Impact of weightbearing on progressive collapsing foot deformity shape

Abstract

Aims

Weightbearing CT (WBCT) has set a new standard for the assessment of foot and ankle alignment in patients with progressive collapsing foot deformity (PCFD) under physiological loading conditions compared with conventional CT. Principal component analysis (PCA) models are currently used for a detailed 3D shape analysis, but are not able to take into account non-linear (e.g. rotational) anatomical variance, which is particularly relevant in PCFD. Innovative advances in geometrical morphometrics by principal polynomial shape analysis (PPSA) are now able to overcome this challenge. Therefore, the objective of this study was to evaluate the use of PPSA in identifying distinct morphological patterns in patients with PCFD under weightbearing conditions.

Methods

In this retrospective comparative study, 40 feet from 20 PCFD bilateral patients imaged by WBCT were confirmed eligible for analysis. Subsequently, matched controls were selected from a cohort of patients who underwent WBCT imaging for clinical follow-up of disorders unrelated to the foot. From the WBCT images, 3D models were reconstructed and registered. PPSA was applied to the 3D foot models to identify and delineate morphology variations in foot shape between the PCFD and control group.

Results

Automated classification of PCFD by linear discriminant analysis using the PPSA model yielded a sensitivity of 92.5% and specificity of 92.5%. Furthermore, PPSA revealed distinct foot morphology components in the PCFD group. Anatomical differences were significant and most pronounced at the level of the talocalcaneonavicular joint, with prominent internal and plantar rotation of the talar bone (p < 0.001).

Conclusion

This study is the first to apply PPSA in patients with PCFD. The findings validate distinct 3D spatial position alterations compared with control subjects. More specifically, they demonstrate that the talocalcaneonavicular joint complex is the most affected structure.

Cite this article: Bone Jt Open 2025;6(12):1566–1574.

Introduction

Progressive collapsing foot deformity (PCFD), formerly known as adult-acquired flatfoot deformity (AAFD), is a complex 3D disorder characterized by valgus of the hindfoot, planus of the longitudinal arch, and abduction of the forefoot.¹ The introduction of weightbearing CT (WBCT) imaging enables the assessment of complex multiplanar deformities and joint subluxations under physiological loading conditions compared with conventional CT.² While WBCT is gaining traction in clinical practice, the understanding of how weightbearing affects the foot’s complex 3D alignment is still developing.^3,4 Previous studies have attempted to characterize the morphological changes in PCFD by means of WBCT using heterogeneous alignment parameters,^5,6 but relied on discrete evaluations (rotations, angles, distances) of the foot, resulting in a somewhat fragmented understanding of the PCFD’s structural complexity due the lack of 3D tools that comprehensively describe 3D shape.⁷

Geometrical morphometrics based on principal component analysis (PCA) provide a robust and accurate statistical shape modelling (SSM) approach to characterize anatomical variations across populations.⁸ By analyzing sets of homologous landmarks, this method extracts quantitative information about shape, enabling the application of conventional multivariate statistical techniques to describe the anatomical variability of an entire population.⁸ Unlike previous methods, this data-driven approach offers precise parametrizations of individual morphologies, opening up new avenues for investigating anatomical distributions and their implications for medical diagnosis, classification, and treatment.⁹ Although the technique has been recently suggested as an innovative alternative to study PCFD, its application should be performed with caution.¹⁰ PCA is a linear dimensionality technique, which will enforce linearity and decompose the shape data in a combination of linear-only shape variants, of which the clinical interpretation is meaningless. Therefore, the technique is inherently limited to study complex anatomical variations that involve mainly rotational and non-linear deformity patterns such as alterations in foot arch geometry.¹¹ This limitation of geometrical morphometric analysis was recently resolved by the introduction of principal polynomial shape analysis (PPSA), capable of capturing complex non-linear patterns by means of polynomial approximations.¹²

The primary objective of this study was therefore to explore the benefits of PPSA in the analysis of foot shape change under weightbearing conditions in patients with PCFD. We hypothesized that adopting a non-linear methodology would significantly benefit the clinical interpretability of the observed structural variations in PCFD, and allow for reliable automated classification between healthy subjects and PCFD patients.

