Computed tomography-based joint locations affect calculation of joint
moments during gait when compared to scaling approaches
Ward Bartelsa*, Jan Demolb, Frederik Gelaudeb, Ilse Jonkersc and Jos
Vander Slotena
a
Department of Mechanical Engineering, Katholieke Universiteit Leuven, Leuven,
Belgium; bMobelife NV, Leuven, Belgium; cDepartment of Biomedical Kinesiology,
Katholieke Universiteit Leuven, Leuven, Belgium
*Corresponding author. Email: ward.bartels@mech.kuleuven.be
Disclosure statement
The authors declare no conflict of interest.
Acknowledgements
The authors extend their gratitude to Dr. Gerlinde Lenaerts for performing the gait analyses,
inverse kinematics and model scaling. Also, Prof. Dr. Michiel Mulier is gratefully
acknowledged for the clinical follow-up of the patients involved in this study.
This research was supported by the Agency for Innovation by Science and Technology (IWT).
CT-based joint locations affect calculation of joint moments during
gait when compared to scaling approaches
Hip joint moments are an important parameter in the biomechanical evaluation of
orthopaedic surgery. Joint moments are generally calculated using scaled generic
musculoskeletal models. However, due to anatomical variability or pathology,
such models may differ from the patient’s anatomy, calling into question the
accuracy of the resulting joint moments.
This study aimed to quantify the potential joint moment errors caused by
geometrical inaccuracies in scaled models, during gait, for eight test subjects. For
comparison, a semi-automatic CT-based workflow was introduced to create
models with subject-specific joint locations and inertial parameters. 3D surface
models of the femora and hemipelves were created by segmentation and the hip
joint centres and knee axes were located in these models.
The scaled models systematically located the hip joint centre (HJC) up to 33.6
mm too inferiorly. As a consequence, significant and substantial peak hip
extension and abduction moment differences were recorded, with respectively up
to 23.1% and 15.8% higher values in the image-based models. These findings
reaffirm the importance of accurate HJC estimation, which may be achieved
using CT- or radiography-based subject-specific modelling. However, obesityrelated gait analysis marker placement errors may have influenced these results
and more research is needed to overcome these artefacts.
Keywords: musculoskeletal modelling; subject-specific; computed tomography;
gait analysis; joint moments
1 Introduction
The combination of musculoskeletal modelling and dynamic motion simulation has
many applications in rehabilitation and orthopaedics, including clinical decision-making
in the surgical treatment of cerebral palsy (Simon 2004), the analysis of postural
stability and the functional evaluation of orthopaedic surgery and prosthetics (SoutasLittle 1998). Specifically, joint moments (gait kinetics) are an important parameter in
the biomechanical evaluation of patients undergoing orthopaedic surgery such as total
hip arthroplasty (THA) (Beaulieu et al. 2010; Klausmeier et al. 2010). To obtain
accurate joint moments, models are needed that realistically describe the patient’s
skeletal geometry, joint kinematics and inertial properties.
In clinical gait analysis, a generic model is usually scaled based on measured
marker locations (Bell et al. 1990; Delp et al. 1990; Davis et al. 1991; Seidel et al. 1995;
Lu & O’Connor 1999; Cappozzo et al. 2005; Leardini et al. 2007). The use of scaled
generic models may introduce geometrical inaccuracies in hip joint locations and knee
joint axes (Della Croce et al. 2005). Errors in marker placement can disrupt the
rescaling procedures. Della Croce et al. (1999) found inter-observer variability up to
25 mm for pelvic marker locations. Additionally, the patient’s anatomy may differ from
the standard model geometry due to anatomical variability or pathology (White 1989;
Scheys et al. 2006; Blemker et al. 2007; Scheys et al. 2008; Lenaerts et al. 2009).
Indeed, even within the group of volunteers used to create regression equations for
locating the hip joint centre (HJC), Bell et al. (1990) found HJC prediction errors up to
34.9 mm. Also, many generic models (Delp et al. 1990; Davis et al. 1991; Lu &
O’Connor 1999) assume the knee flexion-extension axis to be perpendicular to the
mechanical axis of the femur. However, in a cadaver study, Stiehl and Abbott (1995)
found transepicondylar axes inclined up to 5.9° relative to the femur mechanical axis.
The resulting inaccuracies in the joint kinematics of scaled generic models may
compromise the accuracy of the calculated joint moments.
This study aimed to quantify the geometrical inaccuracies in hip joint locations
and knee joint axes for scaled generic models and the resulting errors in calculated joint
moments during gait. Specifically, the generic model presented by Delp et al. (1990)
and the rescaling procedure introduced by Lu and O’Connor (1999) were investigated.
To evaluate the inaccuracies in HJC, knee joint centre and knee axis inclination as well
as the resulting errors in calculated joint moments, we introduced a new method for
constructing image-based, subject-specific models. Based on 3D CT images of the
pelvis and femora, the joint kinematics and inertial parameters of a musculoskeletal
model were semi-automatically individualized. Significant differences in joint
locations, joint axes and calculated joint moments between the resulting image-based
models and the corresponding scaled generic models would emphasize the need for
accurate incorporation of hip and knee joint kinematics in musculoskeletal models for
use in the calculation of joint moments.
2 Materials and methods
2.1 Test subjects and gait analysis
After approval from the institutional review board, one man and seven women gave
informed consent to participate in this study. The subject group’s mean age was 60.7
years (range 41–75) and their mean body mass index (BMI) was 28.0 (range 25.4–33.2).
All subjects were evaluated prior to THA for treatment of osteoarthritis. The mean
femoral neck length on the operated side was 52.6 mm (range 62.5–42.7 mm), the mean
neck-shaft angle was 123.0° (range 105.5°–142.6°) and the mean femoral anteversion
angle was 14.8° (range 6.1°–26.8°).
