Statistical, Morphometric, Anatomical Shape Model (Atlas) of Calcaneus

Symmetry of the left and right tibial plafond; a comparison of 75 distal tibia pairs

PURPOSE

Tibia plafond or pilon fractures present a high level of complexity, making their surgical management challenging. Three-Dimensional Virtual Planning (3DVP) can assist in preoperative planning to achieve optimal fracture reduction. This study aimed to assess the symmetry of the left and right tibial plafond and whether left-right mirroring can reliably be used.

METHODS

Bilateral CT scans of the lower limbs of 75 patients without ankle problems or prior fractures of the lower limb were included. The CT images were segmented to create 3D surface models of the tibia. Subsequently, the left tibial models were mirrored and superimposed onto the right tibia models using a Coherent Point Drift surface matching algorithm. The tibias were then cut to create bone models of the distal tibia with a height of 30 mm, and correspondence points were established. The Euclidean distance was calculated between correspondence points and visualized in a boxplot and heatmaps. The articulating surface was selected as a region of interest.

RESULTS

The median left-right difference was 0.57 mm (IQR, 0.38 - 0.85 mm) of the entire tibial plafond and 0.53 mm (IQR, 0.37 - 0.76 mm) of the articulating surface. The area with the greatest left-right differences were the medial malleoli and the anterior tubercle of the tibial plafond.

CONCLUSION

The tibial plafond exhibits a high degree of bilateral symmetry. Therefore, the mirrored unfractured tibial plafond may be used as a template to optimize preoperative surgical reduction using 3DVP techniques in patients with pilon fractures.

A novel method to perform morphological measurements on three-dimensional (3D) models of the calcaneus based on computed tomography (CT)-imaging

Background

While current preoperative and postoperative assessment of the fractured and surgically reconstructed calcaneus relies on computed tomography (CT)-imaging, there are no established methods to quantify calcaneus morphology on CT-images. This study aims to develop a semi-automated method for morphological measurements of the calcaneus on three-dimensional (3D) models derived from CT-imaging.

Methods

Using CT data, 3D models were created from healthy, fractured, and surgically reconstructed calcanei. Böhler's angle (BA) and Critical angle of Gissane (CAG) were measured on conventional lateral radiographs and corresponding 3D CT reconstructions using a novel point-based method with semi-automatic landmark placement by three observers. Intraobserver and interobserver reliability scores were calculated using intra-class correlation coefficient (ICC). In addition, consensus among observers was calculated for a maximal allowable discrepancy of 5 and 10 degrees for both methods.

Results

Imaging data from 119 feet were obtained (40 healthy, 39 fractured, 40 reconstructed). Semi-automated measurements on 3D models of BA and CAG showed excellent reliability (ICC: 0.87-1.00). The manual measurements on conventional radiographs had a poor-to-excellent reliability (ICC: 0.22-0.96). In addition, the percentage of consensus among observers was much higher for the 3D method when compared to conventional two-dimensional (2D) measurements.

Conclusions

The proposed method enables reliable and reproducible quantification of calcaneus morphology in 3D models of healthy, fractured and reconstructed calcanei.

Talus-derived reference coordinate system for 3D calcaneal assessment: A novel approach to improve morphological measurements

In 3D-analysis of the calcaneus, a consistent coordinate system aligned with the original anatomical directions is crucial for pre- and postoperative analysis. This importance stems from the calcaneus's key role in weight-bearing and biomechanical alignment. However, defining a reliable coordinate system based solely on fractured or surgically reconstructed calcanei presents significant challenges. Given its anatomical prominence and consistent orientation, the talus offers a potential solution to this challenge. Our work explores the feasibility of talus-derived coordinate systems for 3D-modeling of the calcaneus across its various conditions. Four methods were tested on nonfractured, fractured and surgically reconstructed calcanei, utilizing Principal Component Analysis, anatomical landmarks, bounding box, and an atlas-based approach. The methods were compared with a self-defined calcaneus reference coordinate system. Additionally, the impact of deviation of the coordinate system on morphological measurements was investigated. Among methods for constructing nonfractured calcanei coordinate systems, the atlas-based method displayed the lowest Root Mean Square value in comparison with the reference coordinate system. For morphological measures like Böhler's Angle and the Critical angle of Gissane, the atlas talus-based system closely aligned with ground truth, yielding differences of 0.6° and 1.2°, respectively, compared to larger deviations seen in other talus-based coordinate systems. In conclusion, all tested methods were feasible for creating a talus derived coordinate system. A talus derived coordinate system showed potential, offering benefits for morphological measurements and clinical scenarios involving fractured and surgically reconstructed calcanei. Further research is recommended to assess the impact of these coordinate systems on surgical planning and outcomes.

