Abstract
Accurate anatomical coordinate systems for the foot and ankle are critical for interpreting their complex biomechanics. The tibial superior-inferior axis is crucial for analyzing joint kinematics, influencing bone motion analysis during gait using CT imaging and biplane fluoroscopy. However, the lack of consensus on how to define the tibial axis has led to variability in research, hindering generalizability. Even as advanced imaging techniques evolve, including biplane fluoroscopy and weightbearing CT, there exist limitations to imaging the entire foot together with the full length of the tibia. These limitations highlight the need to refine axis definitions. This study investigated various superior-inferior axes using multiple distal tibia lengths to determine the minimal field of view for representing the full tibia long-axis. Twenty human cadaver tibias were imaged and segmented to generate 3D bone models. Axes were calculated based on coordinate definitions that required user manual input, and a gold standard mean superior-inferior axis was calculated based on the population’s principal component analysis axis. Four manually calculated superior-inferior tibial axes groups were established based on landmarks and geometric fittings. Statistical analysis revealed that geometrically fitting a cylinder 1.5 times the mediolateral tibial width, starting 5 cm above the tibial plafond, yielded the smallest angular deviation from the gold standard. From these findings, we recommend a minimum field of view that includes 1.5 times the mediolateral tibial width, starting 5 cm above the tibial plafond for tibial long-axis definitions. Implementing these findings will help improve foot and ankle research generalizability and impact clinical decisions.
Keywords: tibial axis, tibial field of view, principal component analysis, landmark-based axis, geometric-based axis, primary axis
INTRODUCTION
Defining accurate and consistent anatomical coordinate systems for the bones in the foot and ankle is paramount to interpreting the intricate kinematics in this complex multivariant biomechanical system. Specifically, the tibial superior-inferior (SI) axis plays an important role when calculating the kinematics for the tibiotalar and tibiofibular joints, as it serves as a primary axis for joint angle computations. The results from such an analysis can influence the interpretation of data in fields such as bone motion analysis during gait using CT (computed tomography) imaging and biplane fluoroscopy, prosthesis design, and injury assessment (Canton et al., 2020; MacWilliams and Davis, 2013).
However, despite its importance, there remains a lack of consensus regarding the ideal method for defining a tibial axis (Kruger et al., 2019; Lenz et al., 2021). Currently, there are multiple approaches to defining SI tibial axes including principal component analysis (PCA) (Imai et al., 2009; Kai et al., 2014; Mattingly et al., 2006), bony landmark identification (Caputo et al., 2009; Claassen et al., 2019; Ito et al., 2015; Yamaguchi et al., 2009), and fitting geometric shapes to identifiable bony structures (Green et al., 2011; Yamaguchi et al., 2009). This lack of standardization has resulted in variability among studies, specifically when calculating relative joint angles for the tibiotalar and tibiofibular joints, which ultimately hinders the generalizability of findings and comparison of results across sites. Notably, the ISB-recommended definition for a tibia coordinate system, which is based on proximal and distal landmark identification, relies on the full tibia (Wu et al., 2002). This reliance poses challenges in the context of advanced imaging modalities, which may not capture the entire tibia, thus limiting its applicability and precision in certain scenarios.
Additionally, as imaging techniques evolve, especially for the foot and ankle, there is a need to be cognizant of the amount of tibial shaft that is being captured within the field of view of advanced medical imaging machines (Figure 1). While conventional CT allows for full tibia scans, concerns arise regarding the necessary radiation exposure and the non-weightbearing nature of these scans. Conversely, weightbearing CT presents clinical advantages with its lower radiation and capacity to image the joint under load, yet it offers a limited field of view for foot and ankle analysis. With these imaging advances comes the responsibility to critically evaluate and refine axis definitions, primarily because most imaging modalities for the foot and ankle are currently unable to image the full tibia. Therefore, the objective of this study was to investigate the accuracy of multiple SI axis definitions, on varying artificial lengths of distal tibiae, to determine the minimal tibial field of view needed to adequately represent a full tibia long-axis.
Figure 1:
Cropped and full tibiae with various superior-inferior axes calculations highlighting the large variability when there is such a limited field of view.
