3‐D range of motion envelopes reveal interacting degrees of freedom in avian hind limb joints

Abstract

Measuring range of motion (ROM) is a valuable technique that can link bone morphology to joint function in both extant and extinct taxa. ROM results are commonly presented as tables or graphs of maxima and minima for each rotational degree of freedom. We investigate the interactions among three degrees of freedom using X‐ray reconstruction of moving morphology (XROMM) to measure ROM of the main hind limb joints of Helmeted Guineafowl (Numida meleagris). By plotting each rotation on an axis, we generate three‐dimensional ROM volumes or envelopes composed of hundreds of extreme joint positions for the hip, knee, and intertarsal joints. We find that the shapes of ROM volumes can be quite complex, and that the contribution of long‐axis rotation is often substantial. Plotting in vivo poses from individual birds executing different behaviors shows varying use of potential rotational combinations within their ROM envelopes. XROMM can provide unprecedented high‐resolution data on the spatial relationship of skeletal elements and thereby illuminate/elucidate the complex ways in which soft and hard tissues interact to produce functional joints. In joints with three rotational degrees of freedom, two‐dimensional representations of ROM (flexion/extension and abduction/adduction) are incomplete.

Introduction

The relationship between skeletal morphology and function is often clearest at joint surfaces. Diverse articular geometries have evolved to promote and constrain rotation about different degrees of freedom (DoFs). For example, both the human hip and knee are mobile in flexion/extension (FE) and, to a lesser extent, long‐axis rotation (LAR). But the ball‐and‐socket configuration of the hip allows abduction/adduction (ABAD) movements that are resisted at the knee by collateral ligaments combined with a bicondylar shape. Such differences in the maximum and minimum amounts of FE, ABAD, and LAR allowed by each joint can be quantified, with the results collectively termed the joint's range of motion (ROM). Rich ROM datasets on human joints stem from a variety of techniques and approaches (e.g. Markolf et al. 1976; Nielsen et al. 1984; Renström et al. 1986; Sidles et al. 1988), including sophisticated rigs to independently manipulate and load joints along a specific degree of freedom (DoF; Langa, 1963; Wang & Walker, 1974; Blankevoort et al. 1988).

In contrast to the large body of work on humans, the comparative ROM literature is relatively sparse, although it is growing. Vertebrate paleontology is one area of active ROM research. Paleontologists often seek to make inferences about function in extinct taxa known only from skeletal remains (e.g. Galton, 1971; Bramwell & Whitfield, 1974; Stevens & Parrish, 1999; Gishlick, 2001; Senter & Robins, 2005; Senter 2006; Carpenter & Wilson, 2008; Senter, 2009; Mallison, 2010a,b; Pierce et al. 2012; Hutson & Hutson, 2014, 2015, 2017; Nyakatura et al. 2015; White et al. 2015, 2016). An accurate assessment of ROM about each of a joint's DoFs can test hypotheses of behavior by eliminating those that require poses or movements outside the range of accessibility (Senter, 2005, 2009; Brougham & Brusatte, 2010; Pierce et al. 2012). ROM data from extant relatives or analogues are sometimes used to improve and validate the reliability of fossil ROM estimates (Carpenter, 2002; Dzemski & Christian, 2007; Fujiwara et al. 2010; Hutson & Hutson, 2012, 2013; Cobley et al. 2013).

Most dinosaur ROM studies focus on fewer than three rotational DoFs (Gishlick, 2001; Senter & Robins, 2005; Dzemski & Christian, 2007; Senter, 2009; Cobley et al. 2013). Congruent, well‐constrained articulations such as the ginglymoid interphalangeal joints of some theropods lend themselves to measurement of FE alone (1‐DoF: Galton, 1971; Senter, 2009). The zygapophyses and saddle‐shaped centra of ostrich cervicals appear to preclude torsion, leading researchers to measure ROM only in dorsoventral and lateral bending dimensions (2‐DoFs: Dzemski & Christian, 2007; Cobley et al. 2013). In contrast, for a joint such as the theropod glenohumeral articulation, all three rotations are likely required to describe its ROM fully. Estimates of just FE and ABAD (Gishlick, 2001; Carpenter, 2002; Senter & Robins, 2005; Carpenter & Wilson, 2008) are incomplete and ambiguous if LAR is not measured. A few studies have quantified ROM about all three rotational DoFs (3‐DoFs) in joints with more complex shapes (Chan, 2007; Pierce et al. 2012; Hutson & Hutson, 2013; Arnold et al. 2014; Grytsyshina et al. 2016), but the analysis, interpretation, and presentation of these data are difficult.

Two inter‐related issues plague the analysis of 3‐DoF ROM data: data visualization and interaction among DoFs. Results of ROM studies are commonly reported using bar graphs or tables of minima and maxima for each DoF measured. These methods are simple to read and understand, but they treat DoFs independently. In the case of a 1‐DoF joint, a bar graph suffices to describe its ROM completely (Fig. 1A). The position of the joint at maximum flexion and maximum extension, for instance, is easily resolved.

Figure 1.

