Inertial properties of equine limb segments

Authors


Sandra Nauwelaerts, Mary Anne McPhail Equine Performance Center, Department of Large Animal Clinical Sciences, D202 Veterinary Medical Center, East Lansing, MI 48824-1314, USA. T: +1 517 4327238; F: +1 517 3537733; E: nauwelae@msu.edu

Abstract

Quantifying the dynamics of limb movements requires knowledge of the mass distribution between and within limb segments. We measured segment masses, positions of segmental center of mass and moments of inertia of the fore and hind limb segments for 38 horses of different breeds and sizes. After disarticulation by dissections, segments were weighed and the position of the center of mass was determined by suspension. Moment of inertia was measured using a trifilar pendulum. We found that mass distribution does not change with size for animals under 600 kg and report ratios of segmental masses to total body mass. For all segments, the scaling relationship between segmental mass and moment of inertia was predicted equally well or better by a 5/3 power fit than by the more classic mass multiplied by segmental length squared fit. Average values taken from previous studies generally confirmed our data but scaling relationships often needed to be revised. We did not detect an effect of morphotype on segment inertial properties. Differences in segmental inertial properties between published studies may depend more on segmental segmentation techniques than on size or body type of the horse.

Introduction

Quantifying the dynamics of limb movements requires knowledge of the mass distribution between and within limb segments (Schneider & Zernicke, 1992; Crompton et al. 1998). Segment mass, position of segmental center of mass and moment of inertia (i.e. inertial properties) are essential to solve the equations of motion of any moving multi-segmented body.

Even though the horse is one of the best studied models in animal biomechanics, with research dating as far back as Leonardo da Vinci (van Weeren, 2002), data on equine inertial properties are scarce. The distribution of the total body mass over the body segments (Sprigings & Leach, 1986; van den Bogert, 1989; Kubo et al. 1992; Buchner et al. 1997) has received more attention than segmental moments of inertia but even these studies were confined to single breeds, whereas many research studies use horses of mixed or unknown breeds. Full inertial properties have been measured on two extreme populations: ponies and Dutch Warmbloods. One study used five ponies with mass 165–240 kg (van den Bogert, 1989), while Buchner et al. (1997) published data for six Dutch Warmblood horses ranging from 470 to 620 kg. Both datasets have been used to determine regression models to allow the prediction of inertial parameters from measurements in live animals (Minetti et al. 1999; Clayton et al. 2001; Dutto et al. 2004) but the validity of extrapolating these estimates to horses of different breeds and sizes has not been tested.

Horse breeds can be categorized based on morphotype and temperament. Cold-blooded horses are generally more robust in stature and phlegmatic in temperament, whereas hot-blooded horses are more gracile and reactive, with the warm-blooded horse intermediate in morphotype and temperament. These differences in body build are likely to be reflected in mass distribution and inertial properties of the limbs.

Movements of the equine limbs occur predominantly in the sagittal plane, which is energetically advantageous in cursorial species. Indeed, one of the recommendations of the panel of experts at the Havemeyer workshop (2006) on Motion Capture and 3D Analysis of Equine Locomotion was that, for most purposes, 2D analysis in the sagittal plane is adequate in the majority of studies to capture the essential kinematic features. The objective of this study was to provide a larger database of sagittal plane inertial properties that will be used to improve the accuracy of future studies that involve computation or modeling using segmental masses and moments of inertia (mechanical energy, joint work, etc.).

In this paper, we determined inertial properties of the limb segments for 38 horses of different breeds and sizes. We hypothesized that (i) mass distribution will change with size, that (ii) previously reported scaling relationships would have to be redefined when applied to horses from a larger size range and that (iii) differences in morphotypes affect segment inertial properties.

Materials and methods

Subjects

Thirty-eight horses of various breeds, ages (median 10 years ± 9 SD) and sizes (mass 488 kg ± 142 SD; range 217–766 kg) were used in this study. Total body mass was determined prior to euthanasia using a Masstron M5000 scale. Horses were classified into three morphotypes: cold-blooded included all draft horses and Haflingers, hot-blooded were race horse types, Arabians and Hackney ponies, and warm-blooded horses were all horses that did not clearly belong in the other two categories.