METHODS
Image Acquisition and Processing
In this study, we utilized twenty human cadaver full-length tibias (8 female, mean length of 387.24 ± 11.29 mm). Each individual tibia underwent scanning with a clinical computed tomography (CT) machine (Siemens Somatom Definition Flash; 0.6 mm3) and were manually segmented in Mimics (Mimics 24.0; Materialise) to create three-dimensional (3D) bone models. Following segmentation, all bone models were consistently smoothed and decimated in 3-matic (3-matic 16.0; Materialise) and left-sided models were mirrored to match right-sided models to remove laterality as a variable. All models were aligned using an iterative closest point algorithm in MATLAB (R2022b; MathWorks) to prepare the models for data analysis (Wilm, 2023).
Axis Calculations
Prior to manual axes calculation, a gold standard was defined to determine the differences between results. This is achieved by calculating the PCA based axes on each individual full tibia which results in three axes per bone. The PCA axis definition for the tibia, also known as a principal axis (Imai et al., 2009) or principal moment of inertia (Mattingly et al., 2006), has been used in previous studies, similar to a study performed by Kai et al. (Kai et al., 2014), because it is automatically calculated, ensuring consistency and independence from user input. The primary axis, which was the axis along the tibia shaft, was used for each bone to calculate the mean primary PCA axis, which will be referred to as the mean SI PCA axis, across the population. The mean SI PCA axis was used as the gold standard for this study. The angle between the gold standard mean SI PCA axis and each manually calculated axes was used for statistical analysis (Figure 2). This study included four manually calculated SI tibial axes groups per bone: two based on landmarks and two employing geometric fittings (Figure 3).
Figure 2:
Illustration of the angle calculation between the mean principal component analysis (PCA) axis (black) and the various manual axes (green).
Figure 3:
Methods flowchart highlighting the four groups, two landmark-based and two geometrically-based with the nuances between them. The geometrically-based definitions rely on the mediolateral talar width (MTW).
Landmark-Based Axes
The first landmark based axis was an interpretation of the Yamaguchi et al. axis (Yamaguchi et al., 2009). To create this axis in 3-matic, a plane was fitted to the surface of the tibial plafond then translated 5 cm and 10 cm proximally. The line connecting the origins of the translated planes was the first landmark-based axis, which will be referred to as the Yamaguchi adaptation throughout the manuscript. The second landmark-based axis was adapted from, and a combination of, Yamaguchi et al. and Caputo et al. definitions (Caputo et al., 2009; Yamaguchi et al., 2009). To create this axis, first, a line was drawn connecting the medial malleolus and the posterior corner of the lateral edge of the tibial plafond to define the medial-lateral (ML) axis (Caputo et al., 2009). Second, a line was drawn connecting the midpoints of the anterior and posterior ridges of the tibial plafond to define the anterior-posterior (AP) axis (Yamaguchi et al., 2009). Finally, the SI axis was calculated by taking the cross product of these two defined axes for the second landmark-based axis, which will be referred to as the ML/AP cross product.
Geometric-Based Axes
Both geometrically fit axes use the medial-lateral distance between the medial malleolus and the lateral edge of the tibial plafond. This distance will be referred to as the mediolateral tibial width (MTW) throughout the manuscript. All cylindrical axes were calculated in 3-matic using the “Fit cylinder” method on the varying lengths of tibiae and adjusting the origin based on the two geometric axes definitions, as defined below (3-matic 16.0; Materialise).
The first geometric axis was calculated by fitting a cylinder to the tibia with the base of the cylinder 5 cm above the tibial plafond. This 5 cm offset was motivated by the 5–10 cm range from Yamaguchi et al. (Yamaguchi et al., 2009). The height of the cylinder is a ratio of the MTW. The cylindrical height ranged from half of the MTW to four times the MTW, increasing by 0.5 increments (0.5x, 1.0x, 1.5x, 2.0x, 2.5x, 3.0x, 3.5x, 4.0x). The midline of each of the 8 cylinders was used as the SI axes for the first geometric axes. This axis will be referred to as the shaft axis throughout the manuscript. The second geometric axis was calculated by fitting a cylinder to the tibia with the base of the cylinder at the most distal point on the medial malleolus and the height is a ratio of the MTW. The cylindrical height ranged from the MTW to four times the MTW, increasing by 0.5 increments (1.0x, 1.5x, 2.0x, 2.5x, 3.0x, 3.5x, 4.0x). The midline of each of the 7 cylinders was used as the SI axes for the second geometric axes. This axis will be referred to as the distal axis throughout the manuscript.
