Estimation of single-root surface area from true thickness data and from thickness derived from digital dental radiography


Pan, J-H.; Chen, S-K.; Lin, C-H.; Leu, L-C.; Chen, C-M.; Jeng, J-Y.

Dento Maxillo Facial Radiology 33(5): 312-317

2004


The prognosis of a tooth affected by periodontitis may depend on the amount of bone remaining around the root surface. The aim of this study was to find how the surface area of a single root is related to the true thickness data and the calculated thickness data from digital dental radiographs. Eight extracted single-root teeth were digitized three-dimensionally for direct surface area measurement. Meanwhile, they were also exposed to a digital dental X-ray system. The true thickness of the tooth root was measured. The estimated circumference data were calculated from both the measured thickness and the thickness estimated from the digital image and then measured and estimated circumferences were compared. (1) The largest circumference difference mean for measured thickness and for estimated thickness was -4.94% (+/-0.07%) and 23.02% (+/-1.12%) respectively. (2) The largest 95% confidence interval for difference means for measured thickness and for estimated thickness was (-2.82%, -1.87%) and (-5.42%, 2.22%), respectively. When the thickness data are available, the surface area of a single-root tooth can be estimated to an error of less than 5%. Theoretically, the root thickness can be derived from the projected radiological image of the tooth. However, the error of estimated circumference from digital dental radiography may be over 20%. This error can be minimized if the estimated thickness from digital dental radiography can be made more accurate.

Dentomaxillofacial
Radiology
(2004)
33,
312-317
©
2004
The
British
Institute
of
Radiology
http://dmfr.birjournals.org
RESEARCH
Estimation
of
single-root
surface
area
from
true
thickness
data
and
from
thickness
derived
from
digital
dental
radiography
J-H
Pan',
S-K
Chen*.
2
,
C-H
Lin
3
,
L-C
Leu
4
,
C-M
Chen
5
and
J-Y
Jeng
6
'Graduate
Institute
of
Clinical
Dentistry,
College
of
Medicine,
National
Taiwan
University,
Taipei,
Taiwan;
'Division
of
Oral
and
Maxillofacial
Imaging,
School
of
Dentistry,
College
of
Medicine,
National
Taiwan
University,
Taipei,
Taiwan;
'Graduate
Institute
of
Civil
Engineering,
College
of
Engineering,
National
Taiwan
University,
Taipei,
Taiwan;
4
Department
of
Civil
Engineering,
College
of
Engineering,
National
Taiwan
University,
Taipei,
Taiwan;
'Institute
of
Biomedical
Engineering,
National
Taiwan
University,
Taiwan;
6
Department
of
Mechanical
Engineering,
National
Taiwan
University
of
Science
and
Technology,
Taipei,
Taiwan
Objectives:
The
prognosis
of
a
tooth
affected
by
periodontitis
may
depend
on
the
amount
of
bone
remaining
around
the
root
surface.
The
aim
of
this
study
was
to
find
how the
surface
area
of
a
single
root
is
related
to
the
true
thickness
data
and
the
calculated
thickness
data
from
digital
dental
radiographs.
Methods:
Eight
extracted
single-root
teeth
were
digitized
three-dimensionally
for
direct
surface
area
measurement.
Meanwhile,
they
were
also
exposed
to
a
digital
dental
X-ray
system.
The
true
thickness
of
the
tooth
root
was
measured.
The
estimated
circumference
data
were
calculated
from
both
the
measured
thickness
and
the
thickness
estimated
from
the
digital
image
and
then
measured
and
estimated
circumferences
were
compared.
Results:
(1)
The
largest
circumference
difference
mean
for
measured
thickness
and
for
estimated
thickness
was
4.94%
0.07%)
and
23.02%
1.12%)
respectively.
(2)
The
largest
95%
confidence
interval
for
difference
means
for
measured
thickness
and
for
estimated
thickness
was
(-2.82%,
—1.87%)
and
(-5.42%,
2.22%),
respectively.