Morphometric Analysis of the Calcaneus in a Southeast Asian Population

Introduction The calcaneus is the most commonly fractured tarsal bone, accounting for up to 60% of tarsal bone fractures and 2% of all fractures in the body. With the calcaneus playing an important role in maintaining a stable and efficient bipedal gait, the sequelae of these injuries have also been associated with potential long-term disability or discomfort, especially if improperly managed. Incorrectly sized implants similarly cause their own set of complications, such as poor fixation, impingement, or implant prominence. This potentially increases the need for revision surgery or implant removal, with increased morbidity for the patient. As such, a thorough understanding of calcaneal morphology is vital to ensure optimal conservative and surgical management of calcaneal pathology. CT imaging has become an indispensable tool in the evaluation of such a complex three-dimensional structure and allows us to accurately map out calcaneal morphology. This study aims to evaluate calcaneal morphology in the Southeast Asian population using CT imaging and to determine if morphological differences exist between male and female patients. Methods Calcaneus measurements were taken from CT scans of 100 patients with intact calcanei, consisting of 34 female and 66 male patients. Patients who have had fractures or previous calcaneus surgery were excluded. IBM SPSS Statistics for Windows, Version 28.0 (Released 2021; IBM Corp., Armonk, NY, USA) was used for statistical calculations. Mean values were calculated, and t-tests were performed to establish any significant differences between measurements taken from male and female patients. Results were deemed to have a significant difference if the p-value was less than 0.05. Results Males had larger calcanei measurements than females in all parameters included. Calcaneal length in females measured on CT axial views was 66.2 mm, compared to 75.2 mm in males (p < 0.001). Calcaneal height, measured at the medial wall, was 28.2 mm in females and 33.9 mm in males (p < 0.001). Calcaneal height measured at the lateral wall was 33.3 mm and 38.1 mm in females and males, respectively (p > 0.001). Calcaneal width was 33.0 mm in females and 36.9 mm in males (p < 0.001). The mean dimensions measured in the total sample were an axial length of 72.1 mm, a medial wall height of 32.0 mm, a lateral wall height of 36.4 mm, and a width of 35.6 mm. Conclusion There is a significant difference in calcaneal morphology on CT imaging between male and female patients in the Southeast Asian population, which is an important consideration for surgical planning and the selection of appropriately sized implants.

Unique shape variations of hind and midfoot bones in flatfoot subjects-A statistical shape modeling approach

Flatfoot deformity is a prevalent hind- and midfoot disorder. Given its complexity, single-plane radiological measurements omit case-specific joint interaction and bone shape variations. Three-dimensional medical imaging assessment using statistical shape models provides a complete approach in characterizing bone shape variations unique to flatfoot condition. This study used statistical shape models to define specific bone shape variations of the subtalar, talonavicular, and calcaneocuboid joints that characterize flatfoot deformity, that differentiate them from healthy controls. Bones of the aforementioned joints were segmented from computed tomography scans of 40 feet. The three-dimensional hindfoot alignment angle categorized the population into 18 flatfoot subjects (≥7° valgus) and 22 controls. Statistical shape models for each joint were defined using the entire study cohort. For each joint, an average weighted shape parameter was calculated for each mode of variation, and then compared between flatfoot and controls. Significance was set at p < 0.05, with values between 0.05 ≤ p < 0.1 considered trending towards significance. The flatfoot population showed a more adducted talar head, inferiorly inclined talar neck, and posteriorly orientated medial subtalar articulation compare to controls, coupled with more navicular eversion, shallower navicular cup, and more prominent navicular tuberosity. The calcaneocuboid joint presented trends of a more adducted calcaneus, more abducted cuboid, narrower calcaneal roof, and less prominent cuboid beak compared to controls. Statistical shape model analysis identified unique shape variations which may enhance understanding and computer-aided models of the intricacies of flatfoot, leading to better diagnosis and, ultimately, surgical treatment.