Visualizing joint ROM. (A) Bar graph (in degrees) for a single degree of freedom joint. (B) Left: Bar graph for a two degrees of freedom joint. Right: Plot of joints poses for a two degrees of freedom joint. ROM maxima (dotted lines) delimit the area in which joint poses may occur. Actual joint poses (dashed lines) depend on DoF interactions and could widely vary among joints. (C) Left: Bar graph for a three degrees of freedom joint. Right: ROM maxima delimit the volume in which joint poses may occur. Actual joint poses depend on DoF interactions and could be quite complicated due to the increased degrees of freedom.

For a 2‐DoF joint, a bar graph easily plots maxima (Fig. 1B). However, the bar graph hides the complexity that occurs when adding a DoF. Consider a plot of the poses reached by a joint with known maxima where each axis represents the angular value for a DoF (Fig. 1B). The maxima limit the area in which joint motion may occur and it is possible that this rectangular shape represents all poses available to the joint (Fig. 1B, rectangle). However, it seems unlikely that most joints would allow multiple DoFs to reach their maxima simultaneously (e.g. Gishlick, 2001; Arnold et al. 2014). In these cases, it will not be possible to predict what portion of the plot is used by the joint merely from the maxima. For instance, moving one DoF towards its maximum might restrict movement about the other DoF (Fig. 1B, circle). Moving one DoF away from a maximum could increase the mobility of the other DoF (Fig. 1B, triangle). Alternatively, the rotations could remain tightly coupled throughout their range of mobility (Fig. 1B, tilted ellipse). In all these cases, the maxima reported in a bar graph would be the same. A 3‐DoF joint compounds this issue (Fig. 1C). Bar graphs continue to represent only a maxima/minima cubic volume, whereas the actual 3‐D envelope of extreme poses within which the limb works could be quite complex (Fig. 1C, blob).

Here we measure ROM in the Helmeted Guineafowl (Numida meleagris, L.) hind limb joints to investigate how DoFs interact when they are plotted simultaneously. Guineafowl spend substantial time on the ground and are adept walkers and runners. We anticipated that the hip would be capable of substantial rotation about all three DoFs, allowing us to test visualization and analysis techniques on mobile joints. First, we consider ROM data collected postmortem by manipulating joints to the limit of their range. Then we plot in vivo data from the same individuals within the joint's ROM volume to investigate the relationship between the motion a joint passively allows and what portion of that space is used in life.

Materials and methods

All animal experiments were approved by the Institutional Animal Care and Use Committee at Brown University. The three individuals (1.21, 1.51, 1.31 kg at time of surgery) were acquired from a local breeder and housed with food and water ad libitum. They were used previously as part of our study of in vivo terrestrial locomotion in birds (Kambic et al. 2014, 2015).

X‐ray reconstruction of moving morphology (XROMM; Brainerd et al. 2010) methods follow those described in Kambic et al. (2014). Briefly, radiopaque markers hand‐ground from tungsten carbide (0.8 mm diameter unground premium carbide, RR2, California Tool and 390 Engineering, Inc., Riverside, CA, USA) were surgically implanted into pelvis, femur, tibiotarsus, and tarsometatarus. The first two individuals were marked on the right side, and the third was marked on the right side as well as in the left femur. After recovery, in vivo data were collected in the W.M. Keck Foundation XROMM Facility at 250 fps. The X‐ray systems comprised an EMD Technologies model EPS 45–80 X‐ray generator and a Varian model G‐1086 X‐ray tube. The X‐rays were collected by Dunlee model TH9447QXH590 image intensifiers (40.64 cm diameter) backed by Phantom v10 high‐speed digital video cameras (Vision Research, Wayne, NJ, USA). Images were captured at a resolution of 1760 × 1760.

A variety of behaviors were induced, including walking, turning, and other maneuvers. More rarely, sitting to standing, jumping, and other behaviors that might involve unusual postures were recorded. When in vivo data collection was complete, individuals were euthanized with Beuthanasia after isoflurane induction. Euthanized individuals were immediately used for ROM measurements.

ROM data were collected separately for each ankle (intertarsal), knee, and hip joint, from distal to proximal. Since multi‐articular muscles could confound one joint's mobility based on another's position, all muscles spanning these joints were severed before data collection. Muscle mass far from the joints was removed, but it was retained close to the joint to ensure that ligaments and joint capsules were left intact. For each joint measurement, the bone proximal to that joint was fixed via cable ties to a plastic platform attached to a wooden rod. The rod was held in place with a vise, immobilizing the platform. A second dowel was cable‐tied to the distal element, providing a handle for manipulation of the bone within the biplanar X‐ray volume.

A low speed (10 fps) fluoroscopic video was recorded of the distal element being taken through extremes of rotation. Limits of rotations were subjectively assessed by the researcher performing the manipulations; force was applied to the dowel, and thus the joint, until resistance was met. The experimenter generally experienced this resistance as a hard stop, with the impression that farther force would risk breaking ligaments. Multiple sequences were necessary to fully map out the joint's ROM. The researcher first attempted to keep the distal element either maximally internally or externally rotated while the element was moved through its limits of FE and ABAD. This was then repeated for the opposite LAR maximum. Finally, two more sweeps were made, one attempting to maximize ABAD and the other to maximize FE regardless of LAR angle. This whole sequence was repeated at least twice. The goal of this procedure was to keep at least one DoF at its maximum at all times in order to sample the surface of the ROM envelope, rather than internal points of the volume. The knee and ankle flexed too much to be manipulated in a single sweep through their entire ROM while staying clear of the X‐ray equipment. Recording for these joints was split into separate flexion and extension runs, ensuring overlap to minimize any gaps in the ROM envelope.

