Having established a well-defined set of parameters, many possibilities
for their use become apparent. One use is in making comparisons
between horses. This can be extremely useful in assessing how a
particular horse compares to a certain control group.
Another use of the parameters is in tracking change in conformation.
As a part of preventative foot care, or in concert with an attempt
to improve the conformation of the hoof, such a system is invaluable
in tracking progress, or lack of it, in an unbiased way.
Figure 2: Circles defined by three points at the distal ends of
P1 and P2.
The shape of a biomechanical joint, viewed in
the plane perpendicular to the joint’s axis, is circular, at least
in a region local to the joint’s nominal operating point. Only
for large rotations of the joint may the circular approximation
lose validity. That is to say, in it’s normal range of operation,
the coffin joint articulates P3 about a fixed center of rotation
located on P2 as indicated in figure 2. Likewise, the center of
rotation for P2 about the pastern joint is a point located on
P1 as indicated in figure 2.
Note that the biomechanical motion of the limb
involves rotations at these two centers as well as others found
in the proximal direction up the limb (e.g., at the fetlock joint,
at the carpus, etc). The notion of "center of articulation
of the foot" that is sometimes mentioned is hence not well
defined, as the foot articulates due to several rotation centers.
Only with a gross simplification can we speak of a single "center
of articulation" for the foot. One such simplification apparently
sometimes used, is to assume no motion at the pastern joint and
other more proximal joints, and refer the center of rotation of
the coffin joint as the "center of articulation" of
the foot.
While it would make sense to repeat the circle-fitting
procedure at the fetlock joint, in standard practice, many radiographs
of the digit do not fully capture the fetlock joint. Instead,
we propose a method of defining an "axis of P1" which
we will later use in defining the angular position of the pastern-joint.
This technique is as follows: Having found the center of rotation
associated with the pastern joint, we construct a larger circle
of 3 times the radius of the original circle, overlay this circle
on the image, and pick the two points where this circle crosses
P1 as viewed from this lateral aspect. This defines a line segment.
We use the midpoint of this line segment as a point that we will
consider to be on the "axis of P1". By "axis of
P1" we mean a line which is aligned with the major dimension
of P1 as viewed in a lateral radiograph and which is centered
within P1. We use this point, along with the center of rotation
of the pastern joint (as defined previously) to define the "axis
of P1". We will use this axis as a means to describe the
orientation of P1 in the lateral radiograph.
We may now define a precise way to measure value
the rotational position of coffin joint and of the pastern joint
as seen in lateral radiographs. In figure 3 we show these joint-angle
values. To quantify the coffin-joint angle, construct a line from
the rotation center associated with the coffin joint extending
down towards the sole and parallel to our reference orientation
defined on the dorsal aspect of P3. The value of the coffin-joint
angle is the geometric angle formed between this constructed line,
and the line defined by connecting the two rotation centers. In
the example shown in figure 3, this value is 15.22 degrees. The
positive sense is defined such that a positive rotation of the
coffin-joint makes the major axis of P2 become more upright in
the image.
To quantify the pastern-joint angle, construct
a line that connects the two rotation centers. The value of the
pastern-joint angle is the geometric angle formed between this
constructed line and the line representing the "axis of P1"
as previously defined. In the example of figure 3 this value is
7.61 degrees. The positive sense is defined such that a positive
rotation of the pastern-joint makes the axis of P1 become more
upright in the image.
Figure 3: Definition of the coffin-joint angle
and the pastern-joint angle.
We have defined the "P3 Angle" (see
figure 1), the "coffin-joint angle" and the "pastern-joint
angle" (see figure 3) such that they may be summed to obtain
the angle of P2 relative to ground, and a value for the angle
of P1 relative to ground. For example, in the case shown in figures
1 and 3, we compute the orientation of the axis of P1 relative
to ground as 53.13 + 15.22 + 7.61 = 75.96 degrees.
Parameters Involving Length Measurements
In addition to the parameterization of the angulation
of P1, P2, and P3 described in the previous section, it may also
be useful to develop a well-defined, standard method of measuring
the relationship between the exterior hoof wall and the phalanges
which may involve length measurements. This can be done by means
of a set of additional parameters, a sample of which are shown
in figure 4.
