Statistical shape model reconstruction with sparse anomalous deformations: Application to intervertebral disc herniation
Introduction
Prior shape modeling of human organs plays a distinctive role in many medical image processing algorithms, including image registration, segmentation, surgical planning or computer-aided diagnosis (CAD) [1], [2]. Statistical shape models (SSM) of Cootes et al. [3] have become one of the most widely used algorithms for defining anatomical shape spaces and shape similarities [1]. The standard formulation of the SSM using principle component analysis (PCA) captures general anatomical variation by defining a space of plausible shapes (within certain standard deviations from the mean shape). If normal (i.e. healthy) shapes were used in the training, this shape space can be attributed to represent ‘normal’ instances. On the other hand, the SSMs cannot model local shape deformations that are not statistically significant in the training dataset. Many pathological conditions, such as intervertebral disc (IVD) herniation, locally affect the anatomical morphology and challenge automated processing techniques (e.g. segmentation, CAD) that rely on strong prior shape assumptions.
Modeling relevant local information has been attempted with hierarchical shape modeling [4], sparse PCA [5] or medial shape representations [6]. However, these techniques still require the presence of similar shape instances in the training set. Focused shape models of Chandra et al. [7] enable to increase shape modeling sensitivity by targeting specific anatomical sub-regions. This strategy should hypothetically help to improve the modeling of ‘common’ anomalous (e.g. herniated) areas but is unlikely to capture larger pathological deformations (e.g. migrations of disc material) in absence of specific training data.
Sparse optimization techniques have become a popular choice in computer visions and medical image processing applications dealing with modeling of local anomalies. A sparse optimization was used to robustly recognize facial expressions from large training datasets in the presence of occlusions and corrupted data [8]. Sparse representation shape models of Li et al. [9] define the shape space as a convex hull of sparse linear representations of training data which considerably improves accuracy of face localization in images. Sparse shape composition of Zhang et al. [10] represents a test shape instance as a sparse linear combination of training data and defines regions of specific local deformations. It has been successfully applied in several challenging medical image segmentation problems, such as lung localization and liver segmentation [10], [11] or cardiac motion analysis [12], where modeling of previously unseen local shape deformations is required. Further improvements in medical image segmentation were achieved by combining sparse reconstructions of shape subregions [13], [14] and by sparse modeling of the signal intensity appearance in the form of active appearance models [14]. The sparse shape composition and its alternatives have been shown to improve deformable model segmentation of anatomical features with pathologies that substantially alter the shape morphology. However, because the sparse shape composition uses prior information in the form of a linear combination of a subset of training shapes, it is not clear how to anatomically interpret the detected sparse anomalous differences. Unlike the SSMs, the definition of a ‘normal’ shape space and a shape distance metric is not available with the sparse shape composition. While it does not hinder the application to image segmentation, these notions are important for quantification of the pathology and for designing a CAD system.
The aim of this work is to combine the advantages of sparse optimization and SSMs in order to deliver quantitative descriptors suitable for shape comparisons and classifications. The presented method of sparse reconstruction will be applied to the clinical case of IVD herniation. The hypothesis of this research is that the proposed sparse shape reconstruction can deliver sensible CAD of IVD herniation with the potential to provide novel quantitative descriptors of the lesions. The method will preserve the benefits of strong prior knowledge in the form of SSM while being able to automatically identify, quantify and classify areas of local shape abnormalities that cannot be modeled a priori (as is the case with the IVD herniation). As a result, quantitative descriptors of the morphological characteristics of the herniation that can serve as a basis for efficient radiological diagnosis will be readily available.
The clinical application presented in this study, the IVD herniation, figure among the most common causes of low back pain. The term herniation encompasses a range of acute or chronic IVD pathologies (e.g. IVD bulge, protrusion, extrusion or sequestered disc) [15] and the references often differ in the reporting nomenclature and classification of the radiological findings [16]. Accurate and precise descriptions of normal and pathologic conditions of lumbar discs are therefore highly desirable. CAD systems capable to efficiently deliver quantitative information and consistent classification can have a significant impact on clinical diagnostic and therapeutic decision making.