Dissection

One fore limb and one hind limb were removed from each cadaver and disarticulated into segments (Figs 1 and 2). The fore limb was removed by abducting the limb and cutting the pectoral musculature, subclavius and serratus ventralis thoracis as close to the rib cage and sternum as possible. The other extrinsic muscles were severed around the periphery of the scapula and humerus along the lines shown in Fig. 1. The proximal extremity of the segment was the cartilaginous border of the scapula. The scapular segment was removed by disarticulation of the glenohumeral joint. The supraglenoid tubercle of the scapula and the greater tubercle of the humerus were palpated and used as landmarks to locate the joint, then an incision was made through the soft tissues, in the articular plane of the joint to separate the scapula and humerus. The triceps brachii, biceps brachii and brachialis muscles were divided by a linear incision that bisected the angle between the scapula and humerus on the caudal aspect of the limb. The elbow was disarticulated by making an incision that followed the contours of the olecranon process and the articular plane of the humeroradial joint, then cutting the remaining soft tissues horizontally at the level of the proximal radius to remove the brachial segment. Usually, the musculature of both scapula and brachium needed to be trimmed down to ensure that both segments would move as a unit during locomotion. This was done by outlining the bulging of the pectoral and subclavius muscles with a scalpel. The carpus was disarticulated between the proximal and middle rows of carpal bones.

Figure 1.

 Outline drawing showing the skeleton of an equine fore limb and indicating the cuts that were made to remove the limb and disarticulate the limb segments.

Figure 2.

 Outline drawing showing the skeleton of an equine hind limb indicating the cuts that were made to remove the limb and disarticulate the limb segments.

The hind limb was removed by disarticulation of the coxofemoral joint. An incision was made through the soft tissues dorsal to the greater trochanter, and then continued cranially to the tuber coxae and caudally to the tuber ischium. On the medial side, the incision followed the line of the sacrum in a lateral direction toward the coxofemoral joint, and then continued cranially towards the tuber coxae. The joint capsule and the ligament of the femoral head were cut to allow disarticulation. Removal of the limb was completed by cutting through the remaining extrinsic musculature close to the pelvis. Disarticulation of the femorotibial joint began on the cranial aspect by cutting the ligaments, tendons and joint capsule just distal to the femoral trochlea so the patella remained attached to the thigh segment. A horizontal incision was made through the soft tissues on the lateral and medial sides of the joint and continued caudally to completely separate the thigh from the crus. The tarsal joint was disarticulated by making a cut through the calcaneal tendon just proximal to the calcaneus and following the bony contours of the proximal edges of the calcaneus and talus to disarticulate the tarsocrural joint, thus keeping all tarsal bones with the metatarsus.

In both fore and hind limbs, the distal segments (pastern and hoof) were removed by a horizontal incision through the soft tissues to disarticulate the metacarpophalangeal or metatarsophalangeal joint, keeping the sesamoid bones with the proximal segment (metacarpus or metatarsus). The pastern segment (proximal and middle phalanges and proximal interphalangeal joint) was left intact, as it is usually treated as a single segment for kinematic analyses. The hoof (distal phalanx) was removed from the pastern (proximal and middle phalanges) by cutting through the hairline of the coronet and severing the soft tissues to disarticulate the distal interphalangeal joint, leaving the distal sesamoid (navicular) bone and distal phalanx with the hoof segment. All segments were frozen immediately after dissection.

Experiments

For each segment, mass was determined using a Valor 5000 scale (Ohaus) which measures with a precision of 1 g. Total length of the segment between its bony extremities was determined using electronic calipers with a precision of 1 mm (Swiss Precision Instruments), measuring from the middle of the articular surfaces on both ends of the segment. For the scapula, the length was measured from the middle of the glenohumeral joint surface to the top of the cartilage along a line parallel to the spina scapulae. The hoof axis was defined from the middle of the joint articulation surface to the sole of the hoof parallel to the frontal hoof wall. The position of the segmental center of mass (COM) was determined by suspending the frozen segment from a string with the long axis in a horizontal orientation using the same calipers. The string was moved along the long axis of the segment until it was balanced horizontally. Care was taken to ensure no contact remained between the segment and the environment. Under these conditions, the segment was suspended through its COM. The position of the segmental COM along the long axis was measured from the proximal end of the segment. Measurement error associated with this method was tested on dummy segments of simple geometry and was found to be dependent on length and radius: longer and thicker segments were associated with larger errors. By extrapolation, precision of this method was estimated to be within 1 cm.