Methods

Ethical compliance

This investigation complied with the Declaration of Helsinki and its subsequent amendments,¹³ receiving ethical clearance from the Institutional Review Board, and documented with the registration number B6702022000639. All participants signed an informed consent form. Furthermore, compliance with the STROBE (Strengthening the Reporting of Observational Studies in Epidemiology) guidelines ensured complete and adequate reporting on the study design and methodology.

Study design and subjects

We retrospectively reviewed our CT database for subjects who underwent full lower limb or isolated foot and ankle WBCT scanning, performed at the Ghent University Hospital between August 2023 and July 2024. A total of 114 scans were performed during this period, out of which 20 PCFD patients eligible for inclusion were identified.

For the PCFD group, inclusion criteria involved age between 18 and 65 years old, bilateral involvement, and radiological PCFD confirmation. Initial clinical PCFD diagnosis by the referring foot and ankle surgeon (AB) was consequently positively confirmed by the handling musculoskeletal radiologist (AVO) by a hindfoot angle < 0° and a tarsometatarsal angle < -4°. Exclusion criteria were presence of osteoarthritis (Kellgren-Lawrence > grade 1), osseous foot coalitions, previous surgery, and talar tilt within the ankle mortise. According to the Consensus Group Classification of Progressive Collapsing Foot Deformity,^14,15 14 cases were classified as class B and six cases were class C.

Subsequently, matched healthy controls were retrospectively selected from the same WBCT cohort. Inclusion criteria were imaging for clinical follow-up of conditions unrelated to foot and ankle deformity (trauma, follow-up of hip- and knee-related disorders, hip and/or knee cartilage lesions, and sprains to rule out avulsion fractures). Exclusion criteria were presence of osteoarthritis (Kellgren-Lawrence > grade 1), osseous foot coalitions, previous surgery, and planovalgus/cavovarus deformity (hindfoot angle < 0° or > 6° and/or tarsometatarsal angle < -4° or > 4°). The inclusion and exclusion criteria of both the PCFD patients and control subjects on the database cohort were applied by JL (a board-certified orthopaedic surgeon). Two fellowship-trained foot and ankle surgeons (MP, AB) independently validated the patient selection, excluding any inconsistent cases.

The HiRise imaging device (Curvebeam, USA) was used with the following settings: tube voltage: 130 kV; tube current: 6.5 mAs; pixel size: 0.5 mm; and slice thickness: 0.5 mm. The WBCT images were exported in the Digital Imaging and Communications in Medicine (DICOM) format to the commercially available Materialise’s Interactive Medical Image Control System (Mimics v24.0, Materialise, Belgium). In Mimics, relevant bony structures of the hind-, mid-, and forefoot were segmented semiautomatically and manually corrected. The segmented foot bone structures were reconstructed into 3D models and exported in stereolithography (STL) file format for subsequent analysis the dedicated open-source MATLAB toolboxes: PPSA Builder and SSM Builder.

Subject demographic details

No significant demographic differences were found between the PCFD and healthy group. Table I provides a detailed summary of the subject characteristics.

Table I.

Demographic data of the study cohort.

