Automatic construction of statistical shape models using deformable simplex meshes with vector field convolution energy

OpenHands: An Open-Source Statistical Shape Model of the Finger Bones

This paper presents statistical shape models of the four fingers of the hand, with an emphasis on anatomic analysis of the proximal and distal interphalangeal joints. A multi-body statistical shape modelling pipeline was implemented on an exemplar training dataset of computed tomography (CT) scans of 10 right hands (5F:5M, 27-37 years, free from disease or injury) imaged at 0.3 mm resolution, segmented, meshed and aligned. Model generated included pose neutralisation to remove joint angle variation during imaging. Repositioning was successful; no joint flexion variation was observed in the resulting model. The first principal component (PC) of morphological variation represented phalanx size in all fingers. Subsequent PCs showed variation in position along the palmar-dorsal axis, and bone breadth: length ratio. Finally, the models were interrogated to provide gross measures of bone lengths and joint spaces. These models have been published for open use to support wider community efforts in hand biomechanical analysis, providing bony anatomy descriptions whilst preserving the security of the underlying imaging data and privacy of the participants. The model describes a small, homogeneous population, and assumptions cannot be made about how it represents individuals outside the training dataset. However, it supplements anthropometric datasets with additional shape information, and may be useful for investigating factors such as joint morphology and design of hand-interfacing devices and products. The model has been shared as an open-source repository ( https://github.com/abel-research/OpenHands ), and we encourage the community to use and contribute to it.

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.

Statistical shape model of the talus bone morphology: A comparison between impinged and nonimpinged ankles

Diagnosis of ankle impingement is performed primarily by clinical examination, whereas medical imaging is used for severity staging and treatment guidance. The association of impingement symptoms with regional three-dimensional (3D) bone shape variaties visible in medical images has not been systematically explored, nor do we know the type and magnitude of this relation. In this cross-sectional case-control study, we hypothesized that 3D talus bone shape could be used to quantitatively formulate the discriminating shape variations between ankles with impingement from ankles without impingement, and we aimed to characterize and quantify these variations. We used statistical shape modeling (SSM) methods to determine the most prevalent modes of shape variations that discriminate between the impinged and nonimpinged ankles. Results of the compactness and parallel analysis test on the statistical shape model identify 8 prominent shape modes of variations (MoVs) representing approximately 78% of the total 3D variations in the population of shapes, among which two modes captured discriminating features between impinged and nonimpinged ankles (p value of 0.023 and 0.042). Visual inspection confirms that these two shape modes, capturing abnormalities in the anterior and posterior parts of talus, represent the two main bony risk factors in anterior and posterior ankle impingement. In conclusion, in this research using SSM we have identified shape MoVs that were found to correlate significantly with bony ankle impingement. We also illustrated potential guidance from SSMs for surgical planning.

Statistical shape model-based tibiofibular assessment of syndesmotic ankle lesions using weight-bearing CT

Forced external rotation is hypothesized as the key mechanism of syndesmotic ankle injuries, inducing a three-dimensional deviation from the normal distal tibiofibular joint (DTFJ) alignment. However, current diagnostic imaging modalities are impeded by a two-dimensional assessment, without considering ligamentous stabilizers. Therefore, our aim is threefold: (1) to construct an articulated statistical shape model of the normal DTFJ with the inclusion of ligamentous morphometry, (2) to investigate the effect of weight-bearing on the DTFJ alignment, and (3) to detect differences in predicted syndesmotic ligament length of patients with syndesmotic lesions with respect to normative data. Training data comprised non-weight-bearing CT scans from asymptomatic controls (N = 76), weight-bearing CT scans from patients with syndesmotic ankle injury (N = 13), and their weight-bearing healthy contralateral side (N = 13). Path and length of the syndesmotic ligaments were predicted using a discrete element model, wrapped around bony contours. Statistical shape model evaluation was based on accuracy, generalization, and compactness. The predicted ligament length in patients with syndesmotic lesions was compared with healthy controls. With respect to the first aim, our presented skeletal shape model described the training data with an accuracy of 0.23 ± 0.028 mm. Mean prediction accuracy of ligament insertions was 0.53 ± 0.12 mm. In accordance with the second aim, our results showed an increased tibiofibular diastasis in healthy ankles after weight-bearing. Concerning our third aim, a statistically significant difference in anterior syndesmotic ligament length was found between ankles with syndesmotic lesions and healthy controls (p = 0.017). There was a significant correlation between the presence of syndesmotic injury and the positional alignment between the distal tibia and fibula (r = 0.873, p < 0,001). Clinical Significance: Statistical shape modeling combined with patient-specific ligament wrapping techniques can facilitate the diagnostic workup of syndesmosic ankle lesions under weight-bearing conditions. In doing so, an increased anterior tibiofibular distance was detected, corresponding to an "anterior open-book injury" of the ankle syndesmosis as a result of anterior inferior tibiofibular ligament elongation/rupture.

