A computational technique to measure fracture callus in radiographs
Trevor J. Lujana,n, Steven M. Madeya, Dan C. Fitzpatrickb, Gregory D. Byrda, Jason M. Sandersona,
aBiomechanics Laboratory, Legacy Research and Technology Center, Portland, OR 97232, USA
bSlocum Center for Orthopedics and Sports Medicine, Eugene, OR 97408, USA
a r t i c l e i n f o
Accepted 5 October 2009
a b s t r a c t
Callus formation occurs in the presence of secondary bone healing and has relevance to the fracture’s
mechanical environment. An objective image processing algorithm was developed to standardize the
quantitative measurement of periosteal callus area in plain radiographs of long bone fractures.
Algorithm accuracy and sensitivity were evaluated using surrogate models. For algorithm validation,
callus formation on clinical radiographs was measured manually by orthopaedic surgeons and
compared to non-clinicians using the algorithm. The algorithm measured the projected area of
surrogate calluses with less than 5% error. However, error will increase when analyzing very small areas
of callus and when using radiographs with low image resolution (i.e.100 pixels per inch). The callus size
extracted by the algorithm correlated well to the callus size outlined by the surgeons (R2=0.94,
po0.001). Furthermore, compared to clinician results, the algorithm yielded results with five times less
inter-observer variance. This computational technique provides a reliable and efficient method to
quantify secondary bone healing response.
& 2009 Elsevier Ltd. All rights reserved.
The formation of fracture callus occurs in the presence of
secondary bone healing and has relevance to the mechanical
stability at the fracture. For instance, the amount of callus
formation in long bone fractures is predictive of bending stiffness
(Eastaugh-Waring et al., 2009; Marsh, 1998; Tiedeman et al.,
1990). Unfortunately, callus measurement from plain radiographs
is a subjective process, with inter-physician variability of 20–25%
(Bhandari et al., 2002; Whelan et al., 2002). This subjectivity has
implicitly hindered efforts to predict fracture mechanics and
treatment efficacy from radiographs (Corrales et al., 2008; Martin
et al., 2000).
Image processing algorithms have potential to render callus
measurement objective and thereby reduce observer error.
However, previous studies which measured callus with image
processing protocols did not document the accuracy and objec-
tivity of their methods (Augat et al.,1997; Morcuende et al., 2004).
To establish credibility, it is critical that computational techniques
be verified and validated (Anderson et al., 2007). This research
endeavors to verify and validate a novel computational method to
objectify callus measurement from plain radiographs.
The proposed algorithm analyzes fracture callus in digital radiographs using
MATLAB (Mathworks; Natwick, MA). User-defined boundary conditions assist the
demarcation of cortical fragments, and the callus is automatically segmented. To
convert to metric area, a hardware feature of known dimension is chosen as a length
standard. Numerical error was analyzed with two and three-dimensional surrogates.
For clinical validation, callus formation in distal femur fractures was assessed manually
by orthopaedic surgeons and compared to non-clinicians using the algorithm.
2.1. Cortex segmentation
Segmentation of the cortex was guided by user inputs and defined by two-
dimensional intensity gradients (rIxy). First, the user selects a region of interest
(ROI) that encompasses the fracture site and the periosteal callus (Fig.1A). The user
then specifies rectangular regions that enclose the ends of the anterior and posterior
bone fragments (Fig. 1B). The final user input is to connect a user-defined finite
sequence of straight line segments along the external cortices (Fig.1B). The external
cortex is defined for each row as the local rIxymaxima, nearest to this line (Fig.1C).
The inner cortex is automatically defined when the Ixymagnitude reaches a local
maxima (rIxy=0), deep to the external cortex (Fig. 1C). The cortex delineations
originate at the ROI boundary and expand by permitting only a one pixel shift per
row. Cortex endpoints are defined in the user specified regions (Fig. 1B) by a
composite rIxyscore, taken tangential and normal to the cortical bone (Fig. 1D).
Finally, the fracture was bridged by the shortest line connecting the tip of the
outermost cortex with the periosteal surface of the adjacent cortex (Fig. 2A).
Automatic segmentation of callus involved noise reduction, edge detection and
edge localization. To reduce salt-and-pepper noise while maintaining edge
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0021-9290/$-see front matter & 2009 Elsevier Ltd. All rights reserved.
nCorresponding author: Legacy Biomechanics Laboratory, 1225 NE 2nd Avenue,
Portland, OR 97215, USA. Tel.: +1503 413 5487; Fax: +1503 413 4942.
E-mail address: email@example.com (T.J. Lujan).
Journal of Biomechanics 43 (2010) 792–795
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contrast, a median filter was applied over the ROI (Southard and Southard, 1995).
