Statistical shape modeling of multi-organ anatomies with shared boundaries

Statistical shape modeling (SSM) is a valuable and powerful tool to generate a detailed representation of complex anatomy that enables quantitative analysis and the comparison of shapes and their variations. SSM applies mathematics, statistics, and computing to parse the shape into a quantitative representation (such as correspondence points or landmarks) that will help answer various questions about the anatomical variations across the population. Complex anatomical structures have many diverse parts with varying interactions or intricate architecture. For example, the heart is a four-chambered anatomy with several shared boundaries between chambers. Coordinated and efficient contraction of the chambers of the heart is necessary to adequately perfuse end organs throughout the body. Subtle shape changes within these shared boundaries of the heart can indicate potential pathological changes that lead to uncoordinated contraction and poor end-organ perfusion. Early detection and robust quantification could provide insight into ideal treatment techniques and intervention timing. However, existing SSM approaches fall short of explicitly modeling the statistics of shared boundaries. In this paper, we present a general and flexible data-driven approach for building statistical shape models of multi-organ anatomies with shared boundaries that captures morphological and alignment changes of individual anatomies and their shared boundary surfaces throughout the population. We demonstrate the effectiveness of the proposed methods using a biventricular heart dataset by developing shape models that consistently parameterize the cardiac biventricular structure and the interventricular septum (shared boundary surface) across the population data.

A new segment algorithm based on the pixels intensity and spatial information is proposed in this paper. The algorithm has three main steps. The first step is image preprocessing. After the points in the neighborhood of each image pixel are classified, their distributing situation are used to estimate the image pixel's location, in the center or near the boundary of a region. Each pixel's gradient magnitude is adaptively adjusted according to its location. The second step is image segmentation. Watershed transform is performed on the adjusted gradient magnitude image to obtain the initial segmented regions. The last step is regions merging. Pairs of adjacent regions are merged if they have small cost function. For each pair of adjacent regions, the cost function is calculated according to the strength of their shared boundaries, the ratio of smaller region area to shared boundary length, and the homogeneity. Experimental results indicate that this algorithm provides a good segmentation for segment-based image coding.

Patient-specific biomechanical simulations of joints require accurate reconstruction of bony anatomy from medical image data. The articular geometries of the joints may influence their biomechanics. Statistical shape models (SSMs) have become ubiquitous in the literature and aim to capture the natural variation of biological objects. They work by learning the variation from training examples to define the space of valid biological shapes. However, the kinematic information descriptive of the anato-physiological relationship of two interacting objects is not generally encoded in the SSM. Here, we propose a framework for developing combined statistical shape and kinematics models (SSKMs) as Gaussian process morphable models to analyse the shape and kinematics relationship. We demonstrate the framework on a three-dimensional (3D) image data set consisting of ten right-handed cadaveric shoulder joints acquired using computed tomography. Additionally, we simulate specific bone motions to encode kinematics in the combined model. Our SSKM built from shoulder data (matching scapulae and humeri) correctly depicts a correlation between the shape and kinematics as hypothesized. We furthermore demonstrate the ability to marginalize from the SSKM to obtain shape-only variation and kinematics-only variation. Future work aims to use the SSKM framework to understand the relationships between kinematics and shape for various joints as well as to develop patient-specific computational models to evaluate joint biomechanics.

In total hip arthroplasty, the shape of the contra-lateral femur frequently serves as a template for preoperative planning. Previous research on contra-lateral femoral symmetry has been based on conventional hip geometric measurements (which reduce shape to a series of linear measurements) and did not take the effect of subject positioning on radiographic femur shape into account. The aim of this study was to analyse proximal femur symmetry based on statistical shape models (SSMs) which quantify global femoral shape while also adjusting for differences in subject positioning during image acquisition. We applied our recently developed fully automatic shape model matching (FASMM) system to automatically segment the proximal femur from AP pelvic radiographs to generate SSMs of the proximal femurs of 1258 Caucasian females (mean age: 61.3 SD=9.0). We used a combined SSM (capturing the left and right femurs) to identify and adjust for shape variation attributable to subject positioning as well as a single SSM (including all femurs as left femurs) to analyse proximal femur symmetry. We also calculated conventional hip geometric measurements (head diameter, neck width, shaft width and neck-shaft angle) using the output of the FASMM system. The combined SSM revealed two modes that were clearly attributable to subject positioning. The average difference (mean point-to-curve distance) between left and right femur shape was 1.0mm before and 0.8mm after adjusting for these two modes. The automatic calculation of conventional hip geometric measurements after adjustment gave an average absolute percent asymmetry of within 3.1% and an average absolute difference of within 1.1mm or 2.9° for all measurements. We conclude that (i) for Caucasian females the global shape of the right and left proximal femurs is symmetric without isolated locations of asymmetry; (ii) a combined left–right SSM can be used to adjust for radiographic shape variation due to subject positioning; and (iii) adjusting for subject positioning increases the accuracy of predicting the shape of the contra-lateral hip.

