An experimental and morphometric test of the relationship between vertebral morphology and joint stiffness in Nile crocodiles (Crocodylus niloticus)

Modern crocodylians are secondarily adapted to a semi-aquatic mode of life. However, they use a wide range of terrestrial locomotor behaviours, ranging from a sprawling ‘belly crawl’ to more erect ‘high walking’ and asymmetrical gaits such as bounding and galloping that are otherwise found only in mammals (Renous et al., 2002). The terrestrial abilities of modern crocodylians are thought to have been inherited from their Triassic ancestors, which had a more erect posture, possibly great athleticism on land, and more terrestrial lifestyles (Parrish, 1987). While many studies of crocodylian locomotion have sought to unravel the function of the limbs during variable locomotor behaviours (e.g. Blob and Biewener, 1999; Gatesy, 1991; Reilly and Elias, 1998; Reilly et al., 2005; Willey et al., 2004), the importance of the axial skeleton has received far less attention. Yet kinematic studies have revealed an appreciable role for both dorsoventral and mediolateral vertebral movements during terrestrial locomotion in crocodylians (e.g. Carpenter, 2009; Gatesy, 1991; Reilly and Elias, 1998; Renous et al., 2002).

The axial morphology of crocodylians and their ancestors has been proposed to be closely tied to the evolution of locomotor performance (Frey, 1988; Frey and Salisbury, 2001; Salisbury and Frey, 2000; Schwarz-Wings et al., 2009). These studies inferred that a ‘bracing system’ composed of osteodermal armour, vertebrae, ribs and axial musculature keeps vertebral loads low and assists in gravitational support. In contrast to the bracing system of early crocodylomorphs, which ‘nearly prevented’ mediolateral movements and was specialized for cursoriality, that of modern crocodylians is thought to permit both dorsoventral and mediolateral movements during terrestrial and aquatic locomotion (Frey, 1988). Evolutionary changes in the morphology of the bracing system, specifically the opening of the margins of the paravertebral shield and the loss of articulating processes between the osteoderms, may explain why crocodylomorphs transitioned from one vertebral form (amphicoelous) to another (procoelous) and why body size is tightly linked to locomotor ability in some crocodylians (Salisbury and Frey, 2000; Schwarz-Wings et al., 2009). Additionally, the bracing system has been proposed to be the critical anatomical structure influencing athletic capacity, perhaps even more important than other factors such as limb forces (Salisbury and Frey, 2000). The idea that the crocodylian bracing system functions as intuitively as described has long been accepted without quantitative biomechanical testing. Here, we aimed to perform such an experimental test on one component of the bracing system by measuring the stiffness of crocodylian intervertebral joints, as we explain below.

Intervertebral joint stiffness is relevant to locomotion because it affects force transmission, passive maintenance of posture, and the speed and amplitude of travelling or fixed waves of undulation (Gál, 1993a; Hebrank et al., 1990; Long, 1992; Long et al., 1997; McHenry et al., 1995). Consider the mechanical behaviour of a relatively stiff vertebral column versus a more flexible one: the stiff column requires greater work (produced by muscles or external forces such as gravity and inertia) to produce bending, which translates into more powerful (and possibly more energetically costly) active movement. For example, the lumbosacral joint in many terrestrial mammals is less stiff than the other lumbar intervertebral joints, which may enhance pelvic girdle and hindlimb movement (Gál, 1993a). In passive support, a stiff column can sustain greater gravitational moments with smaller displacements, conserving energy in postural muscles. Examples include passive resistance to ‘hogging’ moments of the mid-trunk in terrestrial quadrupeds (Christian and Preuschoft, 1996) and ventral flexion moments produced by the weight of the head and upper body in seated macaques (Gál, 2002). In swimming, stiffness in the vertebral column may serve to decelerate the tail in dolphins, and variation in stiffness along the column may produce patterns of deformation during locomotion, i.e. less stiff regions would have greater angular deflections (Long et al., 1997) [but see Nowroozi and Brainerd for a notable exception (Nowroozi and Brainerd, 2013)]. A stiffer column has a higher undulatory frequency and propagates travelling waves more quickly, resulting in a faster swimming speed (Long, 1992). Mechanically relevant properties such as stiffness and range of motion have also been linked to athletic ability and locomotor habits in several fish and mammalian species (e.g. Gál, 1993a; Hebrank et al., 1990; Long, 1992; Long et al., 1997), but they have not been quantitatively studied in crocodylians.