Conclusions:
When
the
thickness
data
are
available,
the
surface
area
of
a
single-root
tooth
can
be
estimated
to
an
error
of
less
than
5%.
Theoretically,
the
root
thickness
can
be
derived
from
the
projected
radiological
image
of
the
tooth.
However,
the
error
of
estimated
circumference
from
digital
dental
radiography
may
be
over
20%.
This
error
can
be
minimized
if
the
estimated
thickness
from
digital
dental
radiography
can
be
made
more
accurate.
Dentomaxillofacial
Radiology
(2004)
33,
312-317.
doi:
10.1259/dmfr/19746488
Keywords:
root
surface
area,
X-ray
projection,
digital
radiology,
simulation
Introduction
Root
surface
area
(RSA),
or
the
contact
of
a
tooth
root
with
the
surrounding
bone,
plays
an
important
role
in
daily
periodontic
and
prosthodontic
practice.
It
partly
prognos-
ticates
the
results
of
a
tooth
affected
by
periodontitis.'
-3
Moreover,
Ante's
law
is
taken
into
consideration
as
a
conventional
bridge
is
prepared
because
accurate
assess-
ment
of
the
total
root
surface
and
the
amount
of
RSA
that
is
still
supported
is
of
clinical
significance.
4
.
5
Although
radiography
is
the
most
efficient
method
of
recording
tooth
root
dimensions,
it
is
a
two-dimensional
mapping
of
a
three-dimensional
root.
The
alveolar
bone
height
is
frequently
expressed
as
a
percentage
of
the
*Correspondence
to:
Ssu-Kuang
Chen,
No.
1
Chang-Te
Street,
Dentistry,
National
Taiwan
University
Hospital,
Taipei,
Taiwan;
E-mail:
cskchen@ntu.edu.tw
Received
26
March
2004;
revised
20
July
2004;
accepted
9
August
2004
one-dimensional
total
root
length
as
measured
on
the
radiographs."
However,
estimation
of
RSA
from
root
length
caused
much
error
in
a
previous
report.
9
Therefore,
an
alternative
method
is
needed
to
determine
RSA
from
dental
radiographs.
One
possible
method
uses
X-ray
beam
attenuation
information
that
is
embedded
in
digital
radiographs.
Attenuation
is
the
reduction
in
the
intensity
of
an
X-ray
beam
as
it
transverses
matter
by
either
the
absorption
or
deflection
of
photons
from
the
beam,
and
this
follows
a
classic
equation
known
as
Beer's
I=
where
I
is
the
transmitted
X-ray
photon
intensity;
I
o
is
the
initial
X-ray
photon
intensity;
e
is
the
base
of
the
natural
logarithm;
pt
is
the
attenuation
coefficient
and and
L
is
the
Root
surface
area
and
X-ray
projection
J-H
Pan
et
al
313
thickness
of
the
matter
through
which
the
X-ray
photons
are
transmitted.
The
amount
of
transmitted
X-ray
photons
determines
the
optical
density
recorded
on
film
in
the
traditional
way.
When
digital
systems
are
applied,
the
optical
density
is
expressed
as
the
pixel
value
in
the
grey
level
that
results
in
X-ray
images.
Therefore,
by
Beer's
law,
when
the
amount
of
initial
and
transmitted
photons
and
the
linear
attenuation
coefficient
are
known,
the
thickness
of
the
intervening
mass
may
be
derived
from
the
pixel
values.
Since
the
shape
of
the
root
is
recorded
on
radiographs
and
the
amount
of
mass
is
also
recorded,
it
should,
therefore,
be
possible
to
better
estimate
the
RSA
from
the
digital
dental radiograph.
The
aim
of
this
study
was
to
find
how the
surface
area
of
a
single
root
is
related
to
the
true
thickness
data
and
the
calculated
thickness
data
from
digital
dental
radiographs.