Statistical Analysis
For each bone, the seventeen SI axes from the four groups were reconstructed in MATLAB and the angle between each axis and the mean SI PCA axis was calculated. A one-way ANOVA with a Tukey post-hoc analysis was employed to determine statistical significance (p < 0.05) between the seventeen subgroups. Additionally, an omega squared (ω2) was used to quantify effect size with values of 0.01, 0.06, and 0.14 representing small, medium, and large effect sizes (Field, 2013; Kirk, 1996).
RESULTS
The manually calculated SI axis with the smallest angular deviation from that gold standard mean SI PCA axis was the shaft axis at 1.5x the MTW, resulting in an angle of 1.71° ± 0.69° (Figure 4). Six of the subgroups did have significantly different angles than the 1.5x shaft axis. These included the ML/AP cross product axis and first five distal axes calculations (1.0x, 1.5x, 2.0x, 2.5x, 3.0x) with p-values of p<0.0001 for each, and p=0.0012 for the 3.0x axis. In contrast, angles from the remaining shaft axes (0.5x, 1.0x, 2.0x, 2.5x, 3.0x, 3.5x, 4.0x), the remaining two distal axes (3.5x and 4.0x), and the Yamaguchi adaptation did not show significant differences (p > 0.23). The effect size from the ANOVA results had a large effect size, based on an ω2 value of 0.84.
Figure 4:
Chart to illustrate the average angle differences with error bars compared to the mean principal component analysis (PCA) axis. The values with an asterisk (*) indicate they are significantly different from the shaft 1.5 times the mediolateral talar width (MTW) definition (bold). The blue bars represent the tibial shaft only definition, the red bars represent the distal tibia and shaft definition, the purple bar represents the medial-lateral (ML) and anterior-posterior (AP) cross product definition, and the gold bar represents the adapted Yamaguchi approach.
DISCUSSION
This study aimed to determine the minimal tibial field of view to adequately represent a full tibia long-axis. To achieve this, we used four different SI axis definitions and compared them against the mean SI PCA axis of the full tibias. We found that the approach with the smallest angular deviation to the mean SI PCA axis was geometrically fitting a cylinder 1.5 times the MTW starting 5 cm above the tibial plafond and using the long axis of that cylinder as the tibial SI axis (Figure 5). As a result of these findings, we recommend a minimal field of view that extends at least 6.3 cm above the tibial plafond, based on the average MTW. Additionally, a previous study has shown that axial deviations of 2° cause significant shifts in kinematic results (Long et al., 2008). Therefore, if we include all approaches with an angular deviation of less than 2° (shaft axes 1.0x, 1.5x, 2.0x and Yamaguchi adaptation), a range from 4.4 – 10.0 cm above the tibial plafond may be acceptable.
Figure 5:
Illustration of the recommended tibial length field of view and how to calculate it per tibia.
Further notable findings include using the ML or AP axis as the primary axis results in a significantly larger angle deviation than the recommended approach. Similarly, most of the techniques that fit a cylinder to the distal tibia resulted in significantly larger angle deviations compared to the shaft only approaches.
Limitations of this study include a lack of pathological tibia morphologies because only healthy tibias were evaluated. The morphological variations that pathologies present may result in different findings. These morphological variations may include tibial torsion or bowing, which will require additional analyses outside the scope and dataset of this work. Additionally, while this may not be an exhaustive application of every approach, PCA, landmark-based, and geometric-based are the main approaches from the literature. Furthermore, this study employed a method of fitting a cylinder along the long axis of the distal tibia, a technique primarily identified in an extensive literature review by Lenz et al. as the most common approach for defining the SI axis of the distal tibia without using landmarks or PCA (Lenz et al., 2021). While there are alternative methods for deriving an axis from a model of a bone, such as fitting a cylinder to the distal tibial plafond, these were found to be less prevalent. The selection of a cylindrical fit was based on its predominance in current research and its relevance to the objectives of this study.