The parameter "P3 Descent" gives a
measure of the distance from the highest point on the extensor
process of P3 to the hairline on the exterior of the hoof capsule.
The parameters "P3 to Toe" and "P3 to Ground"
may be of interest to a farrier in deciding how much toe to trim.
The "Length of P2" is defined as the distance between
the centers
Figure 4: An example showing four length parameters
of the two fit circles (defined previously), minus
the radius of the circle at the pastern joint, and plus the radius
of the circle at the coffin joint.
For measurements taken from radiographs to be
considered accurate, a number of factors must be considered. Chief
among these factors is the careful set up of the radiographic
machine, the subject, and the film. In the case of the lateromedial
radiograph, we wish to mark the dorsal hoof wall with radio-opaque
material, place a metal marker in the block on which the horse
stands to be able to see the "ground plane" in the resulting
image, and so on. The central X-ray beam should be parallel to
the bulbs so that it is perpendicular to the plane the leg moves
in. These and other important aspects of good technique have been
documented elsewhere.
Additionally, when it is desired to make measurements
of lengths, an additional calibration technique must be used.
All radiographs exhibit a certain degree of magnification. The
amount of magnification present depends on the distance from X-ray
point source to the film, known as the Film-Focal Distance (FFD),
and the distance between the film and the subject, which we will
call the Object-Film Distance (OFD). To be more precise, we define
OFD as the distance from the film to the center of the bone
column. The magnification factor, M, for a given image is
then computed as:
By applying the inverse of this value to all
length measurements made in the image, we obtain length values
which have been scaled to the center of the bone column. Hence
values such as those shown in figure 4 are understood to be length
measures at the center of the leg.
Having established a well-defined set of parameters,
many possibilities for their use become apparent. One use is in
making comparisons between horses. This can be extremely useful
in assessing how a particular horse compares to a certain control
group. For example, as part of a pre-purchase examination, one
could compare the parameters of the subject horse to those of
a control set of 100 horses of the same breed which were previously
judged sound by veterinarians performing pre-purchase examinations.
Such data would be interesting and valuable for the buyer, and
would further protect the veterinarian as it helps make a more
complete disclosure concerning the subject horse.
A major use of the parameters is in tracking
change in conformation. As a part of preventative foot care, or
in concert with an attempt to improve the conformation of the
hoof, such a system is invaluable in tracking progress, or lack
of it, in an unbiased way. One such use of the system has been
for making periodic adjustments to the "rails" of a
special shoeing system used in conjunction with a case of severe
laminitis in which careful and measurable angular changes to P3
were introduced over time to slowly change angulation [b].
We feel that any attempt at corrective shoeing would benefit from
tracking changes to these conformation parameters.
Another use of the parameters is in a scoring
system which rates a given set of parameters (equivalently the
set of parameters can be thought of as a description of one individual’s
conformation) relative to some ideal. Such a use is of
course subjective and judges the conformation relative to a certain
practitioner’s opinion of what constitutes good conformation.
Repeatability of the Method
It can be difficult to achieve consistency in
radiographs of live horses for a number of reasons. In addition,
a user of our method introduces an additional source of non-repeatability
when picking the key points in the radiograph.
By repeatability we mean the ability
of the technique to derive the same parameter values from different
radiographs of the same horse, as well as the ability for different
practitioners to derive the same parameter values from the same
radiographic image. Hence two tests were performed: in the first
test, the technique was used by a single practitioner to measure
a certain biomechanical parameter in eight radiographs of the
same equine digit, taken over several years by various independent
radiographers. Variation in the measured parameter indicate that
we can derive highly repeatable parameter values in such a situation.
In the second test, the same radiographic image was analyzed using
our technique by thirteen different practitioners working independently.
Variation in measured parameters indicate good repeatability of
results in this situation.
In the first test, we estimate the repeatability
of our method for length measurements as follows. Eight radiographs
of the right fore digit of the same horse, taken over a ten year
period (1991 – 2001), were parameterized using our technique.