Materials
and
methods
Eight
extracted
single-root
teeth
without
obvious
curvature
in
their
long
axis
were
employed
in
the
study.
The
RSA
was
calculated
by
dividing
the
tooth
into
thin
slices
perpendicular
to
the
long
axis
of
the
individual
tooth
and
then
adding
up
all
the
circumferences
of
the
slices.
The
circumferences
of slices of
each
tooth
can
be
obtained
by
three
methods
in
this
study.
Method
1
was
direct
contact
measurement
by
three-dimensional
contact
probe
captur-
ing
system.
The
result
from
Method
1
was
considered
the
true
RSA.
In
Method
2
the
RSA
was
estimated
from
the
true
thickness.
In
Method
3
the
RSA
was
estimated
from
the
thickness
derived
from
digital
dental
radiography.
We
will
compare
the
results
of
the
three
methods.
Method
1:
Direct
contact
measurement
of
RSA
(Figure
1)
Three-dimensional
contact
probe
capturing
system
Digitization
of
the
root
surface
was
achieved
by
a
Co-ordinate
Measuring
Machine
(CMM)
system"
(Renishaw
Cyclone
scanning
system;
Renishaw
Plc,
New
Mills,
UK).
CMM,
which
is
used
for
a
wide
variety
of
industry
applications
as
a
quality
reference,
uses
probing
systems
to
replace
traditional
manually
operated
measur-
ing
instruments
such
as
micrometers,
vernier
calipers
and
dedicated
gauges.
The
capturing
system
in
the
study
can
cover
an
axis
travel
of
600
mm
x
500
mm
x
400
mm,
which
can
easily
cover
the
tooth
specimens
in
this
study.
System
repeat-
ability
is
0.005
mm,
with
an
axis
resolution
of
0.001
mm.
The
probe
diameter
is
0.4
mm.
Measurement
procedure
The
tooth
was
positioned
into
a
nut
fixed
with
wax.
After
clamping
the
tooth
and
nut
onto
a
fixture,
the
scanning
range
on
the
appropriate
scope
was
set
to
cover
the
tooth
specimen.
Step
1:
Constraining
best
fit.
The
selected
source
point
set
was
rotated
and
translated
as
specified
by
the
rotation
and
translation
constraint,
so
that
the
mean
square
distance
between
the
points
was
minimized
and
was
within
the
specified
tolerance,
if
possible.
Then
each
data
point
was
shifted
a
distance
that
was
equal
to
the
radius
of
the
probe
tip
in
a
direction
normal
(perpendicular)
to
the
root
surface.
Step
2:
Polygonization.
In
this
step,
rendering
of
arbitrary
point
sets
joined
the
points
to
form
a
closed
mesh
on
the
skin
of
a
shape
represented
by
the
points
by
entering
the
maximum
similar
distance
and
neighbourhood
size
to
control
polygon
size.
Step
3:
Closing
shape.
The
polygonization
process
usually
produces
many
non-closed
areas.
Before
comput-
ing
the
surface
area
this
error
needs
to
be
closed
by
stitching
or
capping
a
polygonized
point
cloud.
The
gap
distance
was
measured
based
on
the
gaps
that
needed
closing
and
the
gap
distance
was
measured
as
the
shortest
distance
between
a
vertex
on
an
open
edge
and
another
open
edge.
Step
4:
Calculating
the
root
surface
area.
The
circumference
of
a
slice
was
calculated
directly
by
summing
up
the
distance
between
the
adjacent
two
data
points
in
the
contour.
The
total
RSA
was
calculated
by
summation
of
the
polygonized
triangles.
Method
2:
RSA
estimated
from
true
thickness
data
(Figure
1)
Step
1
to
Step
3:
same
as
in
Method
1.
Step
4:
Format
conversion
to
stereolithography
(STL)
format.
