%
of the total space closure (4.37 ± 1.37
mm), which is acceptable for maximum
posterior anchorage and comparable to
other methods of space closure.21,22
Root resorption occurs when pressure
on the cementum exceeds its reparative
capacity. Subsequently, dentin is
exposed, thereby allowing multinucleated
odontoclasts to degrade the root surface.
Movement of teeth typically produces
some blunting of root apices independent of the type of appliance used.23 The
relevant literature describes a prevalence
ranging from 3% to 100% of the treated
patients.24,25
Of the 240 roots in this study, 55%
(132) encountered a slight blunting, 20%
(48) showed moderate blunting, and 25%
(60) revealed no apex blunting at all.
Studies by Beck et al24 and McNab et
26
al have shown that among the posterior teeth, the most frequently resorbed
are the mandibular molars followed by
the maxillary molars, mandibular premolars, maxillary first premolars, and maxillary second premolars. In this study,
molars showed significantly greater apical root resorption than premolars and
canines (P < .01), which is confirmed by
the findings of Sharpe et al.11 There was,
however, no difference of resorption
between canines and premolars.
The length of treatment time and root
resorption are positively correlated 27 ;
increased treatment length makes roots
more prone to resorption. If space closure is completed quickly in a controlled
manner as in this study, treatment duration is reduced, as is the risk of root
resorption.
CONCLUSION
Sequential repetitive loading of the periodontal ligament with small and controlled activations (approximately 0.175
mm) is effective for space closure as indicated by a significantly higher increase of
the gingival crevicular fluid–alkaline
phosphatase level if a retraction screw is
used instead of active tie-backs (a superior force application); a shorter treatment length because, with traditional
methods, activation intervals, force levels, and activation length vary significantly; and minimal anchorage loss and
root resorption.
228
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VOLUME 11, NUMBER 3, 2010
Kalha et al
ACKNOWLEDGMENTS
The authors would like to thank the staff of Dental
Sciences, Davangere, India, where the study was
carried out. We would also like to thank Dr Aparna
P for her contributions during the FEM study.
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© 2010 BY QUINTESSENCE PUBLISHING CO, INC. PRINTING OF THIS DOCUMENT IS RESTRICTED TO PERSONAL USE ONLY.
NO PART OF THIS ARTICLE MAY BE REPRODUCED OR TRANSMITTED IN ANY FORM WITHOUT WRITTEN PERMISSION FROM THE PUBLISHER.