Understanding the relationship between bone morphology and functional characteristics, such as intervertebral joint stiffness, is fundamental to our interpretation of fossils, and thus to our understanding of the evolution of locomotion. All such interpretations are complicated by the unknown quantities of soft tissues such as skin and muscle, and they are especially difficult in the vertebral column where mobility is constrained by the intervertebral discs or notochord, fibrous tissues and ligaments (Gál, 1993b; Koob and Long, 2000). Morphometric measurement of vertebrae is a promising approach to this problem, because experimental evidence supports correlation of stiffness with such characteristics as the presence of zygapophyses, intervertebral disc length and width (which can be estimated from centrum dimensions), centrum length, nucleus pulposus length and transverse process height (Hebrank et al., 1990; Long, 1992; Long et al., 1997; Slijper, 1946). The contribution of vertebral processes to joint stiffness has been assessed by testing stiffness before and after their removal, with mixed results; Gaudin and Biewener (Gaudin and Biewener, 1992) found that xenarthrae did not contribute significantly to stiffness in any direction in armadillos, but Hebrank et al. (Hebrank et al., 1990) found that haemal spines and zygapophyses both stiffened intervertebral joints in marlins. However, these laws cannot be indiscriminately applied to crocodylians because stiffness appears to be governed by different structures in different species (Gál, 1993a).

In addition to joint stiffness, vertebral morphology also has been found to correlate with locomotor behaviour and mechanics, including swimming style, habitual spinal loading patterns and arboreal locomotor habits. In pinnipeds, relative centrum length and width, transverse process width and inter-zygapophyseal length were correlated with swimming style (pelvic versus pectoral oscillation) (Pierce et al., 2011), and in whales centrum length and width were correlated with degree of dorsoventral flexion and undulatory wavelength during swimming (Buchholtz, 2001). In a range of mammals, relationships have been found between habitual spinal loading patterns (dorsoventral shear, mediolateral shear, torsion, axial compression) and centrum width, mediolateral spacing of zygapophyses and zygapophyseal angle (Boszczyk et al., 2001), and between arboreal locomotor habits and neural spine height and angle, transverse process width, lamina width and pre-zygapophyseal angle (Shapiro, 2007). The principles drawn from living animals also have been applied to reconstruct locomotor behaviour in extinct relatives (e.g. Buchholtz, 2001; Buchholtz, 2007; Finch and Freedman, 1986; Hua, 2003; Piechowski and Dzik, 2010; Pierce et al., 2011; Pittman et al., 2013; Shapiro et al., 2005).

To test the validity of inferring locomotor biomechanics from vertebral morphology, we quantified the passive stiffness of intervertebral joints along the thoracolumbar region in cadaveric Nile crocodiles (Crocodylus niloticus Laurenti 1768), and we investigated the relationship between intervertebral joint stiffness and vertebral morphological variation. Although our approach measures passive stiffness of individual joints (here simply termed ‘joint stiffness’) and not factors such as muscle-driven mechanics, dynamic behaviour of viscoelastic tissues, or other axial structures such as ribs and osteoderms, it does test how some of the components of the bracing system work. By doing so, we sought to begin to answer fundamental questions about how the crocodylian vertebral column functions in a locomotor context. For instance, do the mechanical properties of the crocodylian vertebral column support a role in locomotion (especially asymmetrical gaits) similar to its role in mammals, or are there marked differences? And if so, can the mechanical differences be correlated with anatomical ones? By comparing regional anatomical variation with direct measurements of joint stiffness in C. niloticus, we also hope to identify those morphological parameters that have the greatest power to predict vertebral mechanics in extant crocodiles, and, with due caution, in their extinct relatives.

Joint stiffness in all directions increased slightly or remained constant along the thoracic vertebral column and increased significantly at the lumbar and lumbosacral joints (Fig. 1). This effect was particularly pronounced in lateral flexion. Stiffness was lowest in lateral flexion in all joints except the lumbosacral, where it was the highest. Significant differences in stiffness were found with position of the joint along the column (‘joint’, P<0.0001) and bending direction (‘direction’, P<0.0001) (Table 1A). Stiffness was significantly lower in lateral flexion than in dorsal extension (P=0.0181) or ventral flexion (P=0.0103). J8 was significantly stiffer than all other joints (P<0.0001); J6 was significantly stiffer than J1 (P=0.0006); J7 was significantly stiffer than each of the four more cranial joints (0.0001<P<0.0242); and J5 was significantly stiffer than J1 (P=0.0068). P-values reflect Bonferroni corrections for multiple comparisons. Severing intervertebral ligaments resulted in a small but significant increase in stiffness (P=0.002), although a substantial increase of 1.8±0.1 deg in the neutral zone (P<0.0001) may account for this effect.

