Rigid motion invariant statistical shape modeling based on discrete fundamental forms data from the osteoarthritis initiative and the Alzheimer' disease neuroimaging initiative

Shape-based disease grading via functional maps and graph convolutional networks with application to Alzheimer's disease

Shape analysis provides methods for understanding anatomical structures extracted from medical images. However, the underlying notions of shape spaces that are frequently employed come with strict assumptions prohibiting the analysis of incomplete and/or topologically varying shapes. This work aims to alleviate these limitations by adapting the concept of functional maps. Further, we present a graph-based learning approach for morphometric classification of disease states that uses novel shape descriptors based on this concept. We demonstrate the performance of the derived classifier on the open-access ADNI database differentiating normal controls and subjects with Alzheimer's disease. Notably, the experiments show that our approach can improve over state-of-the-art from geometric deep learning.

DCES-PA: Deformation-controllable elastic shape model for 3D bone proliferation analysis using hand HR-pQCT images

Bone proliferation is an important pathological feature of inflammatory rheumatic diseases. Although recent advance in high-resolution peripheral quantitative computed tomography (HR-pQCT) enables physicians to study microarchitectures, physicians' annotation of proliferation suffers from slice inconsistency and subjective variations. Also, there are only few effective automatic or semi-automatic tools for proliferation detection. In this study, by integrating pathological knowledge of proliferation formation with the advancement of statistical shape analysis theory, we present an unsupervised method, named Deformation-Controllable Elastic Shape model, for 3D bone Proliferation Analysis (DCES-PA). Unlike previous shape analysis methods that directly regularize the smoothness of the displacement field, DCES-PA regularizes the first and second-order derivative of the displacement field and decomposes these vector fields according to different deformations. For the first-order elastic metric, DCES-PA orthogonally decomposes the first-order derivative of the displacement field by shearing, scaling and bending deformation, and then penalize deformations triggering proliferation formation. For the second-order elastic metric, DCES-PA encodes both intrinsic and extrinsic surface curvatures into the second-order derivative of the displacement field to control the generation of high-curvature regions. By integrating the elastic shape metric with the varifold distances, DCES-PA achieves correspondence-free shape analysis. Extensive experiments on both simulated and real clinical datasets demonstrate that DCES-PA not only shows an improved accuracy than other state-of-the-art shape-based methods applied to proliferation analysis but also produces highly sensitive proliferation annotations to assist physicians in proliferation analysis.

Learning continuous shape priors from sparse data with neural implicit functions

Statistical shape models are an essential tool for various tasks in medical image analysis, including shape generation, reconstruction and classification. Shape models are learned from a population of example shapes, which are typically obtained through segmentation of volumetric medical images. In clinical practice, highly anisotropic volumetric scans with large slice distances are prevalent, e.g., to reduce radiation exposure in CT or image acquisition time in MR imaging. For existing shape modeling approaches, the resolution of the emerging model is limited to the resolution of the training shapes. Therefore, any missing information between slices prohibits existing methods from learning a high-resolution shape prior. We propose a novel shape modeling approach that can be trained on sparse, binary segmentation masks with large slice distances. This is achieved through employing continuous shape representations based on neural implicit functions. After training, our model can reconstruct shapes from various sparse inputs at high target resolutions beyond the resolution of individual training examples. We successfully reconstruct high-resolution shapes from as few as three orthogonal slices. Furthermore, our shape model allows us to embed various sparse segmentation masks into a common, low-dimensional latent space - independent of the acquisition direction, resolution, spacing, and field of view. We show that the emerging latent representation discriminates between healthy and pathological shapes, even when provided with sparse segmentation masks. Lastly, we qualitatively demonstrate that the emerging latent space is smooth and captures characteristic modes of shape variation. We evaluate our shape model on two anatomical structures: the lumbar vertebra and the distal femur, both from publicly available datasets.

Joint reconstruction and segmentation in undersampled 3D knee MRI combining shape knowledge and deep learning

Objective.Task-adapted image reconstruction methods using end-to-end trainable neural networks (NNs) have been proposed to optimize reconstruction for subsequent processing tasks, such as segmentation. However, their training typically requires considerable hardware resources and thus, only relatively simple building blocks, e.g. U-Nets, are typically used, which, albeit powerful, do not integrate model-specific knowledge.Approach.In this work, we extend an end-to-end trainable task-adapted image reconstruction method for a clinically realistic reconstruction and segmentation problem of bone and cartilage in 3D knee MRI by incorporating statistical shape models (SSMs). The SSMs model the prior information and help to regularize the segmentation maps as a final post-processing step. We compare the proposed method to a simultaneous multitask learning approach for image reconstruction and segmentation (MTL) and to a complex SSMs-informed segmentation pipeline (SIS).Main results.Our experiments show that the combination of joint end-to-end training and SSMs to further regularize the segmentation maps obtained by MTL highly improves the results, especially in terms of mean and maximal surface errors. In particular, we achieve the segmentation quality of SIS and, at the same time, a substantial model reduction that yields a five-fold decimation in model parameters and a computational speedup of an order of magnitude.Significance.Remarkably, even for undersampling factors of up toR= 8, the obtained segmentation maps are of comparable quality to those obtained by SIS from ground-truth images.