Gait analysis was performed for all test subjects as part of a previously reported
study (Lenaerts et al. 2009). The analysis was performed with the subject barefoot,
walking at self-selected speed along a 10 m walkway. Walking aids were not used.
During walking, 30 reflective markers were attached to the subject’s skin,
following the full-body marker protocol presented by Davis et al. (1991). During the
static pose used to scale the musculoskeletal model, four additional markers were placed
on the medial epicondyles and malleoli. A VICON system with eight cameras (612
data-capturing system, VICON, Oxford Metrics, Oxford, UK) recorded the 3D marker
trajectories at a sample rate of 120 Hz. Two AMTI force plates (Advanced Mechanical
Technology Inc., Watertown, MA, USA) were used to measure ground contact force.
2.2 Inverse dynamics using scaled generic models
In a first step, scaled generic models were used in an inverse dynamics framework to
determine joint moments. The musculoskeletal model presented by Delp et al. (1990)
was used. This model includes 16 degrees of freedom. The knee is described by the
planar model presented by Yamaguchi and Zajac (1989), with the plane of the motion
perpendicular to the knee axis, which itself is perpendicular to the mechanical axis of
the femur (connecting HJC and knee centre).
Models were scaled to the subjects’ dimensions, based on marker locations
recorded during a static pose (Lu & O’Connor 1999), using the SIMM program
(Musculographics Inc., Motion Analysis, Santa Rosa, CA, USA). Regression equations
(Bell et al. 1990) were used to locate the HJC. Pelvic scale factors were determined
based on the HJC and the markers in the pelvis frame. The resulting model will be
called the “scaled model”.
Gait kinematics (generalized coordinates) were calculated from the 3D marker
trajectories recorded by the VICON system using an inverse kinematics procedure (Lu
& O’Connor 1999). SIMM dynamics pipeline in conjunction with SD/FAST
(Parametric Technology Corporation®, Needham, MA, USA) was used to determine the
joint moments based on the scaled model and the gait kinematics.
2.3 Inverse dynamics using image-based models
2.3.1 Overview
This study introduced a new procedure for constructing an image-based, subjectspecific model. Based on CT images, this model individualized the lumbosacral, hip and
knee joint kinematics as well as the inertial parameters of the femur and pelvis
segments. It will be called the “image-based” model.
The flow diagram in Figure 1 provides an overview of the procedures used to
construct image-based models. These procedures used 3D models, obtained by
segmenting CT images, to individualize the femur and pelvis body segments.
Specifically, the locations of the HJC, knee axis and lumbosacral joint centre as well as
the pelvis and femur centre of mass (COM) were updated to better represent the subject-
specific situation. To construct the image-based model, the resulting femur and pelvis
segments were integrated into the scaled model; other body segments were left
unaltered. These procedures are briefly discussed in the following sections; the
appendix offers a more exhaustive description.
2.3.2 CT imaging and construction of 3D bone models
Pre-operative CT images of the pelvis and femora were acquired using a GE
BrightSpeed (GE Healthcare, Little Chalfont, UK) scanner with a field of view of 440
by 440 mm, producing 0.859 by 0.859 mm pixels. For imaging the pelvis, proximal and
distal femur, the transverse image slices were spaced 2 mm apart. In order to limit
radiation exposure, the inter-slice-distance was increased to 10 mm for the femoral
diaphysis.
3D models representing the bone surface were constructed from the CT images.
Mimics® (Materialise® NV, Leuven, Belgium) was used to perform semi-automatic
segmentation (Gelaude et al. 2008). A threshold of 226 Hounsfield units was applied to
the images’ grey values to segment the bony structures. The resulting voxel masks were
further refined using manual editing and automated tools including morphological
dilation, erosion and region growing. From the final voxel masks, a set of triangulated
surface meshes were constructed using the Marching Cubes algorithm (Lorensen &
Cline 1987).
Using these methods, 3D models of the hemipelves and femora were created for
all subjects. For the sacral bone, a scaled generic mesh was used as this bone was
considered less relevant for the mechanics of gait.
2.3.3 Image-based modelling
A set of anatomical features was automatically identified in the 3D bone models for
both the image-based bone models and the scaled model. These features included a set
of landmarks on the hemipelvis (anterior superior iliac spine – ASIS, posterior superior
iliac spine – PSIS, symphysis pubis) and on the femur (medial adductor tubercle, lateral
epicondyle). Additionally, the pelvic symmetry plane was located by registering the left
hemipelvis model to the right hemipelvis using the iterative closest point algorithm
(Besl & McKay 1992).
The hip was defined as a spherical joint with the kinematics fully determined by
the HJC location, which was determined as a 3D vector within the pelvic coordinate
system. With respect to the femoral coordinate system, flexion-extension occurred
along the medio-lateral axis, ab-adduction along the sagittal axis and rotation along the
longitudinal axis. For the image-based bone models, the HJC was located using a
previously published procedure (Bartels et al. 2012).
The knee kinematics were described by a planar model, with the plane of the
motion perpendicular to the knee axis (Yamaguchi & Zajac 1989). This axis was
defined as a line parallel to the posterior condyle symmetry axis and passing through the
lateral epicondyle landmark. The posterior condyle symmetry axis was located by
manually delineating the posterior condyles and determining their rotational symmetry
axis. To determine the knee centre, the midpoint of the line segment connecting the
medial adductor tubercle and the lateral epicondyle was projected onto the knee axis.
