This paper aims at evaluating the effect of spinal surgery on the torso shape appearance of adolescent patients. Current methods that assess the surgical outcome on the trunk shape are limited to its global asymmetry or rely on unreliable manual measurements. We introduce a novel framework to evaluate pre- to postoperative local asymmetry changes using a spectral representation of the torso shape, more specifically, the Laplacian spectrum (eigenvalues and eigenvectors) of a graph. We conduct a statistical analysis on the eigenvalues to efficiently select the spectral space and determine the significant components between preop and postop groups. On the selected eigenvectors, we propose a local analysis based on the concept of Euler characteristic to detect their local maxima and minima, which are then used to compute local left-right (L-R) asymmetries of torso shape. On 49 patients with a thoracic spinal deformity, the method captures significant pre- to postoperative changes of asymmetry at the waist, shoulder blades, shoulders, and breasts. We have evaluated average correction rates for L-R asymmetry of the waist height (67%), shoulder-blade height (64%) and depth (67%), lateral offset between shoulder and neck (61%), and breast height (52%). Spectral torso shape analysis provides a novel approach to quantify the surgical correction of the scoliotic trunk from local shape asymmetry. The proposed method could help the surgeon to understand the impact of different spinal surgery strategies on the postoperative appearance and choose the one that should provide better patient's satisfaction.

The main objective of this letter is to formulate a new approach of learning a Mahalanobis distance metric for nearest neighbor regression from a training sample set. We propose a modified version of the large margin nearest neighbor metric learning method to deal with regression problems. As an application, the prediction of post-operative trunk 3-D shapes in scoliosis surgery using nearest neighbor regression is described. Accuracy of the proposed method is quantitatively evaluated through experiments on real medical data.

Besides the spinal deformity, scoliosis modifies notably the general appearance of the trunk resulting in trunk rotation, imbalance and asymmetries which constitutes patients' major concern. Existing classifications of scoliosis, based on the type of spinal curve as depicted on radiographs, are currently used to guide treatment strategies. Unfortunately, even though a perfect correction of the spinal curve is achieved, some trunk deformities remain, making patients dissatisfied with the treatment received. The purpose of this study is to identify possible shape patterns of trunk surface deformity associated with scoliosis. First, trunk surface is represented by a multivariate functional trunk shape descriptor based on 3D clinical measurements computed on cross sections of the trunk. Then, the classical formulation of hierarchical clustering is adapted to the case of multivariate functional data and applied to a set of 236 trunk surface 3D reconstructions. The highest internal validity is obtained when considering 11 clusters that explain up to 65% of the variance in our dataset. Our clustering result shows a concordance with the radiographic classification of spinal curves in 68% of the cases. As opposed to radiographic evaluation, the trunk descriptor is three-dimensional and its functional nature offers a compact and elegant description of not only the type, but also the severity and extent of the trunk surface deformity along the trunk length. In future work, new management strategies based on the resulting trunk shape patterns could be thought of in order to improve the esthetic outcome after treatment, and thus patients satisfaction.

Surgical instrumentation for the Adolescent idiopathic scoliosis (AIS) is a complex procedure involving many difficult decisions. Selection of the appropriate fusion level remains one of the most challenging decisions in scoliosis surgery. Currently, the Lenke classification model is generally followed in surgical planning. The purpose of our study is to investigate a computer aided method for Lenke classification and scoliosis fusion level selection. The method uses a self organizing neural network trained on a large database of surgically treated AIS cases. The neural network produces two maps, one of Lenke classes and the other of fusion levels. These two maps show that the Lenke classes are associated with the the proper fusion level categories everywhere in the map except at the Lenke class transitions. The topological ordering of the Cobb angles in the neural network justifies determining a patient scoliotic treatment instrumentation using directly the fusion level map rather than via the Lenke classification.

This paper presents a novel 3-D reconstruction method of the scoliotic spine using prior vertebra models with image-based information taken from biplanar X-ray images. We first propose a global modeling approach by exploiting the 3-D scoliotic curve reconstructed from a coronal and sagittal X-ray image in order to generate an approximate statistical model from a 3-D database of scoliotic patients based on a transformation algorithm which incorporates intuitive geometrical properties. The personalized 3-D reconstruction of the spine is then achieved with a novel segmentation method which takes into account the variable appearance of scoliotic vertebrae (rotation, wedging) from standard quality images in order to segment and isolate individual vertebrae on the radiographic planes. More specifically, it uses prior 3-D models regulated from 2-D image level set functionals to identify and match corresponding bone structures on the biplanar X-rays. An iterative optimization procedure integrating similarity measures such as deformable vertebral contours regulated from high-level anatomical primitives, morphological knowledge and epipolar constraints is then applied to globally refine the 3-D anatomical landmarks on each vertebra level of the spine. This method was validated on twenty scoliotic patients by comparing results to a standard manual approach. The qualitative evaluation of the retro-projection of the vertebral contours confirms that the proposed method can achieve better consistency to the X-ray image's natural content. A comparison to synthetic models and real patient data also yields good accuracy on the localization of low-level primitives such as anatomical landmarks identified by an expert on each vertebra. The experiments reported in this paper demonstrate that the proposed method offers a better matching accuracy on a set of landmarks from biplanar views when compared to a manual technique for each evaluated cases, and its precision is comparable to 3-D models generated from magnetic resonance images, thus suitable for routine 3-D clinical assessment of spinal deformities.