Biomechanical Insights Afforded by Shape Modeling in the Foot and Ankle

Advancements in volumetric imaging makes it possible to generate high-resolution three-dimensional reconstructions of bones in throughout the foot and ankle. The use of weightbearing computed tomography allows for the analysis of joint relationships in a consistent natural position that can be used for statistical shape modeling. Using statistical shape modeling, a population-based statistical model is created that can be used to compare mean bone shape morphology and identify anatomical modes of variation. A review is presented to highlight the current work using statistical shape modeling in the foot and ankle with a future view of the impact on clinical care.

Multi-level multi-domain statistical shape model of the subtalar, talonavicular, and calcaneocuboid joints

Traditionally, two-dimensional conventional radiographs have been the primary tool to measure the complex morphology of the foot and ankle. However, the subtalar, talonavicular, and calcaneocuboid joints are challenging to assess due to their bone morphology and locations within the ankle. Weightbearing computed tomography is a novel high-resolution volumetric imaging mechanism that allows detailed generation of 3D bone reconstructions. This study aimed to develop a multi-domain statistical shape model to assess morphologic and alignment variation of the subtalar, talonavicular, and calcaneocuboid joints across an asymptomatic population and calculate 3D joint measurements in a consistent weightbearing position. Specific joint measurements included joint space distance, congruence, and coverage. Noteworthy anatomical variation predominantly included the talus and calcaneus, specifically an inverse relationship regarding talar dome heightening and calcaneal shortening. While there was minimal navicular and cuboid shape variation, there were alignment variations within these joints; the most notable is the rotational aspect about the anterior-posterior axis. This study also found that multi-domain modeling may be able to predict joint space distance measurements within a population. Additionally, variation across a population of these four bones may be driven far more by morphology than by alignment variation based on all three joint measurements. These data are beneficial in furthering our understanding of joint-level morphology and alignment variants to guide advancements in ankle joint pathological care and operative treatments.

Assessment of Hindfoot Alignment Comparing Weightbearing Radiography to Weightbearing Computed Tomography

BACKGROUND

Hindfoot alignment view (HAV) radiographs are widely utilized for 2-dimensional (2D) radiographic assessment of hindfoot alignment; however, the development of weightbearing computed tomography (WBCT) may provide more accurate methods of quantifying 3-dimensional (3D) hindfoot alignment. The aim of this study was to compare the 2D calcaneal moment arm measurements on HAV radiographs with WBCT.

METHODS

This retrospective cohort study included 375 consecutive patients with both HAV radiographs and WBCT imaging. Measurement of the 2D hindfoot alignment moment arm was compared between both imaging modalities. The potential confounding influence of valgus/varus/neutral alignment, presence of hardware, and motion artifact were further analyzed.

RESULTS

The intraclass correlation coefficients (ICCs) of interobserver and intraobserver reliability for measurements with both imaging modalities were excellent. Both modalities were highly correlated (Spearman coefficient, 0.930; P < .001). HAV radiographs exhibited a mean calcaneal moment arm difference of 3.9 mm in the varus direction compared with WBCT (95% CI, -4.9 to 12.8). The difference of hindfoot alignment between both modalities was comparable in subgroups with neutral/valgus/varus alignment, presence of hardware, and motion artifact.

CONCLUSION

Both HAV radiographs and WBCT are highly reliable and highly correlated imaging methods for assessing hindfoot alignment. Measurements were not influenced by severe malalignment, the presence of hardware, or motion artifact on WBCT. On average, HAV radiographs overestimated 3.9 mm of varus alignment as compared with WBCT.

LEVEL OF EVIDENCE

Level III, retrospective comparative study.

Morphological analysis of Gissane's angle utilising a statistical shape model of the calcaneus

INTRODUCTION

Gissane's crucial angle (GA) facilitates to diagnose calcaneal fractures, and serves as an indicator of the quality of anatomical reduction after fixation. The study aimed to utilise statistical shape models (SSM) for analysing the complex 3D surface anatomy of the calcaneus represented by the simplified GA measurement on lateral radiographs.