In
Method
2,
all
polygonal
data
were
converted
into
a
solid
model
with
"Initial
Graphics
Exchange
Specification"
(IGES)
format
and
then
processed
with
the
program
Pro/ENGINEER
2001
(Parametric
Technology
Corporation,
MA,
USA)
to
further
convert
the
files
into
STL
format.
Step
5:
Deriving
the
contour
data
of
the
slice.
AUTOEDIT2000
(Autostrade
Co.
Ltd.,
Oita,
Japan)
was
then
used
to
process
the
STL
files
to
derive
the
contour
data
of
the
slices
perpendicular
to
the
long
axis
of
the
tooth.
The
interval
of
the
slices
was
set
at
0.07
mm
to
match
the
pixel
height
of
the
direct
digital
X-ray
system
(DDX).
Step
6:
Calculating
the
thickness
data.
An
in-house
program
"Multi-Optical-Source
Stereolithography"
(MOSS)
System
developed
for
laser
path
design
and
rapid
prototyping
was
employed
to
calculate
thickness
data.
This
program
can
calculate
the
distance
between
the
contours
at
certain
distance
intervals
and
in
certain
directions.
This
program
can
also
detect
whether
there
is
a
concavity
of
the
contour
in
the
thickness
path.
Only
the
thickness
of
the
tooth
structure
was
added.
The
interval
of
the
thickness
calculation
was
set
at
0.07
mm
to
match
the
pixel
width
of
the
DDX
system.
Step
7:
Calculating
the
circumference
and
RSA.
Estimated
circumference
was
calculated
by
doubling
the
half
thickness
data
under
the
assumption
of
cross-sectional
symmetry.'
In
addition,
the
total
RSA
was
the
summation
of
each
slice
that
was
the
multiplication
of
the
circumfer-
ence
and
the
height
(0.07
mm)
of
each
slice.
Method
3:
RSA
estimated
from
thickness
derived
from
digital
dental
radiography
(Figure
2)
Step
1:
Setting
of
the
digital
dental
radiography,
tooth
specimen
and
step-wedge.
An
intraoral
X-ray
unit
Heliodent
MD
(Sirona
Dental
Systems
GmbH,
Dentomaxillofacial
Radiology
314
Root
surface
area
and
X-ray
projection
J-H
Pan
et
al
Data
points
measurement
ay
scanning
system
Software
-
Software
Procedure
fConstrained
Best
Fit
Convert
to
IGES
and
STL
Software
Procedure
-
1
11
Derive
the
Contour
of
Slice
Polygoniza
Calculate
the
Thickness
data
Close
Shape Shape
Calculate
the
Circumference
Computes
the
Surface
Area
Method
I
Calculate
the
RCP}
Surface
Area
Method
II
Finishing
measurement
Figure
1
The
flow
chart
for
Method
1
and
Method
2
Figure
2
Method
3.
Tooth
and
bone-simulating
step
wedge
on
imaging
plate,
used
for
calculating
tooth
root
thickness
from
pixel
values
Bensheim,
Germany)
and
Digora
(SOREDEX,
Finland)
intraoral
computed
radiography
system
were
used
to
capture
the
images.
The
tooth
specimen
was
placed
on
the
image
plate
with
the
long
axis
of
the
tooth
parallel
to
the
long
axis
of
the
sensor,
with
the
buccal
side
of
the
tooth
facing
the
X-ray
source.
A
10
mm
x
30
mm
step
wedge
made of
a
bone-simulating
resin'
was
placed
next
to
the
tooth
on
the
image
plate.
The
six
5
mm
long
steps
of
the
wedge
ranged
in
thickness
from
1
mm
to
6
mm
in
increments
of
1
mm.
The
teeth
were
exposed
along
with
this
step
wedge
with
the
focus-to-
film
distance
of
300
mm,
and
the
X-ray
exposure
conditions
of
70
kVp,
8
mA
and
0.12
s.
