A preliminary modelling study on the equine cervical spine with inverse kinematics at walk



Reason for performing study: The motion of the atlanto-occipital, cervical vertebral and cervicothoracic joints play an important role in equestrian sports and they are also common sites for lesions limiting performance in horses.

Objectives: To calculate inverse kinematics based on cervical vertebral motion and to develop a model close to the measured neck movements.

Materials and methods: Measurements were recorded in 6 horses without neck pain. Reflective markers were placed on both cristae facialis, both sides of cervical vertebra 1, 3 and 6 on the withers and hooves. The neck model was reconstructed from CT scans of the osseus structures and was developed in SIMM (Software for Interactive Musculoskeletal Modelling). Inverse kinematics calculation was done in OpenSim. Three degrees of freedom: Flexion-extension (FE), axial rotation (AR) and lateral bending (LB) were considered. The simulated motion was generated from the recorded motion of the skin markers. The differences in angular range of motion (ROM) of the joints were analysed using paired sample t tests.

Results: From the model, the smallest FE ROM was in the C5–C6 joint (2°± 1°) and the largest was in the C3–C4 joint (11°± 5°). The smallest AR ROM was in the C5–C6 joint (2°± 1°) and largest AR ROM was in the atlantoaxial joint (7°± 2°). The smallest LB ROM was in the C5–C6 joint (2°± 1°) and the largest LB ROM was in the cervicothoracic joint (18°± 5°). There were significant differences between the ROM of joints in 51 of 168 comparisons (P<0.05).

Conclusions: The result of the motion of each joint gives an insight into the biomechanics of the equine neck. The small FE ROM at C5–C6 illustrates the pathogenetical relevance of the model for the development of osteoarthritis. The calculated data also provides a source for inverse dynamics.


Computer models are becoming increasingly popular in equine biomechanics. Advantages of computer models include the production of information that cannot be easily obtained by other means, such as internal stresses or strains. They can be used repeatedly for multiple experiments with uniform consistency, which lowers the experimental cost and validated computer models can simulate various conditions easily and quickly. Once developed, a musculoskeletal head-neck simulation model can improve our understanding of the complex cervical spine biomechanics and provide a platform for future model development that integrates muscle excitation functions (Yan 2006).

Head position is fundamental to a broad range of movements, including visual and auditory orientations, feeding and vestibular function. In animals, activities such as grooming, predation and defence are also dependent upon head position and neck movement (Sharir et al. 2006). The allocation and degree of joint mobility within the equine cervical and thoracolumbar spine have an enormous influence on head, neck and trunk movements. Horses built for high running endurance and low energy costs have developed rather rigid vertebral columns, mainly by developing a shorter lumbar region and extending the dorsal vertebral spines to maximum movement (Slijper 1946). Angular position of the head in horses is not closely dependent on cervical column orientation. The equine head reaches and retains head orientation fairly autonomously from the neck to effectively complete a selection of behavioural tasks (e.g. stance and gaze maintenance, locomotion, grazing) (Dunbar et al. 2008).

Buchner et al. (1997) confirmed that the head and neck segments of the horse are cantilevered from the front of the body and represent approximately 10% of the animal's total body mass (TBM). Besides that, the horse neck is larger in mass than the head (6 and 4% TBM, respectively) (Clayton 2004).

The first research on equine cervical spine kinematics was done by Clayton and Townsend (1989a,b). The investigations focused on the cervical vertebral axial rotation, dorsoventral flexion and extension and lateral bending in adult horses and foals. These examinations were done in cadavers. A recent study on in vitro cervical spines found the stiffness of the equine cervical spine depends on the direction of the loading and is 2–7 times lower than thoracolumbar spinal stiffness in horses (Pagger et al. 2009). In vivo studies include experiments done only on the thoracic, lumbar and lumbosacral regions (Faber et al. 1999; Haussler et al. 2001; Licka et al. 2001a,b). While in vitro studies have shown the successful development of a simulated model of the equine thoracolumbar spine (Peham and Schobesberger 2004; Schlacher et al. 2004), until now in vivo intervertebral movements of the cervical region have not been reported.