Moment of inertia (MOI) was measured using a trifilar pendulum (Pal & Gaberson, 1973). Two versions of the pendulum were made to accommodate the wide range in MOI in the different-sized segments. Each pendulum consisted of two parallel plates connected by three long, flexible steel cables, attached at equal distances from the center of the plates. The top plate was fixed rigidly, whereas the lower plate was allowed to rotate freely. The two pendulums differed in size; the small one had a plate with radius 0.067 m and mass 0.361 kg with strings 0.539 m long; the larger version had a plate with radius 0.354 m, mass 3.91 kg and strings 2.15 m long. Knowing the dimensions and weight of the lower plate, the MOI of the empty pendulum could be calculated. The test segment was placed on the lower plate with its COM aligned above the middle of the plate and oriented so that the sagittal plane of the segment (parallel to the median plane of the horse, which is also the plane of movement) was parallel to the plate of the pendulum. The pendulum was set in motion and the period of free rotational vibration was recorded for the pendulum–mass system using a light-emitting diode (LED) light-photodetector system that detected an interruption in the light beam caused by the movements of a small opaque marker attached to the lower plate. The difference between MOI of the segment–pendulum system and the empty pendulum was used to calculate the segmental MOI under the assumption of small angle approximation (sinα approximately equal to α) using the equation:

image

where g = 9.81 m s–2, radius = radius lower plate, mpend = mass lower plate, msegment = mass segment, T1 = period pendulum with segment, and T2 = period empty pendulum. Each pendulum was precalibrated using dummy segments of known MOI.

Statistics

Reduced major axis regressions were performed in spss v. 17.0. Slopes of segmental masses against total body mass were tested for significant deviations from zero. Residuals of these relationships were tested for a size effect. Some horses were excluded from this procedure because we were not able to obtain a total body mass measurement. Some segments were excluded because the dissection was not performed accurately. Effect of breed type was tested by an anova on the residuals, comparing the mean residual value between the three morphological groups. This was repeated for relative position of the COM. Two different functions were fitted to estimate segmental MOIs: (i) a one-variable function using segment mass to the power of 5/3, as would be predicted from scaling relationships (Walter & Carrier, 2002), and (ii) a two-variable function using segment mass multiplied by the squared segment length. Selection of the two-variable function was based on the general equation of moment of inertia, which is the mass times the square of the perpendicular distance to the rotation axis. These two fitted functions were evaluated using the average absolute residual and the squared correlation coefficient to determine the most appropriate fit.

Figs 3A and 4E show the relationships between segmental mass and MOI for each segment. Raw data are shown as circles, color-coded by breed type. The means and standard deviations reported by other researchers are included (van den Bogert, 1989: large white circle; Buchner et al. 1997: large white square). A solid regression line is drawn for all raw data points, not taking breed type into account. The previously reported relationships are shown as a dashed line (Buchner et al. 1997) and a dash-dotted line (van den Bogert, 1989). These plots are useful for evaluating our scaling relationships compared with those of previous research. To determine these mass vs. MOI relationships, we combined reported equations of length vs. mass and MOI vs. length and mass. When length–mass relationships were not reported in the previous publications, we used the regression equation from our own data to build mass vs. MOI relationships.

Figure 3.

 (A) Moment of inertia of the scapula segment plotted against its mass. (B) Moment of inertia of the brachial segment plotted against its mass. Length–mass relationships based on our data were used to enable us to use the equations reported by Buchner et al. (1997) and van den Bogert (1989). (C) Moment of inertia of the antebrachial segment plotted against its mass. Length–mass relationships based on our data were used to enable us to use the equation reported by Buchner et al. (1997). (D) Moment of inertia of the metacarpal segment plotted against its mass. Length–mass relationships based on our data were used to enable us to use the equations reported by Buchner et al. (1997) and van den Bogert (1989). (E) Moment of inertia of the fore pastern segment plotted against its mass. Length-mass relationships of Buchner et al. (1997) were used to enable us to use the equations reported by Buchner et al. (1997) and van den Bogert (1989). Regression model of van den Bogert (1989) is off the chart. (F) Moment of inertia of the fore hoof segment plotted against its mass. Length–mass relationships of Buchner et al. (1997) were used to enable us to use the equations reported by Buchner et al. (1997), while length–mass relationships based on our data were used for the equation of van den Bogert (1989). Raw data points of this study are given as small, color-coded circles. The colors indicate morphotypes: red for hot-bloods, blue for warm-bloods and white for cold-bloods. A solid line shows the 5/3 power fit through all data points. Mean and standard deviations are shown for Buchner et al. (1997) as an open square and for van den Bogert (1989) as an open circle, both with error bars. Their reported relationships between mass and MOI are shown as respectively a dashed line and a dash-dotted line. The equation for Buchner et al. (1997) was corrected into I = 0.191 × l2 × m + 0.10783.