Disarticulated specimens were frozen before being imaged with a medical CT scanner (Philips Medical System, Best, The Netherlands). After segmentation in osirix (v.4.1.2, Geneva, Switzerland; Rosset et al. 2004), bone models were cleaned in geomagic studio 2013 (3D Systems, Morrisville, NC, USA), where fitting of geometric primitives to articular surface features was also performed. Cleaned bone models were brought into maya 2010 (Autodesk Inc., San Rafael, CA, USA) and coordinate systems established as previously described (Kambic et al. 2014). X‐ray videos were calibrated and digitized in matlab (Mathworks, Natick, MA, USA) using the custom X‐ray reconstruction of moving morphology (XROMM) tools bundled as XrayProject (Brainerd et al. 2010; xromm.org). Bone models were animated in maya using transformation matrices produced by the matlab workflow and six DoF kinematics were calculated from each joint coordinate system (Grood & Suntay, 1983).

Sample sizes from the first individual were 780 right hip poses, 905 knee poses, and 1411 ankle poses. The second individual had 967 right hip poses. Analysis revealed multiple unreliable tibiotarsus markers in this individual that prevented the recording of knee and ankle joint angles. The third individual had 801 right hip poses, 597 left hip poses, 1011 knee poses, and 1058 ankle poses. The data from the joint coordinate systems were used to generate particles in maya to create 3‐D graphs. For each pose a joint reached, a spherical particle was emitted at the point defined by the angular value of FE, ABAD, and LAR at that moment. Custom scripts were used to create the 3‐D volumes in the correct coordinate system and to create the 2‐D projections of the volume.

To compare the volume actually occupied by the pose data with a ‘potential’ volume defined by the maximum excursions, the 3‐D point cloud pose data were meshed. The data were exported from maya and imported into meshlab (Cignoni et al. 2008). There, the point cloud was meshed using the convex hull method. The volume of the hull was calculated using the Compute Geometric Measures option in meshlab. This volume was divided by the bounding box volume to express the volume actually occupied as a proportion of the ‘potential’ volume. Finally, this proportion was converted to a percentage. To calculate the area occupied by the pose data, compared with a theoretical rectangular area defined by maxima for two DoFs, the hull was exported as a.obj and imported into maya. There, the hull was rendered from three directions using an orthographic camera. The renders were trimmed in photoshop (Adobe Systems Incorporated, San Jose, CA, USA) and imported into imagej (Abramoff et al. 2004). In imagej, the render was thresholded and the Analyze Particles option was used to measure the area occupied by the hull. The output was given as a percentage.

To compare the volumes of pose data between individuals, one individual was chosen to be the reference individual. The difference between the volume of this convex hull and another joint or individual (the sample joint) was calculated using a Boolean difference operation in the Cork plugin (Bernstein, 2017) for cloudcompare (2017). Finally, to express this difference as a percentage, the result was divided by the average volumes of all observations of the joint and multiplied by 100%.

Results

The ROM results are presented first as bar graphs, then as 2‐D surfaces, and finally as 3‐D plots to compare and contrast each visualization method. ROM data reveal patterns that differentiate the hind limb joints based on DoF ranges (Fig. 2). The hip allows the smallest range of FE (95°–116°), whereas the knee and ankle can undergo amounts that are similar in magnitude (162°–176°). We measured the most ABAD at the hip (35°–45°) with decreasing amounts at the knee and ankle (see Discussion and Kambic et al. 2014). The knee is the most flexible joint in LAR (78°–88°), although the hip can substantially axially rotate as well (57°–67°). LAR at the ankle is smaller (36°–46°).

Figure 2.

Bar graph of ROM results for the hip, knee, and ankle from three individuals, colored gray, purple, and turquoise.

2‐D ROM surfaces

Plotting observed combinations of DoFs reveals substantial interactions. Consider a plot showing FE and LAR simultaneously (Fig. 3); if there were no interactions, then the poses would describe a rectangular area. In contrast, the hip, knee, and ankle areas are all more complicated shapes. These shapes visualize the interactions among DoFs. For instance, the amount of FE permitted at the hip greatly depends on LAR angle (Fig. 3A). When the hip is fully externally rotated, almost no FE is permitted. In contrast, when the hip is internally rotated, the maximum amount of FE is permitted. Intermediate LAR poses allow intermediate amounts of FE. The interaction goes both ways; flexion permits the most LAR, extension the least, and intermediate poses allow some. The knee and ankle also have FE/LAR interactions (Fig. 3B,C), although each differs from the hip and each other.

Figure 3.

Flexion/extension vs. long axis rotation for the hip (A), knee (B), and ankle (C) from a single individual. Each sphere represents an actual pose reached by the joint during manipulation. Ticks mark 20° increments.

To quantify the impact of the interaction between FE and LAR, we calculated the area actually occupied by pose data compared with the rectangular area delineated by maximum and minimum angular values. To ensure that our estimate was conservative, we assumed that unsampled internal poses were achievable and used a convex hull method (see Methods). The results are similar for each joint, despite their varying shapes (Table 1). The measured poses for the hip cover 69% of their ‘potential’ area, and the knee and ankle cover 67 and 68%, respectively.