Our goal was to model the equine neck movements from skin markers representing the movements of the cervical vertebrae without any implantation. We wanted to document normal movement patterns of the cervical spine and then use the model to explore the complexity of the whole cervical spine as a 3-dimensional structure. One of the basic assumptions on which the model is based on is that the cervical intervertebral joints cannot move independently from each other as many of the cervical muscles span several joints (Wissdorf et al. 1998). This dependence has already been demonstrated in the feline cervical spine (Keshner et al. 1997).

Materials and methods


In vivo measurements were taken in 6 horses (2 Thoroughbreds, 2 Trotters and 2 Warmbloods; 2 geldings, 2 mares, 2 stallions; 8–20-years-old; 450–700 kg) without clinical signs of neck and back pain. Clinical examination existed of palpation of the vertebrae and the musculature, as well as evaluation of passive and active neck movement. Horses were without history of neck or back trauma or surgeries.

Data collection

Fourteen reflective skin markers were attached to each horse using adhesive tape. Six markers were symmetrically placed on left and right side of the first, third and the sixth cervical vertebrae. Additional markers were placed on the head (left and right crista facialis), on the highest point of the withers, sacrum and lateral side of each hoof to identify motion cycles, which are defined as the complete sequence of motion from one breakover of the right forefoot to the next, consisting of one swing and one stance phase.

All horses were part of the teaching herd at the university and well accustomed to the experimental set-up on the treadmill (Mustang 2200)1 and they were warmed up prior to the data collection. Each horse walked at its own optimum speed (Peham et al. 1998). Data collection continued until 3 trials (each 10 s) in walk had been recorded.

Three-dimensional kinematic data were collected in a standard right-handed Cartesian coordinate system using 10 digital infrared cameras (Eagle Digital RealTime System)2 recording at 120 Hz.

Data analysis and processing of the kinematic data

The 3-dimensional coordinates of each marker during the time course of each experiment were calculated from the data by Cortex (Cortex 1.3)2 software. The kinematic data has then been smoothed by use of a Butterworth low-pass filtered (cut-off frequency, 10 Hz). Duration of the motion cycle was calculated from the movement of the hoof of the right forelimb by Matlab (MATLAB R2008b)3 software.

Development of the model

The cervical vertebrae were reconstructed from CT scans (Groesel et al. 2009). The equine neck was modelled in SIMM (SIMM 4.2.1.)4 (Software for Interactive Musculoskeletal Modelling)3 and further analysis was done in OpenSim4 (open source software for simulation). The standard right-handed Cartesian coordinate system was applied, where the movements are defined as a rotation about the x, y and z axes, respectively. Three degrees of freedom (DOF) were applied. Flexion-extension (FE) was defined as longitudinal bending in a vertical plane, which flexes or extends the spine, dorsoventral flexion-extension is rotation about the y axis. Flexion causes an increase in the dorsal convexity of the spine, i.e. arching the neck. Extension straightens the convexity or may even cause a dorsally concave outline, i.e. elevation of the head and neck. Axial rotation (AR) was defined as torsion about a longitudinal, horizontal axis (x axis). Lateral bending (LB) was defined as transverse bending in a horizontal plane that curves the spine to the right or left side for each cervical joint. Rotation about z axis is lateral bending. For each modelled vertebra 3 segment axes were manually approximated to the axes of the vertebra. Figure 1 shows the final model with the skull, C1–C7 and the first 5 thoracic vertebrae. Maximum possible ranges of motion of every single DOF accepted for each joint in our model of the equine cervical spine are listed in Table 1. The values were chosen in accordance with Clayton and Townsend (1989b).

Figure 1.

Equine cervical spinal model with the skull, C1 to C7 and the first 5 thoracic vertebrae. Pink markers show the position of the skin markers over the osseous structures, the movement of which was the basis for the development of the model.

