Determining Measurement Error for Bohler's Angle and the Effect of X-Ray Obliquity on Accuracy


Gonzalez, T.A.; Ehrlichman, L.K.; Macaulay, A.A.; Gitajn, I.Leah.; Toussaint, R.James.; Zurakowski, D.; Kwon, J.Y.

Foot and Ankle Specialist 9(5): 409-416

2017


Bohler's angle (BA) is the most commonly utilized radiographic measurement in the study of calcaneus fractures and has been shown to be prognostic in nature. Therefore, it is critical that the measurement of BA be accurate as both therapeutic and prognostic information relies on it. Oblique lateral radiographs can be a cause of error in BA measurements. However, measurement error and the effects of X-ray beam obliquity on BA have not been established in the literature. The purpose of this study was to determine measurement error and understand the effects of X-ray beam's obliquity on the measurement of BA. A cadaver specimen was imaged using a C-arm to obtain a perfect lateral radiograph of the ankle and slightly oblique lateral views in the anterior, posterior, cephalad, and caudad directions in 5° increments (21 images). Metallic beads were then placed on the anterior calcaneal process, posterior facet, and the superior aspect of the posterior tuberosity, and the same 21 images were then obtained. The metallic beads placed on the reference radiographs allowed the authors to accurately measure BA for each image and served as reference for the corresponding test radiographs. Thirty-four orthopaedic staff members participated in the study and used DICOM measurement tool to measure BA on each of the 21 test radiographs. The measurements were then compared to the measurements of BA from the reference radiographs to determine error in measurement. A total of 714 different measurements were obtained. Average measurement error was 6° (95% confidence interval = -4° to 15°). The difference between the observed BA measurements compared to the true BA measurements increased with increasing X-ray obliquity. Measurement error for BA is ±6° and increases most with cephalad oblique radiographs. Orthopaedic surgeons' ability to accurately measure BA significantly decreases with increasing obliquity of the lateral radiograph. Level V: Cadaver bench study.

vol.
XX
/
no.
X
(Clinical
Research
)
Determining
Measurement
Error
for
Bohler's
Angle
and
the
Effect
of
X-Ray
Obliquity
on
Accuracy
Footailde
8pedalst
1
Tyler
A.
Gonzalez,
MD,
MBA,
Lauren
K.
Ehrlichman,
MD,
Alec
A.
Macaulay,
MD,
I.
Leah
Gitajn,
MD,
R.
James
Toussaint,
MD,
David
Zurakowski,
PhD,
and
John
Y.
Kwon,
MD
Abstract:
Background.
Bohler's
angle
(BA)
is
the
most
commonly
utilized
radiographic
measurement
in
the
study
of
calcaneus
fractures
and
has
been
shown
to
be
prognostic
in
nature.
Therefore,
it
is
critical
that
the
measurement
of
BA
be
accurate
as
both
therapeutic
and
prognostic
information
relies
on
it.
Oblique
lateral
radiographs
can
be
a
cause
of
error
in
BA
measurements.
However,
measurement
error
and
the
effects
of
X-ray
beam
obliquity
on
BA
have
not
been
established
in
the
literature.
The
purpose
of
this
study
was
to
determine
measurement
error
and
understand
the
effects
of
X-ray
beam's
obliquity
on
the
measurement
of
BA.
Methods.
A
cadaver
specimen
was
imaged
using
a
C-arm
to
obtain
a
perfect
lateral
radiograph
of
the
ankle
and
slightly
oblique
lateral
views
in
the
anterior,
posterior,
cephalad,
and
caudad
directions
in
increments
(21
images).
Metallic
beads
were
then
placed
on
the
anterior
calcaneal
process,
posterior
facet,
and
the
superior
aspect
of
the
posterior
tuberosity,
and
the
same
21
images
were
then
obtained.
The
metallic
beads
placed
on
the
reference
radiographs
allowed
the
authors
to
accurately
measure
BA
for
each
image
and
served
as
reference
for
the
corresponding
test
radiographs.
Thirty-four
orthopaedic
staff
members
participated
in
the
study
and
used
DICOM
measurement
tool
to
measure
BA
on
each
of
the
21
test
radiographs.
The
measurements
were
then
compared
to
the
measurements
of
BA
from
the
reference
radiographs
to
determine
error
in
measurement.
Results.
A
total
of
714
different
measurements
were
obtained.
Average
measurement
error
was
(95%
confidence
interval
=
—4°
to
159.
The
difference
between
the
observed
BA
measurements
compared
to
the
true
BA
measurements
increased
with
increasing
X-ray
obliquity.
Conclusions.
Measurement
error
for
BA
is
±6°
and
increases
most
with
cephalad
oblique
radiographs.
Orthopaedic
surgeons'
ability
to
accurately
measure
BA
significantly
decreases
with
increasing
obliquity
of
the
lateral
radiograph.
