Statistical Shape Modeling Characterization of Cavovarus Deformity between Demyelinating and Axonal Subtypes of Charcot-Marie-Tooth Disease

Abstract

Background

Charcot-Marie-Tooth disease (CMT) is an inherited peripheral neuropathy that is associated with a cavovarus foot deformity that leads to impaired mobility and pain. Structural differences in the hindfoot, midfoot, and forefoot that contribute to this cavovarus deformity have not been fully characterized or described between disease subtypes. This study aimed to identify structural differences in the foot associated with CMT and between demyelinating and axonal subtypes in a retrospective cross-sectional study.

Methods

In this study, we use statistical shape modeling, a mathematical tool to describe morphologic averages and variation to create a 14-bone model of the tibia through metatarsals from retrospectively identified WBCT images from individuals with CMT and controls, classified as having either demyelinating or axonal disease. We used a Hotelling’s T² test and a principal component analysis followed by statistical tests to identify significant differences in morphology between CMT and control groups and between demyelinating, axonal, and control groups.

Results

Results of this analysis showed similarity in the overall foot deformity between subtypes and supported previous research on foot alignment by highlighting several regions of the foot and ankle with an alignment-driven deformity. Differences in overall cavovarus position were identified between CMT and control groups, with additional increase in hindfoot varus rotation seen in the demyelinating group. Along each component of the deformity, the demyelinating group demonstrated more severe deformity than the axonal group.

Conclusion

There are differences in foot morphology throughout the hindfoot, midfoot, and forefoot that contribute to the cavovarus deformity seen in CMT. Demyelinating CMT presents with severe global deformity with pronounced hindfoot varus while axonal CMT has a more midfoot-centered deformity.

Clinical Relevance

These results demonstrate the importance of disease subtype in treatment planning for individuals with CMT-related cavovarus deformity and support the use of 3-dimensional imaging in characterization of cavovarus foot structure.

Graphical Abstract

Introduction

Charcot-Marie-Tooth disease (CMT) is an inherited progressive neurologic condition that, despite substantial heterogeneity in both genetic cause and expression, commonly presents with a characteristic cavovarus foot deformity consisting of varus hindfoot alignment with a high arch and plantarflexion of the first ray.^{2, 4, 6, 31, 33, 38} This cavovarus foot shape has been associated with CMT since the early identification and writing about the disease by Charcot, Marie, and Tooth and descriptions of the features and surgical treatments of this deformity exist throughout orthopaedic literature.^{1, 4, 20, 22–25, 44, 56} However, there is relatively minimal literature describing detailed skeletal components of this deformity or evaluating differences in foot and ankle structure between genetic subtypes of CMT.^{2, 3, 6, 25, 33, 46, 49, 51} While over 400 genes have been implicated in the disease, three basic categories for CMT have been distinguished (axonal, demyelinating and intermediate). In the demyelinating form (type 1), the protective coating of the nerve (myelin) is predominantly affected. In the axonal form (type 2), the axon which carries the nerve impulse is predominantly affected and patients typically do not have the same pronounced slowing of nerve conduction velocities (NCV) seen in type 1. An intermediate category is assigned when NCV are somewhere in between. Each type is then further broken down into subtypes based on the genetic cause^{4, 5, 25, 38}. Existing research in this area has predominantly utilized WBCT and has studied the correlation between 2D and 3D measures of varus alignment, identified differences in foot and ankle offset and hindfoot alignment angle, and established the talonavicular and naviculocuneiform joints as the major locations for supination and compensatory pronation.^{2, 6, 46, 51, 53}. Differences in individual bone shape have been identified between CMT and control groups throughout the hindfoot, midfoot, and forefoot, while differences between seen types 1 and 2 were primarily located in the midfoot.^{35, 42, 48} Throughout the foot, more severe morphological abnormality was observed in CMT type 1. However, none of these studies have analyzed a combined model of the hindfoot, midfoot, and forefoot or distinguished between types of CMT. This knowledge gap contributes to a lack of consensus on both conservative and surgical management of CMT-related cavovarus deformity.^{10, 25, 28, 30, 37, 43–45, 50, 54, 55}