MATERIALS AND METHODS

SSMs were generated from CT scans of paired adult calcanei from 10 Japanese and 31 Thai specimens. GA measurements in 3D and 2D were obtained for the lateral, central and medial anatomy of the posterior facet and sinus tarsi. The correlation between calcaneal length and GA was analysed. Regression and principal component (PC) analyses were conducted for analysing morphological variability in calcaneal shape relating to GA. The bilateral symmetry of the obtained measurements was analysed.

RESULTS

The mean GA (lateral) for the Japanese specimens was 105.1° ± 7.5 and 105.4° ± 8.5 for the Thai. The projected 2D angles of the central and medial measurements were larger (P < 0.00) than the 3D values. The medial projected 2D angles were larger (P ≤ 0.02) compared to the lateral. Despite the bilateral symmetry of GA and calcaneal length, their correlation displayed clear signs of asymmetry, which was confirmed by regression and PC analyses.

CONCLUSIONS

Japanese and Thai specimens revealed lower GAs (both range and mean) compared to reported reference values of other ethnicities. As a reduced GA is generally indicative of a calcaneal fracture, our results are important to surgeons for their diagnostic assessment of Japanese and Thai patients. The results indicate that the GA measurement on a plain radiograph is a simplified representation of the lateral-to-central 3D calcaneal anatomy but significantly underestimates the angle measurement on the medial aspects of the respective surface areas.

Statistical shape modeling of the talocrural joint using a hybrid multi-articulation joint approach

Historically, conventional radiographs have been the primary tool to morphometrically evaluate the talocrural joint, which is comprised of the distal tibia, distal fibula, and proximal talus. More recently, high-resolution volumetric imaging, including computed tomography (CT), has enabled the generation of three-dimensional (3D) reconstructions of the talocrural joint. Weightbearing cone-beam CT (WBCT) technology provides additional benefit to assess 3D spatial relationships and joint congruency while the patient is load bearing. In this study we applied statistical shape modeling, a computational morphometrics technique, to objectively quantify anatomical variation, joint level coverage, joint space distance, and congruency at the talocrural joint. Shape models were developed from segmented WBCT images and included the distal tibia, distal fibula, and full talus. Key anatomical variation across subjects included the fibular notch on the tibia, talar trochlea sagittal plane rate of curvature, tibial plafond curvature with medial malleolus prominence, and changes in the fibular shaft diameter. The shape analysis also revealed a highly congruent talocrural joint with minimal inter-individual morphometric differences at the articular regions. These data are helpful to improve understanding of ankle joint pathologies and to guide refinement of operative treatments.

Healthy ankle and hindfoot kinematics during gait: Sex differences, asymmetry and coupled motion revealed through dynamic biplane radiography

The aims of this study were to compare male versus female and dominant versus non-dominant kinematics in the ankle and hindfoot, and to characterize coupled motion between the subtalar and tibiotalar joints during the support phase of gait. Twenty healthy adults walked on a laboratory walkway while synchronized biplane radiographs of the ankle and hindfoot were collected at 100 frames/s. A validated tracking technique was used to measure tibiotalar and subtalar kinematics. Differences between male and female range of motion (ROM) were observed only in tibiotalar (AP and ML) and subtalar (ML) translation (all differences<1 mm and all p < 0.04). Statistical parametric mapping identified differences between kinematics waveforms of males and females in tibiotalar translation (AP and ML) and eversion, and subtalar ML translation. No differences between dominant and non-dominant sides were observed in ROM or kinematics waveforms. The average absolute side-to-side difference in the kinematics waveforms was 4.1° and 1.5 mm or less for all rotations and translations, respectively. Tibiotalar plantarflexion was coupled to subtalar inversion and eversion during the impact and push-off phases of stance (r = 0.90 and r = 0.87, respectively). This data may serve as a guide for evaluating ankle kinematics waveforms, ROM, symmetry, and restoration of healthy coupled motion after surgical intervention or rehabilitation. The observed kinematics differences between males and females may predispose females to higher rates of ankle and knee injury and suggest sex-dependent ankle reconstruction techniques may be beneficial.