For descriptive purposes, the vertebral column is divided into four regions, cranial thoracic (T1–T4), caudal thoracic (T5–L1), lumbar (L2–L5) and sacral (S1), based upon changes in the values and trends of morphological measurements (Fig. 2). In the cranial thoracic region, there was a sharp gradient between characteristic cervical and thoracic morphologies. The caudal thoracic region showed a more gradual change: centrum length, width and height, transverse process width and pre-zygapophyseal angle increased in a caudad direction, and neural spine height decreased. Transverse process orientation shifted from being caudally and dorsally directed to approach an angle of 180 deg in both planes. Within the lumbar region, transverse processes decreased in width, increased in length and inclined caudally, while the centra became shorter and wider. The first sacral vertebra showed sharp increases in the length and width of the centrum and transverse processes (related to articulation with the iliac bones). Many of the morphological parameters were strongly inter-correlated (see supplementary material Table S1).

Several morphological parameters were found to be significant correlates of stiffness (Table 2). Pre-zygapophyseal width, inter-zygapophyseal length and ventral deflection of transverse processes were correlated positively with stiffness in all directions (0.0001<P<0.0443), and neural spine angle was correlated negatively with stiffness in all directions (0.0001<P<0.0024). Centrum height was positively correlated with stiffness in dorsal extension (P=0.0048) and ventral flexion (P=0.0116), and lamina width was correlated positively with stiffness in dorsal extension (P=0.0042) and lateral flexion (P=0.0093). Additional parameters were correlated with stiffness in lateral flexion only: pre-zygapophyseal angle (P=0.0058), neural spine length (P=0.0166) and centrum length (P=0.0455) in a positive direction and neural spine height (P=0.0443) in a negative direction.

An initial stepwise linear regression, using all morphometric measurements as potential predictors, resulted in models where dorsal extension was predicted (R²=0.470) by pre-zygapophyseal width (P<0.001) and centrum width (P=0.003); lateral flexion was predicted (R²=0.624) by pre-zygapophyseal width (P=0.001) and transverse process deflection both ventrally (P<0.0001) and caudad (P=0.0002); and ventral flexion was predicted (R²=0.385) by neural spine angle (P<0.0001) and neural spine height (P=0.006) (see supplementary material Table S2). Collinearity statistics indicated problems for the lateral flexion and ventral flexion models, with the majority of tolerances below 0.6; to address this problem, we conducted a principal components analysis (PCA) to uncover uncorrelated morphological parameters. The PCA produced a subset of six measurements (lamina width, neural spine angle, caudal deflection of transverse processes, transverse process tip length, centrum width, centrum height) that were minimally correlated with each other (absolute value of Pearson correlation <0.35) (see supplementary material Table S1), yet each measurement was weighted most heavily in one of the first six principal components (see supplementary material Table S3). A second stepwise linear regression using this subset of measurements predicted stiffness in dorsal extension (R²=0.279) by lamina width (P=0.0078) and centrum height (P=0.0136); stiffness in lateral flexion (R²=0.520) by lamina width (P=0.0051), neural spine angle (P<0.0001) and centrum width (P=0.0068); and stiffness in ventral flexion (R²=0.335) by centrum height (P=0.0490) and neural spine angle (P=0.0003) (Table 3).

We examined the experimental design and found no reason to suspect that methodological errors made any qualitative difference to our results. The estimated standard error of digitization, calculated by digitizing a single random image 10 times, was 0.013 deg of angular deflection, compared with an average of 0.12 deg of deflection produced by loading it with the smallest mass (0.01 kg), which indicates that the digitization process was highly repeatable. The regression lines used to approximate stiffness fitted the displacement curves very well: only four out of 165 cases had adjusted R² values below 0.75, and those cases were excluded from the analysis. An additional 11 cases were excluded because the P-value of the regression line was >0.05. Not counting specimen 8, a total of 19 out of 168 possible stiffness measurements were excluded (Table 4).

The stiffness of a single vertebra (i.e. the entire bony structure) was ~20 times the stiffness of a representative cranial (T4–5) or caudal (T7–8) intact joint (see supplementary material Fig. S1). Thus, we estimate that the actual joint stiffness is about 10% higher than the reported value because deformation of the two vertebral bodies contributed somewhat to deflection of the pins. However, this calculation does not take into account variation in torque along the vertebral segment, which might make both our estimation of vertebral deformation and the actual joint stiffness marginally higher. Exclusion of the two most cranial joints from specimen 7, which corresponded to different vertebral numbers from those in other specimens, did not result in any change in the stiffness patterns or statistical results. The greatest source of error was variation between trials, with a small but significant increase in stiffness between the first and second trials (1.9% of mean normalized stiffness in trial 1; P=0.0030) and between the first and third trials (3.3% of mean normalized stiffness in trial 1; P<0.0001) (see supplementary material Table S4). This effect may be a product of an increase in the neutral zone due to tissue fatigue; however, it should not affect our interpretation because only the first trial was used in subsequent statistical analyses.