Statistical shape models (SSMs) are used in medical imaging to quantify variations in the shape of anatomical structures across a population. This study aimed to understand if lumbar spine shape models obtained using different numbers of landmark points provide similar information. Three SSMs were created by placing landmarks points around the edges of the vertebral bodies in sagittal T2 weighted MR images of the lumbar spine from 30 women. The three SSMs differed in the number of landmark points, with four, eight, and 28 points per vertebra. Modes of variation identified by each model were compared qualitatively by three observers and the scores assigned to the modes were compared quantitatively using Pearson correlation coefficients. The first five modes of variation explained approximately 80 % of the variance in shape for all three models. The first four modes described similar variations in shape (including lumbar curvature and vertebral depth) and correlated strongly (r > 0.9). The only shape descriptor that did not correlate strongly across the three models was the concavity in the edges of the vertebral body. SSMs created using four, eight and 28 landmark points per vertebra characterise similar features of lumbar spine shape, indicating that a small number of landmark points may be used for some applications. However, shape models created using four points are not able to characterise the concavity of the vertebral edges, limiting their use for applications where this anatomical feature is important. Shape models could in the future be used opportunistically to identify and predict several musculoskeletal disorders of the spine. However, the number of landmark points needs to be chosen depending on the application of interest.

Statistical shape modeling (SSM) is an essential tool for analyzing variations in anatomical morphology. In a typical SSM pipeline, 3D anatomical images, gone through segmentation and rigid registration, are represented using lower-dimensional shape features, on which statistical analysis can be performed. Various methods for constructing compact shape representations have been proposed, but they involve laborious and costly steps. We propose Image2SSM, a novel deep-learning-based approach for SSM that leverages image-segmentation pairs to learn a radial-basis-function (RBF)-based representation of shapes directly from images. This RBF-based shape representation offers a rich self-supervised signal for the network to estimate a continuous, yet compact representation of the underlying surface that can adapt to complex geometries in a data-driven manner. Image2SSM can characterize populations of biological structures of interest by constructing statistical landmark-based shape models of ensembles of anatomical shapes while requiring minimal parameter tuning and no user assistance. Once trained, Image2SSM can be used to infer low-dimensional shape representations from new unsegmented images, paving the way toward scalable approaches for SSM, especially when dealing with large cohorts. Experiments on synthetic and real datasets show the efficacy of the proposed method compared to the state-of-art correspondence-based method for SSM.

Active Shape Models (ASM) have been widely used in the literature for the extraction of the tibial and the femoral bones from MRI. These methods use Statistical Shape Models (SSM) to drive the deformation and make the segmentation more robust. One crucial step for building such SSM is the shape correspondence (SC). Several methods have been described in the literature. The goal of this paper is to compare two SC methods, the Iterative Median Closest Point-Gaussian Mixture Model (IMCP- GMM) and the Minimum Description Length (MDL) approaches for the creation of a SSM, and to assess the impact of these SC methods on the accuracy of the femur segmentation in MRI. 28 MRI of the knee have been used. The validation has been performed by using the leave-one-out cross-validation technique. An ASMMDL and an ASMIMCP-GMMM has been built with the SSMs computed respectively with the MDL and IMCP-GMM methods. The computation time for building both SSMs has been also measured. For 90% of data, the error is inferior to 1.78 mm and 1.85 mm for respectively the ASMIMCP-GMM and the ASMMDL methods. The computation time for building the SSMs is five hours and two days for respectively the IMCP-GMM and the MDL methods. Both methods seems to give, at least, similar results for the femur segmentation in MRI. However (1) IMCP-GMM can be used for all types of shape, this is not the case for the MDL method which only works for closed shape, and (2) IMCP- GMM is much faster than MDL.