Based on the anatomical features in the image-based bone models and the scaled
model, the image-based bones were aligned to the scaled model’s body segments. This
alignment transformation consisted of a rotation and a translation. For the pelvis, the
symmetry plane of the image-based pelvis was rotated to lie parallel to that of the scaled
model pelvis. Additionally, the lines connecting the ASIS and symphysis pubis for the
image-based and scaled pelvis were projected onto the pelvic symmetry plane. The
image-based pelvis was rotated to align these projected lines. The subsequent
translation made the projection of the image-based PSIS points on the pelvic symmetry
plane coincident with the projected PSIS point of the scaled model. For the femur, the
image-based mechanical axis was rotated to lie parallel to that of the scaled model
pelvis, and the angle between the image-based and scaled model knee axes was
minimized. A subsequent translation made the image-based HJC coincident with that of
the scaled model. The resulting alignment transformations were used to transform the
HJC, knee axes and 3D bone models into the local coordinate systems of the imagebased model’s pelvis and femur segments.
The lumbosacral joint centre, the body segments’ centres of mass and the
sacrum 3D model were not obtained directly from the CT images. Instead, these data
were obtained by applying re-scaling transformations to the scaled model’s pelvis and
femur segments. These transformations were defined based on the anatomical features
in the image-based bone models and the scaled model. The transformations used for
scaling were the same as those used previously in the construction of the scaled model
(Lu & O’Connor 1999), but the scale factors were different. For the pelvis, a nonuniform scaling was performed, with three scale factors corresponding to the three axes
of the local coordinate system. The scale factors were defined as the proportions
between three distances measured in the image-based bone models and the
corresponding distances in the scaled model. Specifically, the left-right inter-ASIS
distance, the antero-posterior distance from HJC to PSIS and the vertical distance from
HJC to ASIS were used. For the femur, a uniform scaling was used, with the scale
factor calculated from the distance between HJC and knee centre.
The body segment masses and moment of inertia tensors in the scaled model
were not altered, as they had already been scaled based on total body mass.
2.3.4 Inverse kinematics and inverse dynamics
For the inverse kinematics procedure used to determine gait kinematics (generalized
coordinates), the locations of the gait analysis markers had to be expressed in the body
segments’ local coordinate systems. Because the gait analysis markers were not
included in the CT images, we could not reliably locate the markers in the image-based
models.
Initially, inverse kinematics were calculated using markers located on imagebased anatomical landmarks, i.e. the ASIS and PSIS points for the pelvis and two points
on the knee axis for the femur segment. However, the calculated joint angles differed
strongly from the joint angles obtained for the scaled model. In particular, large
differences were found for the forward pelvic tilt (pitch) angles. The largest pertimeframe differences in pelvic tilt between the models ranged from -1.5 to 39.2° with a
mean of 13.0° (indicative of a more anteriorly tilted in the image-based models). Test
subjects presenting excessive anterior pelvic tilt also showed a larger distance between
the ASIS gait analysis markers than between the corresponding bony landmarks. We
therefore concluded that the influence of soft tissue probably shifted the ASIS markers
to a location antero-lateral from the corresponding bony landmarks. In addition, gravity
may have shifted the ASIS markers downward after palpation. These marker placement
errors would disrupt the inverse kinematics procedure, as the pelvis tilts forward to
align the bony landmarks to the recorded marker positions. Because of these
phenomena, we considered the inverse kinematics for the image-based models
unreliable. Therefore, the gait kinematics obtained for the scaled models were imposed
on the image-based models.
Using procedures similar to those discussed in section 2.2, joint moments were
calculated for the image-based models. Rather than scaling the models and using
regression equations to locate the HJC, the image-based models were used directly.
SIMM dynamics pipeline and SD/FAST were used to determine joint moments based
on these models.
2.4 Image-based knee axis reproducibility
The direction of the knee axis was determined by two manually isolated areas on the
posterior condyles. This manual step can potentially introduce a user-dependent error
into the knee axis definition and consequently influence the joint moments investigated
in this study. To evaluate the effect of this user-dependent step, the reproducibility of
the resulting axis was determined. Two observers tested the procedure for locating the
knee axis on nine pairs of femora. Each observer repeated this test three times on
separate days.
The angles between the three knee axes obtained for each observer were
calculated for each knee. The maximum of the three resulting angles was used to
quantify intra-observer variability.
Subsequently, a set of unit vectors was defined parallel to the knee axes. For
each observer and each knee, the mean of the three resulting vectors was calculated and
normalized. To quantify inter-observer variability, the angle was calculated between the
mean vectors for both observers.
2.5 Evaluating model differences
2.5.1 Knee axis inclination
In the scaled models, the knee axis was perpendicular to the mechanical axis by
definition. In the image-based models, due to the rotational alignment of the femur
coordinate system onto the scaled model, the knee axis was parallel to the coronal
plane, at a variable angle with the mechanical axis. The deviation of this angle from 90°
represents the knee axis inclination. This inclination was defined as positive when the
joint tended towards valgus. The knee axis inclination was only determined for the
image-based models, as it was zero by definition in the scaled models.
2.5.2 Joint locations
Because gait analysis markers were not included in the CT images, we could not define
a reference frame common to the image-based and scaled models. Therefore, a set of
frame-invariant measures was used to evaluate the differences in joint locations between
both model types. Different measures were used for the femur and pelvis body
segments.
Changes in joint locations for the pelvic segment were expressed by the relative
positions of the lumbosacral joint centre and HJC. Therefore, vectors were calculated
from the lumbosacral joint centre to the left and right HJC in the coordinate system of
the pelvis segment. The axes of this coordinate system corresponded with the anterior,
lateral and superior anatomical directions. To quantify the differences between imagebased and scaled models, the vectors calculated for the scaled model were subtracted
from the vectors calculated for the image-based model. This yielded the change in HJC
relative to the lumbosacral joint. In order to remove the dependence between the left
and right side, the mean of both sides’ HJC change was calculated for each subject. This
approach was used to avoid treating both sides as statistically independent samples.
