Abstract
The absence of a standardized method for defining hindfoot bone coordinate systems makes it difficult to compare kinematics results from different research studies. The purpose of this study was to develop a reliable and robust procedure for defining anatomical coordinate systems for the talus and calcaneus. Four methods were evaluated based upon their anatomic consistency across subjects, repeatability, and their correspondence to functional axes of rotation. The four systems consisted of: 1) interactively identified bony landmarks, 2) a principal component analysis, 3) automatically identified bony landmarks, and 4) translating the tibial coordinate system to the hindfoot bones. The four systems were evaluated on 40 tali and 40 calcanei. The functional axes of rotation were determined using dynamic biplane radiography to image the hindfoot during gait. Systems 2 and 3 were the most repeatable and consistent due to the lack of operator intervention when defining coordinate systems. None of the coordinate systems corresponded well to functional axes of rotation during gait. System 3 is recommended over System 2 because it more closely mimics established bone angles measured clinically, especially for the calcaneus. This study presents an automated method for defining anatomic coordinate systems in the talus and calcaneus that does not rely on manual placement of markers or fitting of spheres to the bone surfaces which are less reliable due to operator-dependent measurements. Using this automated method will make it easier to compare hindfoot kinematics results across research studies.
Introduction
The hindfoot is composed of the talus and calcaneus bones. Accurately measuring hindfoot joint kinematics is challenging due to the absence of external landmarks (Arndt et al., 2004; Wu et al., 2002), the globular asymmetrical geometry of the bones (Parr et al., 2012), and the complex coupled motion of the tibiotalar and subtalar joints (Koo et al., 2015). In 2002, the Standardization and Terminology Committee (STC) of the International Society of Biomechanics (ISB) proposed a joint coordinate system for the ankle joint complex (Wu et al., 2002) that failed to distinguish between tibiotalar and subtalar joints. The continuing absence of a standardized method for defining hindfoot bone coordinate systems makes it difficult to compare kinematics results from different research studies (Nichols et al., 2016; Peltz et al., 2014; Wainright et al., 2012). Previous techniques for defining anatomic coordinate systems in the hindfoot include using a reference neutral position (Arndt et al., 2004; de Asla et al., 2006; Koo et al., 2015), manually identifying external bony landmarks (Rouhani et al., 2012), manually identifying bony landmarks or fitting spheres to 3D bone models (Gutekunst et al., 2013; Parr et al., 2012), copying a tibia coordinate system to the hindfoot bones (Wang et al., 2015), using the functional axis of motion (Beimers et al., 2008; Sheehan 2010), and co-registering bones to an averaged model (Gutekunst et al., 2013).
The purpose of this study was to develop a reliable and robust procedure for defining anatomical coordinate systems for the hindfoot bones. Four methods were evaluated based upon their anatomic consistency across subjects, repeatability, and their correspondence to functional axes of rotation.
Methods
Data Collection
Data was collected from 20 healthy adults (10 M, 10F; 30.8 ± 6.3 years; range 22–42 years) after obtaining informed consent and following Institutional Review Board approval (IRB approval - PRO16070246). Participants reported no previous serious injuries to their foot or ankle.
Bilateral computed tomography (CT) scans of the distal tibias through the bottom of the feet, in addition to a single slice through the proximal tibia, were collected for each participant (GE LightSpeed Pro 16; radiation dose: 0.03 mSv). Mimics software (Mimics Software, Leuven, Belgium) was used to segment distal tibia, talus, and calcaneus bone tissue in each scan (voxel size 0.658 × 0.658 × 0.658 mm3) using a combination of automated (thresholding and region growing) and manual techniques (Figure 1C). Three-dimensional bone models were then made from the segmented bone tissue (Treece et al., 1999) (Figure 1D).
Fig 1.
Dynamic biplane radiography data collection and processing. A) Participants performed two trials of over-ground walking at a self-selected pace. B) synchronized biplane radiographs were collected during the stance phase of the gait cycle. C) Bilateral ankle CT scans were collected. D) Subject-specific 3D bone models were created. E) 3D bone models were matched to the biplane radiographs using a validated and automated matching process. F) Relative translations and rotations were calculated using standard methods.
Participants walked through the imaging area of a biplane radiography system two times per side at their self-selected pace while synchronized biplane radiographs of the ankle and hindfoot were collected at 100 Hz for one second (maximum 90 kV, 125 mA, 1 ms exposure per image) during the stance phase (heel strike to toe off) (Figure 1A and 1B). At least one static standing trial of each ankle was also captured.
The subject-specific bone models created from CT were matched to the synchronized biplane radiographs using a validated volumetric model-based tracking process with an RMS accuracy of 1.2 mm or better in translation and 1.5° or better in rotation for the tibiotalar and subtalar joints (Pitcairn et al., 2020) (Figure 1E).