We measured passive intervertebral joint stiffness in three bending directions throughout the thoracolumbar vertebral column of C. niloticus to investigate patterns of stiffness and their relationship to vertebral morphology. The intervertebral joints were somewhat stiffer in dorsoventral versus mediolateral bending, except at the lumbosacral joint where mediolateral stiffness was the highest. Joint stiffness increased caudally along the column, particularly in mediolateral bending. Counter-intuitively, severing intervertebral ligaments resulted in a small increase in stiffness, probably as a result of the greater joint excursion angles reached at small weight increments (increase in neutral zone). Several morphometric measurements were correlated with stiffness in ways that agreed with our predictions, as described below.

Like mammals, crocodylians use some degree of axial movement across many modes of locomotion. Kinematic studies reveal moderate mediolateral pelvic/sacral rotations (10–15 deg) during high walk and sprawling locomotion in alligators (Gatesy, 1991; Reilly and Elias, 1998), slight lateral undulations of the body in some types of swimming (Frey and Salisbury, 2001), and speed-dependent dorsoventral movements of the pre-sacral column during bounding and galloping (Renous et al., 2002). However, intervertebral joint angles and the contributions of different regions of the vertebral column to locomotor dynamics are unknown. Our results show that the patterns of joint stiffness for C. niloticus are different from those reported for mammalian vertebral mechanics, suggesting that the mechanical role of the vertebral column also is different between the two groups. This difference is not surprising, because crocodylian and mammalian lineages have evolved independently for ~320 million years. Nonetheless, because some crocodylians use analogous asymmetrical gaits, it might have been expected that they would exhibit similar patterns of dorsoventral stiffness, particularly at the lumbosacral joint.

In the mammalian vertebral column, dorsoventral stiffness is closely tied to locomotor function. Dorsoventral movements of the lumbar region are considered to be important for increasing step length and the speed of the swing leg in asymmetrical gaits (Hildebrand, 1959), and patterns of dorsoventral stiffness mirror patterns of joint flexion/extension during locomotion. In agreement with biomechanical studies showing the lumbosacral joint in several terrestrial mammals to have relatively low dorsoventral stiffness and high mobility (e.g. Gál, 1993a; Jeffcott and Dalin, 1980; Slijper, 1946), kinematic studies have shown that the greatest dorsoventral bending amplitude tends to occur at the lumbosacral joint (e.g. Haussler et al., 2001; Hildebrand, 1959; Nyakatura and Fischer, 2010; Schilling and Hackert, 2006; Slijper, 1946). In contrast, stiffness in all bending directions in C. niloticus increased with craniocaudal position and was highest at the lumbosacral joint (Fig. 1), suggesting that bounding and galloping crocodiles would need to generate very large moments about this joint to produce an appreciable degree of flexion/extension. If the relationship between passive joint stiffness and kinematics that has been observed in mammals also applies to crocodylians, it follows that crocodiles must either rely less upon axial dorsoventral flexion during asymmetrical gaits than mammals do, or distribute the bending more evenly across the trunk. This high stiffness is likely to be useful in supporting their large tails and countering hindlimb forces, which are proportionately greater in crocodilians (Willey et al., 2004).

The trend of increasing intervertebral joint stiffness in a craniocaudal direction is most pronounced in the mediolateral direction (Fig. 1). This result was unexpected, because the few studies of regional vertebral motion during locomotion in non-mammalian tetrapods show the greatest mediolateral flexion occurring in the caudal-most region in trotting lizards (Ritter, 1995) and salamanders (O'Reilly et al., 2000). However, regional axial flexion (either dorsoventral or mediolateral) has not been studied in crocodylians, and they may show a different pattern. Likewise, passive joint stiffness has not been measured in lizards or salamanders. It is even possible that the increased mediolateral stiffness may stabilize the lumbosacral joint against lateral movements during asymmetrical gaits, constraining it to move predominantly in the dorsoventral plane.

Alternatively, the high joint stiffness might indicate higher forces rather than smaller degrees of flexion. It has been suggested that crocodylians experience particularly high craniocaudal shear forces in the lumbosacral region because of the action of epaxial muscles (Salisbury and Frey, 2000), which could be balanced by high stiffness in this region. The osteoderms, which comprise more rows in the mid-thoracic region than in the lumbar region (Ross and Mayer, 1983), and the ribcage likely stiffen the thoracic region and may compensate for the lower stiffness of intervertebral joints, and/or the thoracic region might be stabilized by axial muscles. Finally, the high mediolateral stiffness of the lumbosacral joint might serve to absorb and propagate forces generated by the hindlimbs during terrestrial locomotion (Reilly et al., 2006) or moments generated by undulation of the tail, which is the primary source of thrust in swimming (Fish, 1984; Frey and Salisbury, 2001). Among aquatic mammals, dolphins, which also use tail propulsion for swimming, show increased stiffness in the lumbosacral joints (Long et al., 1997), while phocid seals, which use hindlimb propulsion, do not (Gál, 1993a).