During the rotational alignment of the image-based femur onto the scaled model,
the mechanical axes were made coincident (see appendix, section A.2.3). As the
mechanical axis connects the HJC to the knee joint centre, the relative positions of both
joints only differ along the mechanical axis. Therefore, the length of the femur was
defined as the distance from HJC to knee centre along the mechanical axis, and this
length was used to express changes in joint locations for the femur segment. Changes in
femur length were therefore calculated for the left and right femora. The mean of the
left and right side’s femur length change was calculated for each subject.
2.5.3 Joint moments
To evaluate the mechanical consequences of the joint definition differences between
scaled and image-based models, joint moments were calculated for both modelling
methods. This was done unilaterally for all eight test subjects over the course of one gait
cycle.
For each test subject, proportional differences in peak joint moments between
both model types were determined: for each degree of freedom, the maximum moment
was calculated over the entire gait cycle. Differences in peak moments between the
scaled and image-based model were calculated and normalized to the peak moments in
the scaled model. For the hip, maximal extension, flexion, abduction and endorotation
moments were evaluated whereas for the knee and ankle only peak knee extension and
ankle plantar flexion were evaluated.
To investigate joint moment changes over the entire gait cycle, the maximum
and minimum per-timeframe joint moment differences between scaled and image-based
models were determined. For each time frame, the differences between the joint
moments calculated using the scaled model and the image-based model were
determined. The maximum and minimum values of these moment differences for the
gait cycle are reported.
2.5.4 Statistical analysis
The Wilcoxon signed rank test was used to assess the significance of differences
between image-based and scaled models. Differences were considered significant for pvalues under 0.05.
3 Results
3.1 Image-based knee axis reproducibility
The intra-observer variability of the knee axis was quantified for both observers as the
angles between pairs of knee axes determined for the same knee. For one observer, the
mean intra-observer variability over all knees was 2.0° (standard deviation 1.2°), with a
maximum of 4.3°. For the other, the mean variability was 1.2° (standard deviation 0.7°),
with a maximum of 3.6°.
The inter-observer variability was quantified as the angles between mean knee
axis directions located by both observers for the same knee. The mean inter-observer
variability over all knees was 1.6° (standard deviation 0.9°), with a maximum of 2.9°.
3.2 Model differences
3.2.1 Knee axis inclination
Figure 2 shows the knee axis inclination as box plots calculated over the eight test
subjects (sixteen knees). The knee axis inclination showed a slight tendency towards
positive values (valgus), ranging from -2.5° to 6.6°. The median of the inclination was
2.3°.
3.2.2 Joint locations
Figure 3 shows the changes in HJC location (mean between left and right sides) as box
plots calculated over the eight test subjects. The dominant component of the HJC
change was clearly the superior direction. Image-based musculoskeletal modelling
yielded HJC locations up to 33.6 mm (median 18.7 mm) closer to the lumbosacral joint
in the vertical direction than a scaling approach. This difference was significant
(p = 0.008). The changes in the medio-lateral direction were not significant (p = 0.547).
Their values were roughly centred around 0 (median 2.4 mm), ranging from 8.0 mm
medial to 10.7 mm lateral. A posterior displacement up to 15.7 mm (median 5.6 mm)
was also observed, with an outlier showing a 12.6 mm anterior displacement. However,
this difference was not significant (p = 0.148).
Figure 4 shows the changes in femur length (mean between left and right sides)
as box plots calculated over the eight test subjects. The image-based femora were
systematically longer than the femora obtained by scaling a generic model. Significant
(p = 0.008) length changes up to 95.7 mm (median 14.3 mm) were observed.
3.2.3 Joint moments
Figure 5 shows the proportional peak joint moment differences over the eight test
subjects as box plots, along with the significance of these differences. Also, for scale,
the mean joint moments for the image-based models over the eight test subjects are
shown as a function of the gait cycle’s progress, starting at initial heel contact. To
eliminate the effect of body mass differences, joint moments are expressed in units of
per cent bodyweight-meters (%BW·m).
Significant differences in hip extension (p = 0.016) and abduction (p = 0.016)
moments were observed. In the image-based models, hip extension moments were up to
23.1% higher than in the scaled models, with an outlier of 35.9%. Hip abduction
moments were up to 9.0% higher in the image-based models, with an outlier of 15.8%.
Significant (p = 0.016) differences in knee extension moment were also observed, but
these were limited to -4.9%. For hip rotation and ankle plantar flexion, differences in
joint moments were negligible.
The minimum and maximum per-timeframe joint moment differences (Figure 6)
showed behaviour similar to the peak joint moments. The most extreme changes
appeared in hip flexion, extension and abduction.
4 Discussion
4.1 Results and interpretation
To assess the potential errors in joint moments caused by inaccuracies in the kinematics
of scaled models, differences between image-based and scaled models have been
quantified in terms of hip and knee joint locations, knee joint inclinations and joint
moments. A semi-automatic procedure has been presented for constructing image-based
subject-specific dynamic models from CT images of a subject’s pelvis and femora. The
manual steps required were the segmentation of the pelvis and femora from CT images
and the isolation of the posterior condyles from the resulting 3D femur models.
The joint locations of the image-based models have been compared with those
of scaled models (Delp et al. 1990; Lu & O’Connor 1999) in eight test subjects. The
most important findings resulting from this comparison were large differences in the
vertical components of joint locations. In the pelvis segment, the image-based HJC was
located significantly closer to the lumbosacral joint centre, by up to 33.6 mm (median
18.7 mm). Also, all image-based femora were significantly longer than their scaled
counterparts by up to 95.7 mm (median 14.3 mm), which is roughly a quarter of the
entire femur length.