Figure 4.

 (A) Moment of inertia of the thigh segment plotted against its mass. (B) Moment of inertia of the crural segment plotted against its mass. (C) Moment of inertia of the metatarsal segment plotted against its mass. Length–mass relationships of Buchner et al. (1997) were used to enable us to use the equations reported by Buchner et al. (1997), while length–mass relationships based on our data were used for the equation of van den Bogert (1989). Note that the fit of Buchner et al. (1997) does not pass through its own mean. (D) Moment of inertia of the hind pastern segment plotted against its mass. (E) Moment of inertia of the hind hoof segment plotted against its mass. Length–mass relationships of Buchner et al. (1997) were used to enable us to use the equations reported by Buchner et al. (1997) and van den Bogert (1989). See Fig. 3 for coding of data points and lines.

Results

Segmental masses

Total limb masses were 33 kg ± 9 SD for the fore limb (7 ± 1% body mass) and 40 kg ± 11 SD for the hind limb (8 ± 1% body mass). The proportional mass distribution of the limb segments was close to that found in previous studies (Sprigings & Leach, 1986; van den Bogert, 1989; Kubo et al. 1992; Buchner et al. 1997) (Table 1). The residuals of crus, metacarpus and brachium showed a relationship with total mass, indicating a change in proportion with size. However, when data for six horses weighing over 600 kg were removed, this relationship disappeared (crus and metacarpus) or its sign reversed (brachium). For several segments, the cold-blooded horses had a significantly different residual segment mass from the hot-blooded animals, with warm-blooded horses having intermediate values between the two other groups in some segments. Masses of the antebrachium and crus were significantly smaller in cold-blooded horses than would have been expected from their size (residuals were negative), whereas pastern mass in the hind limb was significantly larger. For the scapula, brachium, fore and hind hooves, segmental masses did not differ between warm-blooded and hot-blooded horses but both were significantly different from cold-blooded horses. Scapular and brachial masses were smaller and hoof masses were larger in cold-blooded breeds than predicted from their size. As four of the five cold-blooded horses were larger than 600 kg, the breed effects on crus, metacarpus and brachium could probably be attributed mostly to a size effect. Metacarpal, fore pastern, thigh, and metatarsal masses did not differ between the three morphotypes.

Table 1.   The proportional mass distribution of the limb segments estimated by the slopes of reduced major axis regressions without intercepts of segmental masses against total body mass.
SegmentMean % (min % 95% CI–max % 95% CI)
n = 35
Mean %
DWB1
n = 12 (6)
Mean %
Pony2
n = 5
Mean %
TB3
n = 2/3
Mean %
TB4
n = 3
  1. Data in the left column show mean and 95% confidence intervals for our study. In the other columns, we provide the data from previous studies for comparison purposes: 1Buchner et al. (1997), 2van den Bogert (1989), 3Sprigings & Leach (1986), 4Kubo et al. (1992).

  2. DWB, Dutch Warm-blood; TB, Thoroughbred. For Buchner et al., sample size is written as 12 (6) because even though 12 limbs were used in this study, the limbs were removed from six subjects.

  3. *Used to show when the mean % from a previous study fell outside the 95% confidence interval of our data.

Scapula2.84 (2.67–3.00)2.14*2.12*4.74.6
Brachium2.23 (2.04–2.42)1.60*1.77*  
Antebrachium1.11 (1.05–1.27)1.251.04*1.3*0.9*
Metacarpus0.26 (0.25–0.27)0.29*0.29*0.45*0.3*
Fore pastern0.12 (0.12–0.13)0.140.11*0.45*0.25*
Fore hoof0.20 (0.17–0.22)0.200.27*  
Thigh6.49 (5.88–7.10)3.46*5.916.66.9
Crus1.06 (1.01–1.12)1.54*1.061.4*1.0*
Metatarsus0.53 (0.49–0.56)0.530.48*0.6*0.4*
Hind pastern0.13 (0.12–0.14)0.170.11*0.4*0.3
Hind hoof0.18 (0.13–0.22)0.180.17  

Position of the COM

Table 2 shows the relative positions of the COM measured from the proximal end of the segment and provides a comparison with similar data available from the literature (Sprigings & Leach, 1986; van den Bogert, 1989; Buchner et al. 1997). The residuals of COM position regressed against segmental length of the pastern and hoof of the fore limb showed a significant decrease when these residuals were in turn regressed against segmental length. This means that the relative position of the COM for these two segments changes to a more proximal position when the segmental length increases. No differences in relative COM position were found between breed types.