Table 1.

Percentage of ROM maxima bounding boxes occupied by pose data in 2‐D projections (area), and in 3‐D (volume)

Joint	Individual	FE/ABAD	ABAD/LAR	FE/LAR	FE/ABAD/LAR
Hip	Gray	64.7	66.0	68.5	30.0
	Purple	70.8	63.2	58.1	30.1
	Turquoise	66.3	66.9	61.2	30.0
Knee	Gray	78.5	61.1	67.4	31.9
	Turquoise	70.3	61.7	68.0	25.7
Ankle	Gray	68.1	50.1	67.6	26.1
	Turquoise	79.0	57.3	64.1	30.8

Plotting the other combinations of two DoFs produces similar results. ABAD and FE interact (Fig. 4), as well as ABAD and LAR (Fig. 5). The area defined by the poses is perhaps most irregular at the hip, reflecting strong interactions among degrees of freedom. However, none of the views reveals symmetrical interactions where one DoF responds in a similar manner to another moving away from a given pose. All have asymmetries. When considering the area sampled by the pose data, for FE vs. ABAD the results are 65–79% (Table 1). The areas covered are lower when considering ABAD vs. LAR: 50–66% (Table 1).

Figure 4.

Flexion/extension vs. abduction/adduction for the hip (A), knee (B), and ankle (C) from a single individual. Each sphere represents an actual pose reached by the joint during manipulation. Ticks mark 20° increments.

Figure 5.

Abduction/adduction vs. long axis rotation for the hip (A), knee (B), and ankle (C) from a single individual. Each sphere represents an actual pose reached by the joint during manipulation. Ticks mark 20° increments.

3‐D ROM envelopes

Every pose figured in the 2‐D plots has a unique 3‐D coordinate in angle‐angle‐angle space, and the volume that these poses create fully encompasses every reachable configuration. In our visualizations (Figs 6, 7, 8), the volume is projected into three 2‐D coordinate spaces to help the viewer visualize the volume and to demonstrate what information is lost if only two DoFs are measured/considered.

Figure 6.

Hip ROM for a single individual. Perspective view of the ROM volume in angle‐angle‐angle space. Grids show 2‐D projections of ROM. Thick grid lines represent zero. Colored spheres represent maximum FE (blue), ABAD (green), and LAR (red). Each light gray sphere represents a single pose reached by the joint at one timestep; dark gray spheres represent the 3‐D joint poses (light gray) projected onto 2‐D grids.

Figure 7.

Knee ROM for a single individual. Perspective view of the knee ROM volume in angle‐angle‐angle space along with 2‐D projections. Grids, colored spheres, and axes follow Fig. 4.

Figure 8.

Ankle ROM for a single individual. Perspective view of the ankle ROM volume in angle‐angle‐angle space along with 2‐D projections. Grids, colored spheres, and axes follow Fig. 4.

Each volume re‐emphasizes that all DoFs interact. For instance, at the hip (Fig. 6), maximum abduction and maximum adduction are separated by ~ 20° of FE. Additionally, as the hip adducts towards its maximum, there is a linear decrease in flexion mobility, whereas extension retains proportionately more mobility until close to maximum adduction. The shape of the ABAD/LAR interaction is quite irregular, with a large concavity on the abduction side.

The 3‐D ROM envelope for the right knee shows similar, if less dramatic, DoF interactions (Fig. 7). It is apparent that there are complex relationships between LAR and the other DoFs. Keeping LAR near 0° allows a large FE excursion, but externally rotating does not restrict FE nearly as severely as at the hip. Over 100° of FE are still possible at maximum external rotation. By contrast, once the knee internally rotates past 0°, FE becomes more and more restricted, eventually causing maximum and minimum FE to converge at maximum internal rotation. The volume is skewed in other dimensions as well. Extending the knee reduces LAR, but asymmetrically, so that internal rotation is restricted more rapidly than external rotation. In contrast, maximum flexion tends to restrict internal and external rotation equally. The volume is tilted in ABAD/LAR space such that adduction and external rotation are associated while abduction and internal rotation are associated.

The ankle presents the simplest 3‐D ROM envelope, but even here there are asymmetries in the way the DoFs interact (Fig. 8). Here, too, there appears to be LAR potential, and there is a relationship between FE and LAR mobility. Extension limits LAR more than flexion, and internal rotation limits FE more than external rotation. The ankle volume is also tilted in ABAD/LAR space, although here, adduction and internal rotation are associated – the opposite of the pattern observed at the knee.

The convex hull method can again be applied, this time to measure the volume occupied by these 3‐D angle data compared with a rectangular prism of maxima and minima (Table 1). Viable hip poses occupy 30% of the hip's ‘potential’ volume; the knee and ankle occupy 32 and 26%, respectively.

Symmetry and repeatability of 3‐D ROM envelopes

One test of the precision of our manipulation method was to compare ROM envelopes in the individual with right and left femora marked (Fig. 9, Table 2). Both sides were quite similar in shape and scale. Another test of our manipulations was to compare ROM volumes across individuals. Initially the hips for different individuals did not align precisely (Fig. 10A). However, the shape of each ROM volume appeared similar. To more easily compare these shapes, the volumes from the first two individuals were aligned to the volume from the individual that had both sides measured (Fig. 10B). This offset was performed by hand but did not involve any rotations of the data. The only manipulation that was performed was to translate the volumes along the LAR axis (by 18° and 5°), equivalent to re‐zeroing the LAR values for the two individuals. With this adjustment, it is apparent that the shapes of the hip ROM envelopes across individuals are quite similar (Fig. 10B, Table 2).