Table 1. Maximum possible ranges of motion of every single DOF accepted for each joint in our model of the equine cervical spine. The values were chosen in accordance with Clayton and Townsend (1989b)

Data analysis, processing and application of the model

The reconstructed vertebra model was built in SIMM and exported into OpenSim. The model was scaled by the use of the OpenSim Scale Tool. The Scale Tool adjusted the anatomy of the model so that it matched the particular subject as closely as possible. Scaling was performed based on a comparison of experimental marker data with virtual markers placed on the model. For each horse the model was scaled individually by the marker data from the recorded motion. After that, the inverse kinematic tool was used to calculate the joint angles. The purpose of the inverse kinematics (IK) step was to find the set of joint angles and positions for the model that best reproduced the experimental kinematics recorded from the in vivo measurements of the neck. The experimental kinematics targeted by IK included experimental marker positions as well as experimental joint angle values. Experimental markers are matched by model markers throughout the motion by varying the joint angles over time. The IK tool computed joint angle values which position the model in a pose that best matched experimental marker and coordinate values for each recorded frame of motion. Mathematically, the best matched was expressed as a weighted least squares problem, whose solution minimised both marker and coordinate errors (Delp et al. 2007).

The model data was split into motion cycles by using the in vivo breakover movement of the right forefoot. At least 5 walking motion cycles for each horse were used to apply the model to determine the individual range of motion (ROM) for each joint angle. The mean values and standard deviations of the ROMs of all 3 DOFs for each joint were calculated over all horses. These values were also represented as a percentage of the summed cervical movement of all 8 joint angles.

Marker error analysis

Skin markers always cause small-sized systematic errors due to skin movement and muscle deformation. In order to represent the 3 dimensional difference between recorded and simulated marker position Root Mean Square Errors (RMSE) were calculated for the marker position of the recorded and simulated motion during the mean motion cycles of all 6 horses. The recorded and the simulated motion of the left C1 marker was plotted to illustrate the difference in all 3 directions. The C1 FE and LB angles were calculated based on the recorded and the simulated motion data for Horse 1.

Statistical analysis

Statistical analysis was carried using SPSS (SPSS 17.0)5. For confirmation of normal distribution of data Kolmogorov-Smirnov test was used. Differences between angles of each joint were tested by use of a Student t test for paired samples. Values of P<0.05 were considered significant.

Results of inverse kinematics

ROM for flexion-extension, axial rotation and lateral bending was calculated at walk.

The angular ROM for each joint is presented in Figure 2, the significant differences between the joints is given in Table 2.

Figure 2.

Mean and standard deviation for range of motion of flexion-extension (FE), axial rotation (AR) and lateral bending (LB) between the vertebral joints occurring during the simulated motion in the model of the equine cervical spine at walk. The model was applied to 6 horses to determine the individual range of motion (ROM) for each joint angle. AO (atlanto-occipital joint) is on the left and for the other joints the involved cervical vertebrae are given.

Table 2. Mean and standard deviation (+/−) for range of motion of flexion-extension (FE), axial rotation (AR) and lateral bending (LB) between the vertebral joints (e.g. AO atlanto-occipital joint, C1–C2 atlantoaxial joint) occurring during the simulated motion in the model of the equine cervical spine at walk. The model was applied to 6 horses to determine the individual range of motion (ROM) for each joint angle. Within one column, superscripts indicate a significant difference (P<0.05) with the joint indicated by the cranial vertebra only (e.g. C1 indicates a significant difference with the value of the C1–C2 joint)
mean ± s.d.
Significant differencesAR
mean ± s.d.
Significant differencesLB
mean ± s.d.
Significant differences
AO4.1 ± 2.4 C1,C2,C3,C4 1.3 ± 0.4 C1,C4,C6,C7 2.6 ± 0.7 C3,C4,C5,C6,C7
C1–C210.1 ± 8.7 AO,C5,C7 6.9 ± 2.4 AO,C2,C3,C4,C5,C6,C7 2.9 ± 1.1 C3,C4,C5,C7
C2–C38.7 ± 5.2 AO,C5 1.8 ± 0.3 C1,C3,C5,C6 4.1 ± 2.0 C4,C5,C7
C3–C410.5 ± 4.9 AO,C5 1.3 ± 0.3 C1,C2,C4,C6,C7 5.4 ± 2.6 AO,C1,C5,C7
C4–C58.4 ± 3.6 AO,C5 2.7 ± 0.9 AO,C1,C3,C5,C6 7.3 ± 2.5 AO,C1,C2,C5,C6,C7
C5–C62.1 ± 0.4 C1,C2,C3,C4,C6,C7 0.9 ± 0.3 C1,C2,C4,C6,C7 1.0 ± 0.2 AO,C1,C2,C3,C4,C6,C7
C6–C77.9 ± 4.5 C5 3.2 ± 0.7 AO,C1,C2,C3,C4,C5 4.0 ± 0.8 AO,C4,C5,C7
C7–T15.7 ± 2.5 C5 2.7 ± 1.0 AO,C1,C3,C5 17.9 ± 5.0 AO,C1,C2,C3,C4,C5,C6