Step
2:
Standardization
of
eight
root
images
with
step
wedge.
Because
the
amount
of
X-ray
exposure
and
the
Finishing
measurement
sensor
response
would
not
be
the
same
in
all
eight
images,
variations
in
pixel
values
would
be
rendered.
Therefore,
the
images
were
adjusting
by
cross-match
for
brightness
and
contrast
via
the
step
wedge.
Step
3:
Calibration
of
canals
in
the
images
by
fourth-
order
polynomial
equations.
It
is
important
to
note
that
the
pixel
values
would
decrease
in
areas
where
the
root
canal
was
imaged,
and
would
therefore
result
in
an
under-
estimation
of
the
thickness
of
the
tooth
structure
in
these
regions.
To
avoid
this
error,
fourth-order
polynomial
equations
were
used
in
each
slice
to
interpolate
pixel
values
in
the
areas
where
the
root
canals
were,
according
to
the
pixel
values
of
the
peripheral
area,
and
then
the
pixel
values
were
adjusted
accordingly.
Step
4:
Transforming
the
pixel
value
into
thickness
data
by
Beer's
law.
Tooth
thickness
was
calculated
based
on
pixel
values
of
the
root
and
the
step
wedge.
Following
Beer's
law,
the
constants
used
for
calculating
the
tooth
thickness
from
the
pixel
values
were
established
through
the
resin
stepwedge
that
had
a
known
attenuation
coefficient
and
thickness.
Bi-linear
interpolation
was
used
to
estimate
the
attenuation
coefficient
of
the
tooth
root.
Tooth
thickness
could
then
be
calculated
with
the
constants
and
the
estimated
attenuation
coefficient.
Step
5:
Calculating
the
circumference
and
RSA.
An
in-house
program
was
developed
to
estimate
slice
circumference
from
pixel
values
in
the
digital
images.
The
projected
objects'
symmetry
across
the
horizontal
long
axis
was
assumed.
The
circumference
in
each
slice
was
obtained
by
doubling
the
half
thickness
data
under
the
assumption
of
cross-sectional
symmetry'
individually.
The
total
RSA
was
the
summation
of
each
slice
that
was
multiplication
of
the
circumference
and
the
height
(0.07
mm)
of
each
slice.
Dentomaxillofacial
Radiology
Difference
mean(%)
=
1
-
n
X
d,
i=i
n
Root
surface
area
and
X-ray
projection
.1-H
Pan
et
al
315
Difference
mean
The
difference
mean
was
defined
as
the
following:
each
slice
in
the
roots
of
the
eight
extracted
teeth
was
compared
in
the
three
methods
as
Method
2
to
Method
1
and
Method
3
to
Method
1.
The
difference
of
circumferences
between
the
two
methods
in
each
slice
of
a
root
was
standardized
as:
Circumference
-
Circumference
Method
II
Method
I
-
Circumference
method
x100%
or
d
-
Circumference
Method
-
Circumference
Method
I
,
Circumference
Method
I
x100%
in
which
subscript
i
means
a
certain
slice,
which
were
then
summed
up
in
each
tooth,
and
averaged.
Then
we
obtained:
Therefore,
this
variable
was
called
"difference
mean".
Simultaneously,
the
standard
error,
and
95%
confidence
interval
of
difference
mean
were
derived.
Results
The
results
are
summarized
in
Tables
1
and
2.
The
difference
means
between
Method
1
and
Method
2
varied
from
-4.94%(±0.07%)
to
-1.05%(±0.06%)
with
an
average
of
-
2.07%.
However,
the
difference
means
between
Method
1
and
Method
3
varied
from
-
1.70%(
±
1.89%)
to
23.02%(±1.12%)
with
an
average
of 8.67%.
In
relation
to
Method
1,
the
largest
95%
confidence
interval
for
the
difference
means
from
Method
2
and
Method
3
is
(-2.83%,
-
1.87%)
and
(-5.42%,
2.02%),
respectively.