Levels
of
Evidence:
Level
Cadaver
bench
study
Keywords:
Bohler's
angle;
measurement
error;
calcaneus
fracture;
radiograph;
X-ray
obliquity;
foot
and
ankle
C
alcaneus
fractures
account
for
approximately
2%
of
all
fractures
and
are
the
most
frequently
fractured
tarsal
bone,
representing
60%
of
all
tarsal
fractures.
1
Intra-articular
calcaneus
fractures
comprise
60%
to
75%
Given
its
importance
in
determining
treatment,
understanding
measurement
error
and
ways
to
decrease
error
is
beneficial
for
the
treatment
of
patients."
DOI:
10.1177/1938640016656236.
From
the
Department
of
Orthopaedic
Surgery,
Massachusetts
General
Hospital,
Boston,
Massachusetts
(TAG,
LKE,
AAM,
ILG);
The
Orthopaedic
Institute,
Gainesville,
Florida
(RJT);
Orthopedic
Center,
Boston
Children's
Hospital,
Boston,
Massachusetts
(DZ);
Department
of
Orthopaedic
Surgery,
Beth
Israel
Deaconess
Medical
Center,
Boston,
Massachusetts
(JYK).
Address
correspondence
to
Tyler
A.
Gonzalez,
MD,
MBA,
Department
of
Orthopaedic
Surgery,
Massachusetts
General
Hospital,
55
Fruit
Street,
White
565,
Boston,
MA
02114;
e-mail:
For
reprints
and
permissions
queries,
please
visit
SAGE's
Web
site
at
http://www.sagepub.com/joumalsPermissions.nay.
Copyright
©
2016
The
Author(s)
Figure
1.
Cadaveric
specimen
showing
exposed
calcaneus
with
placement
of
metallic
beads
on
the
most
superior
portion
of
the
posterior
facet.
ACP,
anterior
calcaneal
process;
PF,
posterior
facet.
Arrow
is
pointing
at
metallic
marker.
2
Foot&Mide
MosclaIst
Mon
MOM
of
these
injuries
and
result
in
depression
of
the
posterior
facet.
2
In
1931,
Bohler
stated
that
measurement
of
the
"tuber-
joint
angle,"
often
defined
as
25°
to
40°,
is
a
useful
radiographic
tool
to
aid
in
the
diagnosis
of
calcaneus
fractures,
and
it
is
now
the
most
commonly
used
parameter
to
measure
the
amount
of
calcaneal
deformity
after
such
injuries.
2
'
3
After
a
calcaneus
fracture,
Bohler's
Angle
(BA)
is
often
used
to
help
determine
treatment,
as
those
with
a
decrease
in
BA
are
more
likely
to
undergo
surgical
fixation
to
restore
normal
posterior
facet
anatomy.
Also,
BA
measurement
after
treatment
has
also
been
shown
in
numerous
studies
to
have
prognostic
value
in
determining
functional
outcomes
after
calcaneus
fractures.
1
'
4-9
Additionally,
BA
is
the
most
commonly
reported
radiographic
parameter
in
the
study
of
calcaneus
fractures.
Therefore,
not
only
is
the
ability
to
accurately
measure
BA
important,
but
understanding
the
error
in
measurement
when
utilizing
this
angular
measurement
is
also
critical.
While
inter-/intraobserver
reliability
has
been
examined
for
BA
and
has
generally
found
to
be
good,
to
our
knowledge
the
concept
of
measurement
error
as
it
applies
to
BA
has
not
been
defined
in
the
literature.
4311-14
Errors
in
measurement
on
X-rays
can
be
due
to
several
factors.
X-ray
beam
direction
can
affect
the
quality
of
the
radiograph,
and
beam
obliquity
can
affect
measurement
errors
for
specific
angle
measurements.
15
Perfect
lateral
X-rays
of
the
foot
are
not
always
obtained
due
to
problems
with
positioning
or
technical
error.
As
obliquity increases,
the
ability
to
measure
precisely
off
of
specific
bony
landmarks
likely
decreases.
Given
its
importance
in
determining
treatment,
understanding
measurement
error
and
ways
to
decrease
error
is
beneficial
for
the
treatment
of
patients.
Additionally,
an
understanding
of
the
measurement
error
is
critical
for
proper
interpretation
of
statistical
findings
when
utilized
for
research
purposes.
The
purpose
of
this
study
was
3-fold:
1.
To
determine
the
measurement
error
in
BA
2.
To
determine
the
effects
of
X-ray
beam
obliquity
on
the
measurement
of
BA
3.
To
determine
if
X-ray
beam
obliquity
affects
the
magnitude
of
measurement
error
in
BA
Methods
A
cadaver
ankle
specimen
was
imaged
using
a
large
C-arm
(General
Electric,
Fairfield,
CD
to
capture
fluoroscopic
images.
