Point-cloud registration using adaptive radial basis functions

A hybrid statistical morphometry free-form deformation approach to 3D personalized foot-ankle models

Foot and ankle joint models are widely used in the biomechanics community for musculoskeletal and finite element analysis. However, personalizing a foot and ankle joint model is highly time-consuming in terms of medical image collection and data processing. This study aims to develop and evaluate a framework for constructing a comprehensive 3D foot model that integrates statistical shape modeling (SSM) with free-form deformation (FFD) of internal bones. The SSM component is derived from external foot surface scans (skin measurements) of 50 participants, utilizing principal component analysis (PCA) to capture the variance in foot shapes. The derived surface shapes from SSM then guide the FFD process to accurately reconstruct the internal bone structures. The workflow accuracy was established by comparing three model-generated foot models against corresponding skin and bone geometries manually segmented and not part of the original training set. We used the top ten principal components representing 85 % of the population variation to create the model. For prediction validation, the average Dice similarity coefficient, Hausdorff distance error, and root mean square error were 0.92 ± 0.01, 2.2 ± 0.19 mm, and 2.95 ± 0.23 mm for soft tissues, and 0.84 ± 0.03, 1.83 ± 0.1 mm, and 2.36 ± 0.12 mm for bones, respectively. This study presents an efficient approach for 3D personalized foot model reconstruction via SSM generation of the foot surface that informs bone reconstruction based on FFD. The proposed workflow is part of the open-source Musculoskeletal Atlas Project linked to OpenSim and makes it feasible to accurately generate foot models informed by population anatomy, and suitable for rigid body analysis and finite element simulation.

Automated 2D and 3D finite element overclosure adjustment and mesh morphing using generalized regression neural networks

Computer representations of three-dimensional (3D) geometries are crucial for simulating systems and processes in engineering and science. In medicine, and more specifically, biomechanics and orthopaedics, obtaining and using 3D geometries is critical to many workflows. However, while many tools exist to obtain 3D geometries of organic structures, little has been done to make them usable for their intended medical purposes. Furthermore, many of the proposed tools are proprietary, limiting their use. This work introduces two novel algorithms based on Generalized Regression Neural Networks (GRNN) and 4 processes to perform mesh morphing and overclosure adjustment. These algorithms were implemented, and test cases were used to validate them against existing algorithms to demonstrate improved performance. The resulting algorithms demonstrate improvements to existing techniques based on Radial Basis Function (RBF) networks by converting to GRNN-based implementations. Implementations in MATLAB of these algorithms and the source code are publicly available at the following locations: https://github.com/thor-andreassen/femors; https://simtk.org/projects/femors-rbf; https://www.mathworks.com/matlabcentral/fileexchange/120353-finite-element-morphing-overclosure-reduction-and-slicing.

Enabling supra-aortic vessels inclusion in statistical shape models of the aorta: a novel non-rigid registration method

Statistical Shape Models (SSMs) are well-established tools for assessing the variability of 3D geometry and for broadening a limited set of shapes. They are widely used in medical imaging due to their ability to model complex geometries and their high efficiency as generative models. The principal step behind these techniques is a registration phase, which, in the case of complex geometries, can be a critical issue due to the correspondence problem, as it necessitates the development of correspondence mapping between shapes. The thoracic aorta, with its high level of morphological complexity, poses a multi-scale deformation problem due to the presence of several branch vessels with varying diameters. Moreover, branch vessels exhibit significant variability in shape, making the correspondence optimization even more challenging. Consequently, existing studies have focused on developing SSMs based only on the main body of the aorta, excluding the supra-aortic vessels from the analysis. In this work, we present a novel non-rigid registration algorithm based on optimizing a differentiable distance function through a modified gradient descent approach. This strategy enables the inclusion of custom, domain-specific constraints in the objective function, which act as landmarks during the registration phase. The algorithm's registration performance was tested and compared to an alternative Statistical Shape modeling framework, and subsequently used for the development of a comprehensive SSM of the thoracic aorta, including the supra-aortic vessels. The developed SSM was further evaluated against the alternative framework in terms of generalisation, specificity, and compactness to assess its effectiveness.