Morphologic analysis of the subtalar joint using statistical shape modeling

Weightbearing computed tomography (WBCT) enables visualization of the foot and ankle as patients stand under load. Clinical measurements of WBCT images are generally limited to two-dimensions, which reduces the ability to quantify complex morphology of individual osseous structures as well as the alignment between two or more bones. The shape and orientation of the healthy/normal subtalar joint, in particular, is not well-understood, which makes it very difficult to diagnose subtalar pathoanatomy. Herein, we employed statistical shape modeling to evaluate three-dimensional (3D) shape variation, coverage, space, and congruency of the subtalar joint using WBCT data of 27 asymptomatic healthy individuals. The four most relevant findings were: (A) talar and calcaneal anatomical differences were found regarding the presence of (a) the talar posterior process, (b) calcaneal pitch, and (c) curvature of the calcaneal posterior facet; (B) the talar posterior facet articular surface area was significantly greater than the calcaneal posterior facet articular surface area; (C) the posterior facet varied in joint space distance, whereas the anteromedial facet was even; and (D) the posterior and anteromedial facet of the subtalar joint was consistently congruent. Despite considerable shape variation across the population, the posterior and anteromedial articular facets of the subtalar joint were consistently congruent. Results provide a detailed 3D analysis of the subtalar joint under a weightbearing condition in a healthy population which can be used for comparisons to pathological patient populations. The described SSM approach also shows promise for clinical evaluation of the subtalar joint from 3D surface reconstructions of WBCT images.

Development and validation of statistical shape models of the primary functional bone segments of the foot

Introduction

Musculoskeletal models are important tools for studying movement patterns, tissue loading, and neuromechanics. Personalising bone anatomy within models improves analysis accuracy. Few studies have focused on personalising foot bone anatomy, potentially incorrectly estimating the foot’s contribution to locomotion. Statistical shape models have been created for a subset of foot-ankle bones, but have not been validated. This study aimed to develop and validate statistical shape models of the functional segments in the foot: first metatarsal, midfoot (second-to-fifth metatarsals, cuneiforms, cuboid, and navicular), calcaneus, and talus; then, to assess reconstruction accuracy of these shape models using sparse anatomical data.

Methods

Magnetic resonance images of 24 individuals feet (age = 28 ± 6 years, 52% female, height = 1.73 ± 0.8 m, mass = 66.6 ± 13.8 kg) were manually segmented to generate three-dimensional point clouds. Point clouds were registered and analysed using principal component analysis. For each bone segment, a statistical shape model and principal components were created, describing population shape variation. Statistical shape models were validated by assessing reconstruction accuracy in a leave-one-out cross validation. Statistical shape models were created by excluding a participant’s bone segment and used to reconstruct that same excluded bone using full segmentations and sparse anatomical data (i.e. three discrete points on each segment), for all combinations in the dataset. Tali were not reconstructed using sparse anatomical data due to a lack of externally accessible landmarks. Reconstruction accuracy was assessed using Jaccard index, root mean square error (mm), and Hausdorff distance (mm).

Results

Reconstructions generated using full segmentations had mean Jaccard indices between 0.77 ± 0.04 and 0.89 ± 0.02, mean root mean square errors between 0.88 ± 0.19 and 1.17 ± 0.18 mm, and mean Hausdorff distances between 2.99 ± 0.98 mm and 6.63 ± 3.68 mm. Reconstructions generated using sparse anatomical data had mean Jaccard indices between 0.67 ± 0.06 and 0.83 ± 0.05, mean root mean square error between 1.21 ± 0.54 mm and 1.66 ± 0.41 mm, and mean Hausdorff distances between 3.21 ± 0.94 mm and 7.19 ± 3.54 mm. Jaccard index was higher (P < 0.01) and root mean square error was lower (P < 0.01) in reconstructions from full segmentations compared to sparse anatomical data. Hausdorff distance was lower (P < 0.01) for midfoot and calcaneus reconstructions using full segmentations compared to sparse anatomical data.

Conclusion

For the first time, statistical shape models of the primary functional segments of the foot were developed and validated. Foot segments can be reconstructed with minimal error using full segmentations and sparse anatomical landmarks. In future, larger training datasets could increase statistical shape model robustness, extending use to paediatric or pathological populations.