Characteristic	PCFD (n = 20)	Healthy controls (n = 20)	FDR
Mean age, yrs (range; SD)	48.1 (18 to 65; 14.0)	43.7 (22 to 64; 12.3)	0.31
Mean weight, kg (range; SD)	85.5 (58 to 125; 20.0)	79.3 (59 to 103; 14.2)	0.36
Mean height, cm (range; SD)	172.7 (152 to 200; 9.9)	168.6 (156 to 183; 7.4)	0.31
Mean BMI, kg/m² (range; SD)	28.4 (20.06 to 40.82; 5.6)	28.0 (19.04 to 41.09; 5.3)	0.74
Side (left/right), n	20/20	20/20
Sex (male/female), n	5/15	5/15

FDR, false discovery rate; PCFD, progressive collapsing foot deformity.;

Registration and shape model construct

Starting from the segmented structures, dense anatomical point correspondence was established using elastic registration of an isotropic template mesh of the foot comprising 34,362 vertices. This was achieved through non-rigid mapping of an anthropometric mask (quasi-landmarks) onto the original 3D reconstructions using established point/surface matching techniques. Consequently, all relevant structures were represented by a homologous series of dense landmarks, essential for geometrical morphometric analysis and the statistical analysis of the foot shape. Following, a robust least squares (Procrustes) superimposition of all feet was performed based on the alignment of the weightbearing tripod (most plantar point of the sesamoids, fifth metatarsal, and calcaneus). For each subject, both right and left morphologies were available. All left geometries were reflected into a right-sided geometry. The corrected mean and shape variation was derived by PPSA, using a second-order polynomial and capturing 95% of the data’s variance. All registration and shape model construct were performed using MATLAB Central File Exchange.¹⁶

Several automated measurements (Kite angle, Calcaneal pitch angle, ….) were performed on all 3D foot models to quantify the alignment, based on previous work.⁵

To quantitatively evaluate the generated 3D shape models, we employed the following performance metrics: root mean squared error (RMSE) between model predictions and in-training-set landmarks to assess in-model accuracy, cumulative variance as an indicator of model compactness, and RMSE of model predictions for unseen samples in a leave-one-out cross-validation framework to evaluate out-of-model accuracy or generalization.

Difference between PCFD and healthy foot models

To analyze differences in foot bone geometry between the PCFD and healthy foot groups, we first calculated and compared the mean shapes of both datasets. Here, a distance map was generated to visualize pointwise surface variations between the mean PCFD and mean healthy foot models. Subsequently, a pointwise statistical analysis using independent-samples t-tests (α = 0.05) was performed to identify significant shape variations between the two groups. This analysis evaluated the distribution of pointwise deviations (residuals) from the combined cohort’s mean shape in the X (mediolateral), Y (anteroposterior), and Z (superoinferior) directions.

The anatomical healthy-disease relationship was evaluated by means of canonical correlation analysis (CCA). In particular, the principal component (PC) weights of the mixed model containing both healthy and PCFD cases was defined as the training data. Following the PC loadings serving as predictor variables for the observed PCFD (+ 1) either healthy (−1), were used. Overall explained variance in the observed shape components of the PCFD patients was evaluated by means of partial least squares (PLS) regression. The diagnostic potential of the constructed models was assessed by training a classifier using linear discriminant analysis (LDA), with classifications accuracy evaluated trough a k-fold leave-one-out cross-validation. The measurements (separately and combined), linear PCA as non-linear PPSA-based predictions, were all tested for their sensitivity and specificity in automated diagnosis.

Statistical analysis

A matched-pair design was employed based on age, weight, height, and BMI. The Shapiro-Wilk test was used to assess data normality for each variable in both cohorts. The Wilcoxon signed-rank test was used to evaluate differences in the matching criteria between the PCFD cases and their matched controls. A p-value < 0.05 was considered statistically significant. Independent-samples t-tests were performed at each vertex to assess pointwise morphological differences between the healthy and PCFD foot models, with statistical significance set at α = 0.05. CCA was used to assess the multivariate association between foot shape and PCFD diagnosis, and the associated p-value was obtained from the canonical correlation test statistics. LDA was used to classify PCFD versus healthy subjects, with classification performance evaluated using sensitivity and specificity. All analyses were performed using MATLAB R2022b (MathWorks, USA) with the Statistics and Machine Learning Toolbox.

Results

Table II presents the values of imaging automated measurements for each group, along with sensitivity and specificity for each separate measurement.

Table II.