All
difference
means
in
Method
2
are
under-estimated.
However,
almost
all
difference
means
in
Method
3
are
over-estimated
except
for
tooth
8.
The
RSA
in
Method
2
and
Method
3
was
calculated
as
the
summation
of
circumference
in
each
slice
(mm)
multiplied
by
slice
height
(0.07
mm).
The
errors
of
RSA
in
Method
2
and
in
Method
3
were
calculated
as
[(RSA
in
Method
2
-
RSA
in
Method
1)
/
RSA
in
Method
1]
X
100%
or
[(RSA
in
Method
3
-
RSA
in
Method
1)
/
RSA
in
Method
1]
x
100%.
The
errors
of
RSA
in
Method
2
(-5.04%
-
-1.01%)
are
in
a
much
narrower
range
than
the
errors
in
Method
3
(-10.83%
-
19.65%).
This
is
similar
to
the
results
of
the
difference
means.
Discussion
The
surface
area
of
a
root
can
be
calculated
from
the
summation
of
the
circumferences
of slices
perpendicular
to
the
long
axis
of
this
tooth.
Three-dimensional
information
would
allow
for
better
estimation
of
the
root
surface
than
the
only
two-dimensional
or
one-dimensional
information
as
projected
area
and
root
length,
respectively.'
Difference
of
thickness
data
between
Method
2
and
3
In
Method
2
and
Method
3,
no
matter
how they
were
derived,
the
thickness
data
played
a
key
role
in
estimating
the
RSA.
Some
differences
were
noted
between
the
two
methods.
In
Method
2,
the
thickness
of
each
slice
was
obtained
from
the
thickness
path,
the
three-dimensional
coordinate
of
two
end
points
on
the
contour
of
the
root.
One
is
the
Table
1
Method
2
is
compared
with
Method
1
Tooth
no.
1
2
3
4
5
6
7
8
Average
Difference
mean
(%)°
-
2.35
-
1.67
-
4.94
-1.07
-1.96
-
2.22
-1.31
-1.05
-
2.07
Standard
error
(%)
0.24
0.08
0.07
0.03
0.11
0.11
0.03
0.06
95%
CI
(%)-upper
limit
-1.87
-1.50
-
4.81
-1.01
-1.75
-
2.01
-1.24
-
0.93
95%
CI
(%)-lower
limit
-
2.83
-1.84
-
5.08
-1.14
-
2.18
-
2.43
-1.37
-1.17
RSA,
Method
2
90.62
123.12
99.83
158.69
180.37
111.91
77.06
201.86
RSA,
Method
1
92.19
124.97
105.13
160.46
183.14
114.18
78.08
203.91
Error
of
RSA
(%)
-1.70
-1.48
-
5.04
-1.10
-1.51
-1.99
-1.31
-1.01
RSA,
root
surface
area;
°Difference
between
root
circumference
for
Method
2
and
Method
1,
averaged
over
all
the
slices
of
the
tooth
root
Table
2
Method
3
is
compared
with
Method
1
Tooth
no.
1
2
3
4
5
6
7
8
Average
Difference
mean
(%)°
2.65
12.77
20.34
5.19
3.74
3.33
23.02
-1.70
8.67
Standard
error
(%)
0.94
1.29 1.29
0.71
1.51
1.19
1.12
1.89
95%
CI
(%)-upper
limit
4.50
15.32
22.89
6.00
6.72
5.68
25.25
2.02
95%
CI
(%)-lower
limit
0.80
10.23
17.80
3.79
0.75
0.97
20.79
-
5.42
RSA,
Method
3
92.18
136.73
122.20
165.87
179.17
113.76
93.42
181.83
RSA,
Method
1
92.19
124.97
105.13
160.46
183.14
114.18
78.08
203.91
Error
of
RSA
(%)
-
0.01
9.41
16.24
3.37
-
2.17
-
0.37
19.65
-10.83
RSA,
root
surface
area;
°Difference
between
root
circumference
for
Method
3
and
Method
1,
averaged
over
all
the
slices
of
the
tooth
root
Dentomaxillofacial
Radiology
Root
surface
area
and
X-ray
projection
316
J-H
Pan
et
al
initial
point,
and
the
other
is
the
final
point
(in
Method
2,
step
6-7).