The
first
image
obtained
was
a
perfect
lateral
of
the
hindfoot,
which
met
the
following
criteria:
the
medial
and
lateral
articular
surfaces
of
the
talar
dome
overlapped
completely,
the
tibiotalar
joint
space
was
symmetric,
and
the
distal
fibula
was
superimposed
on
the
posterior
half
of
the
distal
tibia.
16
A
sequence
of
oblique
images
was
taken
with
the
beam
directed
anteriorly,
posteriorly,
cephalad,
and
caudad
in
increments
from
to
25°
in
each
direction.
The
study
group
consisted
of
34
orthopaedic
surgeons,
of
which
29
were
orthpaedic
surgery
residents
(Postgraduate
Years
[PGYI
1
through
5),
and
all
participants
received
written
instruction
on
how
to
measure
BA
as
originally
described
by
Bohler
in
1931.
2
A
random
order
generator
spreadsheet
function
(Excel,
Microsoft
Corp,
Redmond,
WA)
was
used
to
provide
the
images
in
a
random
order
to
each
surgeon.
Each
surgeon
was
asked
to
measure
BA,
using
the
angle-measuring
tool
found
within
the
Picture
Archiving
and
Communication
System
(PACS),
on
all
images
provided.
To
define
the
true
BA
for
the
perfect
lateral
image
and
also
for
each
oblique
image,
metallic
markers
were
placed
on
the
anterior
calcaneal
process,
the
superior
most
portion
of
the
posterior
facet,
and
the
posterior
superior
tuberosity
(Figure
1).
The
same
series
of
oblique
images
was
obtained
with
the
markers
in
place
to
maintain
a
constant
reference
point
(Figure
2).
Three
of
the
study's
authors
OK,
JT
and
LG)
independently
measured
BA
on
the
marked
specimens
utilizing
the
radiodense
metallic
markers
on
all
oblique
images.
An
average
of
the
measurements
were
taken
to
represent
the
"true"
BA
for
each
oblique
image.
Interobserver
correlation
coefficient
(ICC)
was
calculated
with
ICC
>0.8
defined
as
excellent,
0.6
to
0.8
defined
as
good,
0.4
to
0.6
as
moderate,
and
<0.5
as
poor
agreement.
17
The
true
BA
was
used
as
the
control
value
for
the
observed
BA.
Measurement
error
was
calculated
as
true
BA
measured
BA
I
for
the
measured
values.
For
each
of
the
4
locations
(anterior,
caudad,
cephalad,
posterior)
and
degrees
of
obliquity
(5°,
10°,
15°,
20°,
25°),
an
average
measurement
error
was
derived.
Percent
measurement
error
was
calculated
as
(
I
true
BA—
measured
BA
I)
/
I
true
BA
I
and
reported
in
Table
2.
A
PhD-level
statistician
performed
all
statistical
analysis
using
descriptive
statistics,
and
all
data
were
entered
into
a
statistical
database
(SPSS
v.19.0,
SPSS
Inc,
Chicago,
IL)
for
analysis.
A
P
value
<.05
was
considered
significant
for
all
statistical
values.
Results
Effects
of
X-Ray
Obliquity
on
Bolder's
Angle
Measurement
Thirty-four
orthopaedic
staff
members
and
residents
participated.
A
total
of
714
different
measurements
were
obtained.
od
0
B
Figure
2.
Representative
oblique
lateral
images
of
the
hindfoot
with
X-ray
beam
directed
25°
cephalad:
(A)
Without
metallic
markers;
(B)
With
metallic
markers.
vol.
XX
/
no.
X
Footailde
8pedalst
8
For
all
study
participants,
the
observed
BA
was
statistically
different
from
the
true
value
for
all
images
except
for
the
oblique
image
in
which
the
X-ray
beam
was
directed
20°
posteriorly
(P
=
.43;
Table
1).
Anteriorly
and
caudally
directed
oblique
images
resulted
in
observed
BA
that
were
lower
than
true
values.
Posterior
and
cephalad
oblique
images
resulted
in
observed
BA
that
were
greater
than
true
values
(Figures
3
and
4).
The
true
BA
measured
on
the
perfect
lateral
image
was
determined
to
be
35°.
The
true
BA
was
found
to
increase
with
increasing
obliquity
as
the
X-ray
beam
was
directed
anteriorly
and
caudally,
whereas
the
angle
remained
relatively
constant
when
directed
posteriorly
(Figures
3
and
4).
The
true
BA
decreased
as
the
X-ray
beam
was
directed
cephalad
(Figure
4).
With
increasing
obliquity,
the
difference
between
the
true
BA
on
the
perfect
lateral
and
oblique
laterals
was
found
to
be
smallest
in
the
posterior
direction
(Table
1).
Measurement
Error
for
Bohler's
Angle
Average
measurement
error
was
determined
to
be
(95%
confidence
interval
=
—4°
to
15°).