This paper introduces a method to analyze the variability of the spine shape and of the spine shape deformations using articulated shape models. The spine shape was expressed as a vector of relative poses between local coordinate systems of neighboring vertebrae. Spine shape deformations were then modeled by a vector of rigid transformations that transforms one spine shape into another. Because rigid transformations do not naturally belong to a vector space, conventional mean and covariance could not be applied. The Fréchet mean and a generalized covariance were used instead. The spine shapes of a group of 295 scoliotic patients were quantitatively analyzed as well as the spine shape deformations associated with the Cotrel-Dubousset corrective surgery (33 patients), the Boston brace (39 patients), and the scoliosis progression without treatment (26 patients). The variability of intervertebral poses was found to be inhomogeneous (lumbar vertebrae were more variable than the thoracic ones) and anisotropic (with maximal rotational variability around the coronal axis and maximal translational variability along the axial direction). Finally, brace and surgery were found to have a significant effect on the Fréchet mean and on the generalized covariance in specific spine regions where treatments modified the spine shape.

In this paper, we propose a new and accurate 3D reconstruction technique for the scoliotic spine from a pair planar and conventional radiographic images (postero-anterior and lateral). The proposed model uses a priori hierarchical global knowledge, both on the geometric structure of the whole spine and of each vertebra. More precisely, it relies on the specification of two 3D templates. The first, a rough geometric template on which rigid admissible deformations are defined, is used to ensure a crude registration of the whole spine. 3D reconstruction is then refined for each vertebra, by a template on which nonlinear admissible global deformations are modeled, with statistical modal analysis of the pathological deformations observed on a representative scoliotic vertebra population. This unsupervised coarse-to-fine 3D reconstruction procedure is stated as a double energy function minimization problems efficiently solved with a stochastic optimization algorithm. The proposed method, tested on several pairs of biplanar radiographic images with scoliotic deformities, is comparable in terms of accuracy with the classical CT-scan technique while being unsupervised and requiring a lower amount of radiation for the patient.

This paper presents a new 3D reconstruction method of the scoliotic vertebrae of a spine, using two conventional radiographic views (postero-anterior and lateral), and global prior knowledge on the geometrical structure of each vertebra. This geometrical knowledge is efficiently captured by a statistical deformable template integrating a set of admissible deformations, expressed by the first modes of variation in the Karhunen-Loeve expansion of the pathological deformations observed on a representative scoliotic vertebra population. The proposed reconstruction method consists in fitting the projections of this deformable template with the segmented contours of the corresponding vertebra on the two radiographic views. The 3D reconstruction problem is stated as the minimization of a cost function for each vertebra and solved with a gradient descent technique. The reconstruction of the spine is then made vertebra by vertebra. This 3D reconstruction method has been successfully tested on several biplanar radiographic images, yielding very promising results.

The main objective of this study was to develop a 3D reconstruction technique of the spine and rib cage of idiopathic scoliotic patients using the self-calibration of the imaging system. The proposed approach computes the intrinsic and extrinsic parameters of the radiographic setup with respect to the global coordinate system used at Ste-Justine Hospital. Our approach determines an optimal estimate of the geometrical parameters of the imaging system from a nonlinear minimization of the mean square distance between the observed and analytical projections of a set of matched points identified on a pair of radiographic views. The accuracy of the optimal estimate for the intrinsic parameters was significantly improved when geometric knowledge such as the known length of detectable straight bars is incorporated as a set of equality constraints in the optimization process. Furthermore, in order to retrieve the 3D structure of interest in the global coordinate system, a reference plane including the origin of the global coordinate system is specified. Computer simulations were performed to evaluate the self-calibration procedure and to determine the minimum knowledge required to obtain an accurate 3D reconstruction for clinical applications. An in vitro validation on real images of a dry cadaveric human spine showed that the method is feasible and reaches the expected accuracy.