Existing studies quantifying the overall foot and ankle deformity associated with CMT have predominantly used automatically calculated radiographic measures from WBCT.^{2, 33, 34, 52} In contrast to these overview measures, statistical shape modeling (SSM) allows for more detailed modeling of morphologic differences between three-dimensional structures and has been used to describe foot and ankle manifestations of other diseases.^{12, 13, 17, 26, 29, 36, 39, 41, 47} Specific to CMT, SSM has been utilized to demonstrate differences in individual bone shape that are present in CMT and that exist between CMT types 1 and 2.^{42, 48} However, to date, there is no existing multi-domain SSM of the whole foot and ankle in CMT to characterize full-foot morphology. This approach allows simultaneous investigation of both differences in relative bony alignment and individual bone structure. In this study, we use SSM to analyze structural differences throughout the foot and ankle that contribute to the cavovarus shape associated with CMT and further investigate differences in foot and ankle skeletal morphology between demyelinating and axonal subtypes of CMT.

Methods

Participant Identification and Classification

Retrospective chart review was used to identify 43 WBCT scans from 25 individuals with CMT and a cavovarus foot type, confirmed by a fellowship trained foot and ankle surgeon. Scans from the University of Utah or University of Iowa were analyzed in individuals without history of foot or ankle surgery. There was no exclusion criteria for age, and the only comorbidity excluded was Charcot foot. Chart review was used to determine genetic subtype of CMT through genetic testing results or electromyography. Individuals with genetic results of CMT type 1 or CMT type 4 and/or EMG features of demyelinating disease were classified as demyelinating CMT. Individuals with genetic results of CMT type 2 and/or EMG findings characteristic of axonal disease were classified as axonal CMT⁵. This resulted in 23 scans in the demyelinating group, 16 in the axonal group, and 4 scans with CMTX without EMG, which were not analyzed as part of either group because of the intermediate nature of CMTX.⁵ This model did not have sufficient data to analyze intermediate CMT. 25 Healthy controls were examined consisting of a mix of prospectively-collected adult controls and retrospectively-identified contralateral limbs from acute unilateral foot injuries that were determined by a fellowship trained foot and ankle surgeon to have a rectus foot type. T-tests revealed no significant difference (p = 0.807) in age at scan between the CMT and control groups and one-way ANOVA revealed no significant differences in age between the demyelinating, axonal, or control groups (p = 0.252). Chi-squared test demonstrated no difference in sex distribution between CMT and control groups (p = 0.926) or between demyelinating, axonal, or control groups (p = 0.643). However, the axonal group had a significantly greater age at diagnosis than the demyelinating group (p = 0.013). Demographics for each group are given in Table 1.

Table 1:

Demographics and Genetic Subtype for WBCT scans of individuals with CMT and Controls

	Individuals	Limbs	Sex	Age (Range)	Age at Diagnosis
CMT	25	43	15 F, 28 M	41.9 (13–73)	33.3 (8–71)
Demyelinating	13	23	9 F, 14 M	38.3 (13–71)	26.7 (8–53)
Axonal	10	16	4 F, 12 M	48.1 (14–73)	44.1 (8–71)
Control	25	25	9 F, 16 M	40.8 (17–69)	--

Image Processing

WBCT images were segmented semi-automatically (Bonelogic, DISIOR, Paragon 28, Englewood, CO) and were then manually edited and verified (Mimics, Materialize, Leuven, Belgium). Segmentations were done of the tibia, fibula, talus, calcaneus, navicular, cuboid, cuneiforms, and metatarsals, resulting in 14 bones spanning the ankle through the distal midfoot. Three-dimensional parts were calculated from these segmentations. These 3D parts were smoothed and decimated consistently in 3-Matic to generate clean meshes for shape modeling. An anatomic coordinate system for the tibia was automatically defined and the tibia and fibula were cut 65mm proximal to the tibiotalar articular surface perpendicular to the long axis of the tibia to create a consistent length for analysis.⁴⁰ All left-sided specimens were mirrored so that all models could be aligned as right feet, and the specimens were aligned with each other using an iterative closest point algorithm for the whole 14-bone structure (Figure 1A-1E).