Table 2.   The position of the COM along the segmental long axis as estimated by the slopes of reduced major axis regressions without intercepts of position against total segmental length.
SegmentMean % (min % 95% CI – max % 95% CI)
N = 35
Mean %
Dutch WB1
N = 12(6)
Mean %
Ponies2
N = 5
Mean %
TB3
N = 2/3
  1. Data in the left column show mean and 95% confidence interval for our study. In the other columns, we provide the data from previous studies for comparison purposes: 1Buchner et al. (1997), 2van den Bogert (1989), 3Sprigings & Leach (1986), 4Kubo et al. (1992).

  2. DWB, Dutch Warmblood; TB, Thoroughbred.

  3. *Used to show when the mean % from a previous study fell outside the 95% confidence interval of our data.

Scapula58.9 (56.3–61.5)27Not comparable15
Brachium54.3 (51.3–57.2)5145* 
Antebrachium49.5 (48.4–50.6)35*35*44
Metacarpus50.0 (48.7–50.7)44*47*50
Fore pastern49.4 (47.2–51.5)46*4858
Fore hoof57.5 (48.6–66.4)29*31* 
Thigh53.2 (49.9–56.4)59*5148*
Crus47.1 (45.0–49.3)38*4840*
Metatarsus49.4 (48.2–50.5)32*36*37*
Hind pastern48.4 (46.7–50.1)43*4752
Hind hoof61.7 (58.3–65.0)31*19 

Moment of inertia

Scaling relationships between segmental mass and MOI were found for all limb segments. Table 3 shows a summary of the results of fitting two different functions through the dataset. Average absolute residual was small for most fits, indicating that both fits were appropriate estimates for the relationship between segmental mass and MOI. For all segments, R2 values were larger for the one variable fit between segmental mass and MOI.

Table 3.   Two-variable function fits of segmental MOI calculated from segmental mass and squared segmental length (A*mass*length2 + B) and one-variable fit equations of segmental MOI against segmental mass (A*mass5/3+B) are shown in this Table.
 SegmentA × mass × length2 + BFit parametersA × mass5/3 + BFit parametersn
A ± SDR2ResA ± SDB ± SDR2Res
  1. These two fitted functions were evaluated using the squared correlation coefficient (R2) and the average absolute residual (Res) to determine the most appropriate fit. Sample sizes (n) are shown in the right column. n.s., not significant.

Fore limbScapula0.1252 ± 0.0124n.s.0.750.080.0052 ± 0.0002−0.0433 ± 0.01890.950.0435
Brachium0.1245 ± 0.0149n.s.0.670.040.0034 ± 0.0002−0.0208 ± 0.01100.910.0236
Antebrachium0.0790 ± 0.0065−0.0273 ± 0.00980.800.020.0061 ± 0.0004−0.0243 ± 0.00710.910.0138
Metacarpus0.0510 ± 0.00270.0011 ± 0.00030.90< 0.010.0033 ± 0.00010.0015 ± 0.00020.95< 0.0137
Pastern0.0447 ± 0.00340.0009 ± 0.00000.83< 0.010.0013 ± 0.00000.0009 ± 0.00000.96< 0.0137
Hoof0.0751 ± 0.00700.0011 ± 0.00010.77< 0.010.0011 ± 0.00000.0008 ± 0.00000.97< 0.0137
Hind limbThigh0.1113 ± 0.01310.3734 ± 0.10330.700.240.0036 ± 0.0002n.s.0.930.1133
Crus0.0657 ± 0.0104n.s.0.530.010.0038 ± 0.0005−0.0173 ± 0.00800.670.0137
Metatarsus0.0497 ± 0.0062−0.0117 ± 0.00390.65< 0.010.0050 ± 0.0006−0.0071 ± 0.00330.66< 0.0137
Pastern0.0433 ± 0.00270.0010 ± 0.00000.88< 0.010.0012 ± 0.00000.0010 ± 0.00000.95< 0.0137
Hoof0.0727 ± 0.00440.0011 ± 0.00010.89< 0.010.0010 ± 0.00000.0009 ± 0.00000.98< 0.0137

