Verification of skin-based markers for 3-dimensional kinematic analysis of the equine tarsal joint.
ABSTRACT Kinematic studies are usually based on tracking markers attached to the skin. However, complex joints, such as the tarsal joint, function in 3-dimensions (3D), and have therefore necessitated application of the invasive bone pin technique, limiting kinematic studies to the research laboratory. This study investigates the feasibility of using skin-based markers for 3D analysis of tarsal joint motion.
Three-dimensional motions of the tarsal joint can be measured with an acceptable degree of accuracy using skin markers.
Retroreflective markers were attached over the tibial and metatarsal segments. Markers were tracked automatically at trot. Three-dimensional skin correction algorithms were used for correction of skin displacement, and 3D motions derived from the corrected (CSD) and uncorrected (USD) skin displacement were compared with data from a previous study in which those motions were described using bone-fixed markers (BFM) by correlation, root mean square errors (RMS) and shape agreement (SA) of the curves.
The RMS of BFM and CSD were smaller than those of BFM and USD for all motions. The correlation coefficients of BFM and CSD were higher than those of BFM and USD. SA was good or fair for all motions except internal/external rotation and medial/lateral translation.
With appropriate correction for skin movement relative to skeletal landmarks, skin markers can identify tarsal 3D motions for flexion/extension, abduction/adduction, cranial/caudal translation, and proximal/distal translation, allowing analysis and comparison of information between horses during swing and stance phases.
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ABSTRACT: The problem of determining skeletal movements in three dimensions by using a number of landmarks is treated. We present a method that determines the motion of a rigid body by using the positions of the landmarks in least-squares sense. The method uses the singular value decomposition of a matrix derived from the positions of the landmarks. We show how one can use this method to express movement of skeleton segments relative to each other. As many others have pointed out, the movement can be very ill determined if the landmarks are badly configured. We present a condition number for the problem with good geometrical properties. The condition number depends on the configuration of the landmarks and indicates how to distribute the landmarks in a suitable way.Journal of Biomechanics 01/1994; 26(12):1473-7. · 2.72 Impact Factor
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ABSTRACT: The tarsal joint is a common site of injury for many sport horses. Understanding the biomechanics of this complex joint begins with developing a clear picture of the kinematics during normal locomotion. This study describes the 3D kinematics of the tarsal joint by measuring the motion of the tibia and third metatarsus in 4 sound Quarter Horses with targets attached directly to the bones via steel pins. The objective was to determine if the tarsus had significant motion outside the tarsocrural joint. Two Steinmann pins were inserted into the lateral side of the right hindlimb and marker triads were fixed to the end of each pin. 3D motion of the bones was recorded as each subject trotted in hand. Three rotations were expressed using an attitude vector based on the finite helical angle method. Three translations were calculated as the motion of the tibia relative to the third metatarsus. Angular and translation data were mostly coupled with flexion angle. Internal/external rotation during stance and translations during swing showed evidence of noncoupled motion. Although the majority of tarsal motion occurs in the tarsocrural joint, there is evidence that translations and rotations occur in other locations within the tarsal joint and that some of these are related to the tarsal joint 'snapping' phenomenon. This research provides a set of reference 3D kinematics which will aid in the study of the aetiology and mechanical effects of tarsal joint lameness.Equine veterinary journal. Supplement. 10/2002;
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ABSTRACT: In view of the singularities, asymmetries and other adverse properties of existing, three-dimensional definitions for joint and segment angles, the present paper proposes a new convention for unambiguous and easily interpretable, 3-D joint angles, based on the concept of the attitude 'vector' as derived from Euler's theorem. The suggested standard can be easily explained to non-mathematically trained clinicians, is readily implemented in software, and can be simply related to classical Cardanic/Eulerian angles. For 'planar' rotations about a coordinate system's axes, the proposed convention coincides with the Cardanic convention. The attitude vector dispenses with the 'gimbal-lock' and non-orthogonality disadvantages of Cardanic/Eulerian conventions; therefore, its components have better metrical properties, and they are less sensitive to measurement errors and to coordinate system uncertainties than Cardanic/Eulerian angles. A sensitivity analysis and a physical interpretation of the proposed standard are given, and some experimental results that demonstrate its advantages.Journal of Biomechanics 01/1995; 27(12):1399-414. · 2.72 Impact Factor
EQUINE VETERINARY JOURNAL
Equine vet. J. (2004) 36 (8) 655-658
Reasons for performing study: Kinematic studies are usually
based on tracking markers attached to the skin. However,
complex joints, such as the tarsal joint, function in
3-dimensions (3D), and have therefore necessitated
application of the invasive bone pin technique, limiting
kinematic studies to the research laboratory. This study
investigates the feasibility of using skin-based markers for
3D analysis of tarsal joint motion.
