Accurate and robust reconstruction of a surface model of the proximal femur from sparse-point data and a dense-point distribution model for surgical navigation

EquiSim: An Open-Source Articulatable Statistical Model of the Equine Distal Limb

Most digital models of the equine distal limb that are available in the community are static and/or subject specific; hence, they have limited applications in veterinary research. In this paper, we present an articulatable model of the entire equine distal limb based on statistical shape modeling. The model describes the inter-subject variability in bone geometry while maintaining proper jointspace distances to support model articulation toward different poses. Shape variation modes are explained in terms of common biometrics in order to ease model interpretation from a veterinary point of view. The model is publicly available through a graphical user interface (https://github.com/jvhoutte/equisim) in order to facilitate future digitalization in veterinary research, such as computer-aided designs, three-dimensional printing of bone implants, bone fracture risk assessment through finite element methods, and data registration and segmentation problems for clinical practices.

Pair-wise vs group-wise registration in statistical shape model construction: representation of physiological and pathological variability of bony surface morphology

Statistical shape models (SSM) of bony surfaces have been widely proposed in orthopedics, especially for anatomical bone modeling, joint kinematic analysis, staging of morphological abnormality, and pre- and intra-operative shape reconstruction. In the SSM computation, reference shape selection, shape registration and point correspondence computation are fundamental aspects determining the quality (generality, specificity and compactness) of the SSM. Such procedures can be made critical by the presence of large morphological dissimilarities within the surfaces, not only because of anthropometrical variability but also mainly due to pathological abnormalities. In this work, we proposed a SW pipeline for SSM construction based on pair-wise (PW) shape registration, which requires the a-priori selection of the reference shape, and on a custom iterative point correspondence algorithm. We addressed large morphological deformations in five different bony surface sets, namely proximal femur, distal femur, patella, proximal fibula and proximal tibia, extracted from a retrospective patient dataset. The technique was compared to a method from the literature, based on group-wise (GW) shape registration. As a main finding, the proposed technique provided generalization and specificity median errors, for all the five bony regions, lower than 2 mm. The comparative analysis provided basically similar results. Particularly, for the distal femur that was the shape affected by the largest pathological deformations, the differences in generalization, specificity and compactness were lower than 0.5 mm, 0.5 mm, and 1%, respectively. We can argue the proposed pipeline, along with the robust correspondence algorithm, is able to compute high-quality SSM of bony shapes, even affected by large morphological variability.

Stacked sparse autoencoder networks and statistical shape models for automatic staging of distal femur trochlear dysplasia

BACKGROUND

The quantitative morphological analysis of the trochlear region in the distal femur and the precise staging of the potential dysplastic condition constitute a key point for the use of personalized treatment options for the patella-femoral joint. In this paper, we integrated statistical shape models (SSM), able to represent the individual morphology of the trochlea by means of a set of parameters and stacked sparse autoencoder (SSPA) networks, which exploit the parameters to discriminate among different levels of abnormalities.

METHODS

Two datasets of distal femur reconstructions were obtained from CT scans, including pathologic and physiologic shapes. Both of them were processed to compute SSM of healthy and dysplastic trochlear regions. The parameters obtained by the 3D-3D reconstruction of a femur shape were fed into a trained SSPA classifier to automatically establish the membership to one of three clinical conditions, namely, healthy, mild dysplasia, and severe dysplasia of the trochlea. The validation was performed on a subset of the shapes not used in the construction of the SSM, by verifying the occurrence of a correct classification.

RESULTS

A major finding of the work is that SSM are able to represent anomalies of the trochlear geometry by means of specific eigenmodes of variation and to model the interplay between morphologic features related to dysplasia. Exploiting the patient-specific morphing parameters of SSM, computed by means of a 3D-3D reconstruction, SSPA is demonstrated to outperform traditional discriminant analysis in classifying healthy, mild, and severe trochlear dysplasia providing 99%, 97%, and 98% accuracy for each of the three classes, respectively (discriminant analysis accuracy: 85%, 89%, and 77%).

CONCLUSIONS

From a clinical point of view, this paper contributes to support the increasing role of SSM, integrated with deep learning techniques, in diagnostics and therapy definition as quantitative and advanced visualization tools.

Surgical Navigation in Orthopedics: Workflow and System Review

Orthopedic surgery is a widely performed clinical procedure that deals with problems in relation to the bones, joints, and ligaments of the human body, such as musculoskeletal trauma, spine diseases, sports injuries, degenerative diseases, infections, tumors, and congenital disorders. Surgical navigation is generally recognized as the next generation technology of orthopedic surgery. The development of orthopedic navigation systems aims to analyze pre-, intra- and/or postoperative data in multiple modalities and provide an augmented reality 3-D visualization environment to improve clinical outcomes of surgical orthopedic procedures. This chapter investigates surgical navigation techniques and systems that are currently available in orthopedic procedures. In particular, optical tracking, electromagnetic localizers and stereoscopic vision, as well as commercialized orthopedic navigation systems are thoroughly discussed. Moreover, advances and development trends in orthopedic navigation are also discussed in this chapter. While current orthopedic navigation systems enable surgeons to make precise decisions in the operating room by integrating surgical planning, instrument tracking, and intraoperative imaging, it still remains an active research field which provides orthopedists with various technical disciplines, e.g., medical imaging, computer science, sensor technology, and robotics, to further develop current orthopedic navigation methods and systems.