Moreover,
this
technique
can
also
detect
whether
there
is
a
concavity
of
the
contour
in
the
thickness
path,
and
only
the
thickness
of
the
tooth
structure
was
added.
Therefore,
it
was
considered
as
true
thickness.
In
Method
3,
tooth
thickness
was
estimated
from
the
pixel
values.
There
was
no
information
on
the
three-
dimensional
coordinates
of
a
certain
point
in
the
thickness
path.
The
assumption
of
cross-sectional
symmetry
was
needed
to
estimate
the
RSA.
Errors
were
expected
from
this
assumption,
9
and
it
was
expected
to
result
in
greater
difference
means
in
estimating
RSA.
In
addition
to
the
errors
from
the
missing
information
of
the
three-dimensional
coordination
of
points
in
thickness
path,
other
errors
could
be
attributed
to
two
main
factors:
the
first
is
the
tooth
itself
and
the
second
is
from
the
system
used
in
the
study.
Errors
from
the
tooth
itself
This
type
of
error
mainly
exists
in
Method
3.
Possible
causes
are
the
cross-sectional
shape
of
a
certain
slice
of
the
tooth
root,
and
homogeneity
of
tooth
structure.
The
cross-sectional
shape
of
a
certain
slice
of
the
tooth
root
By
making
assumptions
of
cross-sectional
symmetry
across
the
horizontal
axis,
we
could
follow
Beer's
law to
obtain
the
thickness
of
the
object.
Therefore,
we
trans-
formed
the
thickness
of
a
certain
projection
into
the
circumference measurement
of
a
certain
slice.
Obviously,
cross-sectional
symmetry
did
not
exist
in
most
cases.
The
cross-section
is
not
an
ideal
ellipse
in
most
cases
and
there
are
even
some
concavities.
In
Method
2,
the
thickness
path
can
be
derived
with
the
three-dimensional
coordinate
of
the
end
points,
concavities
can
be
ruled
out,
and
so
the
true
thickness
can
be
calculated.
However,
in
Method
3,
three-
dimensional
coordinates
can
not
be
derived.
Although
different
eccentricities
and
asymmetric
factors
result
in
different
extents
of
error,
they
are
under
a
reasonably
acceptable
limit
for
most
conditions.
In
the
previous
study,
9
the
error
of
the
estimated
circumference
decreased
to
less
than
2%
when
the
asymmetry
factor
was
less
than
0.6
whatever
method
was
applied.
According
to
the
previous
study,
when
other
factors
were
equal,
the
asymmetry
factor
in
the
study
was
less
than
1%.
Homogeneity
of
tooth
In
addition
to
cross-sectional
shape,
tooth
roots
are
not
homogeneous
in
composition.
Cementum,
dentin
and
root
canal
system
should
have
different
attenuation
coefficients.
Each
of
these
components
can
change
with
age,
type
of
tooth,
etc.
Therefore,
in
clinical
settings,
the
thickness
of
the
projected
root
can
not
be
accurately
derived
by
using
simplified
Beer's
law.
In
addition,
it
is
evident
that
the
pixel
values
would
decrease
in
areas
where
the
root
canal
systems
were
imaged,
which
would
result
in
an
under-estimation
of
the
thickness
of
the
tooth
structure
in
these
regions.
To
avoid
this
error,
in
the
study,
fourth-order
polynomial
equations
were
used
in
each
slice
to
interpolate
pixel
values,
according
to
pixel
values
of
the
peripheral
area.