The callus edge was initially approximated by selecting pixels in the periosteal
region that had a rIxy magnitude greater than an empirical threshold of 1.5
(Fig. 2B). After a flood-fill operation, pixel clusters in the periosteal region not
adjacent to the external cortices were eliminated. Morphological opening was
applied and the callus region was approximated (Figs. 2C and D).
For further refinement, pixels in the callus region were deselected if their
intensity was not greater than the sum of a two components threshold (Fig. 2E).
The first component was two standard deviations above the local background
intensity. The second component was five percent of the difference between the
local background intensity and local cortex intensity. Locality was determined
with Euclidean distance. Finally, morphological opening and closing operations
2.3.Verification of algorithm accuracy
To quantify the inherent error caused by filtering, morphological operations
and discretization, the algorithm analyzed sets of manufactured binary images of
semi-circular callus surrogates. Pixels per inch (PPI), length standard and callus
size were varied by two orders of magnitude. To test algorithm sensitivity to callus
maturation and image plane rotation, surrogate models of a fracture callus were
developed. The development of these surrogates was guided by quantitative data
measured from twenty radiographs of femur fractures taken 6 and 24 weeks post-
fracture (Table 1). Surrogates were assembled using callus and cortex components.
The callus components were composed of epoxy and fiberglass (profile area
E180 mm2). To produce low and high density surrogate callus, corresponding to
actual callus at 6 and 24 weeks post-fracture, the weight concentration of
fiberglass beads was set to 12.5% and 50%, respectively (Fig. 3A). Fiberglass mat
was added to create the radiographic effect of callus heterogeneity (Fig. 3B). The
cortical components (Sawbones, Vashon WA) were then press fit into the callus
lumen. Once radiographs of the surrogates were captured (70 kV, 0.06 s) and
digitized, a soft tissue envelope was superimposed upon the image and an
isochoric or volume preserving transformation was applied to give curvature.
These final image processing steps improved the surrogates’ resemblance to
clinical fractures (Fig. 3C, Table 1), while preserving the known size of the callus
surrogate for determination of algorithm accuracy. Radiographs were analyzed by
three different operators using a 5 mm length standard.
Fig. 1. Cortex segmentation. (A) User selects ROI. (B) User defines regions
enclosing fragment ends (dotted) and snaps line segments (dashed) along external
cortex. (C) External cortex (EC) at the local max rIxynearest the point where the
user approximated the EC (n). Inner cortex (IC) deep to EC where rIxyequals zero.
(D) Apex of bone fragment defined at max difference between the intensity
gradients tangent (T) and normal (N) to the external cortex.
Fig. 2. Callus segmentation. (A) Bone fragments connected. (B) Pixels selected
with rIxy greater than 1.5. (C) Opening and flood-fill operations executed on
objects adjacent to bone fragments. (D) Callus perimeter estimated. (E)
Callus perimeter refined by deselecting pixels with intensity values below local
Comparison of the surrogate models to actual fracture callus.
Mean intensity Mean intensity variation Mean intensity Mean intensity variation Mean intensity Mean intensity variation Mean curvature (deg.)
Clinical radiographs in the low and high density groups were from 6 weeks post-fracture (n=10) and 24 weeks post-fracture (n=10), respectively. Intensity values were
normalized by the maximum intensity bin of 255.
Fig. 3. Callus surrogate. (A) Callus fabricated with fiberglass and epoxy. (B)
Radiograph of low density callus. (C) Soft tissue envelope and curvature applied to
T.J. Lujan et al. / Journal of Biomechanics 43 (2010) 792–795
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2.4.Clinical validation of algorithm
Ten antero-posterior and lateral radiographs of distal femur fractures treated
with locked plating were analyzed immediately after surgery and at a post-
operative time point. Five of the fractures were multifragmentary.
Three clinicians manually outlined the area of callus formation. Two clinicians
(DCF, SMM) were senior trauma surgeons, the other was an orthopaedic resident
(GDB). Using a pen tablet, clinicians independently outlined the cortex and
periosteal callus in each digital radiograph (300 PPI). Film radiographs of the
digital images were available for reference. Callus area was computed from the
clinicians’ digitally marked outlines.
Three non-clinicians evaluated the same radiographs using the proposed
algorithm with the following standard operating procedure: (1) orient images to
obtain vertical bone alignment with external cortex facing right; (2) ensure ROI
encompasses the internal cortex and callus; and (3) reference the initial post-
operative radiographs when tracing the external cortex.
The effect of independent factors on accuracy was assessed with one-way and
two-way ANOVAs. If significance was detected (pr0.05), Tukey post-hoc tests
determined significance between factor levels. Differences in callus area between
the clinician and algorithm were tested with a Pearson r correlation, while case-
by-case comparisons were examined with paired t-tests.