Distal Humerus Morphological Analysis of Chinese Individuals: A Statistical Shape Modeling Approach

Objective

A detailed analysis of the morphology of distal humeral articulation can help in the creation of anatomic prostheses of hemiarthroplasty. This study used statistical shape modeling to evaluate the 3D morphology of the distal humerus in healthy Chinese individuals and to investigate the proper articular morphology differences.

Methods

A statistical shape model (SSM) of the distal humerus was created using CT scans of 106 survey‐confirmed nonpathologic elbows. In addition, the articular components of each principal component (PC) were selected and fitted on the mean mode. The Euclidean point‐to‐mesh distance of articular modes was calculated as a measurement the proper change in the morphology of the articulation.

Results

The first seven PCs jointly accounted for 80.9% of the total variation (44.4%, 12.2%, 7.9%, 5.9%, 4.1%, 3.4% and 3%, respectively). In the mean model, the distance between the medial and lateral epicondyles was 57.4 mm, the width of the articulation was 42.1 mm, and the angle of the transepicondylar line (TEL) and C line was 4.8°. The articular surface differences of the first PC were significant (RMS: 1.43 mm in the −3 SD model and 2.38 mm in the +3 SD model), whereas under other conditions, the differences were not remarkable despite the maximum deformation not exceeding 1 mm.

Conclusion

A novel method (SSM) was used to evaluate the 3D morphology of the distal humerus in healthy Chinese individuals and investigate the proper articular shape differences. We found the proper shape of articular surface basically transformed into one variation pattern which was relevant to the bone size, even though the morphology of distal humerus possessed complicated variation modes. The findings of this study can be helpful to design the next generation of elbow hemiarthroplasty in the future.

Principal polynomial shape analysis: A non-linear tool for statistical shape modeling

BACKGROUND AND OBJECTIVES

The most widespread statistical modeling technique is based on Principal Component Analysis (PCA). Although this approach has several appealing features, it remains hampered by its linearity. Principal Polynomial Analysis (PPA) can capture non-linearity in a sequential algorithm, while maintaining the interesting properties of PCA. PPA is, however, computationally expensive in handling shape surface data. To this end, we propose Principal Polynomial Shape Analysis (PPSA) as an adjusted approach for non-linear shape analyzes. The aim of this study was to assess PPSA's features, its model boundaries and its general applicability.

METHODS

PCA and PPSA-based shape models were investigated on one verification and three model evaluation experiments. In the verification experiment, the estimated mean of the PCA and PPSA model on a data set of synthetic lower limbs of different lengths in different poses were compared to the real mean. Further, the PCA-based and PPSA shape models were tested for three challenging cases namely for shape model creation of gait marker data, for regression analysis on aging faces and for modeling pose variation in full body scans. For the latter, additionally a Fundamental Coordinate Model (FCM) and a PPSA model on Fundamental Coordinate(FC) space was created. The performances were evaluated based on model-based accuracy, generalization, compactness and specificity.

RESULTS

In the verification experiment, the scaling error reduced from 75% to below 1% when employing PPSA instead of PCA for a training set with 180° angular variation. For the model evaluation experiments, the PPSA models described the data as accurate and generalized as the PCA-based shape models. The PPSA models were slightly more compact and specific (up to 30%) than the PCA-based models. In regression, PCA and PPSA-based parameterizations explained a similar amount of variation. Lastly, for the full body scans, applying PPSA to parameterizations improved the compactness and accuracy.

CONCLUSIONS

PPSA describes the non-linear relationships between principal variations in a parameterized space. Compared to standard PCA-based shape models, capturing the non-linearity reduced the nonsense information in the shape components and improved the description of the data mean.