Figure 9.

Hip ROM volumes for right (gray) and left (black) sides of a single individual in perspective view. Axes follow Fig. 6. Arrows are 30° long.

Table 2.

Convex hull volumes and overlap between individuals

Reference joint	Sample joint	Volume (degrees3)	Difference (degrees3)	Percent difference (%)
Gray right hip		78 500
	Gray left hip	88 400	4400	5.3
	Turquoise right hip	88 500	40 200	48.6
	Re‐zeroed turquoise right hip	88 500	6500	7.9
	Purple right hip	75 300	23 800	28.8
	Re‐zeroed purple right hip	75 300	12 000	14.5
Gray knee		162 300
	Turquoise knee	136 000	99 700	66.9
	Re‐zeroed turquoise knee	136 000	47 200	31.6
Gray ankle		44 400
	Turquoise ankle	49 700	16 000	34
	Re‐zeroed turquoise ankle	49 700	11 700	24.9

Figure 10.

Hip ROM volumes for three individuals in perspective view. (A) Non‐aligned volumes. (B) Aligned volumes. LAR angles of turquoise and purple were re‐zeroed for alignment, 18° and 5°, respectively. Light gray represents pooled data from the right and left sides of the individual shown in Fig. 9.

Visually, the knee and ankle data from multiple individuals are similar (Figs 11 and 12). When re‐zeroed, the volumes are comparable for both the knee and ankle as well (Table 2) (knee: −15° FE; ankle: 7° FE, −4° ABAD; both: rotated 3° FE, ABAD), although there is less overlap than at the hips. At the knee, the turquoise individual allowed more external rotation when extended, but could not be flexed as far as the gray individual (Fig. 11). Otherwise, the shapes are quite similar, with a bias towards external rotation with extension, a tall middle area where both LAR and FE are relatively free, and with greater flexion increasingly restricting LAR. Both FE and LAR excursions at the knee are substantial.

Figure 11.

Knee ROM volume for two individuals in perspective view. Colors follow Fig. 9.

Figure 12.

Ankle ROM for two individuals in perspective view. Colors follow Fig. 6.

The ankle data across individuals are also similar (Fig. 12, Table 2) with small differences. The turquoise individual allowed more external rotation when flexed, and tended to restrict internal rotation when fully extended, whereas the gray individual tended to restrict external and internal rotation equally. Overall, both ankles show a pattern, extension limiting LAR and flexion allowing more LAR. FE is the dominant rotation allowed at the ankle, but some LAR is also present.

In vivo joint rotations

For every individual, data from previously tracked in vivo sequences were collated to compare the shape of the in vivo volumes with the volumes produced from the postmortem manipulations. More than 39 000 individual joint poses were assembled across individuals. These data were primarily sampled from an array of maneuvering and steady locomotion sequences, but included other behaviors such as jumps and sitting to standing. These poses mostly fell within the manipulated ROM volumes (Fig. 13). FE undergoes the most excursion at every joint, but LAR at the hips and knees is sizable. The hips appear to remain relatively externally rotated when extended, but use a substantial portion of their LAR potential when flexed. The knees use a sizable portion of their LAR volume across the normal range of FE. Contrast the height of the cyclic FE motion at the hips, where most traces remain relatively constrained, with those at the knees, which appear to cover more than half of their potential LAR mobility.

Figure 13.

In vivo ROM volumes for a variety of behaviors (red) plotted with postmortem ROM volumes (gray) for hip (A–D), knee (E–F), and ankle (G–H) for three individuals in perspective view.

The in vivo data do not fill the postmortem ROM volumes in every dimension. The hips provide the most dramatic example of the difference between potential ROM and ROM observed during behaviors. Large portions of extension at the hip go unused during walking, running, turning, and yawing. The most hip extension occurred during two jumps performed by the second subject (Figs 13B and 14A). During the jumps, the pelvis was tilted up at a large angle while the limbs pushed off of the ground. Otherwise, extension of the femur was mostly used during walking and running, resulting in the large numbers of traces that overlap and follow paths that show small deviations in LAR and ABAD (Fig. 13B–D). The breadth of vertical space that the in vivo volume occupies in the first individual (Fig. 10A) demonstrates that LAR is sometimes used at more extended poses. Some individuals flexed farther than we pushed in our manipulations (seen well in Fig. 13C).

Figure 14.

In vivo ROM plotted with postmortem ROM for two behaviors. (A) Hip joint angles during two jumps (red, turquoise). Bone renders show the maximum extension (left) and flexion (right) reached by the individual during the red jump. (B) Knee joint angles during a maneuvering sequence (red). Bone renders show the maximum external (top) and internal (bottom) rotation reached in the course of this long (6.8 s) sequence.