The
potential
for
overlying
bone
to
reduce
the
accuracy
of
the
method
to
assess
RSA
in
vivo
is
of
concern.
Bone
covering
roots
has
enormous
variation
in
thickness,
trabecular
patterns,
mineral
density
and
anatomical
topography.
Theoretically
the
thickness
of
a
root
should
be
calculated
from
the
pixel
values
in
the
projected
digital
dental
radiographs.
However,
in
this
study
the
thickness
of
the
tooth
was
not
well
derived
from
the
pixel
values.
Once
this
factor
is
under
control,
more
complicated
factors
caused
by
overlying
structures
should
be
studied.
There
might
be
a
solution
to
this
problem.
One
might
be
able
to
use
pixel
values
of
the
coronal
portions
of
teeth
to
estimate
the
corresponding
root
thickness.
However,
further
studies
are
needed
to
evaluate
this
feasibility.
Errors
from
the
system
This
type
of
error
exists
both
in
Method
2
and
3,
as
DDX,
CMMs,
and
computer
softwares
(Pro/ENGINEER
2001,
AUTOEDIT
2000,
etc.)
were
all
used
in
the
study.
However,
different
parameters
play
varying
roles
in
the
two
methods.
The
error
in
Method
2
was
mainly
dependent
upon
the
accuracy
of
the
distance
of
the
adjacent
two-point
interval.
The
shorter
the
distance
between
the
two
adjacent
points
measured
at
certain
distance
intervals
of
a
certain
slice,
the
higher
the
accuracy.
In
this
study,
the
system
repeatability
is
0.005
mm,
with
an
axis
resolution
of
0.001
mm,
and
the
probe
diameter
is
0.4
mm,
allowing
for
excellent
accuracy.
The
error
in
Method
3
is
mainly
dependent
upon
the
nature
of
X-ray
in
the
system.
Since
Beer's
law
only
holds
true
under
monochromatism,
which
does
not
occur
in
real
situations,
it
is
expected that
there
should
be
some
errors
when
clinical
polychromatic
X-rays
were
applied.
In
our
previous
study,
9
the
exact
amount
of
X-ray
exposure
and
the
sensor
response
were
not
the
same
in
all
eight
images
even
though
the
homogeneous
resin-made
step
wedge'
was
applied
with
teeth
under
the
same
X-ray
exposure
condition.
These
factors
could
render
variations
in
pixel
values.
Obviously,
not
only
does
this
imply
that
some
calibration or
standardization
processes
should
be
per-
formed,
but
also
that
different
wavelengths
of
X-ray
photons
will
result
in
different
transmitted
photon
intensities.
In
this
study,
we
adjusted
the
pixel
values
by
averaging
the
pixel
values
of
the
whole
area
of
each
step
in
all
eight
images,
and
the
linear
regression
was
used
to
adjust
each
pixel
to
make
the
average
pixel
value
of
the
steps
the
same
in
all
eight
images.
Conclusion
In
Method
3,
due
to
the
lack
of
symmetry
of
cross-sectional
shape
of
certain
slices
of
tooth
root,
the
nature
of
clinical
radiography
and
image
processing,
the
estimated
root
thickness
was
different
from
the
true
root
thickness
in
Method
2.
Dentomaxillofacial
Radiology
Root
surface
area
and
X-ray
projection
J-H
Pan
et
al
317
Although
the
estimated
circumference
(and
RSA)
from
true
thickness
seems
better
than
that
from
pixel
value,
clinically
the
pixel
value
is
easier
to
use,
more
readily
available
and
within
an
acceptable
error.
In
the
present
study,
we
did
not expect
to
measure
the
root
surface
to
full
precision,
but
only
to
estimate
it
to
some
extent
of
accuracy.
Undoubtedly,
further
studies
aimed
at
optimizing
the
derivation
of
thickness
of
root
from
pixel
values
in
various
digital
dental
X-ray
systems
are
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Dentomaxillofacial
Radiology