The horse’s age was 7 in 1991, and so could be considered fully
mature when the first radiograph in the study was taken. The 8
radiographs were taken by 4 different practitioners using different
equipment. We chose a particular parameter (the "Length of
P2" as shown in figure 4) which should be a constant value
in a mature horse. This particular parameter was chosen for this
test because it is not affected by how the hoof is trimmed, nor
by the horse’s stance at the moment the radiograph is taken. The
variations observed in the measured values give an estimate of
the repeatability of our method. The mean value measured was 4.96
cm with a minimum value of 4.88 cm and a maximum of 5.10 cm. Hence,
all values are within 1.46 mm (or 2.94%) of the mean. We could
also say that by these repeated measurements, we have determined
the 95% confidence interval bounds on the mean value to be +/-
0.76 mm.
In the second test, we asked thirteen practitioners
to make measurements following our technique in the same image.
Since the same image was used by all practitioners, this test
was designed to measure the repeatability of the technique as
regards variations introduced by the practitioner following the
procedure. For the purposes of this test, we looked at the repeatability
of the parameters shown in figure 3, namely the coffin joint angle
and the pastern joint angle. The mean value determined for the
coffin joint angle was 14.70 degrees, with a minimum of 13.23
degrees and a maximum of 16.02 degrees. The mean value found for
the pastern joint angle was 7.95 degrees, with a minimum of 6.45
degrees and a maximum of 9.90 degrees. Hence, all measured coffin-joint
values were within 1.5 degrees of their means, and all measured
pastern-joint angles were within 2.0 degree of their means. Combining
all thirteen measurements results in a 95% confidence interval
of +/- 0.50 degrees for the coffin-joint, and +/- 0.68 degrees
for the pastern-joint.
In a software implementation of this
technique, a total of 22 parameters are computed for the lateromedial
radiograph. In the interest of keeping this paper to a reasonable
length, of these 22 parameters, only 7 have been discussed and
are shown in figures 1 through 4. In our repeatability tests,
we only considered a few of these. It is likely that each of the
parameters would be influenced somewhat differently by various
sources of non-repeatability in measurement.
While we feel its important to have well-defined
values for the various geometrical aspects of the hoof and bone,
and our implementation has defined 22 parameters for the lateromedial
radiograph, we do not intend that uniform importance should be
accorded to all these measures. For example, in our opinion, most
practitioners attach relatively too much significance to the values
of the coffin-joint and pastern-joint angles.
These measures are directly affected by how the
horse is stood in preparation for taking the radiograph, and hence
may not carry a great deal of information concerning the horse’s
true conformation. In our software implementation, the 22 parameters
are divided into 3 categories: bone parameters, hoof parameters,
and stance parameters. The ‘bone parameters’ should be unchanging
in a mature horse, the ‘stance parameters’ are the joint angles,
which depend on how the horse was stood for the radiograph. The
‘hoof parameters’ are the most interesting in that they are values
which can be directly affected by trimming the hoof. Hence, they
carry the most information concerning the portion of conformation
over which the practitioner has some control.
In addition to this style of analysis of the
lateromedial radiograph, we have similarly defined, and implemented
in software, a technique for the horizontal dorsopalmar radiograph
of the equine digit. In that case, a total of 16 parameters are
defined. In a similar fashion, we have defined a measurement technique
and associated sets of parameters for three photographic views
of the hoof (lateral, frontal, solar).
More research is needed to determine what constitutes
ideal conformation of the hoof and bones, as a function of the
horse’s breed, intended usage, and other factors. We hope that
the research community will find the proposed method of defining
conformation useful towards this goal.
1. Craig, J. Introduction to Robotics: Mechanics
and Control, 2nd edition, Addison-Wesley, 1989.
2. Page B., Bowker R., Ovnicek G., et al. How to Mark the Foot
for Radiography, in Proceedings 45th Annual
AAEP Convention, Albuquerque, Dec. 1999; 148-150.
[a] Metron, EponaTech, P.O. Box 361, Creston, CA 93432, USA.
www.eponatech.com