As an additional finding, the image-based models showed substantial inclination
of the knee axis (-2.5° to 6.6°), calling into question the representativeness of the
inclination angles in the scaled models, which are zero by definition. The inclination
angles obtained for the image-based models quantify the potential increase in accuracy
obtained by using image-based models. However, for our test subjects, this difference is
not substantially larger than the knee axis reproducibility (4.3°). In a clinical population
presenting excessive varus or valgus angles, image-based modelling may therefore have
a greater effect on the knee axis orientation and the resulting joint moment calculations.
The differences between scaled and image-based models caused significant
changes in the calculated joint moments. The most important of these occurred in the
hip extension moment, which increased by up to 23.1%, and the hip abduction moment,
which increased by up to 15.8% for the image-based models. Joint moment differences
of this magnitude may be clinically relevant for patients suffering from hip
osteoarthritis. Indeed, Beaulieu et al. (2010) found a peak hip abduction moment of
0.90 Nm/kg for healthy control subjects, compared to 0.76 Nm/kg for a group of
patients who underwent THA, representing a 15.6% deficit. In addition, Klausmeier et
al. (2010) recorded a peak abduction moment of 0.96 Nm/kg for healthy controls,
compared to 0.77 Nm/kg for THA patients operated using an anterolateral approach, or
a 19.8% deficit. These clinically significant differences are in the same range as the
differences in joint moments resulting from scaled and image-based models obtained in
the present study.
Taken together, these observations indicate that scaling of generic models
systematically locates the HJC too inferiorly, introducing clinically significant errors in
the resulting joint moments. A possible cause for this is the influence of soft tissue
impeding the accurate localization of markers attached over palpable bony landmarks
during the static pose (Della Croce et al. 2005). In studies performed by Rabuffetti et al.
(2002) and Della Croce et al. (1999), an inter-observer variability ranging from 13 to
25 mm was recorded for the locations of markers placed on the pelvis. For the femur,
the variability ranged from 13 to 19 mm. The pelvic markers are particularly sensitive to
marker misplacement. Especially in obese patients, gravity may shift these markers
downward from their anatomical location. Additionally, the distance between the ASIS
markers – which determines the size of the scaled pelvis segment – may not correspond
to the distance between the corresponding bony landmarks. Using scaled models, these
effects will shift the pelvis downward and increase its size, resulting in an HJC located
too inferiorly. The scaled femur segments will also shorten.
The regression equations used to locate the HJC in the scaled model (Bell et al.
1990) may also cause inaccuracies (Della Croce et al. 2005). Using bi-planar
radiographs to locate the true HJC, Bell et al. (1990) found HJC estimation errors up to
35 mm, with a mean of 19 mm. Leardini et al. (1999) used similar methods to evaluate
the regression equations published by Bell et al. (1990) and Davis et al. (1991), finding
mean errors of respectively 23 and 21 mm. Functional methods were previously
suggested to provide a better HJC estimate. These methods locate the HJC as the pivot
point of a recorded relative motion of the femur with respect to the pelvis (Della Croce
et al. 2005). However, their accuracy depends on the subjects’ range of motion at the
hip joint, which was impaired in the present study due to the subject group’s hip
pathology.
These findings support the need for subject-specific modelling in the
biomechanical evaluation of orthopaedic surgery. In particular, the HJC location plays
an important role, as found previously by Lenaerts et al. (2009).
4.2 Potential limitations
The knee axes are located using a method that relies on manually indicated
posterior condyle areas. This represents a potential limitation: errors in locating the knee
axes in the image-based model could potentially confound the calculation of the
resulting joint moments. However, the knee axis showed good reproducibility. The
intra-observer variability never exceeded 4.3° and the inter-observer variability was
below 1.9°. Furthermore, the range of knee axis inclinations found in this study (-2.5° to
6.6°) (Figure 2) is comparable to the range of inclination angles found by Stiehl and
Abbott (1995) in cadaver experiments involving healthy knee joints (-5.9° to 4.2°).
These findings indicate that excessive errors did not occur in locating the knee axis.
In this study, the femur and pelvis segments of scaled musculoskeletal models
were individualized based on CT images, potentially improving the realism of the
resulting models. The joint centres and axes in the image-based models were
determined from CT images with a repeatability on the order of millimetres, far below
the differences detected between image-based and scaled models. This implies that, at
least concerning the joint locations, the image-based models can be considered the most
realistic. However, the joint moments under investigation cannot be directly measured
and the moments calculated using the image-based models can still be influenced by
errors in the kinematics or inertial properties. Therefore, this study cannot provide gold
standard joint moments for comparison.
As gait analysis markers were removed prior to CT scanning, there was no
reference geometry that could be used to construct a common coordinate frame for both
scaled and image-based models. Therefore, absolute joint locations could not be
compared; distances between joint centres were calculated to overcome this problem.
Future studies should include the gait analysis markers in the medical images whenever
possible.
For the image-based models, a scaling approach was used to locate the body
segments’ centres of mass. These scaling procedures, which allow at most three scale
factors to vary, cannot capture the full anatomical variability of the body segments
under investigation. Furthermore, the centre of mass locations likely depend more on
soft tissue properties than on bone geometry. By consequence, errors may arise in the
image-based centres of mass. However, because similar scaling procedures were used to
locate the centre of mass in the scaled and image-based models, these errors are
probably similar in both models. In future research, the centres of mass could be
computed from soft tissue information in the medical images (Sandoz et al. 2010; Dao
et al. 2012).
The high BMI in the group of test subjects poses potential limitations to this
study as it increases soft tissue artefacts and interferes with marker placement. These
marker placement errors will additionally cause inaccuracies in the HJC location
estimated by the regression equations used (Bell et al. 1990). As these equations were
only used for scaling generic models and not for creating image-based models, the
influence of obesity might exaggerate the differences between both modelling methods.