Generally,
percent
measurement
error
increased
with
increasing
degrees
of
obliquity
for
anterior,
caudad,
and
cephalad
measurements.
Conversely,
percent
measurement
error
was
inversely
related
to
the
posterior
measurement
(Figure
5).
A
mixed
linear
regression
model
was
used
to
assess
whether
location
or
degrees
was
significantly
associated
with
percent
measurement
error.
Both
degrees
(P
<
.001)
and
location
(P
<
.001)
were
determined
to
be
significantly
associated
with
percent
measurement
error
(see
Table
2).
Level
of
'training
and
Measurement
Error
in
Bohler's
Angle
Level
of
training
was
recorded
for
PGY1
to
5
and
attending
staff.
One-way
analysis
of
variance
(ANOVA)
found
a
significant
difference
between
level
of
training
and
percent
measurement
error
(P
=
.035).
An
independent
t
test
between
percent
measurement
errors
for
trainee
and
attending
determined
no
significant
difference
existed
(P
=
0.88).
However,
a
one-way
ANOVA
determined
PGY
year
was
a
significant
predictor
of
percent
measurement
error
for
trainees
(P
=
.021).
PGY1-level
trainees
were
discovered
to
have
the
most
error
(6.7%)
while
PGYS-level
trainees
were
found
to
have
the
least
error
(4.8%).
Likewise,
an
independent
t
test
between
percent
measurement
errors
for
trainees
versus
attending
staff
and
a
one-way
ANOVA
between
PGY
year
and
percent
error
for
trainees
were
performed
for
all
4
locations
and
degrees.
Anterior
20
(P
<
.001)
and
caudad
15
(P
=
.045)
were
both
found
to
have
a
significant
difference
for
percent
measurement
error
between
attending
and
trainee.
Likewise,
anterior
20
(P
=
.040)
and
caudad
15
(P
=
.031)
were,
additionally,
found
to
significantly
differ
in
relation
to
trainee.
Furthermore,
the
attending
staff
appeared
to
have
the
least
error
(angle
measurement
mean
of
5.6
with
an
SD
of
4.4),
and
the
PGY1-level
trainees
had
the
most
error
(angle
measurement
mean
of
6.7
with
an
SD
of
5.8).
There
was
no
significant
difference
between
the
true
BA
values
for
the
3
authors
that
participated
in
establishing
this
value
for
each
radiograph.
The
agreement
between
the
authors
was
excellent
with
an
ICC
of
0.985
(P
<
.001)
for
the
mean
of
the
true
BA.
Discussion
BA
is
the
most
commonly
reported
radiographic
parameter
in
the
calcaneus
fracture
literature,
with
numerous
studies
demonstrating
its
prognostic
value.
5-83
"
In
a
randomized
trial
by
Buckley
et
a1,
18
it
was
suggested
that
anatomic
or
near-
anatomic
reduction
has
a
positive
effect
on
patient
outcomes.
Su
et
a1,
9
in
a
study
of
274
patients
with
intra-articular
calcaneus
fractures
treated
surgically,
demonstrated
that
postoperative
BA
had
a
significant
correlation
with
functional
recovery.
While
the
indication
for
surgical
management
is
still
often
debated
in
the
literature,
a
decrease
in
BA
is
commonly
used
to
determine
the
need
for
surgical
treatment."
Therefore,
accuracy
in
the
measurement
of
BA
is
critical
to
determining
both
functional
outcomes
as
well
as
preventing
over-
or
undertreatment
of
calcaneus
fractures.
It
is
a
common
misconception
that
measurement
error
is
the
same
as
inter-/
intraobserver
reliability.
As
described
by
Bland
and
Altman,
repeated
measurements
on
the
same
subject
vary
around
a
true
value
because
of
measurement
error,
and
the
standard
deviation
of
repeated
measurements
of
Mon
MOM
Table
1.
Observed
and
True
Bohler's
Angles
a
.
rue
Bohler's
Angles
Observed
Bohler's
Angles
I
SD
Perfect
lateral
35
37
5.1
P=
.007
Anterior
5
36
35
4.5
P=
.037
Anterior
10
37
32
6.6
P<
.001
Anterior
15
38
30
7.2
P<
.001
Anterior
20
39
30
8.5
P<
.001
Anterior
25 40
31
3.9
P<
.001
Caudad
5
37 34
3.0
P<
.001
Caudad
10
38
33
3.3
P<
.001
Caudad
15
38
34
2.8
P<
.001
Caudad
20
39
33
4.3
P<
.001
Caudad
25
39
34
3.0
P<
.001
Cephalad
5
34 37
6.5
P=
.039
Cephalad
10
32
36
4.4
P<
.001
Cephalad
15
29
32
5.9
P<
.001
Cephalad
20
27
36
6.0
P<
.001
Cephalad
25
24
35
5.0
P<
.001
Posterior
5
35
41
5.9
P<
.001
Posterior
10
34
36
4.7
P=
.004
Posterior
15
35
37
3.6
P=
.002
Posterior
20
37 37
3.9
P
=
.43
Posterior
25
37
39
4.1
P<
.001
Abbreviation:
SD,
standard
dev'ation.
a
Pvalues
<.05
are
statistically
significant.
