Evaluation of a pictorial method to obtain subject-specific inertial properties in equine limb segments

2.1 Segmental masses

In the standard method, each limb segment was weighed using a Valor 5000 scale (Ohaus) which measures with a precision of 1 g. Segmental masses obtained by this method were considered the standard to which the other methods were compared.

In the scaling method, the mass of each limb segment was estimated as a percentage of body mass using the data from Nauwelaerts et al. (2011). The mass of the limb segment in the individual horses were then calculated by jack-knifing the data set. This involved removing the data for each horse, one at a time, from the data set, then recalculating the segmental mass ratio based on data from the remaining horses. The calculated ratio was multiplied by the total mass of the horse that had been removed to estimate the segmental mass of that horse while avoiding circular reasoning.

In the pictorial method, two orthogonal photographs of each disarticulated segment were taken with the bone axis vertical and a scale placed adjacent to the segment for calibration of linear measurements. The photographs were loaded into a custom Matlab routine. After manual selection of its proximal and distal ends, the software divided the segment along its length into 10 slices of equal height. The proximal and distal periphery of each segment was digitized manually in the two views and then the values were interpolated to obtain 10 ellipsoid disks per slice (100 disks per segment). The volume of each ellipsoid disk was calculated from measurements of the width (mediolateral dimension) and depth (craniocaudal dimension) at the proximal and distal extremities from the digitized outline, multiplied by the disk height which was one one-hundredth of the total segmental length. Segmental mass was calculated as the volume multiplied by the segmental densities reported by Kubo et al. (1992).

2.2 Segmental lengths

In the standard measurement method, segmental lengths were measured between the segment extremities, usually represented by the articular surfaces, using electronic calipers with a precision of 1 mm (Swiss Precision Instruments).

The scaling method used a jack-knifing procedure similar to that described for measuring segment mass. Regression equations were used to obtain segment lengths from the masses estimated by the scaling method omitting the individual subject for which the length was being determined, then recalculated the value based on data for the remaining horses.

In the pictorial method, the two orthogonal photographs of each disarticulated segment were loaded into a custom Matlab routine. After manual selection of the proximal and distal ends of the segment, and scaling of the picture by selecting a known length on the scale bar, the segment length was calculated.

2.3 Moment of inertia

The standard method for measuring the MOI used the data of a trifilar pendulum (Nauwelaerts et al., 2011). The pendulum has two parallel plates; the top plate is fixed in position but the lower plate rotates freely around three long, flexible steel cables attached equidistant from the center of the plates. The MOI of the empty pendulum was calculated based on the dimensions and weight of the lower plate. The segment that was being tested was placed on the lower plate of the pendulum with its COM aligned above the middle of the plate and the segmental sagittal plane parallel to the plate of the pendulum. The pendulum was set in motion, the period of free rotational vibration was recorded and the MOI of the segment-pendulum system was calculated (Nauwelaerts et al., 2011). The difference between MOI of the segment–pendulum system and the empty pendulum was used to calculate the segmental MOI. Since the segment is placed in this position only, only sagittal plane moments of inertia are determined.

In the scaling method, MOI calculated by the standard method were used in a jack-knifing procedure as described for the segmental masses. The MOI of each limb segment in the individual horses was calculated by removing that horse's data from the data set then jack-knifing the remaining data to recalculate the segmental MOI for the individual horse based on data for the remaining horses.

In the pictorial method, the MOI was calculated separately for each of the 100 ellipsoid disks, then the individual values were summed together to determine the overall MOI. The MOI was then expressed in reference to the COM position in accordance with the parallel axis theorem (Eichler, Kronfelt, & Sahm, 2001).

2.4 Statistics

Estimates of segment mass, segment length, and MOI for the scaling method and the pictorial method were compared to the measurements from the standard method using a Bland-Altman approach in MedCalc version 17.6 software. Bias and p-values of biases, intra-class correlations (ICC), and % errors were reported for each segment and each method.