Figure 1:

Workflow for SSM model generation and mode of variation identification from WBCT images showing (A) WBCT image, (B) automatic segmentation in DISIOR, (C) manual cleanup and verification of segmentations, (D) calculation of 3D parts and smoothing and decimation of those parts,(E) alignment by iterative common point algorithm, (F) creation of a multi-domain models containing all 14 bones (tibia through metatarsals) and single-domain models for each individual bone with Procrustes scaling algorithm applied to normalize size of the specimens, and (G) statistical analysis consisting of Hotelling’s T2 test on local and world particles to identify regions with significant differences in shape, alignment, or both and principal component analysis (PCA) with subsequent parallel analysis to identify statistically significant modes of variation for the whole foot model and each individual bone, and Wilcoxon rank sum test or Kruskal-Wallace test, both followed by Holm-Sidak correction, to identify statistically significant differences between groups along each PCA mode.

Statistical Shape Modeling

In order to generate a multi-domain SSM for all 14 bones, single-domain SSMs were first created for each individual bone with a Generalized Procrustes Analysis applied to remove size as a mode of variation.^{15, 16} Particle locations were optimized in the single domain models to allow for greater particle numbers and different optimization parameters for each bone in order to most efficiently achieve good correspondence on each bone. The optimized particle clouds were aligned in the original full-foot coordinate space for each limb to yield the full 14-bone model (Figure 1F). This large SSM consists of 68 clouds of 14,848 particles that represent the size-normalized bony structure of the foot. The three-dimensional particle locations can then be used to calculate average shape and perform statistical tests on this population.

Statistical Analysis

General differences in bony alignment and shape between groups were analyzed using a Hotelling’s T² test, which in this case functions as a multi-dimension generalization of a Student’s T test and test difference in three-dimensional position between two groups of vectors representing the position of an individual particle.¹⁸ While the T² statistic is a parametric test, the test has been demonstrated to be robust to non-parametric data, even at relatively small sample sizes.³² This test was applied at each particle under two conditions: the full-foot coordinate system and the single-bone coordinate system where each individual bone is centered at the origin. A false discovery rate correction was applied due to the number of particles being tested.^{8, 9, 14, 29} Particle distance differences seen when particles were aligned in the individual bone coordinate systems represented a significant difference in shape. Differences between particles aligned in the global coordinate system represented a significant difference in both shape and alignment. Particles that demonstrated significance in the global, but not individual bone, coordinate systems, were assumed to be representative of an isolated difference in alignment. This comparison was conducted between the control and demyelinating groups, control and axonal groups, and demyelinating groups. While this measure provides an overview of the alignment and single-domain shape components of multi-domain models, it fails to identify patterns of morphologic variation because it does not account for the co-occurring difference in position of nearby particles.

A more detailed analysis of foot morphology variation was conducted using principal component analysis (PCA) with subsequent statistical test. PCA identified the modes of variation in full-foot morphology, which consist of concurrent variation in individual bone shape and relative bony alignment. Each mode of variation accounts for a specific portion of the variance in the population included in this model with the first mode explaining the largest portion of variance and each progressive mode explaining a smaller portion. A PCA mode consists of a single symmetrical axis, centered at the mean shape of this population, along which each limb included on the model can be placed. The location of each individual in this distribution is given by the PCA component score. A PCA component 1 standard deviation above the mean represents the exact opposite shape difference from the mean as a PCA component score 1 standard deviation below the mean. Positive and negative directions of these modes are arbitrary and have been set to have the more cavovarus shape represented by positive values in this analysis.