Another consequence of the obesity-related marker placement errors was the
difficulty in calculating gait kinematics. Because the gait analysis protocol was not well
suited for reconstructing anatomical landmark positions in obese test subjects, an
attempt to track the recorded marker locations with image-based bony landmarks
resulted in excessive pelvic forward tilt angles, clearly exceeding the tilt angles for the
scaled models. This problem was probably caused by marker placement errors of the
ASIS markers, which may have shifted downward and antero-laterally due to the
combined effect of gravity and soft tissue covering the bony landmarks. When the
image-based models were used in the inverse kinematics procedure, the pelvis tilted
forward in order to align the (CT-based) bony landmarks to the recorded marker
positions. As we had no alternative for determining gait kinematics with the imagebased model, the scaled model’s motion pattern was imposed on the image-based
model. Imposing the kinematics from a different model introduces errors in the resulting
joint moments. However, the joint moments investigated here are only influenced by the
position and orientation of the segments below the hip; the marker placement errors did
not affect these segments as strongly as the pelvis segment. An alternative approach,
e.g. the use of bony landmarks to track the recorded markers, would likely have
introduced greater errors. Furthermore, registration of the gait analysis markers to the
CT images would not entirely solve this problem: as the test subject lies supine in the
CT scanner, gravity will affect the markers differently than in the upright posture during
a gait analysis trial. Future studies should therefore employ imaging techniques that
work in a standing position, such as upright MRI (Liodakis et al. 2011), upright CT
(Shah et al. 2009) or bi-planar radiography systems (Thelen et al. 2012). Alternatively, a
different gait analysis protocol could be used where anatomical landmark calibration
techniques (Cappello et al. 1997; Stagni et al. 2006; Hara et al. 2013) are applied to the
ASIS points.
The group of test subjects consisted entirely of patients about to undergo surgery
for hip osteoarthritis. As compensatory motions can influence the gait pattern of these
patients (Watelain et al. 2001), our findings might not carry over to a healthy test
population. To confirm the validity of our conclusions for healthy test subjects, the
present study should be reproduced in a healthy test population.
4.3 Suggestions for future work
In future work, the image-based modelling techniques presented in this study
may be modified to improve generic models and the rescaling procedure. Planar
radiographs could be used to individualize joint locations directly or via a statistical
shape model. Considering the substantial discrepancy in the size of the femur and pelvis
segments between the scaled and image-based models investigated in the present study,
this could strongly improve the accuracy of the scaled model. Furthermore, the imagebased joint locations could be used to construct new regression equations for locating
the HJC during gait analysis. However, this would require the gait analysis markers to
be included in the medical images, as bony landmarks locations may differ substantially
from the corresponding marker locations.
Subject-specific musculoskeletal models can also be constructed using MRI
images. A workflow to create subject-specific models from MRI images was presented
by Scheys et al. (2006, 2008). Using this workflow, accurate muscle trajectories were
obtained directly from MRI images. Significant differences in muscle moment arms
were demonstrated when comparing MRI-based models with scaled models. However,
this approach requires expensive MRI imaging which is not always accessible for all
patients due to claustrophobia or implanted devices. Additionally, MRI is poorly suited
for creating accurate models of the outer bone surface (Chen & Wang 2004). Such
models are often necessary for the computer-assisted planning of orthopaedic surgery
(CAOS) (Sugano 2003).
5 Conclusions
We conclude that significant and substantial differences exist between scaled and
image-based models in terms of joint locations and calculated joint moments. The
magnitude of the joint moment differences is comparable to clinically relevant
differences recorded in previous studies (Klausmeier et al. 2010, Beaulieu et al. 2010).
The most important differences in joint location were found in the vertical direction,
with the HJC being consistently located more superiorly in the image-based models.
The strongest differences in calculated joint moments occurred for hip extension and
abduction, and were in the same range as the joint moment differences reported in
literature from comparing healthy control subjects with patients who received a THA.
Our findings underline the importance of accurate HJC estimation during gait
analysis. This may be relevant for the biomechanical evaluation of orthopaedic hip
surgery, where the effect of the method used to locate the HJC may exceed the
differences in joint moments between healthy controls and THA patients. Considering
the differences in joint location observed, even a (suitably calibrated) planar radiograph
could be used to vastly improve the accuracy of musculoskeletal models.
However, more research is needed to overcome the effect of obesity-related
marker placement errors on the recorded kinematics, by using alternative marker
protocols with calibration of the ASIS or by using medical imaging in a standing
position while ensuring that the markers can be located in the images. Also, our
conclusions should be confirmed in a healthy population.
Appendix: Constructing image-based, subject-specific models
A.1 Identifying anatomical features
A.1.1 Landmarks
MATLAB® (The MathWorks®, Inc., Natick, MA, USA) was used to extract imagebased anatomical features from the individual meshes and to create customized models.
Anatomical landmarks on the hemipelvis and femur bones, required to align the bone
models with the musculoskeletal model’s local coordinate systems, were automatically
identified using a set of custom routines.
For the hemipelvis, the landmarks included the anterior and posterior superior
iliac spine (ASIS and PSIS) as well as the symphysis pubis. The hemipelvis was first
separated into a superior and an inferior half along the cranio-caudal axis of the
coordinate frame. The points in the superior part were projected onto a plane
perpendicular to the cranio-caudal axis, and a 2D bounding box analysis was used to
identify the ASIS and PSIS landmarks. For the symphysis pubis, a line was constructed
perpendicular to both the cranio-caudal axis and the line connecting ASIS and PSIS.
Subsequently, for each point in the inferior part, the distance to the ASIS was calculated
parallel to this line. The point with the maximum distance identified the symphysis
pubis.