Bilateral Symmetry, Sex Differences, and Primary Shape Factors in Ankle and Hindfoot Bone Morphology

Background:

Ankle injuries and joint degeneration may be related to ankle bone morphology. Little data exist to characterize healthy hindfoot bone morphology. The purpose of this study was to characterize side-to-side symmetry and sex differences in ankle and hindfoot bone morphology, and to identify the primary shape factors that differentiate ankle and hindfoot bone morphology among individuals.

Methods:

Computed tomography was used to create 3D surface models of the distal tibia, talus, and calcaneus for 40 ankle and hindfoot bones from 20 healthy individuals. Morphologic differences between left and right bones of the same individual and between males and females were determined. Statistical shape modeling was performed to identify primary shape variations among individuals.

Results:

Side-to-side differences in bone morphology averaged 0.79 mm or less. The average distal tibia in males was larger overall than in females. No significant sex difference was noted in the tali. The average female calcaneus was longer and thinner than the average male calcaneus. Variability in ankle and hindfoot bone morphology is primarily associated with articulating surface shape, overall length and width, and tendon/ligament attachment points.

Conclusion:

In general, the contralateral ankle can serve as an accurate guide for operative restoration of native ankle morphology; however, specific regions demonstrate higher asymmetry.

Clinical Relevance:

Knowledge of regions of high and low bilateral symmetry can improve hindfoot and ankle reconstruction. Design of ankle prostheses can be improved by accounting for differences in bone morphology associated with sex and shape differences among individuals.

Hind- and midfoot bone morphology varies with foot type and sex

Foot type has been associated with pain, injury, and altered gait mechanics. Morphological variations in foot bones due to foot type variation may impact surgical and therapeutic treatments. The purpose of this study was to utilize principal component analysis (PCA) to determine how morphology of the hind- and midfoot bones differs among foot types and sex. The calcaneus, talus, navicular, and cuboid were segmented using previously obtained computed tomography (CT) scans and converted to surface models. The CTs were sorted into four foot types-cavus, neutrally aligned, asymptomatic planus, and symptomatic planus. Morphometric shape analysis software (Geomorph) was used to perform a PCA to determine which components varied between foot types and between sexes. The calcaneus showed planus feet of both types to have calcanei that have decreased height and increased length compared to neutrally aligned feet. The talus demonstrated increased posterior mass for cavus feet compared to neutrally aligned feet. For the navicular, symptomatic planus had a more posteriorly positioned tuberosity and were wider than asymptomatic planus feet. The cuboid did not exhibit any differences between foot types. Sex differences, found only at the talus and navicular, were subtle. PCA is an objective technique that helped elucidate differences in bone morphology between foot types and sex without needing to determine the features of interest before comparing groups. Understanding these variations can help inform diagnosis of foot pathologies and surgical protocols as well as improve computer models of the foot. Published 2018. This article is a U.S. Government work and is in the public domain in the USA. J Orthop Res 9999:1-16, 2019.

Statistical shape models of cuboid, navicular and talus bones

BACKGROUND

The aim was to develop statistical shape models of the main human tarsal bones that would result in novel representations of cuboid, navicular and talus.

METHODS

Fifteen right and 15 left retrospectively collected computed tomography data sets from male individuals, aged from 17 to 63 years, with no known foot pathology were collected. Data were gathered from 30 different subjects. A process of model building includes image segmentation, unifying feature position, mathematical shape description and obtaining statistical shape geometry.

RESULTS

Orthogonal decomposition of bone shapes utilising spherical harmonics was employed providing means for unique parametric representation of each bone. Cross-validated classification results based on parametric spherical harmonics representation showed high sensitivity and high specificity greater than 0.98 for all considered bones.

CONCLUSIONS

The statistical shape models of cuboid, navicular and talus created in this work correspond to anatomically accurate atlases that have not been previously considered. The study indicates high clinical potential of statistical shape modelling in the characterisation of tarsal bones. Those novel models can be applied in medical image analysis, orthopaedics and biomechanics in order to provide support for preoperative planning, better diagnosis or implant design.