The PCA component scores along each mode can be compared between groups using numerical statistical tests. Significant modes of variation, which are modes that explain a more than random portion of the variance, were identified using parallel analysis.^{21, 27} Since this data consisted of both unilateral and bilateral scans, these data are not fully independent and thus an assumption of a parametric distribution is inappropriate, so non-parametric statistical analyses were used. Differences in PCA component scores between either CMT and control groups or demyelinating, axonal, and control groups were tested along each mode. For comparisons between two groups, a Wilcoxon rank sum test with Holm-Sidak correction was used. For three-group comparisons, a Kruskal-Wallis test with Dunn-Sidak post-hoc analysis was used.²⁹ All tests employed a significance value of α = 0.05 (Figure 1G). Corrected Hedge’s g effect size was calculated for all comparisons.^{7, 11}

Results

Hotelling’s T² test revealed substantial areas of the foot with significant differences in alignment and/or individual bone structure between CMT and control groups (Figure 2A) and between each subtype and the control group (Figures 2B and 2C). Much of the difference in whole-foot morphology in all three cases was caused by alignment change. Between the CMT and control groups, 76.36% of particles had a significant difference in position attributable solely to alignment. Similarly, between the demyelinating and control groups, 66.82% of particles showed an alignment-related difference and between the axonal and control groups 53.41% of particles had significant differences due to alignment. However, alignment was not the only factor contributing to this deformity. The CMT to control comparison demonstrated 1.51% of particles with a significant difference attributable only to shape variation and 13.36% of particles with combined shape and alignment-related distance differences. Between demyelinating and control groups, 2.13% of particles demonstrated isolated shape difference and 28.54% had combined shape and alignment differences. Comparing axonal and control groups, 1.79% of particles had a significant difference only related to individual bone shape and 1.29% of particles demonstrated combined alignment and shape difference.

Figure 2:

Results from Hotelling’s T² test comparing (A) the overall CMT group to the control group, (B) the demyelinating group to the control group, and (C) the axonal subtype to the control group. Particles in showed a significant difference in particle location in only the single-domain model, representative of shape difference between groups. Cyan particles showed a significant difference in particle location only in the multi-domain coordinate system, indicating a difference only in alignment. Purple particles represent significant differences in both shape and alignment. Underneath the images of the model are the percentage of particles of each color out of the total number of particles in the model for each comparison.

The location of significant differences in particle position was similar between the CMT and demyelinating groups, which both identified alignment differences throughout the majority of the hindfoot, midfoot, and lateral forefoot. Significant differences in shape and in combined shape and alignment were primarily seen on the anterior-medial tibial shaft, medial fibular shaft, medial cuneiform, medial aspect of the subtalar joint, and throughout the metatarsals, with somewhat more particles demonstrating differences related to individual bone shape in the demyelinating-to-control, rather than CMT-to-control, comparison. Between axonal and control groups, alignment differences were identified in the midfoot, medial hindfoot, and lateral forefoot and isolated shape differences and combined shape and alignment change were primarily identified around the medial talonavicular joint and the metatarsal heads.

PCA analysis broadly supports the results from the Hotelling’s T² test with additional details regarding the pattern of morphologic variation. Parallel analysis identified 7 significant modes of variation, but differences between groups were only identified in the first two modes. Explained variance and a brief description of each mode are given in Table 2. The first mode of variation for the 14-bone model (Figure 3) accounted for 53.4% of the morphology variation between limbs included in this model and demonstrated an overall difference between cavovarus and planovalgus alignment. Since this population consists of more than half CMT cavovarus limbs, the average shape is moderately cavovarus. The distributions of the CMT and control groups showed a clustering of the control group around an approximately neutral position with a wide variability in shape in the CMT group ranging from neutral to strongly cavovarus. There was a significant difference in shape between CMT and control groups (p < 0.001) with a large effect size (g = 1.403). Modes 2 through 7, while necessary to explain the population variance, did not show significant differences between CMT and control groups. P-values and effect sizes for PCA component score tests between CMT and control groups are given in Table 2.