For the femur, the medial adductor tubercle and the lateral epicondyle were
located. Therefore, the ‘tabletop’ position (Kingsley & Olmsted 1948) was simulated. In
this position, the femur was laid on a flat surface, lying on both posterior condyles and
the posterior trochanter major. The convex hull of the 3D model was calculated and the
largest posterior-facing triangle in the resulting hull was selected. The points of this
triangle represented the contact points between the femur model and the flat surface.
Subsequently, the line connecting both posterior condyle contact points was
constructed. All points in the inferior half of the femur model were projected onto this
line. The medial adductor tubercle and the lateral epicondyle were identified as the most
medial and the most lateral of these points respectively.
A.1.2 Joint centres and axes
The image-based HJC was located using a procedure published previously (Bartels et al.
2012). Briefly, a threshold of 7.5 mm was applied to the distance between the caput
femoris and the acetabulum. Points on the caput femoris model for which this distance
was within the threshold value, as well as the associated surface normal, were used in
the calculation of the HJC.
The image-based posterior condyle symmetry axis was determined as the
rotational symmetry axis of the posterior condyles (Churchill et al. 1998; Iwaki et al.
2000; Johal et al. 2005). Therefore, the posterior condyles were isolated from the femur
models by use of a graphical user interface (Figure 7) that allows the user to manually
delineate the condyle area on the femur model.
To determine the rotational symmetry axis of the posterior condyles, a set of
springs was defined, located at the vertices in the posterior condyle mesh and directed
along the corresponding vertex normals (Max 1999). The rotational axis was found by
minimizing the energy increase per unit of rotation in the resulting elastic system (Lin et
al. 2000).
The image-based knee axis was defined as a line parallel to the posterior condyle
axis that passes through the lateral epicondyle anatomical landmark. This definition
corresponds with the knee axis used in the scaled model (Delp et al. 1990), which
passes through the gait analysis markers on both epicondyles.
Finally, the image-based knee centre was determined by intersecting the imagebased knee axis with the bisecting plane of the line segment connecting the lateral
epicondyle and the medial adductor tubercle. For the scaled model, the knee centre was
defined as the midpoint of the gait analysis markers on both epicondyles.
A.2 Individualizing the model
A.2.1 Overview
Individualizing body segment kinematics in a musculoskeletal model based on medical
images generally required solving three problems.

The image-based bone models and the anatomical features were described in the
CT scanner’s coordinate system, which is essentially arbitrary. Therefore, in
order to use information contained in the bone models, the bone models needed
to be aligned relative to the local coordinate systems of the body segments in the
scaled model.

The scaled model’s joints, which may be inaccurately located due to errors in
the rescaling procedures, needed to be adapted so they correspond to the
information obtained from the medical images.

Some data, e.g. the centre of mass location, could not be directly located in the
CT images.
In the present work, these problems were solved by defining alignment transformations
from CT coordinates onto the scaled model’s body segment coordinate systems and by
re-scaling the scaled model’s body segments. The alignment transformations were
defined as rigid body rotations and translations. The re-scaling was performed by recalculating the scale factors of the scaled model’s body segments. The parameters for
these alignment and re-scaling transformation were based on anatomical features
identified in both the CT images and the scaled model’s body segments, as explained
below.
To construct the image-based model, the alignment transformations were
applied to the image-based HJC, knee axes and 3D bone models of femora and
hemipelves. Additionally, re-scaling was applied to the lumbosacral joint centre, the
body segments’ centres of mass and the 3D model of the sacrum from the scaled model.
A.2.2 Alignment and rescaling of pelvis
The image-based pelvis was aligned to the scaled model’s pelvis local coordinate
system. The rotation was determined first, after which the scale factors of the scaled
model pelvis were re-calculated. Finally, the translation was determined.
To determine the rotational alignment, the image-based pelvis was rotated so
that the pelvic symmetry plane was coincident with that of the scaled model. In the
image-based bone model, this symmetry plane was located by mirroring the left
hemipelvis model and registering it to the right hemipelvis using the iterative closest
point algorithm (Besl & McKay 1992). After this alignment of symmetry planes, one
rotational and two translational degrees of freedom still had to be determined.
For the image-based hemipelvis models, a line segment was constructed from
the midpoint of the ASIS landmarks to the midpoint of the symphysis pubis landmarks.
This line was then projected onto the pelvic symmetry plane (Figure 8). The imagebased pelvis was rotated so that this line segment was parallel to a similarly defined line
segment in the generic model, constraining the one remaining rotational degree of
freedom. The generic model (without scaling) was used rather than the scaled model, as
the non-uniform scaling of the pelvis body segment would affect the orientation of the
resulting line segment.
With the rotational alignment known, the scale factors of the scaled model’s
pelvis segment could be re-calculated prior to the translational alignment. This involved
a non-uniform scaling defined by three different scale factors corresponding to the three
axes of the local coordinate system.
The three scale factors were calculated as the proportions of specific distances
between the image-based and scaled model pelvis after rotational alignment (Figure 9):

the distance between the left and right ASIS landmarks along the coronal axis;

the distance between the midpoint of both ASIS landmarks and the midpoint of
both posterior superior iliac spine (PSIS) landmarks along the sagittal axis;

the distance between the midpoint of both ASIS landmarks and the midpoint of
the left and right HJC along the longitudinal axis.
The two remaining translational degrees of freedom in the symmetry plane determined
how the image-based pelvis connected to the sacrum at the sacroiliac joint. To this end,
the midpoints of the left and right PSIS landmarks were projected onto the pelvic
symmetry plane for both the scaled model pelvis and the image-based pelvis. The latter
was then translated along the symmetry plane in such a way that the projected points of
the image-based and re-scaled model coincide. This completed the alignment of the
image-based pelvis onto the local coordinate system of the pelvis body segment.