We also observed departures from the general mammalian pattern in relative stiffness in different bending directions. Joint stiffness was significantly lower in lateral flexion than in dorsoventral flexion, though there was no significant difference between stiffness in dorsal extension versus ventral flexion (Table 1B). In contrast, equine vertebral columns are stiffer in mediolateral bending than in dorsoventral bending (Schlacher et al., 2004), and a wide range of mammals have vertebral columns that are significantly stiffer in dorsal extension than ventral flexion (e.g. Gál, 1993a; Gaudin and Biewener, 1992; Jeffcott and Dalin, 1980; Long et al., 1997). Lower mediolateral stiffness in crocodiles was expected because crocodiles employ substantial lateral flexion of the trunk during symmetrical gaits (Reilly and Elias, 1998) and a small amount during swimming (Fish, 1984; Frey and Salisbury, 2001). Uniformly high stiffness in ventral flexion might confer an advantage for crocodylians in terms of passive maintenance of posture. Crocodylians habitually maintain a dorsally convex arch of the vertebral column by contraction of the abdominal and other axial muscles, generating a moment that tends to flex the vertebral column ventrally (that is, increase the dorsal convexity) (Frey, 1988). The metabolic cost of maintaining this posture could be reduced by resisting this moment through intervertebral joint stiffness rather than epaxial muscle contraction.

Regional differentiation in the crocodilian vertebral column is not as pronounced as seen in mammals (Pierce et al., 2011; Slijper, 1946). However, changes in vertebral morphology were evident around T4–T5 (cranial versus caudal thoracic), L1–L2 (caudal thoracic and first lumbar versus remaining lumbar) and L5–S1 (lumbar versus sacral) (Fig. 2). Pre-zygapophyseal angle was always greater than 90 deg and increased slightly throughout the thoracic column, and neural spine inclination shifted gradually from caudal to vertical. Crocodylians do not display a diaphragmatic or anticlinal vertebra, which may explain why we failed to observe some correlations between morphometrics and stiffness that have been documented in mammals, as explained below.

Some, but not all, of our predictions regarding the relationship between vertebral dimensions and stiffness in C. niloticus (see ‘Morphological parameters’ in Materials and methods) were borne out by our analysis. The following hypotheses were supported: (1) stiffness in dorsal extension and ventral flexion was correlated positively with centrum height, and stiffness in dorsal extension was correlated positively with lamina width (Table 2); (2) stiffness in lateral flexion was correlated positively with distance between pre-zygapophyses (Table 2), and centrum width contributed significantly to the prediction model with a positive coefficient (Table 3).

Centrum width was not significantly correlated with mediolateral stiffness, but it was included in the prediction model because it significantly improved the model fit in combination with other measurements. Measurements that were significantly correlated with stiffness, but were not included in the prediction model, such as pre-zygapophyseal width, were highly correlated with other measurements that were included in the model (see supplementary material Table S1).

Our stepwise linear regression prediction models using a subset of morphometric measurements accounted for 28–52% of the variation in stiffness (0.279<R²<0.520) (Table 3). While this result means that ~48–72% of stiffness variation remains unaccounted for, it does not mean that morphology is a poor indicator of stiffness. To reduce multicollinearity and make the prediction models easier for others to use, we only included two to four measurements in each model. A principal components regression using all measurements accounted for 34–82% of the variation (see supplementary material Table S2). The remaining proportion of variation may be explained by variation in properties of the ligaments and joint capsules, and the shape and area of articular surfaces (along with experimental error). Compared with lateral flexion, stiffness in dorsal extension and ventral flexion varied less along the column, which may account for their weaker correlations with morphometric measurements. Also, vertebral morphology might be a more powerful indicator of stiffness across genera and species than within one species of Crocodylus.

Vertebral centra are the primary structures that resist compressive axial forces, and the relationship between dimensions of the centra and stiffness has long been described using beam theory (e.g. Christian and Preuschoft, 1996; Slijper, 1946). Dorsoventrally flattened centra are understood to increase sagittal flexibility by decreasing the moment of resistance in the dorsoventral plane, permitting the dorsoventral motion that characterizes terrestrial locomotion in mammals (Boszczyk et al., 2001; Shapiro, 2007). Spool-shaped centra with a high ratio of length to cross-sectional area are thought to allow greater flexibility than more axially compressed vertebral bodies (Buchholtz, 2001), while relatively short centra promote stability by decreasing bending moments and increasing joint contact area (Pierce et al., 2011; Shapiro, 2007). In line with our initial predictions, we found that an increase in centrum height was significantly correlated with an increase in joint stiffness in dorsal extension and ventral flexion (Table 2) and was a significant predictor of stiffness in both directions, whereas centrum width was a significant predictor of mediolateral stiffness (Table 3). Thus, increases in centrum diameter may be an important mechanism for stiffening the lumbosacral region in crocodylians. Contrary to our predictions and to the results of a similar study on dolphins (Long et al., 1997), centrum length showed either a positive correlation or no correlation with stiffness. This result may simply reflect the relatively small change in centrum length along the vertebral column in C. niloticus (Fig. 2).