Buchner et al. (1997) reported equations of the relationship between the mass of the scapula and its MOI that work well for warm-blooded horses with a scapular mass larger than 9 kg (which corresponds to body masses larger than 317 kg) after correcting the equation to MOI = 0.191 × length2 × mass + 0.10783 (pers. comm. with Buchner). For warm-blooded and cold-blooded horses with a scapula larger than 16 kg, the values yielded from our linear equation between mass and MOI provide a better prediction (Fig. 3A). As van den Bogert (1989) did not find any scaling relationship for the scapular segment, his prediction lacks precision outside the range of his dataset. The mean values reported by both van den Bogert (1989) and Buchner et al. (1997), however, fall into our raw data cloud. The relationships obtained for the brachial segment from previous studies do not provide a good fit with our data (Fig. 3B). The reason is that Buchner et al. (1997) did not find a significant scaling relationship and the equation of van den Bogert (1989) overestimates the moment of inertia compared to our data. Neither equation intersects its own mean value because mass–length relationships were not provided and relationships based on our data were used instead. The same approach was taken for the antebrachial segment (Fig. 3C). For this segment, the equation of van den Bogert (1989) predicts the mass–MOI relationship well when mass is smaller than 5 kg, whereas the equation of Buchner et al. (1997) yields good predictions for larger segmental masses. Unfortunately, this does not hold true for the metacarpal segment (Fig. 3D). van den Bogert (1989) did not find a significant scaling relationship, limiting the predictive value of his measurements outside the size range of his data, while Buchner et al. (1997) overestimates the MOI. Even worse are the predictions for the pastern of the fore limb (Fig. 3E). The regression model provided by van den Bogert (1989) falls outside the region shown in our plot, and that of Buchner et al. (1997) does not follow our data at all. A similar problem but to a lesser degree arises with the hoof of the fore limb, with both studies underestimating the MOI of the fore hoof (Fig. 3F). For the thigh segment, a significant effect of size is present, whereas both previous studies reported a constant MOI without mass effect (Fig. 4A). Their means do fall within our data cloud. The crus is variable in its mass–MOI relationship (Fig. 4B). The equations presented here and those of Buchner et al. (1997) perform equally well in their predictive power, although ours performs a little better at the very low range of crural mass. To determine the mass–MOI relationship for the metatarsus (Fig. 4C), we used our length–mass relationship with the predictions from van den Bogert (1989), but for the equation reported by Buchner et al. (1997), we used their reported length–mass relationship. In the latter case, this still caused the reported mean values to fall far from the equation values, possibly indicating an error in the mean values reported by Buchner et al. (1997). The mean values of van den Bogert (1989) are close to ours but his scaling relationship largely overestimates the metatarsal MOI. Both previous studies lacked a scaling relationship between mass and MOI for the pastern of the hind limb, in contrast to what we found (Fig. 4D). The mean values estimated by Buchner et al. (1997) confirm our measurements, whereas van den Bogert (1989) underestimates the MOI. A similar effect as the one for the fore hoof occurs in the hind hoof: both previous studies underestimate the MOI and neither scaling equation fits our findings (Fig. 4E).

Discussion

The main uses of segmental inertial properties are in inverse dynamic analyses and modeling studies. Accuracy of individualized inertial data is important for the heaviest, proximal segments in the stance phase and for the most distal segments during the swing phase. Despite some variation, the relative mass distribution over the limb segments in our study generally confirmed the findings of previous studies (Sprigings & Leach, 1986; van den Bogert, 1989; Kubo et al. 1992; Buchner et al. 1997). The major sources of the differences are in (i) the amount of muscle retained with the segment, (ii) the level at which the cuts were made in respect to the joints, and (iii) the amount of tissue lost in the dissection process.