Hypothesis: Three-dimensional motions of the tarsal joint can
be measured with an acceptable degree of accuracy using
Methods: Retroreflective markers were attached over the tibial
and metatarsal segments. Markers were tracked automatically
at trot. Three-dimensional skin correction algorithms were
used for correction of skin displacement, and 3D motions
derived from the corrected (CSD) and uncorrected (USD) skin
displacement were compared with data from a previous study
in which those motions were described using bone-fixed
markers (BFM) by correlation, root mean square errors
(RMS) and shape agreement (SA) of the curves.
Results: The RMS of BFM and CSD were smaller than those
of BFM and USD for all motions. The correlation coefficients
of BFM and CSD were higher than those of BFM and USD.
SA was good or fair for all motions except internal/external
rotation and medial/lateral translation.
Conclusions and potential relevance: With appropriate
correction for skin movement relative to skeletal landmarks,
skin markers can identify tarsal 3D motions for
translation, and proximal/distal translation, allowing analysis
and comparison of information between horses during swing
and stance phases.
The application of gait analysis as a clinical tool requires the use of
accurate, noninvasive methods of data collection. Movements of
the equine limb joints distal to the shoulder and hip are primarily
those of flexion and extension and, consequently, published
kinematic studies have focused on 2-dimensional analysis in the
sagittal plane. However, complex joints, such as the tarsal joint,
may not function as simple hinges. Three-dimensional (3D)
motions of the equine tarsal joint complex have been described by
tracking the movements of marker triads fixed to the tibia and
metatarsus (Lanovaz et al. 2002a). Measurable amounts of tarsal
joint motion were found in the frontal (abduction and adduction)
and transverse (axial rotation) planes, some of which occurred
outside the tarsocrural joint. The invasiveness of the bone pin
technique limits its application to the research laboratory. In the
clinical gait laboratory, kinematic studies are usually based on
tracking markers attached to the skin. Verification of the accuracy
of skin markers for measuring motion of the tarsal joint complex
outside the sagittal plane is an important step towards using this
technique in the evaluation of performance and lameness.
The objective of this study was to verify the feasibility of
using skin-based markers to evaluate 3D movements of the tarsal
joint. The hypothesis was that 3D rotational and translational
motions of the equine tarsal joint complex can be measured with
an acceptable degree of accuracy using skin markers.
Materials and methods
Four sound horses were selected on the basis of physical
evaluation, combined with radiography and nuclear scintigraphy
of the tarsal joints (Khumsap et al. 2003). Six Falcon infrared
video cameras (Motion Analysis System)1collected data at
120 frames/sec. Twelve retroreflective skin-based markers, which
could be viewed from the lateral side, were attached to the skin
over anatomical landmarks of the tibial and metatarsal segments
of the right hindlimb, as described by Lanovaz et al. (2004). Two
additional reference markers were attached on the medial
malleolus of the tibia and the dorsal edge of the head of the second
metatarsal bone (MtII). The horse was positioned obliquely to the
longitudinal axis of the data collection volume so all the markers
could be seen by at least 2 cameras. A video recording, named the
reference pose, was captured and the 2 reference markers on the
medial side of the limb were then removed. The handler led the
horse at trot through the data collection volume. To ensure that all
horses moved at an equivalent speed, data collection was
performed as described in Khumsap et al. (2003) until at least
5 successful trials had been obtained from each horse. Mean ± s.d.
speed for the 4 horses was 2.87 ± 0.05 m/sec.
Verification of skin-based markers for 3-dimensional
kinematic analysis of the equine tarsal joint
S. KHUMSAP*, J. L. LANOVAZ†and H. M. CLAYTON‡
*Faculty of Veterinary Medicine, Chiang Mai University, Thailand; †Department of Mechanical and Material Engineering, Queen’s University,
Kingston, Ontario, Canada; and ‡McPhail Equine Performance Center, Michigan State University, East Lansing, Michigan, USA.
Keywords: horse; hock; kinematic; 3-dimensional; trot
*Author to whom correspondence should be addressed.