Zygapophyseal orientation is considered by many authors to be one of the best osteological clues to axial flexibility and function because the close contact between zygapophyses constrains the range and direction of movement of the intervertebral joint (Holmes, 1989; Pierce et al., 2011). It is widely accepted that more horizontally oriented pre-zygapophyses (>90 deg) permit greater mediolateral flexion, whereas more vertically oriented ones (<90 deg) permit greater dorsoventral flexion (Boszczyk et al., 2001; Finch and Freedman, 1986; Hua, 2003). Wider mediolateral spacing of pre-zygapophyses is thought to increase joint stability (Boszczyk et al., 2001; Holmes, 1989) and craniocaudal distance between zygapophyses may increase dorsoventral range of motion (Shapiro, 2007). Our results showed significant correlation of pre-zygapophyseal angle only with increased mediolateral stiffness, suggesting that it is not an important determinant of dorsoventral stiffness in crocodiles. However, like centrum length, pre-zygapophyseal angle did not vary greatly along the column (Fig. 2), and so this result should not be overstated. In contrast, mediolateral spacing of the pre-zygapophyses was highly correlated with stiffness in all directions (Table 2). It was also highly correlated with lamina width, an important predictor of stiffness in dorsal extension and lateral flexion in mammals (Shapiro, 2007) (Table 3). In combination, wider laminae and greater mediolateral spacing of pre-zygapophyses appear to increase the stiffness of the crocodylian vertebral column in both the mediolateral and dorsoventral planes.

The lengths of vertebral processes (neural spines and transverse processes) affect axial bending by determining the leverage of muscles that flex and extend the vertebral column, with longer processes being associated with more powerful active extension of intervertebral joints (Frey, 1988; Pierce et al., 2011; Shapiro et al., 2005; Slijper, 1946). Longer vertebral processes also provide greater areas of attachment and leverage for intervertebral ligaments and encompass larger axial musculature, which increases passive stiffness (Valentin et al., 2012). Long et al. (Long et al., 1997) proposed that very stiff intervertebral joints were likely to have wide transverse processes, although they admitted that the relationship between transverse process width and stiffness was not explained by their results. We recorded marked variation in transverse process width and neural spine height along the vertebral column in C. niloticus (Fig. 2); however, neither of these was correlated with stiffness in any direction (except for neural spine width and height in lateral flexion, probably as a result of their high correlation with other factors), nor did either contribute to the prediction models. This lack of correlation might have been caused by the use of isolated vertebral columns devoid of muscles and tendons. Because back stiffness can be much greater in live animals than in excised vertebral columns (Ritruechai et al., 2008), moment arms of vertebral processes may be more important for predicting dynamic rather than passive stiffness. As we did not examine live animals and we removed the axial musculature prior to testing, this effect could not be evaluated.

The angles of vertebral processes also affect muscular leverage, and some authors have suggested that they affect joint stiffness and range of motion as well; transverse processes that are oriented more cranially and ventrally are postulated to increase sagittal plane mobility, as are longer and more cranially deflected neural spines (Jeffcott and Dalin, 1980; Shapiro, 2007; Slijper, 1946). Unexpectedly, we obtained the opposite result: ventral deflection of the transverse processes was positively correlated with stiffness, and caudal deflection of the neural spines was negatively correlated with stiffness (Table 2). This result may reflect another difference from many mammals; crocodylian neural spines are never cranially deflected, so an increase in cranial deflection is actually an approach to a vertical orientation. These two measurements also were highly correlated with each other, so it was not clear which, if either, had a direct effect upon joint stiffness.

Severing the intervertebral ligaments (inter-spinous and inter-transverse) resulted in a small but significant increase in joint stiffness, in contrast to its effect on the intervertebral joints of dolphins (Long et al., 1997). A similar effect was observed in repeated trials on the same joint without severing ligaments (see supplementary material Table S4). The most likely reason for this counter-intuitive result was an increase in the neutral zone of about 1.5 deg due to tissue fatigue. It appears that these ligaments may operate within a limited range of forces that were too small to be detected by our methods. Beyond that range, increases in joint stiffness may be governed by other vertebral structures, such as zygapophyseal capsules. Another potential influence on stiffness to consider is that the water used to hydrate the joints between trials may have caused connective tissue to swell (e.g. around zygapophyseal joint capsules), resulting in an increase in stiffness over repeated trials.