2D/3D reconstruction of the distal femur using statistical shape models addressing personalized surgical instruments in knee arthroplasty: A feasibility analysis

BACKGROUND

Personalized surgical instruments (PSI) have gained success in the domain of total knee replacement, demonstrating clinical outcomes similar or even superior to both traditional and navigated surgeries. The key requirement for prototyping PSI is the availability of the digital bony surface. In this paper, we aim at verifying whether the 2D/3D reconstruction of the distal femur, based on statistical shape models (SSM), grants sufficient accuracy, especially in the condylar regions, to support a PSI technique.

METHODS

Computed tomographic knee datasets acquired on 100 patients with severe cartilage damage were retrospectively considered in this work. All the patients underwent total knee replacement using the PSI-based surgical technique. Eighty out of 100 reconstructed distal femur surfaces were used to build the statistical model. The remaining 20 surfaces were used for testing. The 2D/3D reconstruction process was based on digital reconstructed radiographies (DRRs) obtained with a simulated X-ray projection process. An iterative optimization procedure, based on an evolutionary algorithm, systematically morphed the statistical model to decrease the difference between the DRR, obtained by the original CT dataset, and the DRR obtained from the morphed surface.

RESULTS

Over the 80 variations, the first ten modes were found sufficient to reconstruct the distal femur surface with accuracy. Using three DRR, the maximum Hausdorff and RMS distance errors were lower than 1.50 and 0.75 mm, respectively. As expected, the reconstruction quality improved by increasing the number of DRRs. Statistical difference (P < 0.001) was found in the 2 vs 3, 2 vs 4 and 2 vs 5 DRR, thus proving that adding just a single displaced projection to the two traditional sagittal and coronal X-ray images improved significantly the reconstruction quality. The effect of the PSI contact area errors on the distal cut direction featured a maximum median error lower than 2° and 0.5° on the sagittal and frontal plane, respectively. Statistical difference was found (P < 0.0001) in the reconstruction accuracy when comparing SSM built using pathologic with respect to non-pathologic shapes (cadavers), meaning that, to improve the patient-specific reconstruction, the morphologic anomalies, specific to the pathology, must be embedded into the SSM.

CONCLUSIONS

We showed that the X-ray based reconstruction of the distal femur is reasonable also in presence of pathologic bony conditions, featuring accuracy results similar to earlier reports in the literature that reconstructed normal femurs. This finding discloses the chance of applying the proposed methodology to the reconstruction of bony surfaces used in the PSI surgical approach.

Analysis of Uncertainty and Variability in Finite Element Computational Models for Biomedical Engineering: Characterization and Propagation

Computational modeling has become a powerful tool in biomedical engineering thanks to its potential to simulate coupled systems. However, real parameters are usually not accurately known, and variability is inherent in living organisms. To cope with this, probabilistic tools, statistical analysis and stochastic approaches have been used. This article aims to review the analysis of uncertainty and variability in the context of finite element modeling in biomedical engineering. Characterization techniques and propagation methods are presented, as well as examples of their applications in biomedical finite element simulations. Uncertainty propagation methods, both non-intrusive and intrusive, are described. Finally, pros and cons of the different approaches and their use in the scientific community are presented. This leads us to identify future directions for research and methodological development of uncertainty modeling in biomedical engineering.

Computer-Assisted Orthopedic Surgery: Current State and Future Perspective

Introduced about two decades ago, computer-assisted orthopedic surgery (CAOS) has emerged as a new and independent area, due to the importance of treatment of musculoskeletal diseases in orthopedics and traumatology, increasing availability of different imaging modalities, and advances in analytics and navigation tools. The aim of this paper is to present the basic elements of CAOS devices and to review state-of-the-art examples of different imaging modalities used to create the virtual representations, of different position tracking devices for navigation systems, of different surgical robots, of different methods for registration and referencing, and of CAOS modules that have been realized for different surgical procedures. Future perspectives will also be outlined.

Fluoroscopy-based tracking of femoral kinematics with statistical shape models

PURPOSE

Precise knee kinematics assessment helps to diagnose knee pathologies and to improve the design of customized prosthetic components. The first step in identifying knee kinematics is to assess the femoral motion in the anatomical frame. However, no work has been done on pathological femurs, whose shape can be highly different from healthy ones.