Previous CAD approaches for IVD herniation utilized a variety of algorithmical strategies. Herniation detection has been performed using features derived from the appearance of the IVD in magnetic resonance imaging (MRI) (e.g. raw intensity [17], mean intensities of IVD subregions [18], textural features [18], [17]) and morphological features describing the IVD shape in a two-dimensional (2D) cross-section (major and minor axis [19], [18], statistical models of global shape variations [20], geodesic distance to a healthy shape space [21]). The presented output of the classification is usually a binary decision about the normality of the IVD. To the best of our knowledge, computer-based reporting of quantitative characteristics of the herniation or sub-classification of the herniation to one of the clinically used nomenclatures has not been previously presented. Moreover, previous methods of computerized assessment of IVD herniation from MRI have been based on analyses of one (typically the mid-sagittal) 2D slice. However, IVD herniation is a three-dimensional (3D) pathology that affects the IVD in diverse locations in various forms and shapes. An evidence of improving CAD by 3D analysis of IVD volumes has been previously presented for the case of the degenerative disc disease [22] but not applied for CAD of IVD herniation.
Classification of IVD herniation has been based on features extracted from pre-segmented IVDs. MRI segmentation of IVDs relies on signal intensity appearance cues and strong shape priors that in combination increase the segmentation performance. Several studies generated and employed prior probabilistic atlases of the spine shape in the segmentation [23], [24], or created parametric models of the IVD anatomical structure [25], [26]. The SSMs have also been a popular approach to modeling the prior shape constraints in the lumbar spine. They have been employed in the MRI segmentation of IVDs [27], [28], [20], vertebrae [29], [28] and other musculoskeletal structures [7], [30], [31] but their use in CAD of IVD herniation remain largely unexplored.
Section snippets
Methods
The sparse reconstruction algorithm is presented in Section 2.1. The reconstruction was first evaluated using simulated data (Section 2.2). Validation on real data is presented in Section 2.3 where the sparse reconstruction was incorporated into an image segmentation algorithm (Section 2.3.2) and into a herniation classification pipeline (Section 2.3.3).
Simulated data
Histogram of distances between simulated and detected center points of the herniation are presented in Fig. 5. Correlation between the simulated and detected mean displacements per vertex of the herniated region was R = 0.73 (Fig. 4b).
The majority of center points of the detected herniated regions were within 15 mm of the original center points (Fig. 5). For comparison, the average transversal diameter of the cartilage end-plates have been reported between 36.3 and 44.6 mm in lumbar IVDs [51]. This
Conclusion
Anatomical features with local pathological deformations challenge existing shape modeling techniques based on strong shape priors. This study introduced a sparse reconstruction method that is capable to overcome this limitation. It employs prior morphological knowledge in the form of statistical shape models and detects local anomalous deformations with sparse optimization. It can infer shape instances globally similar to training data, while allowing to quantify specific local deformations,
Conflict of interest
The authors have no conflict of interest to disclose.
Acknowledgments
This research was supported under Australian Research Council's Linkage Projects funding scheme LP100200422.
The authors would like to thank Dr. Mark W Strudwick from the University of Queensland for performing manual segmentation.
References (56)
- et al.
Statistical shape models for 3D medical image segmentation: a review
Med Image Anal
(2009) - et al.
Active shape models – their training and application
Comput Vis Image Underst
(1995) - et al.
Musculoskeletal MRI segmentation using multi-resolution simplex meshes with medial representations
Med Image Anal
(2010) - et al.
Focused shape models for hip joint segmentation in 3D magnetic resonance images
Med Image Anal
(2014) - et al.
Towards robust and effective shape modeling: sparse shape composition
Med Image Anal
(2012) - et al.
Deformable models with sparsity constraints for cardiac motion analysis
Med Image Anal
(2014) - et al.
Deformable segmentation via sparse representation and dictionary learning
Med Image Anal
(2012) - et al.
Active learning based intervertebral disk classification combining shape and texture similarities
Neurocomputing
(2013) - et al.
A new method for lumbar herniated inter-vertebral disc diagnosis based on image analysis of transverse sections
Comput Med Imaging Graph
(2002) - et al.
Parametric modeling of the intervertebral disc space in 3D: application to CT images of the lumbar spine
Comput Med Imaging Graph
(2014)