This study is the first to quantitatively examine stiffness of crocodylian intervertebral joints, and the first to rigorously test whether it can be predicted by morphometric measurements. Patterns of intervertebral joint stiffness in crocodiles differ from those reported for mammals both along the column and between bending directions. The contrasting patterns imply that crocodylians have either a different relationship between joint stiffness and axial bending or a different role for the axial column during locomotion, even within similar gaits. Some, but not all, of our predictions regarding the relationship between vertebral dimensions and joint stiffness in C. niloticus were borne out in our analysis, indicating a complex relationship between bony morphology and the surrounding soft tissue. Nonetheless, this study represents a key step towards understanding the functional role of the vertebral column in crocodylian locomotion, from which broader evolutionary questions can be addressed.

We excised and examined eight vertebral columns from cadaveric specimens of juvenile Nile crocodiles (C. niloticus) with body masses ranging from 1.3 to 15.6 kg (Table 4). The animals, provided by conservation centre La Ferme aux Crocodiles (Pierrelatte, France), had died of natural causes and were sealed in airtight plastic bags and frozen immediately thereafter. They were thawed at room temperature for ~24 h before dissection. Only the thoracic and lumbar vertebrae were tested because their primary function is body support and body mobilization during terrestrial locomotion. Cervical morphology is likely to be influenced by the requirements of feeding, and caudal morphology by the requirements for swimming, although the thoracolumbar column also contributes to some types of swimming (Frey and Salisbury, 2001). Following excision, the thoracolumbar region of the vertebral column was divided into eight segments (Fig. 3), each consisting of two vertebrae (i.e. one intervertebral joint) and the intervening intact ligaments and joint capsule. The segments were immediately enclosed in airtight plastic bags and re-frozen.

Before an experiment was run, each joint segment was thawed at room temperature for 1–4 h, depending on the size of the specimen. Small holes were drilled into the centres of the vertebral centra: one on the cranial aspect of the cranial-most vertebra, and one on the caudal aspect of the caudal-most vertebra, and wood screws were inserted. Drill bits and screws were carefully measured and marked so that they penetrated ~2/3 of the centrum while stopping well short of the joint capsule. Each joint was X-rayed to confirm that the screws were in the proper positions. Finally, pins were anchored in the neural spine and right transverse process of each vertebra to aid in visually tracking the positions and angles of the vertebrae over the course of the experiment (Fig. 4A). Joint segments were kept moist with water throughout the experiments.

The cranial-most screw was clamped to immobilize one vertebra in each pair while leaving the other free to move around the joint, similar to Long et al. (Long et al., 1997). Change in intervertebral joint angle was recorded using high-resolution photography, provided by a tripod-mounted camera with a zoom lens set to 107 mm. To minimize optical distortion, the height, angle and position of the tripod head were adjusted so that the lens was aimed in a horizontal plane perpendicular to the long axis of the vertebrae and the intervertebral joint was in the centre of the field of view. At the beginning of each round of testing, the unloaded joint was photographed with a spirit level marked in centimetre increments. This reference image allowed us to calculate initial joint angle, scale and orientation with respect to gravity (Fig. 4A).

Each joint was loaded with metric weights suspended from the head of the screw in the caudal-most vertebra. The exact weights used were adjusted based upon the size of the specimen, but each joint was loaded with a minimum of 10 different weights (Table 4). Between measurements, the joint was unloaded and returned to an approximately neutral position by gently nudging it back into place.

For all joints in three of the specimens, the experiment was repeated after the ligaments between the neural spines and transverse processes had been severed (in ventral flexion and lateral flexion only). The same specimens were used to test both ventral flexion and lateral flexion, but the order of the tests was varied so that we could assess whether severing interspinous ligaments affected mediolateral stiffness or vice versa; no such effects were detected. This test was used to assess the contribution of intervertebral ligaments to joint stiffness. Repeatability and the effect of fatigue induced by repeated loading of the joint were examined for all joints in three specimens by repeating the loading experiment two or three times with the ligaments intact. Because vertebrae of juvenile crocodiles might not behave as true rigid bodies, an additional test was performed to quantify the change in angle caused by deformation of the vertebral bodies rather than flexion/extension of the joint. The sixth thoracic vertebra from specimen 7 was isolated, drilled and loaded in the same manner as the joints had been.