IntroductionVideo urodynamic studies (VUDS) use fluoroscopic imaging to visualize the bladder and multichannel urodynamics to assess its function. Qualitative assessment of bladder shape is used to identify abnormal features (e.g., diverticula) that correspond with pathophysiology; however, this assessment is limited in its ability to predict bladder function. Therefore, we developed a novel quantitative approach to assess bladder shape obtained from fluoroscopic VUDS images utilizing statistical shape modeling. This method was compared to existing binary and continuous shape quantification methods and used to identify relationships between bladder shape and measures of bladder physiology categorized as related to sensation, incontinence, or emptying.MethodsThis was a retrospective, cross-sectional study of 49 participants. Bladder walls were segmented from fluoroscopic images at rest with the bladder filled to approximately 300 mL. Bladder shape was evaluated in three ways: 1) binary categorization as typical or atypical based on clinical assessment, 2) quantification of height-to-width ratios, and 3) quantification by statistical shape modeling. Independent t-tests and correlations were used to assess associations between the three shape evaluation methods and to define relationships between shape and physiologic measures: 3 volumetric measures describing sensation, 2 dichotomous variables addressing incontinence, and 1 volumetric measure representing emptying.ResultsThe statistical shape model generated 5 modes of variation. Mode 1 corresponded with height-to-width ratio (r=0.920, p<0.001), modes 2 and 3 with diagonal height-to-width ratio (r=0.66 and -0.585, p<0.001 and <0.001), and mode 3 with binary shape categorization (p<0.001). In terms of function, those with atypical bladder shape had impaired emptying (p=0.010), modes 4 and 5 were significantly associated with measures of bladder sensation, mode 3 with urodynamic stress urinary incontinence, and mode 3 with emptying in those able to void (r=0.368, p=0.021). The relationship between mode 3 and emptying across all patients is best fitted by a quadratic function (p<0.001).DiscussionOur results demonstrate that binary shape categorization and bladder shape quantified by statistical shape modeling correspond with measures of bladder physiology. This foundational study establishes statistical shape modeling as a robust bladder shape quantification method that can be used to relate bladder shape with physiology.

Segmentation of the left ventricular endocardium from magnetic resonance images by using different statistical shape models

Background: Craniosynostosis is a condition caused by the premature fusion of skull sutures, leading to irregular growth patterns of the head. Three-dimensional photogrammetry is a radiation-free alternative to the diagnosis using computed tomography. While statistical shape models have been proposed to quantify head shape, no shape-model-based classification approach has been presented yet. Methods: We present a classification pipeline that enables an automated diagnosis of three types of craniosynostosis. The pipeline is based on a statistical shape model built from photogrammetric surface scans. We made the model and pathology-specific submodels publicly available, making it the first publicly available craniosynostosis-related head model, as well as the first focusing on infants younger than 1.5 years. To the best of our knowledge, we performed the largest classification study for craniosynostosis to date. Results: Our classification approach yields an accuracy of 97.8 %, comparable to other state-of-the-art methods using both computed tomography scans and stereophotogrammetry. Regarding the statistical shape model, we demonstrate that our model performs similar to other statistical shape models of the human head. Conclusion: We present a state-of-the-art shape-model-based classification approach for a radiation-free diagnosis of craniosynostosis. Our publicly available shape model enables the assessment of craniosynostosis on realistic and synthetic data.

Poster 139: Utilization of 3D Statistical Shape Modeling of Anatomic Variation Across a Cohort of Patella Instability Patients

We present a computer vision-based approach to estimating the projected frontal surface area (pFSA) of cyclists from unconstrained images. Wind tunnel studies show a reduction in cyclists’ aerodynamic drag through manipulation of the cyclist’s pose. Whilst the mechanism by which reduction is achieved remains unknown, it is widely accepted in the literature that the drag is proportional to the cyclist’s pFSA. This paper describes a repeatable automatic method for pFSA estimation for the study of its relationship with aerodynamic drag in cyclists. The proposed approach is based on finding object boundaries in images. An initialised curve dynamically evolves in the image to minimise an energy function designed to force the curve to gravitate towards image features. To overcome occlusions and pose variation, we use a statistical cyclist shape and appearance models as priors to encourage the evolving curve to arrive at the desired solution. Contour initialisation is achieved using a discriminative object detection method based on offline supervised learning that yields a cyclist classifier. Once an instance of a cyclist is detected in an image and segmented, the pFSA is calculated from the area of the final curve. Applied to two challenging datasets of cyclist images, for cyclist detection our method achieves precision scores of 1.0 and 0.96 and recall scores of 0.68 and 0.83 on the wind tunnel and cyclists-in-natura datasets, respectively. For cyclist segmentation, it achieves 0.88 and 0.92 scores for the mean dice similarity coefficient metric on the two datasets, respectively. We discuss the performance of our method under occlusion, orientation, and pose conditions. Our method successfully estimates pFSA of cyclists and opens new vistas for exploration of the relationship between pFSA and aerodynamic drag.