Probably the largest source of variation is the amount of tissue retained with the segment. Our goal was to retain the muscle tissue that moves with the segment in order to create segments that can be considered rigid bodies for modeling. Cutting frozen cadavers with a saw makes a straight cut between the segments which does not allow detailed dissection. Using fresh tissue and a dissection approach allows identification of individual muscles and disarticulation of the segments using precise dissection rather than linear cuts through the articular surface using a bandsaw. The dissection method respects the joint anatomy, making the segmentation process more anatomically relevant. This is important in regard to using the data to build accurate 3D musculoskeletal models that take into account 3D movements of the instantaneous joint centers of rotation. The saw method also causes some material to be lost through cutting and it is difficult to avoid distortion of the soft tissues during the freezing process. Freezing also makes it difficult to palpate the tissue to locate bony landmarks. Previous studies did not provide details on how it was decided where to make the cuts. We suggest, if this approach is used, marking the bony landmarks on the live animal. One benefit to using the freezing method is that it avoids blood loss, which is not possible using the dissection approach. However, the amount of blood lost represents a very small mass. We compared the masses of the entire limbs to the sum of the segmental masses after dissection and found a 7% decrease in mass. This tissue loss is similar to the error reported by Bogert et al. but considerably more than reported by Buchner et al. (2.4%). Being able to freeze the entire horse prior to disarticulation seems to result in a significant reduction in tissue loss. However, measurement bias caused by tissue loss is probably not the largest source of measurement error in disarticulation studies; errors caused by deviations in the cutting protocol, especially for the more distal segments, and measurement error in determining the MOI using a trifilar pendulum are likely to be more important.

The proximal segments of the fore limb (scapula and brachium) in our study were relatively heavier than what has been reported by Buchner et al. (1997) and van den Bogert (1989) but were comparable to the findings of Sprigings & Leach (1986) and Kubo et al. (1992), who combined scapula and brachium into one segment. Specifically for the scapular segment, our mass measurements are likely heavier than previous estimates due to the inclusion of extrinsic muscles that were cut close to the trunk. We also had heavier brachial segments compared to Buchner et al. (1997) and van den Bogert (1989). Those authors gave only a fairly brief explanation of segmentation but we assume that the greater mass in our study resulted from including more of the pectoral muscles and latissimus dorsi. The metacarpi were slightly lighter, while the antebrachium, pastern and hoof segments of the fore limb were similar in mass regardless of the manner of disarticulation.

Overall, the mass distribution was found to be fairly consistent across morphotypes for horses up to 600 kg body weight. The fact that some differences were found for cold-blooded horses could be an effect of size, as three of seven horses larger than 600 kg were cold-bloods and we only had two data points for cold-blooded horses below this weight limit. The cold-blood morphotype group had an additional possible sample problem. For us to obtain animals that were still measurable in our setup, we had to resort to using fairly young animals. Two of the five cold-bloods, both larger than 600 kg, were younger than 2 years old. This means that, although the intralimb proportions had mostly reached adult size, they lacked muscle mass. Mass and moment of inertia would be expected to be less than predicted for their size, and as muscle mass is mostly located on the proximal end of the segment, the location of the COM is expected to lie more distally in young animals (Muri et al. 2008). This phenomenon could also contribute to scapular, brachial, antebrachial and crural masses being significantly smaller in cold-blooded horses than would be expected from their size. However, this decrease in mass did not affect the position of the segmental COM of cold-bloods. Apart from age and breed, gender could potentially affect inertial properties (Cervantes et al. 2009). As we only had data for mares and geldings and not for stallions, we could not test the effects of the androgenic influence of male hormones on body morphotype and specifically muscle mass. Previous studies did not include stallions either, so it is not known whether males differ from other horses.

A sensitivity analysis showed that for the fore limb swing phase, the inverse dynamics approach was most sensitive to segment mass, particularly the mass of the hoof (Lanovaz & Clayton, 2001). It is therefore unfortunate for calculations during the swing phase that the segment with the most variable mass is the hoof. This is most likely due to variations in farriery and trimming style. The larger horses are mostly draft horses, which tend to have flat feet, and the hooves, especially the fore hooves, are trimmed ‘pancake’ style (Thomas, 2006) to distribute the weight over a larger area (Fig. 5). When the draft horse outliers are taken out of the dataset, the linear fit between mass and MOI for the fore hoof segment has a slope of 0.0014 and an intercept of 0.0005. Although this linear equation is a much better fit, considerable variation in the hoof shape remains. Simple scaling relationships as we are proposing here for the other limb segments might not be adequate for the hoof segment. We suggest, therefore, applying the method proposed by Arabian et al. (2001) to obtain individualized inertial properties for the hoof segment in live horses. It should be noted that most researchers are more interested in the stance phase in which the hoof is stationary, so inaccuracies of hoof mass are less important.

Figure 5.

 Lateral (above) and dorsal (below) views on disarticulated fore hoof segments; left from a draft horse, right from a Dutch Warmblood. Note the differences in shape.