[Paper received for publication 10.05.04; Accepted 25.10.04]
656Three-dimensional analysis of the equine tarsal joint
The tibial segmental coordinate system (SCS) was constructed
from the markers at the distal attachment of the lateral collateral
ligament of the femorotibial joint, lateral malleolus and medial
malleolus (Fig 1). The first axis to be defined was the
flexion/extension axis (y), which was a vector running from lateral
malleolus to medial malleolus. This vector was positive in a lateral
to medial direction. The second axis was the abduction/adduction
axis (x), which was calculated as a vector perpendicular to both
the y-axis and a line from the lateral malleolus to the proximal
tibial marker. This axis was positive in a caudal to cranial
direction. The third axis was the internal/external rotation axis (z),
which was calculated as a vector perpendicular to both x- and
y-axes that was positive in a distal to proximal direction. The
origin of the tibial SCS was embedded in the bone midway
between lateral and medial malleoli.
The metatarsal SCS was constructed using markers over the
dorsal edges of the heads of the fourth and second metatarsals, and
the lateral condyle on the distal McIII (Fig 1). The flexion/extension
(y) axis was a vector from McIV to the McII, which was positive in
a lateral to medial direction. The abduction/adduction (x) axis was
perpendicular to the y-axis and to a line from the head of McIV to
the distal condyle of the McIII. The y-axis was positive in a plantar
to dorsal direction. The internal/external rotation (z) axis was
mutually perpendicular to x- and y-axes, and was positive in a distal
to proximal direction. The origin of the metatarsal SCS was
embedded in the bone midway between the dorsal edges of the
heads of McIV and McII.
The reference pose was used to relate the location of the skin
markers overlying each segment to its SCS. During the trotting
trials, skin markers were tracked and expressed in terms of the
global coordinate system (GCS). A singular-value decomposition
method (Söderkvist and Wedin 1993) was used to transform the
skin marker locations from the GCS to their corresponding SCS
for each frame during the stride. Skin marker corrections were
applied using mean skin displacement values (Lanovaz et al.
2002b) to restore the tibial and metatarsal SCSs.
Complete 3D kinematic analysis of the tarsal joint complex
involved the measurement of relative rotational and translational
motions between the tibial and metatarsal SCSs. In this study, all
motions were measured as movement of the metatarsus relative to
the fixed tibia, expressed in terms of spatial attitude vectors
(Woltring 1994). There were 3 relative rotational motions between
the 2 segments: flexion/extension, abduction/adduction and
internal/external rotation. Flexion/extension was motion around
the y-axis; negative values were assigned for flexion, and positive
values were assigned for extension. Abduction/adduction was
motion around the x-axis; negative values were assigned for
abduction and positive values for adduction. Internal/external
rotation was motion around the z-axis; negative values were
assigned for external rotation and positive values for internal
rotation. Translational motions were measured in 3 directions;
cranial/caudal, medial/lateral and proximal/distal translations.
Cranial/caudal translation was motion along the x-axis; negative
values were assigned for caudal translation and positive values for
cranial translation. Medial/lateral translation was motion along the
y-axis; negative values were assigned for lateral and positive
values for medial translation. Proximal/distal translation was
motion along the z-axis; negative values were assigned for distal
and positive values for proximal translation.
Rotational and translational motions, both before and after the
application of skin correction algorithms, were obtained
separately for stance and swing phases, and expressed relative to
the values at the start of the stance phase of that stride. Data
derived from 5 strides were combined and a mean curve for each
horse was constructed to represent that horse’s movement pattern.
The true rotational and translational motions of the tarsal joint,
derived from bone-fixed markers data (BFD) (Lanovaz et al.
2002a) from the same group of horses, were used as reference
values. The mean curves for the 3D motions from the corrected
(CSD) and uncorrected (USD) skin displacement data of each
horse were compared with the true motions of the tarsal joint.
Root mean square (RMS) errors were calculated for each horse,
and the mean RMS errors for the group were then calculated.
Pearson product moment correlation was used to compare BFD
and CDS or USD at a significance level of P<0.05. To explore
similarities and differences in the shape of the curves, the true
motion of the joint was plotted together with uncorrected and
Fig 1: Cranial views of a) the right tibia and b) the right metatarsal bone
showing positions of retroreflective markers (●) used to establish the
segmental coordinate systems. Origins of the coordinate systems were
located midway between the distal tibial markers and midway between the
proximal third metatarsal markers. The positive directions were medial for
the flexion/extension axis (y), craniodorsal for the abduction/adduction
axis (x) and proximal for the internal/external rotation axis (z).