A lumbar spine statistical shape model (SSM) was developed to explain morphological differences in a population with adolescent idiopathic scoliosis (AIS). Computed tomography (CT) was used to collect data on the lumbar spine vertebrae and curvature of 49 subjects. The CT data were processed by segmentation, landmark identification, and template mesh mapping, and then SSMs of the individual vertebrae and entire lumbar spine were established using generalized Procrustes analysis and principal component analysis (PCA). Scaling was the most prevalent variation pattern. The weight coefficient was optimized using the Levenberg-Marquardt (LM) algorithm, and multiple regression analysis was used to establish a prediction model for age, sex, height, and body mass index (BMI). The effectiveness of the SSM and prediction model was quantified based on the root-mean-square error (RMSE). An automatic measurement method was developed to measure the anatomical parameters of the geometric model. The lumbar vertebrae size was significantly affected by height, sex, BMI, and age, with men having lower vertebral height than women. The trends in anatomical parameters were consistent with previous studies. The vertebral SSMs characterized the shape changes in the processes, while the lumbar spine SSM described alignment changes associated with translatory shifts, kyphosis, and scoliosis. Quantifying anatomical variation with SSMs can inform implant design and assist clinicians in diagnosing pathology and screening patients. Lumbar spine SSMs can also support biomechanical simulations of populations with AIS.

Silicon has long been the material of choice for detectors for many applications, from space astronomy to synchrotron research. When operating in space, or within a synchrotron or other accelerator, the detector can be subjected to a harsh radiation environment. The presence of these high energy electrons, protons and gammas can lead to radiation-induced damage within the silicon lattice of the detector, creating further defects or ``traps'' in addition to any defects intrinsic to the lattice.Charge-Coupled Devices (CCDs) have been used for many years to populate the focal planes of space telescopes, with recent examples ranging from the Hubble Space Telescope to the more recently launched ESA Gaia mission. The radiation environment in such missions is often dominated by high-energy protons, and leads to traps which act to capture electrons from signal charge packets as they are transferred through the device. Any captured electrons are then released later in time, with this time determined by the emission time constant of the trap species in question. The repeated capture and release of signal as it is transferred through the CCD produces a ``smearing'' effect, resulting in a change in shape of the objects imaged. This change in shape is not only undesirable, but has particular importance to future applications such as the ESA Euclid mission, in which the subtle shape changes due to weak gravitational lensing are to be measured.In order to correct for any radiation damage present in a CCD, one must be able to produce a model that accurately represents the transfer of charge through a device containing such traps. While current models are often based on fits to observed data, it is now highly desirable to be able to actively predict the effects of any radiation on the device through a deeper understanding of the defects present in the lattice, at a sub-pixel, single-trap level. However, currently our understanding of defects within silicon has been based largely on techniques which analyse the average properties of many traps, often over several trap species.Here is presented a selection of methods, both experimental and simulated, that can be used to begin to study populations of lattice defects down to individual defects themselves. These studies have enabled the investigation of not only the defect densities and the device-averaged trap parameters, but also the properties of individual lattice defects in the device, en route to actively predicting the impact of the radiation environment before launch.

We present an automatic segmentation and statistical shape modeling system for the paranasal sinuses which allows us to locate structures in and around the sinuses, as well as to observe the natural variations that occur in these structures. This system involves deformably registering a given patient image to a manually segmented template image, and using the resulting deformation field to transfer labels from template to patient. We use 3D snake splines to correct errors in the deformable registration. Once we have several accurately segmented images, we build statistical shape models for each structure in the sinus allowing us to observe the mean shape of the population, as well as the variations observed in the population. These shape models are useful in several ways. First, regular video-CT registration methods are insufficient to accurately register pre-operative computed tomography (CT) images with intra-operative endoscopy video because of deformations that occur in structures containing high amounts of erectile tissue. Our aim is to estimate these deformations using our shape models in order to improve video-CT registration, as well as to distinguish normal variations in anatomy from abnormal variations, and automatically detect and stage pathology. We can also compare the mean shape and variances of different populations, such as different genders or ethnicities, and observe the differences and similarities, as well as of different age groups, and observe the developmental changes that occur in the sinuses.