The algorithm’s inherent error in measuring callus area was a
function of PPI (po0.001) and callus size (po0.001) (Fig. 4A).
When image resolution was upgraded from 100 to 200 PPI, the
average error was reduced by 31% (po0.001). Callus areas of
1 mm2were detected on average with 30% larger error than areas
of 5 mm2(p=0.01). Although the size of length standard did not
have an overall effect onerror
improvement in error was observed when increasing the length
standard from 1 to 5 mm. Further increase to the length standard
only reduced error by an additional 0.3%.
The low and high density surrogate models were a good
approximation of actual callus at 6 and 24 weeks post-fracture,
respectively (Table 1). Relative to the adjacent cortex, the radio-
densities of the low and high density callus surrogates were 47%
and 81%, respectively. At low and high densities, the algorithm
was accurate within 5% of the actual surrogate area (Fig. 4B). The
algorithm predicted a significantly greater area for the high
density callus than the low density callus (po0.001). Rotation of
the radiograph in the image plane did not affect accuracy (p=0.9).
The average inter-observer standard deviation for the low and
high density surrogate was 0.8% and 1.1%, respectively.
(p=0.78), a notable13%
Overall, the clinician and algorithm groups had a high positive
correlation when analyzing area of fracture callus (R2=0.94,
po0.001). There was no significant difference between the two
groups in analyzing any specific case (Fig. 5). For all ten cases, the
average standard deviation or inter-observer variation in the
algorithm group was 4% and in the clinician group was 22%. At
200 PPI, the algorithm on average analyzed images in 60 s on a
standard computer (2.80 GHz processor).
The algorithm estimated callus area in long bone fractures
with good precision and accuracy. Area was over-predicted by
?3% in surrogate callus with a high radiodensity, while area was
under-predicted by ?3% in surrogate callus with low radio-
density. To minimize error implicit in the image processing
technique, the length standard and image resolution should be at
least 5 mm (roughly the diameter of plate screws) and 200 PPI
(typical for digital radiographs), respectively.
The callus size extracted by the algorithm correlated extremely
well with an independent analysis by orthopaedic surgeons. By
limiting subjective user interaction, the computational method
Fig. 4. Accuracy and sensitivity of the algorithm. (A) Numerical error of algorithm when using a 5 mm length standard. Callus size and PPI significantly affect error
(po0.001). (B) Error when analyzing radiographic images of callus surrogates (n=3). Accuracy was slightly affected by callus density (p=0.01), but not image plane rotation
Fig. 5. Fracture callus outlined manually by clinicians (n=3) and outlined with the
algorithm by non-clinicians (n=3). There was no statistical difference between the
groups. The algorithm had five times less inter-observer variance. Bars=standard
T.J. Lujan et al. / Journal of Biomechanics 43 (2010) 792–795
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had five times less inter-observer variance relative to the
surgeons. This technique provides a reliable measure of callus
size without requiring time-consuming and prohibitive consulta-
tions with physicians.
Limitations exist with this technique. Accuracy results are
based on surrogates that model a simplified fracture callus and
should be interpreted accordingly. Also, the segmentation of the
cortex required some user interaction. Although user input did not
result in large variations between observers, it nevertheless
inhibits objectivity and processing speed. To further improve
objectivity, a region growing procedure could automate cortex
segmentation (Gelaude et al., 2006). User interaction was not
required to segment the callus, since constant thresholds were
automatically applied. To make more robust, the algorithm could
be iterated to optimize these thresholds. The algorithm requires
the external cortex to be vertically aligned. However, since the
functions used for callus segmentation were invariant to rotation,
moderate variations in vertical alignment did not affect accuracy.
Finally, two-dimensional projections are not ideal in measuring a
three-dimensional biological process. Nevertheless, radiographs
do adequately approximate callus growth at the fracture site
(Augat et al., 1997) and require 45 times less radiation exposure
than equivalent computed tomography scans (Chauhan et al.,
In summary, the proposed algorithm presents a reliable and
valid technique to measure a radiographic feature with biome-
chanical and clinical relevance. By reducing the inter-observer
variation in callus measurement, this technique may improve the
utility of radiographs to predict bending stiffness at fracture sites
(McClelland et al., 2007). Furthermore, the influence of fracture
fixation constructs on secondary bone healing can now be
efficiently analyzed in large prospective and retrospective cohort
Conflict of interest
The authors have no conflict of interest.
We wish to thank Dr. Larry Marsh for his clinical insight and
recommendations. This project was supported by a grant from the
Legacy Research Advisory Committee.
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