A Statistical Shape Model of the Morphological Variation of the Infrarenal Abdominal Aortic Aneurysm Neck

Hostile aortic neck characteristics, such as short length and large diameter, have been associated with type Ia endoleaks and reintervention after endovascular aneurysm repair (EVAR). However, such characteristics partially describe the complex aortic neck morphology. A more comprehensive quantitative description of 3D neck shape might lead to new insights into the relationship between aortic neck morphology and EVAR outcomes in individual patients. This study identifies the 3D morphological shape components that describe the infrarenal aortic neck through a statistical shape model (SSM). Pre-EVAR CT scans of 97 patients were used to develop the SSM. Parameterization of the morphology was based on the center lumen line reconstruction, a triangular surface mesh of the aortic lumen, 3D coordinates of the renal arteries, and the distal end of the aortic neck. A principal component analysis of the parametrization of the aortic neck coordinates was used as input for the SSM. The SSM consisted of 96 principal components (PCs) that each described a unique shape feature. The first five PCs represented 95% of the total morphological variation in the dataset. The SSM is an objective model that provides a quantitative description of the neck morphology of an individual patient.

Fast and Accurate Craniomaxillofacial Landmark Detection via 3D Faster R-CNN

Automatic craniomaxillofacial (CMF) landmark localization from cone-beam computed tomography (CBCT) images is challenging, considering that 1) the number of landmarks in the images may change due to varying deformities and traumatic defects, and 2) the CBCT images used in clinical practice are typically large. In this paper, we propose a two-stage, coarse-to-fine deep learning method to tackle these challenges with both speed and accuracy in mind. Specifically, we first use a 3D faster R-CNN to roughly locate landmarks in down-sampled CBCT images that have varying numbers of landmarks. By converting the landmark point detection problem to a generic object detection problem, our 3D faster R-CNN is formulated to detect virtual, fixed-size objects in small boxes with centers indicating the approximate locations of the landmarks. Based on the rough landmark locations, we then crop 3D patches from the high-resolution images and send them to a multi-scale UNet for the regression of heatmaps, from which the refined landmark locations are finally derived. We evaluated the proposed approach by detecting up to 18 landmarks on a real clinical dataset of CMF CBCT images with various conditions. Experiments show that our approach achieves state-of-the-art accuracy of 0.89 ± 0.64mm in an average time of 26.2 seconds per volume.

2D Statistical Lung Shape Analysis Using Chest Radiographs: Modelling and Segmentation

Accurate information of the lung shape analysis and its anatomical variations is very noticeable in medical imaging. The normal variations of the lung shape can be interpreted as a normal lung. In contrast, abnormal variations of the lung shape can be a result of one of the pulmonary diseases. The goal of this study is twofold: (1) represent two lung shape models which are different at the reference points in registration process considering to show their impact on estimating the inter-patient 2D lung shape variations and (2) using the obtained models in lung field segmentation by utilizing active shape model (ASM) technique. The represented models which showed the inter-patient 2D lung shape variations in two different forms are fully compared and evaluated. The results show that the models along with standard principal component analysis (PCA) can be able to explain more than 95% of total variations in all cases using only first 7 principal component (PC) modes for both lungs. Both models are used in ASM-based segmentation technique for lung field segmentation. The segmentation results are evaluated using leave-one-out cross validation technique. According to the experimental results, the proposed method has average dice similarity coefficient of 97.1% and 96.1% for the right and the left lung, respectively. The results show that the proposed segmentation method is more stable and accurate than other model-based techniques to inter-patient lung field segmentation.

Combining statistical shape modeling, CFD, and meta-modeling to approximate the patient-specific pressure-drop across the aortic valve in real-time

BACKGROUND

Advances in medical imaging, segmentation techniques, and high performance computing have stimulated the use of complex, patient-specific, three-dimensional Computational Fluid Dynamics (CFD) simulations. Patient-specific, CFD-compatible geometries of the aortic valve are readily obtained. CFD can then be used to obtain the patient-specific pressure-flow relationship of the aortic valve. However, such CFD simulations are computationally expensive, and real-time alternatives are desired.

AIM

The aim of this work is to evaluate the performance of a meta-model with respect to high-fidelity, three-dimensional CFD simulations of the aortic valve.

METHODS

Principal component analysis was used to build a statistical shape model (SSM) from a population of 74 iso-topological meshes of the aortic valve. Synthetic meshes were created with the SSM, and steady-state CFD simulations at flow-rates between 50 and 650 mL/s were performed to build a meta-model. The meta-model related the statistical shape variance, and flow-rate to the pressure-drop.

RESULTS

Even though the first three shape modes account for only 46% of shape variance, the features relevant for the pressure-drop seem to be captured. The three-mode shape-model approximates the pressure-drop with an average error of 8.8% to 10.6% for aortic valves with a geometric orifice area below 150 mm² . The proposed methodology was least accurate for aortic valve areas above 150 mm² . Further reduction to a meta-model introduces an additional 3% error.