Image
obliquity:
true
BA
and
observed
BA
values
are
listed
in
degrees.
True
Bohler's
Angles
represent
the
mean
of
the
3
authors'
measurements.
The
interobserver
correlation
was
excellent,
ICC
=
0.985
(P<
.001).
Observed
Bohler's
Angles
are
listed
as
the
mean
value
of
all
observers.
the
same
subject
allows
us
to
measure
the
size
of
the
measurement
error?'
Measurement
error
is
defined
as
the
difference
between
the
actual
value
of
a
quantity
and
the
value
obtained
by
a
measurement.
It
differs
from
interobserver
reliability
in
that
it
is
not
the
difference
between
2
measurements
from
2
or
more
observers
but
rather
the
difference
of
a
measurement
relative
to
a
true
measurement
value.
21
As
it
applies
to
the
measurement
of
BA
in
this
study,
measurement
error
is
defined
as
the
difference
between
the
actual
value
of
the
angle
and
the
value
that
was
measured
by
the
study
participants.
The
main
components
of
measurement
error
are
systematic
bias
and
random
error
due
to
biological
or
mechanical
variation.
22
When
describing
categorical
data,
the
kappa
statistic
(lc)
provides
a
measure
of
the
proportion
of
times
that
the
observers
agree,
modified
to
take
into
account
the
agreement
that
would
occur
by
chance
alone.
For
numerical
data,
however,
reliability
can
be
assessed
with
a
variety
of
methods
from
a
simple
Student's
t
test
to
the
Bland-Altman
approach
to
the
British
Standards
repeatability/reproducibility
coefficient.21
vol.
XX/
no.
X
Foot&Aille
Spaded
Table
2.
Percent
Measurement
Error
Based
on
Radiograph
Obliquity
a
.
Perfect
lateral
35
3
±
3
—3
to
10
8.57
Anterior
5
36
4
±
2
—1
to
9
11.11
Anterior
10
37
7
±
5
—3
to
16
18.92
Anterior
15
38
9
±
6
—3
to
21
23.68
Anterior
20
39
10
±
7
—4
to
24
25.64
Anterior
25
40
10
±
4
1
to
18
25.00
Caudad
5
37
3
±
2
—1
to
8
8.11
Caudad
10
38
5
±
3
—1
to
11
13.16
Caudad
15
38
4
±
3
—1
to
9
10.53
Caudad
20
39
6
±
5
—4
to
15
15.38
Caudad
25
39
6
±
3
0
to
11
15.38
Cephalad
5
34
5
±
5
—5
to
15
14.71
Cephalad
10
32
4
±
4
—4
to
12
12.50
Cephalad
15
29
5
±
5
—5
to
14
17.24
Cephalad
20
27
9
±
5
—2
to
20
33.33
Cephalad
25
24
12
±
5
2
to
21
50.00
Posterior
5
35
7
±
5
—2
to
16
20.00
Posterior
10
34
4
±
3
—3
to
11
11.76
Posterior
15
35
3
±
3
—4
to
9
8.57
Posterior
20
37
3
±
3
—3
to
9
8.11
Posterior
25
37
3
±
3
—4
to
10
8.11
Total
(N
=
714)
35
6
±
5
—4
to
15
17.14
Abbreviations:
SD,
standard
deviation;
CI,
confidence
interval.
a
Results
indicate
mean
difference
from
true
Bohler's
Angle
±
SD
based
on
34
observers
for
each
position.
Roughly
70%
measurements
are
within
1
SD
of
the
mean
difference
and
95%
within
2
SDs
(95%
CI).
As
discussed
by
Bartlett
and
Frost,
one
challenge
in
understanding
measurement
error
is
the
number
of
different
terms
used
to
describe
it.
23
Terms
commonly
used
in
the
medical
literature
with
varying
degrees
of
interchangeability
include
agreement,
reliability,
reproducibility,
and
repeatability.
Agreement
quantifies
how
close
2
measurements
made
for
the
same
observation
are
and
can
vary
depending
on
the
conditions
under
which
the
measurements
were
made
or
due
to
biases
between
observers.
Reliability
relates
the
magnitude
of
the
measurement
error
in
observed
measurements
to
the
inherent
variability
in
the
true
level
of
the
quantity
between
subjects.
Reliability
measures
the
reproducibility
of
a
measurement,
24
with
reproducibility
referring
to
the
variation
in
measurements
made
on
a
subject
under
changing
conditions.