Table 2:

P-values and corrected Hedge’s g effect size for CMT versus control PCA component score tests and the explained variance and brief description of variance described by each of the 7 significant modes. P-values less than 0.05 are noted in bold with an asterisk and highlighted in yellow. Large effect size (g > 0.8) is shaded green, medium effect size (g > 0.5) is shaded in yellow, and small effect size (g > 0.2) is shaded in blue with smaller effect sizes shaded in gray.

PCA Mode	p-value	Effect size g	Explained Variance	Morphology Variation Described by Mode
Mode 1	<0.001*	1.403	53.4%	Extreme cavovarus to mild planovalgus overall foot position
Mode 2	0.197	0.332	17.7%	Varus hindfoot with lateral rotation of subtalar joint to neutral hindfoot and subtalar joint
Mode 3	0.793	0.175	6.4%	Valgus hindfoot to neutral hindfoot
Mode 4	0.793	0.067	6.0%	High arch with dorsiflexion of the ankle to neutral arch height with neutral ankle
Mode 5	0.679	0.315	4.5%	Increased calcaneal pitch with dorsiflexion of MTP joints
Mode 6	0.772	0.287	1.9%	Neutral to lateral shift of cuneiforms with corresponding internal rotation at tarsometatarsal joints
Mode 7	0.793	0.041	1.8%	Posterior-medial to anterior-lateral positioning of the talus relative to the tibia and calcaneus

Figure 3:

First PCA mode of variation, which describes a spectrum from planovalgus (−2 standard deviations) to extremely cavovarus (+2 standard deviations). The mean shape is mildly cavovarus, the control group (shown in purple with circles for each limb) is distributed roughly around a neutral position and the CMT group (shown in red with diamonds for each limb) has a more cavovarus distribution. Bars indicate the mean and +/− 2 standard deviations for each group. Distributions of the demyelinating, axonal, and control groups are given in green, orange, and purple where each diamond, triangle, or circle represents one limb. An asterisk represents a statistically significant difference for the indicated comparison.

This first mode of variation also demonstrated a significant difference between each subtype and the control group, with both the demyelinating (p < 0.001) and axonal (p = 0.006) groups having a more cavovarus position than controls. P-values and effect sizes for PCA component score tests between demyelinating, axonal, and control groups are given in Table 3. Additionally, the second mode of variation (Figure 4) demonstrated a significant difference between the demyelinating and control groups (p = 0.049). This mode accounted for 17.7% of the overall variance and revealed differences in calcaneal varus rotation and subtalar joint alignment. The −2 standard deviation shape showed a more neutral hindfoot with a slightly valgus calcaneal position while the +2 standard deviation shape showed a varus calcaneal rotation with a corresponding lateral rotation of the anterior talus relative to the calcaneus and resulting medial displacement of the posterior talus relative to the posterior facet. There was no significant difference identified along this mode between the CMT and control groups or axonal and control groups, likely due to two outliers in the axonal group.

Table 3:

P-values and corrected Hedge’s g effect size for post-hoc tests comparing between demyelinating, axonal, and control groups. P-values less than 0.05 are noted in bold with an asterisk and highlighted in yellow. Large effect size (g > 0.8) is shaded green, medium effect size (g > 0.5) is shaded in yellow, and small effect size (g > 0.2) is shaded in blue with smaller effect sizes shaded in gray.