CONCLUSIONS

Statistical shape modeling can be used to capture shape variation of the aortic valve. Meta-models trained by SSM-based CFD simulations can provide an estimate of the pressure-flow relationship in real-time.

Contour-based lung shape analysis in order to tuberculosis detection: modeling and feature description

Statistical shape analysis of lung is a reliable alternative method for diagnosing pulmonary diseases such as tuberculosis (TB). The 2D contour-based lung shape analysis is investigated and developed using Fourier descriptors (FDs). The proposed 2D lung shape analysis is carried out in threefold: (1) represent the normal and the abnormal (i.e. pulmonary tuberculosis (PTB)) lung shape models using Fourier descriptors modeling (FDM) framework from chest X-ray (CXR) images, (2) estimate and compare the 2D inter-patient lung shape variations for the normal and abnormal lungs by applying principal component analysis (PCA) techniques, and (3) describe the optimal type of contour-based feature vectors to train a classifier in order to detect TB using one publicly available dataset-namely the Montgomery dataset. Since almost all of the previous works in lung shape analysis are content-based analysis, we proposed contour-based lung shape analysis for statistical modeling and feature description of PTB cases. The results show that the proposed approach is able to explain more than 95% of total variations in both of the normal and PTB cases using only 6 and 7 principal component modes for the right and the left lungs, respectively. In case of PTB detection, using 138 lung cases (80 normal and 58 PTB cases), we achieved the accuracy (ACC) and the area under the curve (AUC) of 82.03% and 88.75%, respectively. In comparison with existing state-of-art studies in the same dataset, the proposed approach is a very promising supplement for diagnosis of PTB disease. The method is robust and valuable for application in 2D automatic segmentation, classification, and atlas registration. Moreover, the approach could be used for any kind of pulmonary diseases. Graphical abstract Contour-based lung shape analysis in order to detect tuberculosis: modeling and feature description.

Predicting Knee Joint Instability Using a Tibio-Femoral Statistical Shape Model

Statistical shape models (SSMs) are a well established computational technique to represent the morphological variability spread in a set of matching surfaces by means of compact descriptive quantities, traditionally called "modes of variation" (MoVs). SSMs of bony surfaces have been proposed in biomechanics and orthopedic clinics to investigate the relation between bone shape and joint biomechanics. In this work, an SSM of the tibio-femoral joint has been developed to elucidate the relation between MoVs and bone angular deformities causing knee instability. The SSM was built using 99 bony shapes (distal femur and proximal tibia surfaces obtained from segmented CT scans) of osteoarthritic patients. Hip-knee-ankle (HKA) angle, femoral varus-valgus (FVV) angle, internal-external femoral rotation (IER), tibial varus-valgus (TVV) angles, and tibial slope (TS) were available across the patient set. Discriminant analysis (DA) and logistic regression (LR) classifiers were adopted to underline specific MoVs accounting for knee instability. First, it was found that thirty-four MoVs were enough to describe 95% of the shape variability in the dataset. The most relevant MoVs were the one encoding the height of the femoral and tibial shafts (MoV #2) and the one representing variations of the axial section of the femoral shaft and its bending in the frontal plane (MoV #5). Second, using quadratic DA, the sensitivity results of the classification were very accurate, being all >0.85 (HKA: 0.96, FVV: 0.99, IER: 0.88, TVV: 1, TS: 0.87). The results of the LR classifier were mostly in agreement with DA, confirming statistical significance for MoV #2 (p = 0.02) in correspondence to IER and MoV #5 in correspondence to HKA (p = 0.0001), FVV (p = 0.001), and TS (p = 0.02). We can argue that the SSM successfully identified specific MoVs encoding ranges of alignment variability between distal femur and proximal tibia. This discloses the opportunity to use the SSM to predict potential misalignment in the knee for a new patient by processing the bone shapes, removing the need for measuring clinical landmarks as the rotation centers and mechanical axes.

Statistical Modeling of Lower Limb Kinetics During Deep Squat and Forward Lunge

Purpose

Modern statistics and higher computational power have opened novel possibilities to complex data analysis. While gait has been the utmost described motion in quantitative human motion analysis, descriptions of more challenging movements like the squat or lunge are currently lacking in the literature. The hip and knee joints are exposed to high forces and cause high morbidity and costs. Pre-surgical kinetic data acquisition on a patient-specific anatomy is also scarce in the literature. Studying the normal inter-patient kinetic variability may lead to other comparable studies to initiate more personalized therapies within the orthopedics.