Beyond these scientific findings, the clinical relevance of our work extends to in vivo bone kinematics. The importance of defining tibial axes consistently and accurately, even with a limited imaging field of view, plays a pivotal role in interpreting kinematic results. If the tibia SI axis definition from a smaller field of view varies greatly from an axis defined from the full-length tibia it will inevitably introduce error as well as make it difficult to draw comparisons between different studies. These results in turn inform clinical decisions in various domains, including orthopaedics, gait analysis, and device design. These insights not only enhance the precision of biomechanical studies in the foot and ankle, but also can play a role in future advancements in clinical imaging protocols to ensure great consistency for providers and their patients.
CONCLUSIONS
When evaluating in vivo tibiotalar kinematics, a standardized coordinate system is essential to compare across patient groups as well as studies from multiple locations. We have shown that with too limited tibia imaging field of views, it is not possible to create a consistent SI axis for the tibia. Therefore, we recommend a minimum field of view to include 1.5 times the MTW starting 5 cm above the tibial plafond.
ACKNOWLEDGEMENTS
Funding provided by Shriners Hospitals for Children (#79146), the University of Utah Undergraduate Research Opportunity Program, and the National Institutes of Health (NIAMS – R01AR083490).
Disclosure of funding
Funding provided by Shriners Hospitals for Children (#79146) and the University of Utah Undergraduate Research Opportunity Program.
ABBREVIATIONS
- AP
Anteroposterior or Anterior/Posterior
- CT
Computed Tomography
- ICP
Iterative Closest Point
- ML
Medial/Lateral
- MTW
Mediolateral Tibial Width
- PCA
Principal Component Analysis
- SI
Superior/Inferior
- 3D
Three-Dimensional
Footnotes
Credit Author Statement
Erika P. Muhlrad: Methodology, Software, Validation, Formal analysis, Writing – Original Draft, Visualization
Andrew C. Peterson: Validation, Writing – Original Draft, Writing – Review & Editing, Visualization
Abigail M. Anderson: Validation, Investigation
Katelyn C. Aragon: Validation, Investigation
Rich J. Lisonbee: Software, Validation, Data curation, Writing – Review & Editing
Bruce A. MacWilliams: Conceptualization, Resources, Writing – Review & Editing
Karen M. Kruger: Conceptualization, Methodology, Resources, Writing – Review & Editing, Supervision, Project administration, Funding acquisition
Amy L. Lenz: Conceptualization, Methodology, Resources, Writing – Review & Editing, Supervision, Project administration, Funding acquisition
Declaration of generative AI and AI-assisted technologies in the writing process
During the preparation of this work the authors used ChatGPT in order to improve the readability and clarity of the work. After using this tool/service, the authors reviewed and edited the content as needed and take full responsibility for the content of the publication.
Declaration of Interest Statement
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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Contributor Information
Erika P. Muhlrad, Department of Orthopaedics, University of Utah, 590 Wakara Way, Salt Lake City, UT 84108, USA.
Andrew C. Peterson, Department of Orthopaedics, University of Utah, 590 Wakara Way, Salt Lake City, UT 84108, USA.
Abigail M. Anderson, Department of Biomedical Engineering, Marquette University, 1515 W Wisconsin Ave, Milwaukee, WI 53233, USA
Katelyn C. Aragon, Department of Biomedical Engineering, Marquette University, 1515 W Wisconsin Ave, Milwaukee, WI 53233, USA.
Rich J. Lisonbee, Department of Orthopaedics, University of Utah, 590 Wakara Way, Salt Lake City, UT 84108, USA.
Bruce A. MacWilliams, Department of Orthopaedics, University of Utah, 590 Wakara Way, Salt Lake City, UT 84108, USA; Motion Analysis Center, Shriners Hospitals for Children-Salt Lake City, 1275 Fairfax Rd, Salt Lake City, UT 84103, USA.
Karen M. Kruger, Department of Biomedical Engineering, Marquette University, 1515 W Wisconsin Ave, Milwaukee, WI 53233, USA; Motion Analysis Center, Shriners Hospitals for Children-Chicago, 2211 N Oak Park Ave, Chicago, IL 60707, USA.
Amy L. Lenz, Department of Orthopaedics, University of Utah, 590 Wakara Way, Salt Lake City, UT 84108, USA; Department of Biomedical Engineering, University of Utah, 36 S Wasatch Dr, Salt Lake City, UT 84112, USA.
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