The knees and ankles used more of their FE and LAR potential than the hips. For instance, during the course of a long maneuvering sequence, one individual used almost its entire knee LAR ROM (Figs 13F and 14B). Both individuals measured appear to have internally rotated their knees somewhat farther than our manipulations (Fig. 13E,F). Similar to the hips, FE in vivo appears to be more restricted than the potential FE we measured, although a larger proportion of the volume was used. The knees rotated through large amounts of both FE and LAR during various behaviors. The ankle and knee in vivo data follow the same tilt in LAR vs. ABAD space that the postmortem ROM measured.

Discussion

Plotting DoFs simultaneously provides the most realistic guide to poses that an animal may adopt in life. Treating the hind limb joints as if they had two DoFs (Figs 3, 4, 5), the area actually covered by poses inhabits 50–80% of the ‘potential’ space delimited by maxima and minima. If the bar graph minima and maxima were used to constrain poses, at best 20% and at worst 50% of those poses would be unrealistic/impossible. The 3‐D envelopes reveal that even these are overestimates for 3‐DoF joints. The volumes of 3‐DoF pose data occupy ~ 30% of the rectangular prism defined by the maxima and minima. Therefore, ~ 70% of the poses that may have been considered possible when just using maxima and minima as guides are not reproducible by the animal.

Plotting poses as 3‐D envelopes does not remove traditional metrics of joint mobility. Maxima and minima of each DoF can still be measured, and the volume can be rotated or projected to examine interactions between two DoFs, ignoring the effects of the third. The strength of the 3‐D representation is that in addition to allowing these analyses, it reveals patterns that maxima and minima or 2‐D surfaces miss. Only in a 3‐D representation can the interaction between all three DoFs be represented simultaneously. For instance, the guineafowl hip can only be highly externally rotated when it is also flexed and adducted. Attempting to rotate an abducted hip around the long axis will only allow one‐third of its maximum potential.

Degrees of freedom interact in complex ways

The volumes created by the ROM data for each joint describe shapes that reveal complex interactions among DoFs. The maximum excursion of a single DOF can vary widely depending on the angles of the other two DoFs. What could account for these interactions at motion limits?

Soft tissues likely interact with each other and the morphology of the joint to produce complex ROM envelopes. For instance, other studies have reported increases in mobility with removal of muscle (Hutson & Hutson, 2012, 2013; Pierce et al. 2012; Cobley et al. 2013; Arnold et al. 2014). However, our de‐muscled joint manipulations did not result in additional excursion in every dimension compared with in vivo results. At the hip, individuals flexed their hips farther than we pushed in our cadaveric specimens, and at the knee in at least two instances the individual internally rotated its knee farther than we were willing to spin. This suggests that ROM along these axes was not increased by the removal of muscle. In contrast, it is entirely possible that more extension was permitted at every joint by the removal of muscles. These results suggest that different DoFs are controlled by different soft tissues, which may account for the complex interactions among DoFs.

At the hip, another reason for the complexity of the ROM envelope is the complexity of the articular geometry. The guineafowl hip is a ball‐and‐socket joint, but in birds an additional pelvic process named the antitrochanter has been hypothesized to articulate with the femur (Hutchinson & Gatesy, 2000; Hertel & Campbell, 2007; Troy et al. 2009). In the course of our ROM manipulations, the femur could be felt to lock into place and become restricted in its rotation when abducted at certain FE and LAR angles. It seems likely that abduction engaged the femur with the antitrochanter, and that this additional point of contact reduced the femur's mobility. Specifically, this contact appeared to restrict further abduction. These observations are consistent with a second point of contact forcing the femur to act as a 2‐DoF joint while engaged. We hypothesize that the concave wall in the ROM volume on the abduction side reflects this area of engagement with the antitrochanter.

An additional reason for the complexity of the hip ROM is that the body seems to obstruct adduction. When sufficiently adducted, the distal femur would contact the body wall. This varied according to the amount of FE, since the body is roughly ellipsoidal. It is likely that we overestimated adduction potential, given that the distal end of the femur was cleared of soft tissue to disarticulate the tibiotarsus before data collection on the hip. This additional soft tissue would add bulk to the distal femur, which would be stopped by the body wall at even smaller angles than those we measured.

It is not clear why the ankle and knee have such different LAR potentials. In gross anatomy, they share many similarities, including collateral ligaments and menisci. While the knee contains two cruciate ligaments, the ankle contains only one. In his survey of tetrapod knees, Haines (1942) hypothesized that possessing two cruciates allowed more LAR than in the single cruciate condition, but he did not state a mechanism. Perhaps it is easier to twist these ligaments when they are also lengthening, allowing the paired cruciates to permit more LAR than a single centrally located ligament. Another hypothesis for the difference between the two joints is that the mobile fibula (Fuss, 1996) allows for increased LAR at the knee, whereas the rigid elements that constitute the ankle prevent similar motion.

