A shape-partitioned statistical shape model for highly deformed femurs using X-ray images

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

Clinical relevance of augmented statistical shape model of the scapula in the glenoid region

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.

Legg-Calvé-Perthes Disease (LCPD) often results in a permanent residual hip deformity, with long-term impacts on hip function. In the clinic, decisions on how to manage LCPD deformity are based on 2D radiographic measures such as the Stulberg grades. It is unclear whether these measures accurately represent complex, patient-specific 3D deformity, making it difficult to determine the best treatment approach. Statistical shape modeling (SSM) provides an objective and compact description of variability, but there is currently no 3D SSM that focuses solely on describing shape variability in LCPD. In this study, we have constructed an SSM of femurs with LCPD deformity, which will provide a foundation for future research into how deformity is measured in the clinic. Clinical magnetic resonance (MR) images (N=13 hips, 11 patients, 3 F/8 M) of affected hips were obtained in patients with stage IV LCPD (age range: 6–12 years, estimated Stulberg grades: II-V). MR volumes were resampled isotropically to the smallest voxel dimension (.47 – .63 mm), and two raters manually segmented the proximal femurs. ShapeWorks (SCI Institute, University of Utah, Salt Lake City, UT) was used to produce an SSM with 512 particles using an incremental optimization routine: corresponding particles were initially distributed and optimized on a subset of the five most similar femurs. The mean particle distribution of the initial model was then used to initialize the remaining eight shapes, followed by an additional optimization of the particle distribution. Differences in pose and scale between shapes were removed with generalized Procrustes analysis. Modes of shape variation were quantified using principal component analysis. The first four shape modes described 87.5% of the population variability, and qualitatively captured clinically relevant variables such as femoral head width and articular-trochanteric distance (see Figure 1). A significant association (p=0.04) was observed between shape mode 4 and asphericity of the femoral head (rho=0.58). A leave-one-out cross-validation of the model demonstrated good generalizability to unseen shapes, with a mean point-to-point reconstruction error of < 1 mm if > 4 modes were included. This SSM provides a continuous, accurate, and compact representation of 3D shape variation in LCPD. Limitations to this model include a small sample size, and thus the inability to control for age. In addition to expanding this model, future work will incorporate the acetabular side to describe joint congruence, and associate shape modes with radiographic parameters. For any figures or tables, please contact the authors directly.

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.

The aim of this article is to investigate the feasibility of using a statistical shape model (SSM)-based reconstruction technique to derive a scaled, patient-specific surface model of the pelvis from a single standard anteroposterior (AP) x-ray radiograph and the feasibility of estimating the scale of the reconstructed surface model by performing a surface-based 3D/3D matching. Data sets of 14 pelvises (one plastic bone, 12 cadavers, and one patient) were used to validate the single-image based reconstruction technique. This reconstruction technique is based on a hybrid 2D/3D deformable registration process combining a landmark-to-ray registration with a SSM-based 2D/3D reconstruction. The landmark-to-ray registration was used to find an initial scale and an initial rigid transformation between the x-ray image and the SSM. The estimated scale and rigid transformation were used to initialize the SSM-based 2D/3D reconstruction. The optimal reconstruction was then achieved in three stages by iteratively matching the projections of the apparent contours extracted from a 3D model derived from the SSM to the image contours extracted from the x-ray radiograph: Iterative affine registration, statistical instantiation, and iterative regularized shape deformation. The image contours are first detected by using a semiautomatic segmentation tool based on the Livewire algorithm and then approximated by a set of sparse dominant points that are adaptively sampled from the detected contours. The unknown scales of the reconstructed models were estimated by performing a surface-based 3D/3D matching between the reconstructed models and the associated ground truth models that were derived from a CT-based reconstruction method. Such a matching also allowed for computing the errors between the reconstructed models and the associated ground truth models. The technique could reconstruct the surface models of all 14 pelvises directly from the landmark-based initialization. Depending on the surface-based matching techniques, the reconstruction errors were slightly different. When a surface-based iterative affine registration was used, an average reconstruction error of 1.6 mm was observed. This error was increased to 1.9 mm, when a surface-based iterative scaled rigid registration was used. It is feasible to reconstruct a scaled, patient-specific surface model of the pelvis from single standard AP x-ray radiograph using the present approach. The unknown scale of the reconstructed model can be estimated by performing a surface-based 3D/3D matching.

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.

