Reasons for performing study: Bending of the equine metacarpal bones during locomotion is poorly understood. Cantilever bending, in particular, may influence the loading of the metacarpal bones and surrounding structures in unique ways.
Hypothesis: We hypothesised that increased amounts of sagittal-plane cantilever bending may govern changes to the shape of the metacarpal bones of Thoroughbred racehorses during training. We hypothesised that this type of bending would require a linear change to occur in the combined second moment of area of the bones for sagittal-plane bending (I) during race training.
Methods: Six Thoroughbred racehorses were used, who had all completed at least 4 years of race training at a commercial stable. The approximate change in I that had occurred during race training was computed from radiographic measurements at the start and end of training using a simple model of bone shape.
Results: A significant (P<0.001), approximately linear pattern of change in I was observed in each horse, with the maximum change occurring proximally and the minimum change occurring distally.
Conclusions: The pattern of change in I was compatible with the hypothesis that sagittal-plane cantilever bending governed changes to the shape of the metacarpal bones during race training.
The mechanical loading of the equine third metacarpal bone (MC3) during locomotion has been investigated using strain gauge methods (Turner et al. 1975; Rybicki et al. 1977; Biewener et al. 1983; Gross et al. 1992; Merritt et al. 2006) and studies of limb dynamics (Biewener et al. 1983; Merritt et al. 2008). These studies all agreed that axial compression dominated MC3 loading at various gaits and speeds. Sagittal plane bending, although reported in many of these studies, did not appear to be consistent in nature and is still poorly understood. For example, Rybicki et al. (1977) found that bending of the MC3 at walk and trot was directed such that the dorso-medial side of the bone was under tension. Biewener et al. (1983) used 2 different methods to compute loading of the MC3: a bone strain analysis which did not reveal substantial bending, and a biomechanical model driven by force plate and kinematic data, which predicted substantial sagittal plane bending. The differences between the results of the 2 models were partially ascribed to the simplicity of the latter model, which lacked a representation of the force acting upon the distal metacarpus due to the paired proximal sesamoid bones (Biewener et al. 1983).
The dominance of axial compression was explained by Thomason (1985), who investigated the trabecular structure of the MC3 condyle and described a mechanism in which the paired proximal sesamoid bones and the first phalanx created a dorso-palmar force balance. The net force on the distal MC3, arising from the sum of articular contact forces, was thus proximally directed and aligned with the MC3 axis, resulting in axial compression. Merritt et al. (2008) showed that this mechanism was mechanically valid throughout the stride at walk and trot, using a model that incorporated the major bones, ligaments and tendons of the distal limb.
Due to the strong fibrous union between the 3 metacarpal bones, which often becomes ossified, they have previously been treated as a single beam (Piotrowski et al. 1983), which we shall refer to in this paper as the metacarpal complex (MC). The MC experiences mechanical loads due to its proximal and distal articulations, the tendons and ligaments which insert upon it, and gravitational and inertial effects due to the mass and acceleration of the MC itself. Anatomically, the points at which external mechanical loads may act are restricted to the proximal third of the MC and the region around the distal MC3 condyle. Therefore, the MC may be treated as an end-loaded beam (Piotrowski et al. 1983). In this end-loaded beam model, the proximal end of the MC experiences a point load which represents the sum of all forces and moments applied by structures in its proximal region, while the distal end experiences a second point load which corresponds to the sum of all forces and moment applied by structures in its distal region. Further, due to the relatively small magnitude of inertial effects during the stance phase of the stride (Merritt et al. 2008), the end-loaded beam model will exist in conditions approximating static equilibrium (Merritt et al. 2006). Under these approximations, the loading state at the proximal MC is entirely determined by the loading state at the distal MC, using the equations of static equilibrium for a rigid body. Therefore, the net loading applied to the MC by the structures related to the carpus and suspensory ligament at the proximal end are uniquely determined by knowing the net loading applied to the MC by structures at its distal end (Merritt et al. 2006). Under these approximations, it is mathematically sufficient to investigate mechanical loading at only one of the 2 ends of the bone to reach a conclusion regarding the other.