Coordinate System Definitions
The anatomic coordinate system for the tibia was created by placing markers on the center of the tibia plateau, medial malleolus, anterior fibular notch, and posterior fibular notch. The tibia anatomic origin was defined as an average point between the sagittal midpoint (average of the anterior fibular notch and posterior fibular notch) and the medial malleolus. The anatomic Z-axis was defined as the vector between anatomic origin and the center of the tibia plateau, and the anatomic X-axis and Y-axis were determined through cross-products, similar to previous studies (Caputo et al., 2009; Wang et al., 2015).
Four methods were evaluated for determining anatomic coordinate systems in the talus and calcaneus (Table 1). All four methods defined the anatomic axes in the same general orientation, with the X-axis in the medial to lateral direction, the Y-axis in the posterior to anterior direction, and the Z-axis in the inferior to superior direction.
Table 1:
The four methods for creating hindfoot bone anatomic coordinate systems. Red, green, and blue arrows correspond to X, Y, and Z-axes, respectively, for each bone. Black markers indicate the landmarks used to create the axes. Corresponding bones are shown from the same viewpoint so that differences in the anatomic coordinate system orientation can be appreciated.
| System 1 | System 2 | System 3 | System 4 | |
|---|---|---|---|---|
| Description | Interactively identified landmarks | Principal component analysis | Automatically identified landmarks | Tibial coordinate system translated from static standing trial |
| Talus |  |
 |
 |
 |
| Calcaneus |  |
 |
 |
 |
System 1 required manually identifying four points that correspond to specific anatomical landmarks on each 3D bone surface, as described in Table 2 (Figure 2A, 2B).
Table 2:
Anatomical landmarks on the 3D bone surface of the talus and calcaneus.
| Bone | Landmark | Description |
|---|---|---|
| Talus | Anterior | Central point on the anterior articular surface for the navicular |
| Posterior | Posterior point at the apex of the posterior process | |
| Medial | Superior point on the edge of the medial trochlea | |
| Lateral | Superior point on the edge of the lateral trochlea | |
| Calcaneus | Anterior | Central point on the anterior surface |
| Posterior | Central point on the posterior surface | |
| Inferior | Inferior point on the posterior surface | |
| Superior | Superior point on the posterior surface | |
Fig 2.
Anatomic landmarks used to define coordinate systems on the talus and calcaneus (A, B). Table 2 provides a descripton of each landmark location. System 4 coordinate system that applied the tibia coordinate system to the talus and calcaneus (C).
System 2 used principal component analysis. The primary axis for the talus was oriented in the posterior-anterior direction, and the secondary axis in the medial-lateral direction. The primary axis for the calcaneus was oriented in the posterior-anterior direction, and the secondary axis in the inferior-superior direction (Figure 3). This system was completely automated.
Fig 3.
The principal component analysis for the talus and calcaneus showing the primary (A), secondary (B), and (C) tertiary principal components to create the X (red), Y (green), and Z (blue) axes.
System 3 was a completely automated system that used a combination of principal component analysis (PCA), bone surface location, and shape to identify the same anatomic landmarks as System 1. The automated process comprised four steps to identify each anatomical landmark on the 3D bone models, as described in Figure 4. PCA was used to generate an initial orientation, followed by a user prompt to confirm anterior/posterior and superior/inferior bone surfaces were identified correctly regardless of the original CT scan orientation. Sensitivity to 3D bone model mesh resolution was also evaluated for Systems 2 and 3 by increasing and decreasing mesh resolution by 50% for 5 tali and 5 calcanei and comparing coordinate system orientations among the three resolutions.
Fig 4.
The automated process for identifying the lateral marker on the talus (top) and the superior marker on the posterior calcaneus (bottom): (A) Bone surface geometry was used to define principal axex to provide initial bone orientation, (B) The region of interest on the bone surface was isolated based upon location relative to the principal axes, (C) A set of points within each region that coincide with a fitted convex hull were identified, and (D) The maximum point within each region was identified as the landmark location.
System 4 translated the tibia coordinate system to the center of the talus and calcaneus based on the orientation of the bones during the static standing trial, as has been done previously (Wang et al., 2015) (Figure 2C). Three subjects were excluded from analysis with this system because they were not standing with their feet side-by-side in a neutral position during the static imaging.
Coordinate System Evaluation
The four systems were compared by assessing their repeatability, axis consistency across subjects, and correspondence to the functional axes of rotation.
Repeatability was assessed for System 1 by having 3 operators interactively identify landmarks on the 10 tali and 10 calcanei. Repeatability for System 4 was assessed by using multiple static standing trials from 4 subjects and therefore quantified standing posture repeatability rather than marker placement repeatability. Repeatability was quantified by the pooled standard deviation of the deviation angles between coordinate system axes.