TABLE 1: Pearson correlation coefficients (r) and root mean square
(RMS) errors between bone-fixed marker data (BF) from Lanovaz et al.
(2002) and data corrected (C) or uncorrected (U) for skin displacement
in the tarsal joint. Correlation coefficients shown are statistically
significant (P<0.05). Nonsignificant correlation coefficients are shown
as NSD. Shape agreement (SA) was evaluated qualitatively for similarity
in shape and magnitude between BF and C curves
r RMS errors
BF vs. C
MotionBF vs. C BF vs. UBF vs. UBF vs. C
Internal/external rot NSD
Cranial/caudal trans 0.82
Proximal/distal trans 0.6
Internal/external rot NSD
Cranial/caudal trans 0.93
Proximal/distal trans 0.91
2.38 ± 0.82
1.19 ± 1.02
2.29 ± 0.10
5.06 ± 2.10
1.83 ± 0.37
2.51 ± 0.32
3.05 ± 1.24
1.45 ± 0.67
8.62 ± 0.81
5.89 ± 1.65
4.36 ± 0.96
6.18 ± 0.57
2.83 ± 0.82
1.63 ± 0.70
2.73 ± 1.49
6.56 ± 3.26 10.58 ± 2.96
2.89 ± 1.59
5.19 ± 2.84 12.29 ± 4.52
3.55 ± 1.67
5.93 ± 0.61
9.35 ± 1.35
NSD7.54 ± 2.97
trans = translation; rot = rotation.
Fig 3: Mean curves of 3D rotational and translational motions of the tarsal joints during swing. For details see Figure 2.
S. Khumsap et al.
corrected skin data. Agreement between BFD and CSD curves
was evaluated qualitatively and assessed as ‘good’when the shape
and direction of the curves were similar for the 2 sets of data;
‘fair’ when the curves showed minor differences in direction or
magnitude; and ‘poor’when neither the shape nor direction of the
curves were similar.
The RMS errors of BFD and CSD were smaller than those
of BFD and USD for all motions (Table 1). The correlation
coefficients of BFD and CSD were higher than those of BFD and
USD for cranial/caudal translation, flexion/extension and
abduction/adduction (P<0.05) during stance and swing phases.
Visual comparison of the curves for CSD and USD with the curve
for BFD (Figs 2 and 3) shows a much closer agreement following
correction for skin displacement, especially for abduction/adduction
in swing. In general, shape agreement between BFD and CSD was
better during swing than during stance. Stance phase data indicated
good shape agreement between BFD and CSD for flexion/extension
and fair shape agreement for abduction/adduction, cranial/caudal
translation and proximal/distal translation. During the swing
phase (Fig 3), there was good shape agreement between the
curves representing BFD and CSD for flexion/extension,
abduction/adduction and cranial/caudal translation and fair shape
agreement for proximal/distal translation. These results support
acceptance of the experimental hypothesis for all motions except
internal/external rotation and medial/lateral translation.
The tarsal joint complex consists of 4 joints. The major motion is
flexion/extension at the tarsocrural joint. The motions at the other
3 joints, proximal intertarsal, distal intertarsal and tarsometatarsal
joints, are considered to be small. Due to the oblique orientation
of the talar ridges, flexion/extension of the tarsocrural joint is
accompanied by translational motion, which is characteristic of
helical motion (Badoux 1987). The largest force loading the distal
tibia is a torsional force (Schneider et al. 1982; Hartman et al.
1984). The combination of torsional loading from the tibia and the
Fig 2: Mean curves of 3D rotational and translational motions of the tarsal joints during stance: a) extension(+)/flexion(-) angle;
b) adduction(+)/abduction(-) angle; c) internal(+)/external(-) rotation angle; d) cranial(+)/caudal(-) translation; e) medial(+)/lateral(-) translation; and
f) proximal(+)/distal(-) translation. Solid line = corrected skin data; dashed line = uncorrected skin data; dotted line = bone-fixed marker data from
Lanovaz et al. (2002). Zero indicates the impact value.