Methods

Trials are performed by 50 healthy young males who were not overweight and approximately of the same age and activity level. Spatial marker trajectories and ground reaction force registrations are imported into the Anybody Modeling System based on subject-specific geometry and the state-of-the-art TLEM 2.0 dataset. Hip and knee joint reaction forces were obtained by a simulation with an inverse dynamics approach. With these forces, a statistical model that accounts for inter-subject variability was created. For this, we applied a principal component analysis in order to enable variance decomposition. This way, noise can be rejected and we still contemplate all waveform data, instead of using deduced spatiotemporal parameters like peak flexion or stride length as done in many gait analyses. In addition, this current paper is, to the authors’ knowledge, the first to investigate the generalization of a kinetic model data toward the population.

Results

Average knee reaction forces range up to 7.16 times body weight for the forwarded leg during lunge. Conversely, during squat, the load is evenly distributed. For both motions, a reliable and compact statistical model was created. In the lunge model, the first 12 modes accounts for 95.26% of inter-individual population variance. For the maximal-depth squat, this was 95.69% for the first 14 modes. Model accuracies will increase when including more principal components.

Conclusion

Our model design was proved to be compact, accurate, and reliable. For models aimed at populations covering descriptive studies, the sample size must be at least 50.

Statistical Shape Modeling of Skeletal Anatomy for Sex Discrimination: Their Training Size, Sexual Dimorphism, and Asymmetry

Purpose: Statistical shape modeling provides a powerful tool for describing and analyzing human anatomy. By linearly combining the variance of the shape of a population of a given anatomical entity, statistical shape models (SSMs) identify its main modes of variation and may approximate the total variance of that population to a selected threshold, while reducing its dimensionality. Even though SSMs have been used for over two decades, they lack in characterization of their goodness of prediction, in particular when defining whether these models are actually representative for a given population.

Methods: The current paper presents, to the authors' knowledge, the most extent lower limb anatomy shape model considering the pelvis, femur, patella, tibia, fibula, talus, and calcaneum to date. The present study includes the segmented training shapes (n = 542) obtained from 271 lower limb CT scans. The different models were evaluated in terms of accuracy, compactness, generalizability as well as specificity.

Results: The size of training samples needed in each model so that it can be considered population covering was estimated to approximate around 200 samples, based on the generalizability properties of the different models. Simultaneously differences in gender and patterns in left-right asymmetry were identified and characterized. Size was found to be the most pronounced sexual discriminator whereas intra-individual variations in asymmetry were most pronounced at the insertion site of muscles.

Conclusion: For models aimed at population covering descriptive studies, the number of training samples required should amount a sizeable 200 samples. The geometric morphometric method for sex discrimination scored excellent, however, it did not largely outperformed traditional methods based on discrete measures.

Pair-wise vs group-wise registration in statistical shape model construction: representation of physiological and pathological variability of bony surface morphology

Statistical shape models (SSM) of bony surfaces have been widely proposed in orthopedics, especially for anatomical bone modeling, joint kinematic analysis, staging of morphological abnormality, and pre- and intra-operative shape reconstruction. In the SSM computation, reference shape selection, shape registration and point correspondence computation are fundamental aspects determining the quality (generality, specificity and compactness) of the SSM. Such procedures can be made critical by the presence of large morphological dissimilarities within the surfaces, not only because of anthropometrical variability but also mainly due to pathological abnormalities. In this work, we proposed a SW pipeline for SSM construction based on pair-wise (PW) shape registration, which requires the a-priori selection of the reference shape, and on a custom iterative point correspondence algorithm. We addressed large morphological deformations in five different bony surface sets, namely proximal femur, distal femur, patella, proximal fibula and proximal tibia, extracted from a retrospective patient dataset. The technique was compared to a method from the literature, based on group-wise (GW) shape registration. As a main finding, the proposed technique provided generalization and specificity median errors, for all the five bony regions, lower than 2 mm. The comparative analysis provided basically similar results. Particularly, for the distal femur that was the shape affected by the largest pathological deformations, the differences in generalization, specificity and compactness were lower than 0.5 mm, 0.5 mm, and 1%, respectively. We can argue the proposed pipeline, along with the robust correspondence algorithm, is able to compute high-quality SSM of bony shapes, even affected by large morphological variability.