The study documented that there was the largest FE between the third and the fourth cervical vertebra. At each of these joints 18% of the total cervical movement in that direction was found. The results also showed that 33% of the overall axial rotation of the head and neck segment occurred at the atlantoaxial joint (C1–C2). Of the lateral bending of the cervical spine, 40% took place at the joint between the last cervical vertebra and the first thoracic vertebra.

Error analysis results

The highest 3-dimensional marker errors were documented at the withers and the left and right C6 markers (Table 3). Comparison of the recorded and the simulated motion of the left C1 marker of Horse 1 showed relatively small errors in all 3 directions, with the largest error in craniocaudal direction (Fig 3). The left C1 flexion-extension and lateral bending angles based on the recorded and simulated motion data of Horse 1 showed a maximum difference of less than 2° throughout the motion cycle.

Table 3. The minimum (min), maximum (max), mean and standard deviation (s.d.) of the difference between recording and simulation within the mean motion cycle at walk is shown. For the calculation of the mean motion cycle, the mean of the recordings of all 6 horses and the mean of the simulations of all 6 horses were used. Markers are indicated as crista facialis (CF), first cervical vertebra (C1), third cervical vertebra (C3), sixth cervical vertebra (C6) and withers (W). Left markers (L) and right markers (R) are listed separately
Three dimensional difference (mm) between recorded and simulated marker position
Figure 3.

Comparison of the recorded (dashed line) and the simulated motion (continuous line) of the marker placed on the skin over the left wing of the atlas (C1L) and the flexion-extension and lateral bending angles between the marker on the left crista facialis, C1L, and the marker on the left transverse process of C3. Shown is the recorded and simulated motion data for Horse 1. The difference between the curves indicates the error between the recorded and simulated motion.


The atlanto-occipital (AO) and atlantoaxial (C1–C2) joints are dedicated to particular movements in all 3 directions by their anatomical shape. The AO joint is classified as a ginglymus with a hinge-like action and its movements are mainly flexion and extension, with some lateral oblique gliding (Getty 1975). In our model, only 7% of the overall cervical flexion-extension occurs at AO and lateral bending of this joint is small. This fits well with the anatomical description of the AO joint, as it is inhibited by the impingement of the jugular process on the lateral arch of the atlas. Axial rotation at AO is small, this agrees with functional anatomical findings (Clayton and Townsend 1989a,b). The C1–C2 joint consists of 2 large articular areas with little congruence. It is described as a trochoid or pivot joint (Getty 1975). Our findings show that most of the axial rotation of the cervical spine occurs at C1–C2 similar to earlier in vitro studies on specimens of the dissected equine cervical spine (Clayton and Townsend 1989a,b). Flexion-extension is relatively large in this joint, which supports the studies of Gellman and Bertram (2002a,b). Lateral bending is small at this joint, but not the smallest in the whole cervical region.

In a previous study, the cervical joints between C2 and T1 were described to be relatively similar in shape, and this was interpreted as the reason for showing relatively similar ROMs in all 3 directions (Clayton and Townsend 1989a,b). In our model, there are fewer significant differences between the ROMs of these joints than in the comparisons with AO and C1–C2 joints. The position of the vertebral articular surfaces is progressively more lateral from C2–C7, being again close to the midline on T1. This orientation influences the amount and type of movement. In our model ROM of FE is large throughout this region, it is largest at C3–C4 and the smallest at C5–C6. In our modelling study, the shapes of the vertebrae have no direct influence on the range of motion. In this study, the anatomically correct osseous contours are only used for defining the segment and joint axes, and in future studies they will be necessary for the location of insertions and origins of muscles.