While
interobserver
reliability
refers
to
the
reliability
between
measurements
made
by
2
or
more
observers,
intraobserver
reliability
assesses
the
reliability
between
Figure
3.
True
and
observed
Bohler's
Angles
based
on
obliquity
of
the
lateral
radiographs
in
the
anterior
and
posterior
directions.
Note
the
overestimation
in
the
posterior
group
and
the
underestimation
in
the
anterior
group.
True
Bohler's
Angles
Observed
Bohler's
Angles
34
33
32
31
30
29
43
42
41
40
9
3
37
36
Bo
hler
's
Ang
le
(
deg
rees)
-25
-20
-15
-10
-5
0
5
10
15
20
25
Posterior
Anterior
Obliquity
of
Lateral
Radiographs
(degrees)
42
40
Observed
Bohler's
Angles
38
34
32
30
28
True
Bohler's
26
Angles
24
Figure
4.
True
and
observed
Bohler's
Angles
based
on
obliquity
of
the
lateral
radiographs
in
the
cephalad
and
caudad
directions.
Note
the
overestimation
in
the
cephalad
group
and
underestimation
in
the
caudad
group.
-25
-20
-15
-10
-5
0
5
10
15
20
25
Caudad
Cephalad
Obliquity
of
Lateral
Radiographs
(degrees)
a
Bo
hler
's
Ang
le
measurements
made
by
1
observer
at
2
different
points
in
time.
Finally,
repeatability
of
measurements
refers
to
the
variation
in
different
measurements
made
on
the
same
subject
under
identical
conditions.
6
Foot&Mide
8peclaist
Mon
MOM
Measurement
error
is
therefore
an
important
concept
for
treating
orthopaedic
surgeons
to
understand.
Knowledge
of
measurement
error,
both
the
understanding
of
its
definition
as
well
as
its
value
for
specific
measurements
used,
is
vital
as
many
of
these
radiographic
measurements
are
used
to
determine
treatment.
Furthermore,
an
understanding
of
measurement
error
allows
for
a
more
complete
interpretation
of
statistical
findings.
Measurement
error
is
also
encountered
in
other
commonly
used
radiographic
measurements.
In
their
2013
study,
for
example,
Sardjono
et
al
used
a
charged
particle
model
(CPM)
to
automatically
determine
the
Cobb
angle,
then
compared
this
measurement
to
3
curve-fitting
methods
to
evaluate
the
best
fit.
25
Using
this
model,
the
error
of
the
manual
Cobb
angle
determinations
among
observers
was
calculated.
Likewise,
Zhang
et
al
sought
to
reduce
variability
of
the
Cobb
angle
measurement
using
a
computer-aided
method,
assessing
both
intra-
and
interobserver
reliability
of
their
technique
as
well
as
factors
that
contribute
to
measurement
error.
27
Similarly,
Wall
et
al
assessed
measurement
error
of
slip
angles
in
spondylolisthesis
and
determined
that
the
measurement
error
in
the
slip
increased
as
the
obliquity
of
the
beam
away
from
the
true
lateral
increased.
15
In
the
present
study,
we
found
the
measurement
error
for
Bohler's
angle
to
be
6°.
Two
factors
that
statistically
increased
error
included
a
lower
training
level
of
the
observer
as
well
as
increasing
obliquity
of
the
lateral
radiograph.
Our
analysis
revealed
that
although
attending
staff
were
more
accurate
in
assessing
BA
than
were
PGY1-level
trainees,
this
difference
was
only
seen
when
X-rays
were
taken
at
very
oblique
angles
(anterior
20°
and
caudad
at
15°).
More
important,
although
a
statistical
difference
was
noted,
the
clinical
implications
of
a
mean
1.1°
difference
is
likely
insignificant.
Increasing obliquity
of
lateral
radiographs
was
the
main
contributor
to
measurement
error.
Perfect
lateral
0—
Anterior
Ca
udad
A—
Cephalad
N—
Posterior
Perfect
Lateral
Figure
5.
Percent
measurement
error
(y-axis)
based
on
radiograph
obliquity
(x-axis).
0
5
10
15
20
25
30
Degrees
100
Pe
rce
n
t
Measu
rme
n
t
Error
80
60
40
20
0
001.
XX
fie.
X
Foot&ilidde
8peclalst
7
radiographs
can
be
technically
difficult
to
obtain,
especially
in
a
traumatized
patient.
The
presence
of
overlying
plaster,
associated
injuries,
and
patient
discomfort
may
also
decrease
the
ability
to
properly
position
the
extremity.
Even
with
fluoroscopy,
obtaining
a
perfect
lateral
view
intraoperatively
can
be
difficult.
Surgeons
should
recognize
the
effect
of
increasing
obliquity
on
their
ability
to
accurately
measure
BA
and
thus
maximize
its
prognostic
value.