In studies of MC shape, the structure has often been treated as having a cross-section that is optimised to allow local regions of the bone to resist their peak strains (Piotrowski et al. 1983). Given this treatment, mechanical beam theory predicts that, were axial compression to dominate the peak loading, then we would expect the MC to have a uniform cross-sectional area along its length (Benham et al. 1996). However, instead of a uniform area, studies of MC geometry found that both the area and second moment of area to resist sagittal-plane bending (I) varied along the length of the bone (Piotrowski et al. 1983; Nunamaker et al. 1989). Piotrowski et al. (1983) described a variation in I along the MC that was approximately linear, with a maximum proximally and a minimum distally. This indicated a structure that was best shaped to resist a cantilever load (Piotrowski et al. 1983) rather than pure axial compression. In this cantilever bending scenario, a net dorsally-directed force component would exist at the distal MC3. Applying the conditions of static equilibrium described above, the carpus would have to induce both a moment and a palmarly-directed force at the proximal end of the MC. Axial compression could be superposed on this loading without affecting this conclusion, to produce the full sagittal-plane loading shown in Figure 1. In this paper, we presume the direction of the hypothetical cantilever force to be directed dorsally, as shown in Figure 1. If the cantilever force were applied in the opposite (palmar) direction, then the carpus would not lock in extension and support a moment, but instead would be free to flex.
These 2 areas of study are therefore not fully reconciled: the shape of the MC indicated a structure that was optimised to resist cantilever bending superposed on axial compression. However, bending in general was not observed with any consistency during in vivo studies.
We hypothesised that cantilever bending may dominate the peak strain state of the MC and may therefore be a key driver of shape change in the bones. In order to reduce the peak strains caused by an increased cantilever bending, the MC cross-section would need to increase its value of I in a linear fashion, with a maximum increase in I occurring proximally and a minimum (possibly zero) increase occurring distally (for a treatment of beam section properties and their relationship to strains please refer to texts such as Benham et al. 1996). Such a linear pattern in changes to I would be a necessary condition if cantilever bending dominated shape change within the MC. We therefore wished to discover whether race training and fast exercise induced changes to I in this linear pattern in individual horses.
Materials and methods
Six Thoroughbred horses from a commercial racing stable were used for this study. All horses were geldings and their racing histories are shown in Table 1. Most horses in this stable were measured on a weekly basis using various modalities over a period of more than 10 years, in support of various research projects. From the total set of horses in the stable, those that had been in training for more than 4 years were selected for this study.
Table 1. Numbers of race starts, number of places (first, second or third in the race) and total prize money (in Australian dollars) of the horses used in this study
Number of race starts
Number of places
Prize money (to nearest thousand)
Radiographic examinations of the horses were available at the start and end of their period in training, which varied from a total of 4–5 years. Each radiographic study consisted of a lateromedial radiograph of the left MC and a mediolateral radiograph of the right MC, both taken at a distance of 1 m, according to a standardised method described by Walter and Davies (2001). Metallic circular markers were affixed to the skin over the flexor tendons of each forelimb to enable measurements of the radiographs to be scaled to account for magnification effects.
The second moment of area to resist sagittal-plane bending (I) was computed by assuming a double-ellipse cross-section for the MC3 (Bynum et al. 1971), in which one ellipse represented the periosteal boundary and another represented the endosteal boundary. The projected widths of the dorsal cortex, medulla and palmar cortex were measured on the radiographs and then scaled appropriately to produce scaled dorsal cortex (D), scaled medulla (Ml) and scaled palmar cortex (P) values. Unfortunately, because only lateral views of the MC3 were available, dorsal projections of cortical and medullary widths could not be measured. Instead, these widths were taken at mid-shaft from the CT scan of the left MC3 of a single Thoroughbred racehorse that was not otherwise a part of this study (medial cortex width = M = 11 mm; lateral cortex width = L = 10 mm; dorsopalmar projection of medulla = Md= 19 mm). With this limitation, which is discussed later, changes to I could only arise from changes to the laterally-projected dimensions.