Our findings agree with the results of Gellman and Bertram (2002b) that at the walk the head and neck oscillate around an almost horizontal position, very close to the same height at the withers and tuber sacrale. Using the motion data, our model also shows this horizontal position of the neck during walking.

The equine cervical spine is the foremost place for spinal trauma, as well as degenerative and developmental processes (Speltz et al. 2006). Traumatic fractures not due to known external forces such as kicks have been described in several foals and horses at the level of C3–C4 and C4–C5 (Mayhew 2009; Muno et al. 2009; Withers et al. 2009). These joints are in the middle between the heavy head and the trunk and at both these joints large ROMs for LB and for FE are present. Both of these factors may make a fracture due to internal trauma more likely at this site.

Fürst (2006) in his review article focused on the increasing incidence of equine cervical vertebral osteoarthritis (OA). Hett et al. (2006) also reported a tendency for arthritic changes in the caudal cervical spine of horses. Arthritic changes are seen most commonly between the 5th, 6th and 7th cervical vertebrae and they occur in both young and old horses. In our study, C5–C6 has the smallest ROM in all 3 movement directions, which indicates that it is functionally a ‘low motion, high pressure’ joint, as the heavy head and neck segment is levered from the caudal cervical spine. Such joints, where large pressures are distributed over a small area of cartilage with little movement during the motion cycle, are prone to develop OA (Jansson 1996). Pressure as such is also important in joints with larger mobility within the motion cycle, such as the carpal joints, where the area along the dorsal joint edge that is under the largest pressures degenerates first (Kawcak et al. 2008).

The equine cervical spine has most commonly been investigated in horses with ataxia localised to the cervical spinal cord (Hahn et al. 2008). These biomechanical conditions are broadly differentiated as increased mobility and impingement of the spinal cord in the mid-cervical region, and static compression and/or stenosis of the spinal cord in the caudal cervical region. Levine et al. (2007, 2008) found that the caudal cervical spine was the area most commonly affected by cervical vertebral compressive myelopathy (CVCM) lesions in 2 studies investigating neck problems in horses. In Levine's studies, Warmblood horses, which are generally thought to have heavier head and neck segments, were significantly overrepresented in the diseased group, compared to control horses. Many cases of CVCM are characterised by spinal cord compression due to osteoarthritic enlargement of articular processes (Van Biervliet et al. 2006). Such osteoarthritic enlargement is also frequently seen in older horses without neurological signs. The CVCM seen in older horses is usually due to severe OA of the articular processes and is associated with extensive bone proliferation and joint capsule thickening, compressing the spinal cord in a dorsolateral direction (Van Biervliet et al. 2006). Hahn et al. (2008) also found that older horses show ataxia resulting from OA of caudal cervical articular process joints. The model presented in this study documents the movements of the intervertebral joints of the caudal cervical spine and allows interpretation of the forces present within these joints, explaining the development of OA shown in all of the above studies.

In younger horses, presumably prior to the onset of the typical degenerative osteoarthritic changes, spinal cord lesions are centred in the more mobile mid-cervical region primarily at C3–C4 and C4–C5. Van Biervliet et al. (2004) detected spinal cord compression mainly at C3–C4 (18%) and at C4–C5 (13%) in their study. These joints have much larger ROMs in FE and in LB than C5–C6. This explains the development of osteochondrosis or malformation of the articular processes of young horses, which is a commonly identified lesion on cervical vertebra radiographs in young horses with cervical ataxia (Nout and Reed 2003). Osteochondrosis and malformation are related conditions which are commonly the consequence of higher motion within juvenile joints. Such a development can be expected in the mid-cervical region similar to the development of osteochondrosis in, for example, stifles (Foerner 2003).

The computer model presented in this study is valuable to demonstrate the movement of the equine cervical spine in vivo. In several clinical conditions of the equine cervical spine the range of motion of the vertebrae is implicated as a factor in the development of the condition, and the presented model is a suitable tool to explore the pathogenesis of these conditions further.