PCA Mode	Demyelinating v. Control		Axonal v. Control		Demyelinating v. Axonal
	P-value	Effect size g	P-value	Effect size g	P-value	Effect size g
Mode 1	< 0.001*	2.150	0.006*	1.285	0.265	0.567
Mode 2	0.049*	0.800	0.969	0.145	0.234	0.606
Mode 3	0.992	0.052	0.978	0.337	0.999	0.216
Mode 4	0.992	0.232	0.310	0.594	0.215	0.583
Mode 5	0.896	0.231	0.301	0.398	0.681	0.147
Mode 6	0.980	0.147	0.708	0.337	0.892	0.238
Mode 7	0.992	0.126	0.933	0.186	0.836	0.236

Figure 4:

Second PCA mode of variation, which consists of concurrent variation in hindfoot rotation and ankle dorsiflexion where +2 standard deviations represents a more cavus hindfoot with a more dorsiflexed position of the ankle and −2 standard deviations represents a more neutral hindfoot with a more plantarflexed ankle. Distributions of the CMT and control groups are given in red and purple and distributions of the demyelinating, axonal, and control groups are given in green, orange, and purple where each diamond, triangle, or circle represents one limb, and the bars show mean and +/− 2 standard deviations for each group. An asterisk represents a statistically significant difference for the indicated comparison.

Discussion

The alignment differences seen between CMT and control groups support previous studies that have shown altered alignment at the talonavicular joint, naviculocuneiform joint, and in hindfoot alignment angle.^{2, 6, 42, 46, 48} The overall CMT group, including demyelinating and axonal types, as well as each individual type showed differences from the control group in overall foot morphology that can be primarily explained by differences in alignment. In the CMT group as a whole and in the demyelinating group, these alignment changes were seen throughout the hindfoot, midfoot, and forefoot joints, but in the axonal group, alignment changes were more localized to the midfoot and lateral forefoot, providing further evidence that these midfoot joints may be the locus of supination and adduction deformity and suggesting that both the hindfoot and midfoot are relevant in surgical correction of this deformity^{2, 19, 34}.

PCA analysis aligned with the clinically described cavovarus deformity, with a difference between CMT and control groups and between each subtype and control groups in overall cavovarus shape. Mode 1, describing this cavovarus position, accounted for over 50% of the population variance, but it is worth nothing the substantial variability in both CMT and control groups that is described by modes 2 through 6, indicating that normal variation in foot structure still impact the overall presentation of the foot in individuals with CMT. The second mode identified variability in the varus rotation of the hindfoot without associated differences in arch height, and demonstrated a significant difference between demyelinating and control groups, but not in any other comparisons, which may be due to the large distribution and outliers in the axonal group. This difference between only demyelinating and control groups supports the theory that CMT-related cavovarus deformity is more severe in demyelinating cases, and suggests that, within demyelinating CMT, the overall cavovarus foot position and varus rotation of the hindfoot are not fully linked. Specifically, clinically similar cavovarus feet may have varying degrees of hindfoot rotation.

While this study provides a comprehensive computational model of foot morphology in CMT, there are several important limitations. Firstly, there is a wide variation in age in the subjects included in this study. No differences in age were identified between groups, but normal morphologic adaptation with age and potential pre-arthritic changes in the older individuals in either group may interfere with identification of morphologic variation caused by CMT. CMT is a progressive disease, and this singe time-point study provides information about foot morphology in CMT broadly, but not at different ages or different points in disease progression. Additionally, there was a difference in age at diagnosis with the individuals with demyelinating CMT being diagnosed, on average, 7.5 years earlier than those with axonal disease. The classification of disease subtypes into demyelinating and axonal is a simplification of the hundreds of genetic mutations implicated in CMT, and a more detailed analysis of genotypes may provide additional information about the relationship between genetic variation and expression in this disease.

Conclusion

These data identify a spectrum of cavovarus foot morphology in CMT that is primarily driven by alignment differences, especially in the midfoot. The degree of overall cavovarus deformity and the alterations in isolated varus rotation were more severe in demyelinating than axonal subtypes of CMT. Clinically, this emphasizes the need for treatment genetic subtype in understanding the foot and ankle manifestations of CMT.