Using the double-ellipse model of Bynum et al. (1971), I was computed as follows. The outer ellipse major and minor radii (a1 and b1) were found by:
Similarly, the inner ellipse major and minor radii (a2 and b2) were found by:
The centre of the inner ellipse relative to the outer ellipse, d1, was found by:
d1= (P – D)/2
Then, using standard equations for ellipse geometry (Merritt 2007), the centroid of the section, x, was found by computing:
The area was computed using:
Finally, the second moment of area for bending in the sagittal plane, I, was found by computing:
I was computed at 5 sites, spaced at 2 cm intervals in the range from 4–12 cm distal to the nutrient foramen of the MC3. This distal region was chosen because the second and fourth metacarpal bones were either absent or very small in this area. Piotrowski et al. (1983) reported that the linear pattern in I was only apparent in the proximal half of the bone when the second and fourth metacarpal bones were included in the calculation. Since it was thought that these bones would cause the cross-section to deviate strongly from the double-ellipse approximation, the distal region of the metacarpus was chosen for analysis.
Changes to I that occurred during race training, ΔI, were found by subtracting site-specific values at the end of training from the same values at the start of training. ΔI values were then averaged between left and right limbs to produce a representative set of site-specific values for each horse. Then, the site-specific values were normalised by dividing them by the largest ΔI across all sites for each horse. This produced a pattern of changes that were scaled individually for each horse, where the site with the largest ΔI had a value of 1, and 0 represented no change. Negative values would indicate decreases in I over the training period. The raw (non-normalised) values for ΔI were not analysed because the study sought only to determine whether the pattern of ΔI with respect to distance along the MC was linear.
The normalised results for each horse were analysed using linear regression, to examine the individual horse relationships between ΔI and position along the bone. The data were then pooled and a one-tailed t test conducted to assess whether the normalised ΔI values at the site 40 mm distal to the nutrient foramen came from a different distribution to those at the site 120 mm distal to the nutrient foramen.
The horses exhibited a significant linear relationship between normalised ΔI and position distal to the MC3 nutrient foramen.
The normalised ΔI were positive at all sites in all horses. This indicated that I had increased at all sites. The average R-squared value for the linear fits was 0.75. All slopes were found to be in the expected direction (the maximum ΔI occurred proximally and the minimum ΔI occurred distally) and were significantly different from zero (P<0.001 in all cases). The one-tailed t test showed that the pooled results for normalised ΔI from the site 40 mm distal to the nutrient foramen came from a different distribution to those from the site 120 mm distal to the nutrient foramen (P = 0.00016). Figure 2 shows mean and standard deviation at each site.
This study found that, for sagittal-plane bending, changes to the second-moment of area of the MC3 (ΔI) that occurred during race training had a linear relationship with position along the bone axis. ΔI had a maximum proximally and a minimum distally. This linear relationship was compatible with the proposition that the metacarpus experienced cantilever bending during race training, which governed peak strain conditions and thus changes to the shape of the bone.
The model used for this study had many limitations. Most important was the lack of measurements of medial and lateral MC3 cortex widths. Instead of individual measurements of these values from the horses in the study, a uniform, prismatic set of values were used. This lack of data is ameliorated by the observation that the dorsal and palmar cortex widths affected I in a cubic fashion (Bynum et al. 1971), whereas medial and lateral cortex widths only affected I in a linear fashion (Bynum et al. 1971). Therefore, changes in the dorsal and palmar cortex dimensions effected changes in the true value of I to a much greater extent than any changes which may have occurred in medial and lateral cortex widths. The lack of medial and lateral cortex widths also prompted the use of normalised ΔI values. Since these cortex dimensions act as linear coefficients in the computation of ΔI, normalisation had the effect of further reducing their influence. However, the strength of the linear relationship between ΔI and axial position along the bone may have been reduced if the true values for the medial and lateral cortices were included. The use of a double-ellipse approximation for the cross-section also represented a substantial limitation and further limited the region of the MC that could reasonably be examined. Both limitations were brought about by the lack of any additional data regarding the cross-sections of the bones in the study.
The repeatability of the radiographic technique used for this study was previously examined by Walter and Davies (2001). The technique and quality of materials used for the radiographic procedure may have varied slightly over the period of the study, resulting in additional errors in the computation of I. These errors could be reduced by the use of modalities which produce a more complete geometric representation of the bone, such as CT and MRI.
The study incorporated many of the assumptions present in earlier work regarding the shape of the MC. It was assumed that the geometry of the MC should somehow be optimal to resist the peak strains experienced by local regions of the bone. It was also assumed that the material properties of bone did not vary substantially within the cross-section, to the extent that the strength of the MC was substantially determined by its shape.