The value of the third dimension

The interactions among DoFs can be lost or distorted when one dimension is ignored (Fig. 6). The points plotted on the bottom 2‐D projection capture the combination of FE and ABAD that produce poses, but do not capture the variety of LAR angles used. For instance, the two maximum and minimum LAR poses are close together in the FE/ABAD projection (Fig. 6, red spheres) but are actually separated by more than 50° of LAR. The LAR/ABAD surface does not reflect the limitation on extension at large external rotations or large adductions (Fig. 6). The FE/LAR surface misses the sizeable concavity on the adduction surface of the volume. ABAD varies more than threefold between maximum external rotation and zero LAR. The FE/ABAD surface similarly misses large variations in LAR depending on the other two rotations. LAR excursion varies more than threefold over the course of FE range. Measuring just the FE/ABAD surface could lead one wrongly to conclude that the hip is most mobile when extended, since more ABAD is available than when the hip is flexed. The 3‐D volume illustrates that in fact the hip is more mobile in ABAD when extended, but more mobile in LAR when flexed. Simply, no 2‐DoF distribution captures the 3‐D ROM volume of the hips. Furthermore, representing these surfaces merely as maximum and minimum excursions would preclude recognition of any interactions.

The situation at the knee and ankle is less dire, although there are still 2‐D surfaces that miss the shape of the ROM volume. In both joints, the LAR/ABAD surface misses variation in FE due to LAR. This is more subtle at the ankle, but substantial at the knee. There, FE varies by almost half over mid‐range LAR values, and more if measured towards the limits of LAR. Similarly, the FE/ABAD surface misses interactions at both joints. At the ankle, smaller non‐FE excursions result in the FE/ABAD surface more closely resembling the 3‐D volume, but at the knee, substantial information is lost. There is a large reduction in LAR as the knee is flexed from 100°, as well as some reduction as the knee is extended. At both joints, the FE/LAR surface best captures the shape of the ROM volume. The major interactions of each joint (between FE/LAR) are captured. Of course, this assessment can only be made confidently given that the 3‐D volume has first been measured.

Measuring ROM around three DoFs is not necessary for every joint or study. Measuring 3‐DoF ROM of the ankle and knee reveals that they seem to operate as 2‐DoF joints. Hinge‐like, 1‐DoF joints can be accurately described with only maxima and minima. Many studies do not require the type of high‐accuracy kinematics reported here. We hope that our results illuminate some of the strengths, weakness, and underlying assumptions in different methods for measuring joint motion and ROM, and help other researchers choose the methods best suited to answering their research questions. Note that our hip results caution against over‐simplification. Accurate measurement of all joint rotations will be required to understand fully the contributions of soft and hard tissues to joint mobility. Interpretations that overlook relevant DoFs will provide incomplete pictures of joint function.

3‐D ROM envelopes are reproducible

Our methodology, although based on the subjective assessment of rotation limits by the experimenters, produced similar patterns across individuals. One reason for this consistency was the highly accurate bone motion derived from the XROMM workflow, which avoids some errors caused by using skin markers or optical techniques (Lanovaz et al. 2004; Miranda et al. 2013). The hip was the best sampled joint, with three separate individuals and four hips represented. The shapes of the 3‐D ROM envelopes recovered across individuals (Fig. 10) and between two sides of a single individual (Fig. 9) were strikingly similar. Likewise, both knee and ankle envelopes had characteristic shapes that were easy to recognize. The major difference across individuals was that the zero point for hip LAR was not consistent.

At least four factors may have given rise to differences across individuals. First, there may have been some inconsistency in creating joint coordinate systems. For example, determining the zero point for hip LAR requires fitting a cylinder to the geometry of the femoral condyles, which are cropped by hand. This could have led to an apparent offset among limits that were actually the same. Second, real differences in morphology among individuals may contribute. The orientation of anatomical features may differ among individuals due to developmental or environmental variability. Third, our data may reflect real differences in ROM among individual joints. Finally, experimenters found ROM limits manually by rotating the joint until resistance was detected. A rig that could measure torque about each rotational axis might have yielded more consistent results with less noise. However, even if torque could be measured, the actual peak values selected for each DoF at each joint are not obvious. Nevertheless, feedback on what loads we impose would be valuable, both for repeatability and to avoid damage to soft tissues mid‐recording.

Ankle and knee data from different individuals produced similarly shaped ROM volumes that did not require re‐zeroing. Variations here were also likely the result of errors introduced by the researchers and real morphological variation among individuals. Measurement error is another possible source of variation but it was small in our results using similar techniques (Kambic et al. 2014).

Knee and ankle ABAD and LAR

The ABAD measured at the knee and ankle does not indicate that the condyles of the femur or tibiotarsus normally disarticulate. Instead, the coupling of LAR and ABAD suggest that the articular surfaces are not completely orthogonal to the long axis of the bone, generating some kinematic cross‐talk (see Piazza & Cavanagh, 2000; Rubenson et al. 2007; Kambic et al. 2014 for further discussion).

Given the closely matched condyles and cotyles, and the single cruciate present in the joint, it may be surprising that we report so much LAR capacity at the ankle (Fig. 8). We were initially skeptical of this result, but after reviewing digitized trials of maneuvering, we believe ankle LAR occurs in vivo; small amounts of in vivo LAR have also been reported in ostriches (Rubenson et al. 2010). It seems unlikely that LAR is actively controlled (Kambic et al. 2014), but passive ankle LAR may have uses for the individual. Ankle LAR may allow the foot to remain planted through a maneuver that rolls the tarsometatarsus. Alternatively, the laterally spread toes may provide long moment arms that make eliminating ankle LAR too costly. It is also possible that true hinge joints are rare in vertebrates, and that other hinge‐like joints actually allow substantial displacement around multiple axes.