3.1 Segment masses

There was no systematic bias in the mass estimates of the scaling method (see p-values Table 1, third column). Relative errors were in the same range for both methods. The measured segmental masses were highly correlated with the scaling method and even slightly higher with the pictorial method, but the latter method showed a bias for the brachium (Figure 1b), the metacarpus (Figure 1d), the pasterns (Figures 1e and 2d), the hooves (Figures 1f and 2e), and the thigh (Figure 2a). The pictorial method overestimated the mass by 0.90 kg in the brachium, 88 g in the metacarpus, and 2.6 kg in the thigh. Rather than being a flaw in the pictorial method, however, these overestimations of mass by the pictorial method might actually reflect an underestimated mass in the reference data since van den Bogert (1989) reported that blood loss during disarticulation of the segments decreased segmental masses by 10%. The biases for the brachium, metacarpus, and thigh showed that their masses were over-estimation by around 10% of the average mass of the data set. If this were true, it could even suggest that the pictorial method is better at estimating the true masses of these segments. However, blood loss is unlikely to explain the differences in pastern and hoof masses, which also tended to be overestimated by the pictorial method. We used average segmental densities provided by Kubo et al. (1992) which reports density for the pastern and hoof as one segment. Buchner et al. (1997) reported densities for these two segments separately, with pastern density being higher, and hoof density slightly lower than the values we used. Since the difference amounted to only 5%, however, it seems unlikely that this explains the overestimation. Even though the pictorial method captures the contours of the segment adequately, the flat disc method does not work well when the joint surfaces at the segmental extremities are irregular, especially when the segment is small, as in the hoof and pastern.

When van den Bogert (1989) took a similar approach to obtaining inertial properties using the outlines of pictures, he concluded that the method performed poorly in estimating the scapula, brachium, and thigh masses. Since we obtained better results for these segments, it is possible that the problem was not in the elliptic zone model approach but rather the fact that his pictures were taken on live horses. These three segments are surrounded by large muscle masses, including the extrinsic limb musculature, that are difficult to include in photos of the live horse. Since we removed the segments from the body before tracing the contours, we did not encounter this particular problem.

Data from the pictorial method fall within the higher range of the data cloud from the scaling method. The scaling method did not show a bias but the data had more variation (e.g., pastern mass Figure 1e). In that sense, the pictorial method is better at individualizing the segments masses, but a correction factor accounting for the bias should probably be included to make the estimates more precise.

3.2 Segment lengths

Segment length estimates show a similar pattern to segment masses. There was no bias in the scaling data except for the length of the fore hoof for which percentage errors were acceptable but ICC were fairly low (Table 2). The lowest ICCs were found in the pastern and the hoof of the forelimb. The lengths estimated by the scaling method for both these segments have a much lower range in magnitude than the actual measurements, causing the lengths to be overestimated in the smaller segments. Even though the pictorial method had a consistent underestimation of 8 mm for the fore hoof, it did capture the full range of lengths and had a higher ICC. The lengths of the scapula (Figure 3a), brachium (Figure 3b), and thigh (Figure 4a) were overestimated while the lengths of the antebrachium (Figure 3c), crus (Figure 4b), and metatarsus (Figure 4c) were underestimated. This might be an effect of the way the program worked. The pictures were taken in two orthogonal planes with the segments upright. It is possible that when the segmental extremities were digitized, the points selected were different from those chosen in the caliper method.

The pictorial method overestimated the length of the hind hoof (Figure 4e) and underestimated the length of the fore hoof (Figure 3f). Since both hooves are so similar in shape, this seems to be a random effect rather than a methodological issue.

3.3 Moment of inertia

Both the scaling and pictorial methods were only capable of providing a rough estimate of the MOI, but the percentage error was particularly high in the pictorial method (Table 3). A bias was present in all segments estimated by the pictorial method, except for the hooves (Figures 5 and 6). Since the mass estimate of the hooves had the highest percentage error, it is a little surprising that the segments with the worst estimations of the MOI by the pictorial method are the metacarpus and the metatarsus (Figure 5 and 6). Correcting the metatarsal data for its large bias (0.023), brings the error down to 34%. The bias may be caused by the irregular shape of the proximal end of this segment, which includes the calcaneus. This has a relatively large effect on the MOI since it is so far from the COM. The MOI estimates for this segment might be improved by using more than 10 outline measurements to represent its shape.