It is possible that the observed changes in I were not caused by cantilever bending, but instead occurred due to other types of shape change. For example, if the MC in the untrained horses already had a linear distribution of I then it is conceivable that uniform increases to the cross-sectional area of the bone may have increased I in the way that was observed. In that scenario, the bone would coincidentally become better able to resist cantilever bending, in the absence of cantilever bending itself. The changes to I that were observed are therefore a necessary, but not sufficient condition for the proposition that cantilever bending dominated shape changes. We thus describe them as merely compatible with the cantilever bending proposition.
No control group of untrained horses was used in this study, which meant that training itself could not be described as associated with the observed changes. However, previous reports have indicated that the magnitude of bone shape change with age is related to training (Nunamaker et al. 1989). It is possible that a similar change in I occurs with a smaller magnitude in untrained horses, or that untrained horses show a different pattern in the changes to I. Neither result would affect the major conclusion of this paper, which is that the changes to I in race-trained horses are compatible with cantilever bending.
Hypothetical cantilever bending of the MC agrees with some other intriguing observations. Inverse dynamics studies of the carpus have revealed that the joint complex experiences an extensor moment during the stance phase of the stride, which is supported at least partially by tension produced in the carpal flexor muscles (Merritt et al. 2008). However, the existence of cantilever bending in the MC suggests that the structures of the joint itself, perhaps via tension in the palmar carpal ligament, also support some of the extensor moment applied to it. This behaviour of the carpus is readily seen in vitro: if the flexor tendons are cut and dissected free from the joint, it does indeed ‘lock’ at full extension, and hyperextension is only possible with the application of a substantial moment. However, the authors are not aware of any report in which the relationship between applied moment and carpal hyperextension has been quantified. If peak loading of the metacarpus in race training were associated with cantilever bending, then the locking behaviour and forced hyperextension of the carpus would also occur at this point of peak loading. This type of carpal hyperextension is often thought to be observed in racing Thoroughbred horses at high speed and Burn et al. (2006) found that, for treadmill exercise, carpal hyperextension was proportional to exercise speed and increased with treadmill incline.
Cantilever bending would provide a putative purpose for the second and fourth metacarpal bones. As described by Piotrowski et al. (1983), the linear pattern in I was only present when these bones were included in the MC. Thus, it could be argued that the second and fourth metacarpal bones provide additional support for bending in the proximal part of the MC, where the bending moment due to cantilever action is the largest (see Fig 1). Furthermore, this support is only possible if the second and fourth metacarpal bones are mechanically bonded to the MC3 in a strong fashion, enabling transfer of the internal stresses that are generated in a bending beam (Bynum et al. 1971). This could provide a reason for the existence of the strong fibrous union between these bones, which can become inflamed and ossified.
Exercise-related changes to the carpal bones may be related to cantilever bending of the metacarpus. If the metacarpus were to apply a moment to the carpus, as would arise in cantilever bending, then the carpus would have to support this moment. With analogy to beam bending (Benham et al. 1996), moment support would then induce a stress gradient within the carpus itself, with peak stresses occurring on the dorsal aspect of the joint. Such a stress gradient would help to explain the sclerotic changes that have been observed in the carpal bones, associated with fast exercise (Firth et al. 2000).
Finally, we address the question of why in vivo studies of the MC3 have not observed consistent bending. One possible explanation may lie in the ‘sensitivity’ of the MC3 to bending as opposed to compression. Due to its length and cross-section properties, the MC3 can support a relatively large compressive force without experiencing large strains. In contrast, only a small cantilever force applied to the MC3 can generate large strains. It was previously estimated that a unit cantilever force would produce peak mid-shaft strains in the MC3 more than 10 times larger than a unit compressive force (Merritt 2007). Hence, for the range of possible physiological strains, the magnitudes of possible compressive forces are probably intrinsically much larger than those of possible cantilever forces. It also seems likely that the magnitude of cantilever bending may increase with increasing exercise speed, as suggested by the observed increases in carpal hyperextension with speed (Burn et al. 2006). Thus, previous investigations of bone loading at walk and trot may not correctly represent the loading conditions at the faster speeds that induce peak strains during race training.
Further work is being undertaken to quantitatively establish the relationship between carpal hyperextension angle and applied moment. In combination with in vivo kinematic studies of carpal hyperextension, such a relationship will establish the magnitude of moment loading that the carpus supports and therefore the magnitude of cantilever bending in the metacarpus.