This paper describes a new method of non-rigid registration using the combined power of elastic and statistical shape models. The transformations are constrained to be consistent with a physical model of elasticity to maintain smoothness and continuity. A Bayesian formulation, based on this model, on an intensity similarity measure, and on statistical shape information embedded in corresponding boundary points, is employed to find a more accurate and robust non-rigid registration. A dense set of forces arises from the intensity similarity measure to accommodate complex anatomical details. A sparse set of forces constrains consistency with statistical shape models derived from a training set. A number of experiments were performed on both synthetic and real medical images of the brain and heart to evaluate the approach. It is shown that statistical boundary shape information significantly augments and improves elastic model based non-rigid registration.KeywordsControl PointBoundary PointElastic ModelSynthetic ImageShape InformationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Ascertaining the detailed shape and spatial arrangement of anatomical structures is important not only within diagnostic settings but also in the areas of planning, simulation, intraoperative navigation, and tracking of pathology. Robust, accurate and efficient automated segmentation of anatomical structures is difficult because of their complexity and inter-patient variability. Furthermore, the position of the patient during image acquisition, the imaging device and protocol, image resolution, and other factors induce additional variations in shape and appearance. Statistical shape models (SSMs) have proven quite successful in capturing structural variability. A possible approach to obtain a 3D SSM is to extract reference voxels by precisely segmenting the structure in one, reference image. The corresponding voxels in other images are determined by registering the reference image to each other image. The SSM obtained in this way describes statistically plausible shape variations over the given population as well as variations due to imperfect registration. In this paper, we present a completely automated method that significantly reduces shape variations induced by imperfect registration, thus allowing a more accurate description of variations. At each iteration, the derived SSM is used for coarse registration, which is further improved by describing finer variations of the structure. The method was tested on 64 lumbar spinal column CT scans, from which 23, 38, 45, 46 and 42 volumes of interest containing vertebra L1, L2, L3, L4 and L5, respectively, were extracted. Separate SSMs were generated for each vertebra. The results show that the method is capable of reducing the variations induced by registration errors.

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.

Morphological study of lateral meniscus using statistical shape modelling: a study using data from the osteoarthritis initiative

Posture normalisation of 3D body scans

Accurate Humeral Version Angle Prediction From Limited Anatomical Data Using Statistical Shape Models.

In this article, we propose a unified statistical framework for image segmentation with shape prior information. The approach combines an explicitely parameterized point-based probabilistic statistical shape model (SSM) with a segmentation contour which is implicitly represented by the zero level set of a higher dimensional surface. These two aspects are unified in a Maximum a Posteriori (MAP) estimation where the level set is evolved to converge towards the boundary of the organ to be segmented based on the image information while taking into account the prior given by the SSM information. The optimization of the energy functional obtained by the MAP formulation leads to an alternate update of the level set and an update of the fitting of the SSM. We then adapt the probabilistic SSM for multi-shape modeling and extend the approach to multiple-structure segmentation by introducing a level set function for each structure. During segmentation, the evolution of the different level set functions is coupled by the multi-shape SSM. First experimental evaluations indicate that our method is well suited for the segmentation of topologically complex, non spheric and multiple-structure shapes. We demonstrate the effectiveness of the method by experiments on kidney segmentation as well as on hip joint segmentation in CT images.

BackgroundComplex bilateral midface fractures necessitate a surgically challenging procedure to preserve or restore the occlusion and the sensitive eye area. In this case control study, we aim to show the potential of a statistical shape model (SSM) for measuring the quality of the midface reconstruction, compared to the estimated preoperative situation.MethodsAn individualized SSM was postoperatively registered on 19 reconstructed complex bilateral midface fractures. Using this SSM, the distances from the simulated preoperative situation to the postoperative positions of the fracture segments were calculated. The fracture lines for Le Fort II, Le Fort III, and NOE fractures were chosen as reference points for the distance measurements.ResultsThe SSM could be registered on all 19 complex bilateral midface fractures. All analyzed fractures showed a dorsal impaction (negative values) of the midface. Le Fort II fractures showed deviation values of –0.98 ± 4.6 mm, Le Fort III fractures showed values of –3.68 ± 3.6 mm, NOE type 2 fractures showed values of –0.25 ± 4.6 mm, and NOE type 1 fractures showed values of –0.25 ± 4.6 mm.ConclusionsThe SSM can be used to measure the quality of the achieved reduction of complex bilateral midface fractures based on the estimated preoperative situation.Trial registrationDRKS00009719.