Observed in vivo ROM was reduced compared with postmortem ROM

In general, actual joint positions reached during walking, running, and maneuvering behaviors were a subset of the potential joint angle space that we measured, agreeing with results from Arnold et al. (2014). The hips used the least amount of their postmortem ROM, whereas the in vivo knees and ankles used a larger portion of their potential space. There are a number of reasons that could combine to explain this result.

One likely reason for the difference in potential ROM and in vivo volumes is that we did not sample all the behaviors that a guineafowl performs, such as non‐locomotor behaviors. Although we attempted to record standing to sitting, sitting to standing, and jumping and landing behaviors, these were still poorly sampled. Maximum performance of behaviors that we did sample may also use joint angles that we did not measure – a hypothesis difficult to test without reliable ways to elicit maximum performance.

A second reason for the smaller in vivo joint angles may be constraints on ROM from both active and passive muscle. To avoid the joint coupling that biarticular muscles can cause, we severed muscles crossing the joints before measuring ROM. Other studies (Hutson & Hutson, 2012, 2013; Pierce et al. 2012; Cobley et al. 2013; Arnold et al. 2014) have found increased joint mobility after muscle removal. This may be the case for joint angle combinations that live animals did not approach. When fully muscled, the hip may simply be unable to extend as far as the reduced, ligamentous preparation.

A final reason for the difference in potential ROM and in vivo ROM may be that the hand manipulation of the joints forced them too far, exerting higher moments on the joints than the subject could produce in life. We find this explanation less likely than the others listed here, the main reason being that individuals sometimes reached joint angles that exceeded the postmortem ROM envelopes. A good example of this phenomenon is at the hips, where most subjects flexed their femora beyond the hand‐manipulated ROM volume. Figure 13B shows another example, where the individual internally rotated its knee beyond the postmortem envelope. These examples, along with the similar shapes of the ROM envelopes across individuals, make it unlikely that we pushed the soft tissues farther than the individuals are able to in life.

Regardless of reasons, it is important to note that we cannot say that guineafowl use only a portion of their potential ROM. We can only report that in the behaviors we observed, which included common tasks such as walking, running, and maneuvering while standing, a portion of potential ROM was used.

Paleontological implications

Many studies use inferred ROM as inputs for modeling or analysis of extinct taxa. Evaluating plausible joint poses using biomechanical constraints (Hutchinson, 2006; Gatesy et al. 2009) requires accurate joint ROM estimates. To bring such techniques to 3‐D, estimates of joint excursion and interactions around all mobile axes will be required. Reconstructions of muscle moment arms use ROM estimates to constrain the joint poses examined, or to eliminate degrees of freedom from consideration (Hutchinson et al. 2005; Bates et al. 2015). We suggest that studies of theropod moment arms include consideration of LAR moments for both the hip and knee going forward.

ROM inference in fossil taxa is challenging given the lack of intact soft tissues. Intuitively, soft tissues seem likely to decrease ROM compared with ROM estimated from skeletal elements (e.g. Carpenter & Wilson, 2008; Cobley et al. 2013). However, researchers investigating ROM in other taxa and joints have sometimes recovered little difference between the two (Jones, 2015), or even decreased ROM from skeletal measurements (Hutson & Hutson, 2012, 2013). The closest to our study was that of Carpenter & Wilson (2008), who reported on hindlimb FE in chickens. Given their results, it seems most likely that our ROM estimates are more conservative than estimates derived from bones alone. The relationship between ROM estimates from bones and ROM measurements taken with soft tissues intact deserves more study.

Conclusions

ROM data can demarcate complex regions of angle‐angle‐angle space (Figs 6, 7, 8). The 3‐D ROM envelopes for the hip, knee, and ankle demonstrate that DoFs interact in ways that may not be easily captured by only measuring minima and maxima. Particularly, without explicit measurements of what angles other DoFs are held to or moved through while measuring ROM for a DoF, it is impossible to tell which 2‐D slice of the 3‐D volume is being measured, or whether it is planar. In short, 1‐D and 2‐D measurements and representations of 3‐D (3‐DoF) data are always incomplete. Understanding the relationship between joint shape and function in 3‐DoF joints requires understanding their full 3‐D function.

Plotting in vivo ROM with this degree of accuracy has the potential to demonstrate when passive soft tissue constraints are used to guide joint rotations. In these cases, in vivo rotations should follow the edges of the ROM envelope. For example, many of the in vivo hip data appear to lie along an edge of abduction. It is possible that passive structures are limiting abduction while muscles work to flex/extend and internally/externally rotate. Joint angle volumes at the knees also have flat sides, suggesting extremely limited mobility in ABAD.

Performing ROM studies with explicitly defined and highly accurate coordinate systems opens up a new avenue for the exploration of joint structure and function. We have shown that the power of XROMM can be leveraged accurately to compare joint motion across individuals and compare how joints behave in vivo with results acquired postmortem from the same individual in the same coordinate system. Logical next steps include studying individual joints in more detail, to understand how individual soft tissues contribute to joint stability, and investigating how muscles and particularly biarticular muscles limit ROM.

Author contributions

R.E.K., T.J.R., and S.M.G. contributed to study conception, experimental design, and manuscript preparation. R.E.K. and S.M.G. performed the data collection and XROMM analysis.

Conflict of interest

The authors declare no conflict of interest.