The effect of slight differences in the location of the intersegmental cuts and the resulting differences in the estimation of the relative mass of the limb segments seem to be amplified in differences in the position of the segmental COM. Another source of differences between studies relates to the protocol of determining the segment lengths. In this study, the actual lengths of the segments were measured after they were disarticulated, rather than estimating the lengths based on anatomical landmarks. We believed that this method would improve the accuracy of the regression models that are based on both segment mass and segment length, as we used the actual length of the segment rather than a proxy. As it turned out, for most segments, MOI can be estimated equally well or better by using just segment mass as an estimator. As segmental mass remains consistent throughout almost the entire size range, this finding means that both segmental masses and moments of inertia can be predicted easily from total body mass. However, the procedure of estimating the position of the segmental COM needs to be changed for most segments in comparison with previous studies and care has to be taken to estimate the position along the geometric length axis, rather than a chosen axis through two anatomical landmarks.

The crus turned out to be the most variable segment in terms of the relationship between mass and moment of inertia. This is probably due to variability in mass and mass distribution as a consequence of variability in muscle development associated with the recent level of athletic activity. These effects are most obvious in the more proximal segments, where the bulk of the locomotor muscles are located. In addition, the muscle mass is concentrated on the craniodorsal side of the crus, which gives the segment an inherent asymmetry compared with the relatively evenly distributed muscle mass in the more proximal segments. This asymmetry could be variable in itself or could cause the measurement error to increase, resulting in more variable data. As the segments seem to be highly variable in shape, we lean towards the first explanation.

The use of our length–mass relationship in the equation between MOI and mass in some of the segments might theoretically be the cause of a mismatch between our raw data and the predictions of the equations reported in previous studies (van den Bogert, 1989; Buchner et al. 1997) since our length measure is the real segment length from the proximal to the distal end of the disarticulated segment, whereas previous studies determined the position of the joint center based on anatomical landmarks prior to disarticulation. We only expected this to have a large effect on the scapular segment, as previous studies used the end of the spina scapulae as the proximal landmark, whereas we used the top of the cartilage, but determining the position of the joint centers prior to dissection might cause a bias in the segment length data.

One drawback to the methodology used in this study is that it was suitable only for determining COM and MOI along the long axis of the segment, which is the largest inertial component. As the vast majority of equine locomotor movements are confined to the sagittal plane, this is the most important axis. However, when aiming for a full 3D mechanical analysis of equine locomotion taking the smaller components of abduction–adduction and endo- and exorotation into account, we refer to the studies of Buchner et al. (1997) and van den Bogert (1989). Along these axes, experimental measurement errors are likely to exceed errors due to inaccurate extrapolation.

In conclusion, mass distribution over the equine limb segments is consistent between horses of different breeds and sizes but caution is warranted when studying horses larger than 600 kg. Segmental masses can be easily determined from total body mass. For most segments, moments of inertia can be accurately obtained from segmental masses without the need to include information on segmental lengths. Segmental COM positions are consistent between horses of different sizes when measured along the geometric length of the segment rather than along a line between two anatomical landmarks. Regression models obtained for the mass–MOI relationships were significantly different from previous studies, which is to be expected when sampling from a more diverse breed population representing a considerably larger range of sizes. The dissection method allowed a more anatomically correct representation of segmental boundaries, which had an effect on mass distribution between segments. Differences in segmental inertial properties between published studies may depend more on segmental segmentation techniques than on size or body type of the horse. We did not detect an effect of morphotype (hot-blooded, warm-blooded and cold-blooded) on segment inertial properties and morphotype may only need to be considered in horses above 600 kg.

Acknowledgements

The authors thank Narelle Stubbs, Claus Toftgaard Jørgensen, Rachel Wright, Lila Zarski, Katherine O’Connor and Kelly Smith for help with the experiments. Shannon Griffin from the necropsy lab at the Diagnostic Center for Population and Animal Health was a tremendous help in obtaining and removing limbs from the cadavers, while Sharon Thon facilitated the experiments by accommodating the use of the anatomy room to our unpredictable work schedule. LeeAnn Kaiser, Courtney Huff and Kimberly Kurtz helped with the administration. S.N. is a postdoctoral fellow of the FWO-Flanders. The research reported in this paper was funded by the McPhail endowment to H.M.C. and a Professorial Assistantship at Michigan State University to W.A.

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