Anatomic axis consistency, a measure of variation among subjects, was assessed by co-registering the talus and calcaneus 3D bone models of each subject to an averaged bone model created from all subjects (Myronenko and Xubo 2010) (Figure 5). The anatomic axes of the averaged bone were created using the four methods described above. Then, XYZ deviation angles were calculated (i.e. the difference in a subject’s XYZ coordinate system and the coordinate system of the average 3D bone model) (Reinschmidt and Bogert 1995).
Fig 5.
Consistency evaluation. The bones were co-registered to the average bone (rotation only) and the difference between a subjects’s coordinate system (black arrows) and the average bone coordinate system (red, green, blue arrows) was calculated for each system. Only 5 bone models are shown for clarity, however all 40 bone models were included in the evaluation.
Correspondence to functional axes of rotation was evaluated by comparing the helical axis of motion (HAM) for tibiotalar and subtalar joints during walking to anatomic axes (Figure 6). Six-degree-of-freedom kinematics between the tibia and talus, and between the talus and calcaneus, were calculated using the ISB-recommended ordered rotations (Wu et al., 2002). Kinematics were filtered using a fourth-order low-pass Butterworth filter at 9 Hz with the filter frequency determined using residual analysis (Winter 2009). The plantarflexion/dorsiflexion (X-axis) was used as the anatomic reference axis for the talus and the inversion/eversion (Y-axis) was used as the anatomic reference axis the calcaneus. The helical axis of motion was calculated following established protocols (Spoor and Veldpaus 1980) from the maximum and minimum plantarflexion/dorsiflexion and inversion/eversion angles in the tibiotalar and subtalar joints, respectively, during the support phase of gait. The average magnitude of the deviation angle between the helical axis and the anatomic axis was determined for each subject (two trials per side) and compared among systems.
Fig 6.
The helical axis of motion (black) from minimum flexion (teal) to maximum flexion (purple) compared to the anatomical X (red), Y (green), and Z (blue) axes for the (A) tibiotalar joint and (B) subtalar joint.
Analysis of variance (ANOVA) and post-hoc Tukey tests were used to identify differences in consistency and correspondence to functional axes among systems (α = 0.05) (SPSS Statistics, IBM Corp, Armonk, NY).
Results
Repeatability
System 1 repeatability ranged from 2.8° to 7.4°, while System 4 repeatability encompassed a larger range, from 1.0° to 16.1°. Systems 2 and 3 were automated and therefore had perfect repeatability (Table 3).
Table 3:
Euler angles [X,Y,Z] for the repeatability (pooled standard deviation of deviation angles) and consistency (average absolute deviation angle) measures, and helical axis deviation angles for each coordinate system. Bold text denotes the best system(s) for each parameter and Euler component.
| System 1 | System 2 | System 3 | System 4 | |
|---|---|---|---|---|
| Talus | ||||
| Repeatability [X,Y,Z] axes (°) | [4.5, 4.0, 2.9] | [0, 0, 0] | [0, 0, 0] | [16.1, 7.7, 9.6] |
| Consistency [X,Y,Z] Abs. Avg. (°) | [4.2, 2.9, 4.4] | [1.8, 3.2, 1.6] | [3.2, 3.0, 3.9] | [4.5, 6.1, 5.3] |
| Helical Axis Deviation Angle (°) | 37.3 ± 9.7 | 43.7 ± 10.6 | 38.7 ± 8.2 | 38.2 ± 9.2 |
| Calcaneus | ||||
| Repeatability [X,Y,Z] axes (°) | [4.2, 7.4, 5.2] | [0, 0, 0] | [0, 0, 0] | [1.0, 4.9, 1.3] |
| Consistency [X,Y,Z] Abs. Avg. (°) | [2.8, 6.3, 3.4] | [0.9, 6.5, 1.1] | [2.4, 4.7, 3.5] | [2.5, 4.8, 3.7] |
| Helical Axis Deviation Angle (°) | 35.8 ± 7.1 | 33.4 ± 5.5 | 32.8 ± 8.0 | 34.0 ± 6.7 |
Consistency
For the talus, System 2 was found to have better consistency than Systems 1 and 4 along the X-axis (all p<0.002), and better consistency than all other systems along the Z-axis (all p<0.003) (Table 3). System 4 was found to have poorer consistency than all other systems along the Y-axis for the talus (all p<0.006). For the calcaneus, System 2 was found to have better consistency along the X- and Z-axes than all other systems (all p<0.002).
Correspondence to Axes of Rotation
None of the anatomic coordinate systems corresponded well to the functional axes of rotation for any of the coordinate systems, with deviation angles ranging from 33° to 44° (Table 3). No statistically significant differences were observed among system deviation angles for the tibiotalar joint (p=0.149) or the subtalar joint (p=0.546).