A.2.3 Alignment and rescaling of femur
For the image-based femur, the mechanical axis was constructed by connecting the knee
centre to the HJC. To facilitate aligning the image-based femur onto the scaled femur
body segment, the same axis was constructed for the scaled femur, with the knee centre
defined as the midpoint between the medial and lateral epicondylar gait analysis
markers.
The image-based femur was first rotationally aligned to the scaled model femur.
It was rotated so that its mechanical axis was parallel with that of the scaled model
femur. An additional rotation around the mechanical axis was performed to ensure that
the plane formed by the knee axis and the mechanical axis was parallel to the equivalent
plane in the scaled musculoskeletal model (Figure 10(a)).
Subsequently, the image-based femur was translated so that its HJC coincided
with the model’s hip centre, which acted as the origin of the femur segment’s local
coordinate system. In effect, this translation connected the image-based femur to the
pelvis.
Finally, the scale factor of the scaled model’s femur segment was re-calculated.
The femur body segment scaling was a uniform scaling utilizing a single scale factor for
the three coordinate axes. To re-calculate the scale factor, the distance between the HJC
and the knee joint centre was calculated for both the image-based femur and the scaled
model femur. The proportion of both calculated distances determined the new scale
factor (Figure 10(b)).
The femur body segment contains two joints: the HJC and the knee joint. As
discussed above, the translational alignment moved the image-based HJC to the origin
of the body segment coordinate system, which individualized the HJC in the femoral
frame.
In the model used here (Delp et al. 1990), the knee kinematics were described
by a planar model (Yamaguchi & Zajac 1989) with all motion taking place in a plane
perpendicular to the knee axis. The same planar model was used for the image-based
knee. However, knee kinematics were individualized by rotating this plane around an
antero-posterior axis into an orientation perpendicular to the image-based knee axis.
Additionally, the translations of the tibia relative to the femur that occur during knee
flexion were rescaled by applying the previously determined re-calculated scale factors.
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Figures
CT coordinates
Segmentation
Femur &
hemipelvis
3D models
Femur & pelvis
segments
Identifying
anatomical
features
Anatomical
features
Identifying
anatomical
features
~
Sacrum 3D
model
Anatomical
features
Alignment
Femur & hemipelvis 3D models
Other
segments
Scaled model coordinates
Scaled model
CT
Re-scaling
HJC &
knee axis
LJC &
COM
Femur & pelvis
segments
Sacrum 3D
model
Image-based
model
Image-based model coordinates
Figure 1. Flow diagram describing the different steps required for creating image-based
models. The procedure started from a CT scan and a scaled model, each with its own
coordinate system. 3D bone models were obtained from the CT images by
segmentation. Based on a comparison of anatomical features identified in the imagebased bone models and the scaled model, alignment and re-scaling transformations were
defined. The alignment was used to transform image-based data, including the bone
models, HJC and knee axes, onto the image-based model’s body segment coordinate
systems. A re-scaling of the model’s body segments was applied to the lumbosacral
joint centre (LJC), body segment centres of mass (COM) and the 3D model of the
sacrum.
Figure 2. Knee axis inclination angles for the image-based models, shown as box plots.
Figure 3. Difference in HJC location relative to the lumbosacral joint centre between
image-based models and scaled models, shown as box plots. The differences were
averaged over the left and right. An asterisk (*) indicates significant differences.
Figure 4. Difference in femur length (distance from HJC to knee centre) between
image-based models and scaled models, shown as box plots. The differences were
averaged over the left and right femora. An asterisk (*) indicates significant differences.
Figure 5. Proportional differences in peak joint moments calculated over a gait cycle,
between scaled and image-based models, shown as box plots (left). P-values below the
0.05 significance level are shown in bold for significant differences (centre). Mean joint
moments for the image-based models are shown for scale (right). Joint moments and
peak moment differences are given for hip extension (ext), flexion (flex), abduction
(abd) and endorotation (ER) as well as knee extension (knee ext) and ankle plantar
flexion (ank PF).
Figure 6. Minimum (left) and maximum (right) per-timeframe difference in joint
moments calculated over a gait cycle, between scaled and image-based models, shown
as box plots. Differences are shown for hip extension (ext), abduction (abd) and
endorotation (ER) as well as knee extension (knee ext) and ankle plantar flexion (ank
PF).
Figure 7. User interface for isolating posterior condyles, with resulting knee axis. The
two areas bordered by black lines represent the medial and lateral posterior condyles;
they were delineated manually. The dashed line is the rotational symmetry axis of this
area, which was used to locate the knee axis.
Figure 8. Line used to align pelvis. The midpoints between the ASIS and symphysis
pubis landmarks of both hemipelves (shown here as dots) were connected by a line
(vertically oriented solid line). This line was then projected onto the symmetry plane
(dashed line). The pelvis model obtained from CT was rotated in the symmetry plane so
that this line was parallel to the corresponding line in the generic model pelvis (with no
scaling applied to the latter).
PSIS
ASIS
ASIS
HJC
HJC
Figure 9. Image-based hemipelvis models with distances used to scale the pelvis
segment (double-headed arrows). The ASIS, PSIS and hip joint centres (HJC) were
used to determine these distances, as well as the midpoints of both hip centres and the
midpoint of the PSIS landmarks (circles). Dashed lines lie in a coronal and in a
transverse plane; two of the distances were measured perpendicular to these planes.
Figure 10(a). Alignment of image femur onto model femur. The model femur is
visualized using a darker colour; its knee axis is the dashed line. The image-based femur
is represented using a lighter colour; its knee axis is the horizontal solid line. The
vertical line is the shared mechanical axis.
Figure 10(b). Rescaling of model femur to image-based femur length. The model femur
is visualized using a darker colour; its knee axis is the dashed line. The image-based
femur is represented using a lighter colour; its knee axis is the horizontal solid line. The
vertical line is the shared mechanical axis.