Shape modelling of the oropharynx distinguishes associations with body morphology but not whiplash-associated disorder

Characterization of the oropharynx, a subdivision of the pharynx between the soft palate and the epiglottis, is limited to simple measurements. Structural changes in the oropharynx in whiplash-associated disorder (WAD) cohorts have been quantified using two-dimensional (2D) and three-dimensional (3D) measures but the results are inconsistent. Statistical shape modelling (SSM) may be a more useful tool for systematically comparing morphometric features between cohorts. This technique has been used to quantify the variability in boney and soft tissue structures, but has not been used to examine a hollow cavity such as the oropharynx. The primary aim of this project was to examine the utility of SSM for comparing the oropharynx between WAD cohorts and control; and WAD severity cohorts. The secondary aim was to determine whether shape is associated with sex, height, weight and neck length. Magnetic resonance (MR) T1-weighted images were obtained from healthy control (n = 20), acute WAD (n = 14) and chronic WAD (n = 14) participants aged 18-39 years. Demographic, WAD severity (neck disability index) and body morphometry data were collected from each participant. Manual segmentation of the oropharynx was undertaken by blinded researchers between the top of the soft palate and tip of the epiglottis. Digital 3D oropharynx models were constructed from the segmented images and principal component (PC) analysis was performed with the PC weights normalized to z-scores for consistency. Statistical analyses were undertaken using multivariate linear models. In the first statistical model the independent variable was group (acute WAD, chronic WAD, control); and in the second model the independent variable was WAD severity (recovered/mild, moderate/severe). The covariates for both models included height, weight, average neck length and sex. Shape models were constructed to visualize the effect of perturbing these covariates for each relevant mode. The shape model revealed five modes which explained 90% of the variance: mode 1 explained 59% of the variance and primarily described differences in isometric size of the oropharynx, including elongation; mode 2 (13%) primarily described lateral (width) and AP (depth) dimensions; mode 3 (8%) described retroglossal AP dimension; mode 4 (6%) described lateral dimensions at the retropalatal-retroglossal junction and mode 5 (4%) described the lateral dimension at the inferior retroglossal region. There was no difference in shape (mode 1 p = 0.52; mode 2 p = 0.96; mode 3 p = 0.07; mode 4 p = 0.54; mode 5 p = 0.74) between control, acute WAD and chronic WAD groups. There were no statistical differences for any mode (mode 1 p = 0.12; mode 2 p = 0.29; mode 3 p = 0.56; mode 4 p = 0.99; mode 5 p = 0.96) between recovered/mild and moderate/severe WAD. Sex was not significant in any of the models but for mode 1 there was a significant association with height (p = 0.007), mode 2 neck length (p = 0.044) and in mode 3 weight (p = 0.027). Although SSM did not detect differences between WAD cohorts, it did detect associations with body morphology indicating that it may be a useful tool for examining differences in the oropharynx.

Development of predictive statistical shape models for paediatric lower limb bones

BACKGROUND AND OBJECTIVE

Accurate representation of bone shape is important for subject-specific musculoskeletal models as it may influence modelling of joint kinematics, kinetics, and muscle dynamics. Statistical shape modelling is a method to estimate bone shape from minimal information, such as anatomical landmarks, and to avoid the time and cost associated with reconstructing bone shapes from comprehensive medical imaging. Statistical shape models (SSM) of lower limb bones have been developed and validated for adult populations but are not applicable to paediatric populations. This study aimed to develop SSM for paediatric lower limb bones and evaluate their reconstruction accuracy using sparse anatomical landmarks.

METHODS

We created three-dimensional models of 56 femurs, 29 pelves, 56 tibias, 56 fibulas, and 56 patellae through segmentation of magnetic resonance images taken from 29 typically developing children (15 females; 13 ± 3.5 years). The SSM for femur, pelvis, tibia, fibula, patella, haunch (i.e., combined femur and pelvis), and shank (i.e., combined tibia and fibula) were generated from manual segmentation of comprehensive magnetic resonance images to describe the shape variance of the cohort. We implemented a leave-one-out cross-validation method wherein SSM were used to reconstruct novel bones (i.e., those not included in SSM generation) using full- (i.e., full segmentation) and sparse- (i.e., anatomical landmarks) input, and then compared these reconstructions against bones segmented from magnetic resonance imaging. Reconstruction performance was evaluated using root mean squared errors (RMSE, mm), Jaccard index (0-1), Dice similarity coefficient (DSC) (0-1), and Hausdorff distance (mm). All results reported in this abstract are mean ± standard deviation.