Mesh Resolution
The average edge length in the original tali and calcanei was 1.1mm and 1.3mm, respectively. Increasing mesh resolution by 50% had a minimal effect on tali and calcanei coordinate system orientation (Table 4). Decreasing mesh resolution by 50% changed coordinate system orientation by up to 3°.
Table 4:
Mesh sensitivity analysis. The bone mesh edge lengths were decreased by 50% (higher resolution model) and increased by 50% (lower resolution model). Coordinate systems determined using the higher and lower resolution models were compared to the original models using System 2 and System 3. The average and standard deviation (SD) of the Euler angles between the original model and new models are provided.
| Description | System 2 | System 3 | |||
|---|---|---|---|---|---|
| principal component analysis | automatically placed markers on bone surface | ||||
| Edge Length | 50% | 150% | 50% | 150% | |
| Talus deviation [X, Y, Z] (°) |
Average | [−0.5, −0.6, 0.1] | [0.1, −0.4, −0.9] | [0.3, −0.2, −0.1] | [0.3, −3.0, 0.2] |
| SD | [0.8, 1.9, 1.0] | [1.3, 1.8, 1.3] | [0.7, 1.0, 0.8] | [1.1, 6.4, 1.7] | |
| Calcaneus deviation [X, Y, Z] (°) | Average | [0.6, −1.3, −0.1] | [0.3, 0.6, 0.1] | [0.1, 0.0, −0.1] | [0.4, −0.4, −0.6] |
| SD | [0.5, 2.0, 0.7] | [1.0, 4.3, 0.9] | [0.4, 0.8, 0.3] | [1.1, 3.0, 1.5] | |
Discussion
The purpose of this study was to identify a reliable and robust procedure for defining clinically meaningful anatomical coordinate systems for hindfoot bones. Four methods for creating anatomical coordinate systems in the talus and calcaneus were evaluated by their repeatability, anatomic consistency across subjects, and their correspondence to functional axes of rotation. The automated methods, System 2 and System 3, were the most repeatable due to the lack of operator intervention when defining the coordinate systems. System 2 had the best consistency along the X- and Z-axis. None of the coordinate systems corresponded well to the functional axes of rotation. Systems 2 and 3 appear to be the most repeatable and consistent across subjects. System 3 offers the advantage of establishing hindfoot bone coordinate systems that correspond to established bone angles used in clinic. In particular, the calcaneus anatomic coordinate system as determined by System 2 fails to mimic established bone angles used in orthopaedics. For example, although the primary axis approximates calcaneal pitch measured on lateral radiographs, the second and third principal axes do not accurately represent the medial-lateral and superior/inferior axes used to characterize frontal plane anatomy (such as tibial-calcaneal angle) (Lamm et al., 2016) and transverse plane deformities (Gutekunst et al., 2013). Considering that System 2 and 3 are similar in terms of quantitative performance, the fact that System 3 more closely replicates axes used for clinical measurements suggest System 3 is preferred.
Agreement between the anatomic and functional axis of rotation was selected as an evaluation criterion because if one of the tested anatomic axes aligned well with the functional axis, that anatomic coordinate system may be a preferable option for providing an unambiguous description that minimizes kinematic crosstalk (Piazza and Cavanagh 2000). Due to the high variability in functional axis directions among subjects, it is unlikely that a single algorithm based upon bone morphology could be devised to align well to the functional axis of rotation for all subjects. This finding of high variability among subjects further supports the need for a consistent and standardized method for reporting joint rotations so results can be compared across studies.
It is important to consider the strengths and limitations of this study when interpreting the results. Strengths include a sample of 40 hindfoot bones, which demonstrates the robustness of the automated algorithms, and in vivo helical axis of motion data determined during gait for each foot. The study was limited to a sample of healthy young adult feet which may differ in terms of kinematics and morphology from feet in older individuals or patients with symptomatic pathology. Therefore, the generalizability of these results to older bones containing osteophytes remains to be demonstrated.
This study presents an automated method for defining anatomic coordinate systems in the talus and calcaneus that is repeatable and consistent. The automated method does not rely on manual placement of markers or fitting of spheres to the bone surfaces which are less reliable due to operator-dependent judgements. Using this automated method will make it easier to compare hindfoot kinematics results across research studies. The source code for this project will be made freely available to the biomechanics community through the Mendeley Data Repository.
Acknowledgements
This research was supported by NIH Grant R44 HD066831
Conflict of Interest Statement
None of the authors have financial or personal relationships with other people or organizations that could inappropriately influence (bias) this work. The study sponsors had no influence on the data collection methods, data analysis, or interpretation of the data.
Sources of Support: This work was supported in part by Grant R44 AR064620 from NIH/NIAMS
Footnotes
Conflicts of Interest: None.
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