When
encountering
this
clinical
situation,
repeat
lateral
radiographs
with
surgeon
assistance
and/or
advanced
imaging
such
as
computed
tomography
should
be
considered.
There
are
several
potential
limitations
of
this
study
that
we
recognize.
While
more
than
700
observations
were
made
by
34
observers,
only
one
cadaver
specimen
was
utilized.
The
study
was
designed
in
this
manner
as
we
felt
that
increasing
the
number
of
cadavers
was
less
important
and
of
limited
utility
than
increasing
the
number
of
observable
radiographs.
Our
goal
was
to
mimic
the
common
clinical
situation
wherein
perfect
lateral
radiographs
are
not
obtained,
and
we
presented
a
multitude
of
oblique
radiographs
to
our
study
participants.
As
our
hypothesis
was
that
increasing
obliquity
leads
to
increased
measurement
error,
the
use
of
a
single
cadaver
was
important
to
decrease
a
source
of
potential
variability.
Per
our
study
findings,
utilizing
multiple
cadavers
but
only
showing
perfect
lateral
radiographs
would
have
only
demonstrated
the
error
in
measurement
when
perfect
X-rays
are
obtained
and
thus
would
not
have
been
applicable
to
clinical
practice.
Another
weakness
of
this
study
is
the
inclusion
of
only
orthopaedic
attending
staff
and
trainees
as
participants,
thus
limiting
the
applicability
of
our
findings
to
orthopaedic
surgeons.
Inclusion
of
radiology
staff
and
trainees
may
have
been
able
to
elucidate
whether
differences
in
training
could
account
for
measurement
error.
Conclusion
Measurement
error
for
BA
as
assessed
by
a
group
of
orthopaedic
surgery
attending
staff
and
trainees
is
±6°
and
increases
most
significantly
with
cephalad
oblique
radiographs.
Orthopaedic
surgeons'
ability
to
accurately
measure
BA
significantly
decreases
with
increasing
obliquity
of
the
lateral
radiograph.
Attending
staff
were
statistically
more
accurate
in
assessing
BA
than
were
PGY1-level
trainees,
although
the
clinical
implications
of
this
finding
is
likely
insignificant.
This
study
defines
the
measurement
error
for
BA
and
should
aid
surgeons
and
researchers
when
considering
treatment
options
or
when
using
BA
for
statistical
purposes.1311
References
1.
Browner
B,
Levine
A,
Jupiter
J,
Trafton
P,
Krettek
C.
Skeletal
Trauma:
Expert
Consult.
Philadelphia,
PA:
Saunders
Elsevier;
2009.
2.
Bohler
L.
Diagnosis,
pathology,
and
treatment
of
fractures
of
the
os
calcis.
J
Bone
Jt
Surg.
1931;13(1):75-89.
http://jbjs.
org/content/13/1/75.abstract
.
Accessed
November
25,
2014.
3.
Loucks
C,
Buckley
R.
Bohler's
angle:
correlation
with
outcome
in
displaced
intra-articular
calcaneal
fractures.
J
Ortbop
Trauma.
1999;13:554-558.
4.
Bakker
B,
Hahn
JA,
Van
Lieshout
EMM,
Schepers
T.
The
fate
of
Biller's
angle
in
conservatively-treated
displaced
intra-
articular
calcaneal
fractures.
Int
Orthop.
2012;36:2495-2499.
doi:10.1007/s00264-012-
1706-3.
5.
Barla
J,
Buckley
R,
McCormack
R,
et
al.
Displaced
intraarticular
calcaneal
fractures:
long-term
outcome
in
women.
Foot
Ankle
Int.
2004;25:853-856.
6.
Brauer
CA,
Manns
BJ,
Ko
M,
Donaldson
C,
Buckley
R.
An
economic
evaluation
of
operative
compared
with
nonoperative
management
of
displaced
intra-articular
calcaneal
fractures.
J
Bone
Joint
Surg
Am.
2005;87:2741-2749.
doi:10.2106/
JBJS.E.00166.
7.
Buckley
RE.
Evidence
for
the
best
treatment
for
displaced
intra-articular
calcaneal
fractures.
Acta
Chir
Orthop
Traumatol
Cech.
2010;77:179-185.
8.
Matheme
TH,
Tivorsak
T,
Monu
JU.
Calcaneal
fractures:
what
the
surgeon
needs
to
know.
Curr
Probl
Diagn
Radiol.
2007;36:1-10.
doi:10.1067/j.
cpradio1.2006.07.006.
9.
Su
Y,
Chen
W,
Zhang
T,
Wu
X,
Wu
Z,
Zhang
Y.
Bohler's
angle's
role
in
assessing
the
injury
severity
and
functional
outcome
of
internal
fixation
for
displaced
intra-articular
calcaneal
fractures:
a
retrospective
study.
8
Footaldo
8poda8st
Mon
MOM
BMC
Sutg.