020 4060 80100
0 2040 60100
0 20 40 60100
0 20 40 60100
0 20 40 6080 100
% Stance duration
0 20 40 60100
% Swing duration
0 2040 60 80100
% Swing duration
020 40 60100
% Swing duration
020 40 60 100
% Stance duration
0 20 4060 80100
% Stance duration
0 20 40 60 80100
0 20 4060 80100
658Three-dimensional analysis of the equine tarsal joint
oblique orientation of the talus may lead to motion at the other
3 low-motion joints in the tarsal joint complex. The objective of
this study was to develop a noninvasive method of measuring 3D
motion of the tarsal joint complex. Since the segments between
the 3 distal tarsal joints are extremely short it is not possible to
attach skin markers to represent each segment of the tarsal joint
complex, although some assumptions could be made regarding the
motion of these joints. The tarsocrural joint has a screw motion
(Badoux 1987; Lanovaz et al. 2002a), which implies that
rotational and translational motions of the tarsocrural joint in any
direction are highly coupled with flexion/extension of this joint.
Loss of coupling between flexion/extension and the other motions
suggests movement at tarsal joints outside the tarsocrural joint
(Lanovaz et al. 2002a).
The use of correction algorithms for skin displacement is
important for obtaining accurate kinematic data from skin-based
markers. In order to study 3D kinematics of the tarsal joints using
skin-based markers, it was necessary to develop 3D skin correction
algorithms based on knowledge of the motion of the underlying
bones. The advantage of this study was that the data were obtained
from the same horses that had been used to construct skin
correction algorithms in a previous study (Lanovaz et al. 2002a,b,
2004). By using the same horses for both studies, it enhanced the
ability to test how closely the skin correction algorithms could
correct skin marker data to real bone motion in an individual horse.
Data from bone-fixed markers indicated that there was some
variation among horses in rotational and translational motions, as
shown by the relatively wide s.d. for abduction/adduction and
proximal/distal translation. Therefore, the skin correction
algorithms, which were calculated as the best fit for a group of
horses, might not be able to account for individual variation in all
motions. Nevertheless, the comparison between BFD and CSD
showed higher correlation coefficients and smaller RMS errors
than the comparison between BFD and USD, indicating that the
application of skin correction algorithms enhances the quality of
motions derived from skin-based markers. Improvements in the
shape of the curves following correction for skin displacement are
clearly visible in Figures 2 and 3.
During stance, shape agreement between BFD and CSD was
assessed as good for flexion/extension, fair for 3 other degrees of
freedom, and poor for the other 2 degrees of freedom. Even though
the RMS errors for internal/external rotation and medial/lateral
translation between BFD and CSD were small, there was no
statistically significant correlation between those motions.
In addition, shape agreement between BFD and CSD of those
motions was poor. Therefore, it is not suggested that this 3D skin-
marker set be used for testing changes in these 2 motions. For
abduction/adduction and proximal/distal translation, the directions of
motion were correct, but differences in the magnitude of the
movement resulted in the shape agreement being assessed as fair. For
cranial/caudal displacement, the fair assessment was due to
differences in shapes of the curves in early stance, whereas in
midstance the curves were quite similar. Therefore, comparisons
between conditions for these ranges of motion within an individual
horse should be acceptable, but direct comparisons between different
horses should be avoided due to the possibility of under- or
overestimation of joint motion from skin-based data.
The curves showed better shape agreement during swing than
during stance. During swing, assessment of shape agreement was
good for 3 motions, fair for one motion and poor for 2 motions.
Internal/external rotation and medial/lateral translation showed poor
shape agreement for the same reasons as described during stance.
Therefore, it is not suggested that this 3D skin marker set be used to
obtain information describing these 2 motions during swing.
Proximal/distal translation showed fair agreement in shape, mainly
due to overestimation of proximal displacement in mid swing,
although the value still fell within 1 s.d. of the real bone motion from
Lanovaz et al. (2002a). Therefore, swing phase flexion/extension,
abduction/adduction, cranial/caudal translation and proximal/distal
translation ranges of motion can be estimated with acceptable
accuracy from corrected skin data. The relatively good 3D
information obtained from this skin marker set during swing allows
analysis and comparison of information between horses.
From this study, it is concluded that, with appropriate
correction for skin displacement, skin-based markers can
identify tarsal 3D motions with acceptable accuracy for
flexion/extension, abduction/adduction, cranial/caudal translation
and proximal/distal translation, but not for internal/external
rotation or medial/lateral translation.
This study was funded by the McPhail Endowment and the
Department of Large Animal Clinical Sciences, Michigan State
1Motion Analysis Corporation, Santa Rosa, California, USA.
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