Values of imaging automated measurements for the healthy and progressive collapsing foot deformity (PCFD) groups, along with the sensitivity and specificity for each separate measurement to classify PCFD.

Measurement	PCFD values	Healthy values	Sensitivity, %	Specificity, %
AP view
Meary’s angle, ° (- = abduction, + = adduction)	-22.01 (-45.86 to 1.25)	-3.98 (-26.38 to 42.53)	82.5	62.5
Kite angle, ° (- = abduction, + = adduction)	-30.01 (-40.02 to -13.27)	-25.05 (-43.59 to -5.07)	60	50
Hindfoot alignment, ° (- = varus, + = valgus)	1.23 (-7.87 to 8.72)	-2.54 (-10.40 to 5.62)	62.5	70
TNCA, ° (- = adduction, + = abduction)	13.51 (3.63 to 23.13)	8.19 (-16.95 to 22.77)	67.5	55
Lateral view
Meary’s angle, ° (+ = cavus, - = planus)	-9.05 (-27.82 to 5.46)	10.93 (-0.20 to 34.67)	87.5	97.5
Kite angle, °	-35.89 (-50.65 to -28.22)	-33.97 (-43.26 to -24.03)	55	57.8
Calcaneal pitch angle, °	15.85 (9.38 to 22.54)	24.74 (9.13 to 37.92)	87.5	75
Total			92.5	87.5

AP, anteroposterior; PCFD, progressive collapsing foot deformity; TNCA, talonavicular coverage angle.

Principal components of foot models

PPSA was used to determine the principal components of foot morphology in the PCFD, and healthy feet (Figure 1 and Figure 2). In the healthy group, the first three PCs explained 75.1% of the total variance. PC1 (40.6%) primarily represented abduction/adduction variability of the talus. PC2 (21.4%) was predominantly associated with the inclination (pitch) of the calcaneus and overall foot size. PC3 (13.1%) did not correspond to a distinct morphological variation. Within the PCFD group, the initial three PCs accounted for 66.3% of the total variance. PC1 (36.0%) primarily captured varus/valgus deviations in calcaneal morphology and midfoot abduction. PC2 (17.8%) was mainly associated with joint space width at the metatarsophalangeal level, while PC3 (12.5%) predominantly reflected variations in foot bone width.

Fig. 1.

Superior view on the principal polynomial shape analysis (PPSA) results for the healthy (top) and progressive collapsing foot deformity (PCFD; bottom) models. Each model illustrates the mean shape along with its first three principal modes of variation within its 98% CI limits.

Fig. 2.

Medial view on the principal polynomial shape analysis (PPSA) results for the healthy (top) and progressive collapsing foot deformity (PCFD; bottom) models. Each model illustrates the mean shape along with its first three principal modes of variation within its 98% CI limits.

Mean differences between PCFD and healthy control group

Significant morphological differences were identified between the average models of the PCFD (right) group and the healthy (left) control group. Overlaying the healthy models onto the PCFD models (right) and plotting the distance maps revealed deviations of up to 19.80 mm, primarily at the talonavicular joint (Figure 3). Figure 4 shows the calculated differences along the three coordinate axes (X, Y, and Z).

Fig. 3.

Distance plot between the average healthy and progressive collapsing foot deformity (PCFD) shape, highlighting the most pronounced difference at the talonavicular level.

Fig. 4.

Pointwise significance plot between the healthy and progressive collapsing foot deformity groups for each directional axis. Statistically significant regions are coloured in yellow.

Shape model evaluation

Figure 5 presents the model compactness as cumulative explained variance of the healthy and PCFD models as a function of the increasing number of PCA either PPSA components. Model compactness mounted to 36% in the PCFD model for the first PC when applying the non-linear PPSA method, as opposed to 29.9% in case linear PCA was used. The RMSE of the PPSA model, averaged 2.68 mm for the PCFD model and 2.65 mm for the healthy model when evaluating in-sample model accuracy, whereas the out-of-sample accuracy (generalizability) was 2.71 mm for the healthy and 2.75 mm model for the PCFD model.