RESULTS

Femurs, pelves, tibias, fibulas, and patellae reconstructed via SSM using full-input had RMSE between 0.89 ± 0.10 mm (patella) and 1.98 ± 0.38 mm (pelvis), Jaccard indices between 0.77 ± 0.03 (pelvis) and 0.90 ± 0.02 (tibia), DSC between 0.87 ± 0.02 (pelvis) and 0.95 ± 0.01 (tibia), and Hausdorff distances between 2.45 ± 0.57 mm (patella) and 9.01 ± 2.36 mm (pelvis). Reconstruction using sparse-input had RMSE ranging from 1.33 ± 0.61 mm (patella) to 3.60 ± 1.05 mm (pelvis), Jaccard indices ranging from 0.59 ± 0.10 (pelvis) to 0.83 ± 0.03 (tibia), DSC ranging from 0.74 ± 0.08 (pelvis) to 0.90 ± 0.02 (tibia), and Hausdorff distances ranging from 3.21 ± 1.19 mm (patella) to 12.85 ± 3.24 mm (pelvis).

CONCLUSIONS

The SSM of paediatric lower limb bones showed reconstruction accuracy consistent with previously developed SSM and outperformed adult-based SSM when used to reconstruct paediatric bones.

Cartilage thickness and bone shape variations as a function of sex, height, body mass, and age in young adult knees

The functional relationship between bone and cartilage is modulated by mechanical factors. Scarce data exist on the relationship between bone shape and the spatial distribution of cartilage thickness. The aim of the study was to characterise the coupled variation in knee bone morphology and cartilage thickness distributions in knees with healthy cartilage and investigate this relationship as a function of sex, height, body mass, and age. MR images of 51 knees from young adults (28.4 ± 4.1 years) were obtained from a previous study and used to train a statistical shape model of the femur, tibia, and patella and their cartilages. Five multiple linear regression models were fitted to characterise morphology as a function of sex, height, body mass, and age. A logistic regression classifier was fitted to characterise morphological differences between males and females, and tenfold cross-validation was performed to evaluate the models’ performance. Our results showed that cartilage thickness and its distribution were coupled to bone morphology. The first five shape modes captured over 90% of the variance and described coupled changes to the bone and spatial distribution of cartilage thickness. Mode 1 (size) was correlated to sex (p < 0.001) and height (p < 0.0001). Mode 2 (aspect ratio) was also correlated to sex (p = 0.006) and height (p = 0.017). Mode 4 (condylar depth) was correlated to sex only (p = 0.024). A logistic regression model trained on modes 1, 2, and 4 could classify sex with an accuracy of 92.2% (95% CI [81.1%, 97.8%]). No other modes were influenced by sex, height, body mass, or age. This study demonstrated the coupled relationship between bone and cartilage, showing that cartilage is thicker with increased bone size, diaphysis size, and decreased femoral skew. Our results show that sex and height influence bone shape and the spatial distribution of cartilage thickness in a healthy young adult population, but body mass and age do not.

Glenohumeral joint reconstruction using statistical shape modeling

Evaluation of the bony anatomy of the glenohumeral joint is frequently required for surgical planning and subject-specific computational modeling and simulation. The three-dimensional geometry of bones is traditionally obtained by segmenting medical image datasets, but this can be time-consuming and may not be practical in the clinical setting. The aims of this study were twofold. Firstly, to develop and validate a statistical shape modeling approach to rapidly reconstruct the complete scapular and humeral geometries using discrete morphometric measurements that can be quickly and easily measured directly from CT, and secondly, to assess the effectiveness of statistical shape modeling in reconstruction of the entire humerus using just the landmarks in the immediate vicinity of the glenohumeral joint. The most representative shape prediction models presented in this study achieved complete scapular and humeral geometry prediction from seven or fewer morphometric measurements and yielded a mean surface root mean square (RMS) error under 2 mm. Reconstruction of the entire humerus was achieved using information of only proximal humerus bony landmarks and yielding mean surface RMS errors under 3 mm. The proposed statistical shape modeling facilitates rapid generation of 3D anatomical models of the shoulder, which may be useful in rapid development of personalized musculoskeletal models.