2013;13:40.
doi:10.1186/1471-
2482-13-40.
10.
Clint
SA,
Morris
TP,
Shaw
OM,
Oddy
MJ,
Rudge
B,
Barry
M.
The
reliability
and
variation
of
measurements
of
the
os
calcis
angles
in
children.
J
Bone
Joint
Surg
Br.
2010;92:571-575.
doi:10.1302/0301-
620X.92B4.22565.
11.
Willmott
H,
Stanton
J,
Southgate
C.
Bohler's
angle-what
is
normal
in
the
uninjured
British
population?
Foot
Ankle
Surg.
2012;18:187-189.
doi:10.1016/j.
fas.2011.10.005.
12.
Sayed-Noor
AS,
Agren
PH,
Wretenberg
P.
Interobserver
reliability
and
intraobserver
reproducibility
of
three
radiological
classification
systems
for
intra-articular
calcaneal
fractures.
Foot
ankle
Int.
2011;32:861-866.
13.
Lauder
AJ,
Inda
DJ,
Bott
AM,
Clare
MP,
Fitzgibbons
TC,
Mormino
MA.
Interobserver
and
intraobserver
reliability
of
two
classification
systems
for
intra-
articular
calcaneal
fractures.
Foot
Ankle
Int.
2006;27:251-255.
14.
Howells
NR,
Hughes
AW,
Jackson
M,
Atkins
RM,
Livingstone
JA.
Interobserver
and
intraobserver
reliability
assessment
of
calcaneal
fracture
classification
systems.
J
Foot
Ankle
Surg.
2014;53:47-51.
doi:10.1053/j.
jfas.2013.06.004.
15.
Wall
MS,
Oppenheim
WL.
Measurement
error
of
spondylolisthesis
as
a
function
of
radiographic
beam
angle.
J
Pediatr
Orthop.
1995;15:193-198.
16.
McQuillen-Martensen
K.
Radiographic
Critique.
Philadelphia,
PA:
Saunders;
1996.
17.
Landis
JR,
Koch
GG.
The
measurement
of
observer
agreement
for
categorical
data.
Biometrics.
1977;33:159-174.
18.
Buckley
R,
Tough
S,
McCormack
R,
et
al.
Operative
compared
with
nonoperative
treatment
of
displaced
intra-articular
calcaneal
fractures:
a
prospective,
randomized,
controlled
multicenter
trial.
JBone
Joint
Surg
Am.
2002;84:
1733-1744.
19.
Knight
JR,
Gross
EA,
Bradley
GH,
Bay
C,
LoVecchio
F.
Boehler's
angle
and
the
critical
angle
of
Gissane
are
of
limited
use
in
diagnosing
calcaneus
fractures
in
the
ED.
Am
J
Emetg
Med.
2006;24:423-427.
doi:10.1016/j.
ajem.2005.12.013.
20.
Bland
JM,
Altman
DG.
Measurement
error.
BMJ.
1996;313:744.
21.
Petrie
A.
Statistics
in
orthopaedic
papers.
JBone
Joint
Surg
Br.
2006;88:1121-1136.
doi:10.1302/0301-620X.88B9.17896.
22.
Atkinson
G,
Nevill
AM.
Statistical
methods
for
assessing
measurement
error
(reliability)
in
variables
relevant
to
sports
medicine.
Sports
Med.
1998;26:217-238.
23.
Bartlett
JW,
Frost
C.
Reliability,
repeatability
and
reproducibility:
analysis
of
measurement
errors
in
continuous
variables.
Ultrasound
Obstet
Gynecol.
2008;31:466-475.
doi:10.1002/
uog.5256.
24.
Kocher
MS,
Zurakowski
D.
Clinical
epidemiology
and
biostatistics:
a
primer
for
orthopaedic
surgeons.
J
Bone
Joint
Surg
Am.
2004;86:607-620.
25.
Sardjono
TA,
Wilkinson
MHF,
Veldhuizen
AG,
van
Ooijen
PMA,
Pumama
KE,
Verkerke
GJ.
Automatic
Cobb
angle
determination
from
radiographic
images.
Spine
(Phila
Pa
1976).
2013;38:E1256-E1262.
doi:10.1097/
BRS.0b013e3182a0c7c3.
26.
Jalba
AC,
Wilkinson
MHF,
Roerdink
JBTM.
CPM:
a
deformable
model
for
shape
recovery
and
segmentation
based
on
charged
particles.
IEEE
Trans
Pattern
Anal
Mach
Intell.
2004;26:1320-1335.
27.
Zhang
J,
Lou
E,
Shi
X,
et
al.
A
computer-
aided
Cobb
angle
measurement
method
and
its
reliability.
J
Spinal
Disord
Tech.
2010;23:383-387.
doi:10.1097/BSD.0b013e3
181bb9a3c.