Fig. 5.

Cumulative variance of the principal component analysis (PCA; red) and principal polynomial shape analysis (PPSA; blue) by increasing number of components, for the healthy (left) and progressive collapsing foot deformity (PCFD; right) model.

Effect size and automated PCFD classification

Based on CCA, the relationship between foot shape and PCFD diagnosis showed a strong canonical correlation (r = 0.87, p < 0.001). Using the same ten shape modes, PLS regression demonstrated that these modes explained 76.3% of the variance in the PCFD outcome. Impact of PCFD on foot morphology (mean shape model consisting of the first ten principal components) obtained following the CCA is demonstrated in Figure 6. Canonical scores were tripled to enhance visualization of collapse effects. For automated classification of PCFD using LDA, both the PCA and PPSA models using the first PC achieved a sensitivity and specificity of 92.5% (95% CI 80.1% to 97.4%). In comparison, when using all seven measurements (Table II), the classification achieved sensitivity of 92.5% (95% CI 80.1% to 97.4%) and specificity of 87.5% (95% CI 75.0% to 94.6%).

Fig. 6.

Progressive collapsing foot deformity (PCFD) compared with healthy foot shape obtained following canonical correlation analysis. Canonical scores were amplified with a factor 3.

Discussion

The recent advent of WBCT imaging has enabled alignment assessment of PCFD under physiological loading conditions.^4,17 However, the integration of complete 3D weightbearing evaluation in routine clinical practice is yet to be fully realized.⁴ By adopting the recently introduced non-linear PPSA approach in combination with WBCT, this study provides a complete mapping of the morphological variations in the PCFD under weightbearing conditions. Our principal finding highlights important changes in PCFD shape compared with the control foot upon weightbearing conditions. The talocalcaneonavicular joint is the most significant affected structure, with prominent internal and plantar rotation of the talar bone. This concurs with a previous study describing the talocalcaneonavicular joint or ‘coxa pedis’ as one of the key stabilizers of the longitudinal arch by counteracting the pressure of the talar head during weightbearing.¹⁸

Further morphological differences at the hindfoot were present at the level of the posterior facet of the subtalar joint. These findings are consistent with previous morphological analyses of the talus/calcaneus,^19-22 which reported that variations in the talus/calcaneus complex can lead to subtalar joint subluxation. In our study, we also observed that the PCFD often exhibited a reduced calcaneal pitch angle, which is an important parameter in diagnosing PCFD and is consistent with the findings of Noh et al.²³ A comparison of the variations between the healthy and PCFD models for each PC revealed a strong correlation between the severity of calcaneal valgus, talar internal rotation, and talar subluxation with the degree of arch collapse. These findings suggest that alterations in the subtalar joint impact the morphology and overall deformity of the longitudinal arch.

At the midfoot, differences were most obvious on the superior and anterior surfaces of the cuboid and navicular bones, possibly due to plantar flexion and abduction of these bones in PCFD. These findings are in line with previous studies demonstrating medial and lateral longitudinal arch lowering via planarization of the navicular and cuboid bone, respectively.²⁴ The obtained results also demonstrate similarities to another study that linked increased talar uncoverage in PCFD patients with increased navicular and cuboid abduction.²⁵

At the level of the forefoot, PCFD distance colour maps demonstrated differences on the articular bases of the metatarsals. These could be attributed to the abduction in the transverse plane and dorsiflexion in the sagittal plane. A previous study used both transverse foot arch collapse and forefoot dorsiflexion in the sagittal plane to assess the severity of PCFD deformity.²⁶

Beyond characterizing shape variation in PCFD using geometrical morphometrics, this study also aimed to enhance the clinical interpretability of shape analysis by adopting the non-linear PPSA approach. Notably, model compactness was significantly increased in the PCFD cohort when compared with traditional PCA, suggesting the presence of important non-linear shape variations and positioning PPSA as a potentially superior method for analyzing and interpreting individual shape components in clinical settings, whereas this advantage was minimal in healthy controls.