A Method to Compare Heterogeneous Types of Bone and Cartilage Meshes

Accurately capturing the bone and cartilage morphology and generating a mesh remains a critical step in the workflow of computational knee joint modeling. Currently, there is no standardized method to compare meshes of different element types and nodal densities, making comparisons across research teams a significant challenge. The aim of this paper is to describe a method to quantify differences in knee joint bone and cartilages meshes, independent of bone and cartilage mesh topology. Bone mesh-to-mesh distances, subchondral bone boundaries, and cartilage thicknesses from meshes of any type of mesh are obtained using a series of steps involving registration, resampling, and radial basis function fitting after which the comparisons are performed. Subchondral bone boundaries and cartilage thicknesses are calculated and visualized in a common frame of reference for comparison. The established method is applied to models developed by five modeling teams. Our approach to obtain bone mesh-to-mesh distances decreased the divergence seen in selecting a reference mesh (i.e., comparing mesh A-to-B versus mesh B-to-A). In general, the bone morphology was similar across teams. The cartilage thicknesses for all models were calculated and the mean absolute cartilage thickness difference was presented, the articulating areas had the best agreement across teams. The teams showed disagreement on the subchondral bone boundaries. The method presented in this paper allows for objective comparisons of bone and cartilage geometry that is agnostic to mesh type and nodal density.

Statistical shape modelling reveals large and distinct subchondral bony differences in osteoarthritic knees

Knee osteoarthritis (OA) results in changes such as joint-space narrowing and osteophyte formation. Radiographic classification systems group patients by the presence or absence of these gross anatomical features but are poorly correlated to function. Statistical-shape modelling (SSM) can detect subtle differences in 3D-bone geometry, providing an opportunity for accurate predictive models. The aim of this study was to describe and quantify the main modes of shape variation which distinguish end-stage OA from asymptomatic knees. Seventy-six patients with OA and 77 control participants received a CT of their knee. 3D models of the joint were created by manual segmentation. A template mesh was fitted to all meshes and rigidly aligned resulting in a set of correspondent meshes. Principal Component Analysis (PCA) was performed to create the SSM. Logistic regression was performed on the PCA weights to distinguish morphological features of the two groups. The first 7 modes of the SSM captured >90% shape variation with 6 modes best distinguishing between OA and asymptomatic knees. OA knees displayed sub-chondral bone expansion particularly in the condyles and posterior medial tibial plateau of up to 10 mm. The model classified the two groups with 95% accuracy, 96% sensitivity, 94% specificity, and 97% AUC. There were distinct features which differentiated OA from asymptomatic knees. Further research will elucidate how magnitude and location of shape changes in the knee influence clinical and functional outcomes.

The morphology of the human mandible: A computational modelling study

Cephalometric methods have been used to evaluate morphometric measurements of the mandible and quantify sex-related anatomical features; however, most studies to date employ a limited set of location-specific measurements without considering the entire three-dimensional anatomy of the mandible. The aims of this study were to develop statistical shape models (SSMs) of partially edentulous male and female mandibles to evaluate inter-subject morphological variability and secondly to assess the effectiveness of discrete clinical morphometric measurements in prediction of complete three-dimensional mandible geometry. Computed tomography images of forty partially edentulous female and twenty-five male subjects were obtained, and SSM developed using mesh fitting, rigid body registration and principal component analysis. Analysis of female and male SSMs showed that the variation along their first principal components was size-related. Sex-differentiating pure shape variations were found along the first principal component of size-normalised SSM and were observed to be most prominent in the symphysis and posterior ramus regions of the mandible. Seven morphometric measurements were found to characterise female and male shape prediction optimally. The capability to rapidly generate accurate patient-specific shape-predictive models of the mandible may be useful for implant development and pre-operative planning, particularly in the absence of bony structures following trauma or tumour resection.