Eight reference points on the vertebrae, pins and screws were digitized from each photograph in ImageJ software (http://rsbweb.nih.gov/ij) to track displacement of the vertebrae under load. An additional four points were digitized from the initial unloaded image to calculate scale and orientation with respect to gravity. Observer error was quantified by digitizing all points on a single randomly chosen photograph 10 times and reporting the standard deviation of the calculated deflection angles.

Stiffness was calculated by taking the linear regression of normalized moment versus angular deflection over a small initial range of moments. Moments were normalized based on geometric similarity theory (Hof, 1996) by dividing by the product of specimen mass and thoracolumbar length (approximated by summed centrum length). The slopes of the regression lines were then log-transformed to normalize their distribution. The range of moments used to determine the slope was defined by the approximate linear region of the graph, covering a small initial range of values (e.g. Ianuzzi et al., 2009; Long et al., 1997; Schlacher et al., 2004); in this case, <0.1 normalized moment, which corresponds to ~0.15 N m in a 4.6 kg specimen (Fig. 5). The first weight increment was excluded because it includes the neutral zone, i.e. the presumed range of angles over which the joint can move without the application of force (Panjabi, 1992). Cases were excluded from the analysis if the regression lines had P>0.05 or R²<0.75.

Based upon previous studies of intervertebral joint stiffness and locomotion cited in the Introduction, we made the following predictions about how the various morphometric measurements would relate to stiffness in different bending directions (see Discussion): (1) stiffness in dorsal extension and ventral flexion is expected to correlate positively with centrum height, neural spine length and height, caudal deflection of the neural spine, pre-zygapophyseal angle, dorsal and caudal deflection of the transverse processes, and lamina width; (2) stiffness in dorsal extension and ventral flexion is expected to correlate negatively with centrum length and craniocaudal spacing of the zygapophyses; (3) stiffness in lateral flexion is expected to correlate positively with centrum width, transverse process width, and distance between pre-zygapophyses; and (4) stiffness in lateral flexion is expected to correlate negatively with pre-zygapophyseal angle.

Variation in intervertebral joint stiffness was examined by joint number and bending direction to determine whether stiffness changed along the vertebral column and whether the column was stiffer in different bending directions. This analysis used a two-way ANOVA with normalized stiffness as the dependent variable and joint (J1–J8) and bending direction (ventral flexion, dorsal extension, lateral flexion) as the independent variables. Post hoc pair-wise comparison tests (with a Bonferroni correction) were conducted to identify which groups were significantly different. The effects of severing intervertebral ligaments and multiple trials on joint stiffness were examined using repeated-measures ANOVA.

To determine which morphological parameters were the best predictors of joint stiffness, we first looked at Pearson's correlations between all 14 normalized morphometric measurements and normalized stiffness in each bending direction. Next, we conducted a stepwise linear regression for each bending direction using all morphometric measurements as independent variables, similar to a previous study (Long et al., 1997). However, the regression models displayed potential problems with multi-collinearity, making it difficult to confidently determine which morphometric measurements were contributing to the regression model.

To address this problem, we performed a principal components analysis to generate a set of uncorrelated factors. Then, a second stepwise linear regression was conducted using only those morphometric parameters weighted most heavily in one of the first six principal components, which accounted for >90% of the variance in the morphometrics data. We chose this method rather than a principal components regression because the principal components are not directly comparable to anatomical measurements. For each bending direction, the model reported was the one that had the highest R² value and where tolerances (a measure of non-collinearity) of all factors were greater than 0.6. All statistical analyses were conducted in IBM SPSS version 20 (http://www-01.ibm.com/software/analytics/spss/) and assessed at a significance level of P<0.05.

Some values were missing or excluded from the analyses. Specimen 8 was excluded from stiffness calculations (but not from severed ligament tests) because the moments used did not cover the full range needed to calculate stiffness. Because of the preservation quality of specimen 7, J1 was not measured, and J2–J3 were defined differently: J2 was T2–T3 and J3 was T4–T5 (see Fig. 3). To determine whether this difference affected the statistical results, the analyses were run with and without J2 and J3 from specimen 7. Also excluded was J5 of specimen 2, which was found to be malformed after soft tissue was removed.

We thank Samuel Martin, Eric Fernandez and other staff of La Ferme aux Crocodiles (Pierrelatte, France) for providing the cadaveric specimens. Phil Pickering is gratefully acknowledged for his technical assistance with the experimental apparatus design, setup and data collection, as well as analysis code. Richard Prior and staff of the post-mortem facility at The Royal Veterinary College assisted with dissections and facility access. We thank Vivian Allen, Stephen Amos, Luis Lamas, Michael Pittman, Emily Sparkes and Renate Weller for discussions and other assistance with this study, and Ruby Chang, Heather Paxton and Simon Wilshin for advice on statistical analyses. Finally, we thank our two anonymous reviewers, whose helpful suggestions greatly improved this manuscript.