The error of the model is a sum of errors of the measurements, e.g. skin displacement, scaling errors (adaption of the model to a given marker set) and orientation errors of the segments. In our model, we used 9 segments (skull, C1–C7, withers), where the withers segment consisted of the first 5 thoracic vertebras without any DOF between their joints. In summary, we worked with 24 DOF and 9 skin markers. The result is a mathematically underdetermined system. Ideally, the number of unknowns should be decreased and/or the number of system equations should be increased until the number of unknowns and system equations match (Morrison 1968; Pierrynowski and Morrison 1985).

To be able to calculate the exact position of each segment in space at all times, a minimum of 3 markers per segment is recommended. It is well known that skin markers always cause small-sized systematic errors in calculation of movements, forces and torques as a consequence of skin deformation with respect to the underlying bone (Kingma et al. 1996; Leardini et al. 2005). Especially on the equine neck, skin movement will prevent the perfectly correct calculation of vertebral motion from skin markers. Marker movements could be corrected based on algorithms developed from studies using bone-fixed markers (van Weeren and Barneveld 1986; Faber et al. 2000, 2001a), but such investigations are highly invasive. Besides the animal welfare considerations, the use of bone pins also creates other errors as bone pins will influence the physiological movement because of the unnatural unyielding attachment of the soft tissue structures such as muscles and ligaments to the bone. In studies into the kinematics of the thoracolumbar spine, both bone pins and skin markers have been used with roughly similar results (Licka et al. 2001a,b; Faber et al. 2001a) and the same can be assumed for the equine cervical spine. A study looking into the validity of skin based markers for the measurement of the movements of the thoracolumbar spine found them to be satisfactory for the determination of FE and AR, as well as accurate for the determination of lateral bending at the walk (Faber et al. 2001b). From this it could be assumed that using skin markers may be adequate for the determination of the movements of the equine cervical spine, even though a study into the validity of the skin markers for the equine neck is still missing. If the placement of 3 skin markers for each bone is unrealisable in further studies, another option would be combining joints of nonmarked segments to decrease the number of DOF; e.g. between C3 and C6, where 3 joints with 9 DOF have only 4 markers available for inverse kinematic calculations.

In the study presented the error of the model was tested by comparing the recorded motion of the skin markers and the simulated motion. This was also done in another study on the simulation of the human knee to show the accuracy of the simulation (Anderson and Pandy 2001; Piazza and Delp 2001). Also, the influence of this error was demonstrated for a composite angle of 3 joints, the atlantooccipital joint and the intervertebral junctions between atlas and axis as well as axis and C2. This form of error analysis has the disadvantage that it does not show the magnitude of errors in each of the joints; however, it is an indication of the susceptibility of the model to the error originating from using skin markers. The location of the segment's centre of rotation has a large influence on the accuracy of a biomechanical model (Delp et al. 1994; Pandy 1999). Nevertheless, we are convinced that the potential error in segment and joint axes estimation is small in comparison to skin marker deformation or errors during scaling.

While a system like the equine neck may have a large number of kinematic DOF, its functional degrees of freedom are usually very limited (Li 2006). A mathematical approach to improve the results would be the calculation of a polynomial curve of second order (LB) and third order (FE). This would reduce the underdetermination of the system. However, we are not aware of a simple and adequate mathematical curve that would be suitable to reduce the AR underdetermination in a similar way. Similar to many complex modelling tasks, several other algorithms may be found to be suitable to determine equine cervical spine movements in the future. Validation is a common problem in biomechanical models (Griffin 2001) and the plausibility of the results is often the only indication of the possible validity of the model (Blana et al. 2008). In our case, the results are expected to be plausible for horses within the anatomical and age range of the animals on which the model was based, but not beyond this.

This is the first documentation of the development of a model of the equine cervical spine that results in modelled FE, LB and AR movements that are within physiological limits.

Conflicts of interest

The authors have no potential conflicts.

Manufacturers' addresses

1 Kagra AG, Fahrwangen, Switzerland.

2 Motion Analysis Corp., Santa Rosa, California, USA.

3 The MathWorks Inc., Natick, Massachusetts, USA.

4 OpenSim 1.8, Stanford University, Stanford, California, USA.

5 SPSS 17.0, SPSS Inc., Chicago, Illinois, USA.