Contribution of Shape Features to Intradiscal Pressure and Facets Contact Pressure in L4/L5 FSUs: An In-Silico Study

Finite element models (FEMs) of the spine commonly use a limited number of simplified geometries. Nevertheless, the geometric features of the spine are important in determining its FEM outcomes. The link between a spinal segment's shape and its biomechanical response has been studied, but the co-variances of the shape features have been omitted. We used a principal component (PCA)-based statistical shape modelling (SSM) approach to investigate the contribution of shape features to the intradiscal pressure (IDP) and the facets contact pressure (FCP) in a cohort of synthetic L4/L5 functional spinal units under axial compression. We quantified the uncertainty in the FEM results, and the contribution of individual shape modes to these results. This parameterisation approach is able to capture the variability in the correlated anatomical features in a real population and sample plausible synthetic geometries. The first shape mode ([Formula: see text]) explained 22.6% of the shape variation in the subject-specific cohort used to train the SSM, and had the largest correlation with, and contribution to IDP (17%) and FCP (11%). The largest geometric variation in ([Formula: see text]) was in the annulus-nucleus ratio.

Skeletons, Object Shape, Statistics

Objects and object complexes in 3D, as well as those in 2D, have many possible representations. Among them skeletal representations have special advantages and some limitations. For the special form of skeletal representation called "s-reps," these advantages include strong suitability for representing slabular object populations and statistical applications on these populations. Accomplishing these statistical applications is best if one recognizes that s-reps live on a curved shape space. Here we will lay out the definition of s-reps, their advantages and limitations, their mathematical properties, methods for fitting s-reps to single- and multi-object boundaries, methods for measuring the statistics of these object and multi-object representations, and examples of such applications involving statistics. While the basic theory, ideas, and programs for the methods are described in this paper and while many applications with evaluations have been produced, there remain many interesting open opportunities for research on comparisons to other shape representations, new areas of application and further methodological developments, many of which are explicitly discussed here.

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.

Towards novel osteoarthritis biomarkers: Multi-criteria evaluation of 46,996 segmented knee MRI data from the Osteoarthritis Initiative

Convolutional neural networks (CNNs) are the state-of-the-art for automated assessment of knee osteoarthritis (KOA) from medical image data. However, these methods lack interpretability, mainly focus on image texture, and cannot completely grasp the analyzed anatomies' shapes. In this study we assess the informative value of quantitative features derived from segmentations in order to assess their potential as an alternative or extension to CNN-based approaches regarding multiple aspects of KOA. Six anatomical structures around the knee (femoral and tibial bones, femoral and tibial cartilages, and both menisci) are segmented in 46,996 MRI scans. Based on these segmentations, quantitative features are computed, i.e., measurements such as cartilage volume, meniscal extrusion and tibial coverage, as well as geometric features based on a statistical shape encoding of the anatomies. The feature quality is assessed by investigating their association to the Kellgren-Lawrence grade (KLG), joint space narrowing (JSN), incident KOA, and total knee replacement (TKR). Using gold standard labels from the Osteoarthritis Initiative database the balanced accuracy (BA), the area under the Receiver Operating Characteristic curve (AUC), and weighted kappa statistics are evaluated. Features based on shape encodings of femur, tibia, and menisci plus the performed measurements showed most potential as KOA biomarkers. Differentiation between non-arthritic and severely arthritic knees yielded BAs of up to 99%, 84% were achieved for diagnosis of early KOA. Weighted kappa values of 0.73, 0.72, and 0.78 were achieved for classification of the grade of medial JSN, lateral JSN, and KLG, respectively. The AUC was 0.61 and 0.76 for prediction of incident KOA and TKR within one year, respectively. Quantitative features from automated segmentations provide novel biomarkers for KLG and JSN classification and show potential for incident KOA and TKR prediction. The validity of these features should be further evaluated, especially as extensions of CNN-based approaches. To foster such developments we make all segmentations publicly available together with this publication.