In a second experiment, we investigated the potential for automated diagnosis by using shape decompositions as predictors for LDA. Both PPSA and PCA models using the first PC achieved sensitivity and specificity values of 92.5%. In comparison, when using all seven measurements, the classification achieved a sensitivity of 92.5% and specificity of 87.5% (Table II). Since classification relies on the combined set of shape components, PCA appears to offer a valid approximation of patient geometry, making it a viable alternative to PPSA in this context.

PPSA facilitates the analysis of principal components in healthy and pathological feet with 3D geometrical morphometric properties, enhancing timeliness, reproducibility, consistency, and objectivity in clinical decisions (Figures 1 to 3). In PCFD diagnostics, PPSA accurately detects subtle morphological changes in the talocalcaneonavicular complex, enabling timely conservative and surgical interventions before irreversible joint degeneration occurs (Figure 6). For PCFD surgical planning, PPSA provides individualized deformity mapping across multiple planes, quantifying hindfoot valgus, talar rotation, and subluxation correlates with arch collapse, thereby guiding the required correction achieved through calcaneal osteotomy or subtalar realignment, while midfoot and forefoot changes alert clinicians to address talonavicular instability or medial column collapse via specific orthotics or targeted osteotomies (Figure 3). This comprehensive approach optimizes the choice between joint-preserving and joint-sacrificing procedures while minimizing correction errors.

This study has several limitations. First, minor geometrical discrepancies may have arisen from segmentation inaccuracies during CT scan analysis or slight variations in foot positioning within the scanner (i.e. positional noise). Second, shape modelling is an inherently data-intensive technique. While there are no strict guidelines for the required sample size in SSM, model performance—evaluated retrospectively for accuracy and generalizability—was considered adequate. Nonetheless, larger sample sizes in future studies would enhance statistical power and improve the robustness of group comparisons.

Finally, to develop an automated screening tool based on shape modelling methodology, a larger training dataset will be essential before translational applications can be realized. Moreover, our case-control design assumes an equal diagnostic probability distribution (p = 0.5), which artificially inflates the a priori likelihood given that the true prevalence of flat foot deformity has been estimated at 15.6%.²⁷

In conclusion, this study is the first to apply PPSA in patients with PCFD and provides a significant step forward in our understanding of foot arch geometry and its clinical implications. While there are limitations and areas for improvement, the potential applications of SSM in clinical settings are promising. Future research should aim to integrate PPSA-based 3D modelling into biomechanical simulations and clinical workflows, while expanding datasets to include more diverse populations, incorporating cartilage thickness variations, and refining automated diagnostic classification algorithms based on distinct morphological patterns. By generating patient-specific digital models, PPSA has the potential to significantly improve personalized orthotics and implant design, precisely accommodating individual deformity patterns and corrected anatomical alignments. Regarding the surgical management, PPSA based identification of distinct morphological patterns in PCFD could mitigate the decision process towards specific osteotomies at level of the hind- and midfoot. Collectively, these advancements will enhance diagnostic precision and treatment efficacy in foot pathology, ultimately improving patient outcomes.

Take home message

- Progressive collapsing foot deformity (PCFD) is a complex, multiplanar, 3D deformity with its most pronounced alterations centred at the talocalcaneonavicular joint complex.

- Non-linear, shape-based modelling techniques—unlike traditional linear clinical measurements (e.g. distances, ratios)—effectively capture the rotational and multistructural collapse patterns of PCFD.

- When combined with weightbearing CT, 3D morphometrics offer enhanced anatomical resolution, underscoring the critical role of talocalcaneonavicular joint in the failure of the medial longitudinal arch.

Data Availability

The data that support the findings for this study are available to other researchers from the corresponding author upon reasonable request.