METHODS

We propose a new femoral tracking technique based on statistical shape models and two calibrated fluoroscopic images, taken at different flexion-extension angles. The cost function optimization is based on genetic algorithms, to avoid local minima. The proposed approach was evaluated on 3 sets of digitally reconstructed radiographic images of osteoarthritic patients.

RESULTS

It is found that using the estimated shape, rather than that calculated from CT, significantly reduces the pose accuracy, but still has reasonably good results (angle errors around 2[Formula: see text], translation around 1.5 mm).

Low-dose three-dimensional reconstruction of the femur with unit free-form deformation

PURPOSE

This paper describes a low-dose method for reconstructing three-dimensional models of femur, using a standard shape model (SSM) and two conventional x-ray images.

METHODS

The x-ray images were taken in two orthogonal directions. The x-ray source and sensor configurations were documented. An optimized algorithm was employed to align the x-ray image to the three-dimensional model. A method of direct correspondence building is proposed for linking two-dimensional images with three-dimensional projections of a SSM. The reconstruction method proposed in this paper is based on a SSM, which was adapted for x-ray images of individual bones. The adaption was executed by deforming the template bone shape until its silhouette boundary exactly matched the x-ray image of the individual bone. A silhouette-based unit free-form deformation method was evaluated for its suitability in the adaption of the SSM for x-ray images. Comprehensive experiments were designed and conducted for 35 specimens.

RESULTS

The validity of the low-dose reconstruction method was demonstrated for the femur, with good results for accuracy (mean error of 1.1 mm, root-mean-square error of 2.1 mm), reproducibility (intraobservation coefficient of variation of 1.1%, interobservation coefficient of variation of 1.4%), and time consumption (mean of 5 min for a full femur).

CONCLUSIONS

Once this approach has been validated in vivo, it should be suited to multiple applications of routine clinical and research practices.

Statistical shape and appearance models of bones

When applied to bones, statistical shape models (SSM) and statistical appearance models (SAM) respectively describe the mean shape and mean density distribution of bones within a certain population as well as the main modes of variations of shape and density distribution from their mean values. The availability of this quantitative information regarding the detailed anatomy of bones provides new opportunities for diagnosis, evaluation, and treatment of skeletal diseases. The potential of SSM and SAM has been recently recognized within the bone research community. For example, these models have been applied for studying the effects of bone shape on the etiology of osteoarthritis, improving the accuracy of clinical osteoporotic fracture prediction techniques, design of orthopedic implants, and surgery planning. This paper reviews the main concepts, methods, and applications of SSM and SAM as applied to bone.

Statistical shape modeling of cam femoroacetabular impingement

Statistical shape modeling (SSM) was used to quantify 3D variation and morphologic differences between femurs with and without cam femoroacetabular impingement (FAI). 3D surfaces were generated from CT scans of femurs from 41 controls and 30 cam FAI patients. SSM correspondence particles were optimally positioned on each surface using a gradient descent energy function. Mean shapes for groups were defined. Morphological differences between group mean shapes and between the control mean and individual patients were calculated. Principal component analysis described anatomical variation. Among all femurs, the first six modes (or principal components) captured significant variations, which comprised 84% of cumulative variation. The first two modes, which described trochanteric height and femoral neck width, were significantly different between groups. The mean cam femur shape protruded above the control mean by a maximum of 3.3 mm with sustained protrusions of 2.5-3.0 mm along the anterolateral head-neck junction/distal anterior neck. SSM described variations in femoral morphology that corresponded well with areas prone to damage. Shape variation described by the first two modes may facilitate objective characterization of cam FAI deformities; variation beyond may be inherent population variance. SSM could characterize disease severity and guide surgical resection of bone.

Robustness and accuracy of feature-based single image 2-D-3-D registration without correspondences for image-guided intervention

2-D-to-3-D registration is critical and fundamental in image-guided interventions. It could be achieved from single image using paired point correspondences between the object and the image. The common assumption that such correspondences can readily be established does not necessarily hold for image guided interventions. Intraoperative image clutter and an imperfect feature extraction method may introduce false detection and, due to the physics of X-ray imaging, the 2-D image point features may be indistinguishable from each other and/or obscured by anatomy causing false detection of the point features. These create difficulties in establishing correspondences between image features and 3-D data points. In this paper, we propose an accurate, robust, and fast method to accomplish 2-D-3-D registration using a single image without the need for establishing paired correspondences in the presence of false detection. We formulate 2-D-3-D registration as a maximum likelihood estimation problem, which is then solved by coupling expectation maximization with particle swarm optimization. The proposed method was evaluated in a phantom and a cadaver study. In the phantom study, it achieved subdegree rotation errors and submillimeter in-plane ( X- Y plane) translation errors. In both studies, it outperformed the state-of-the-art methods that do not use paired correspondences and achieved the same accuracy as a state-of-the-art global optimal method that uses correct paired correspondences.

Automated preoperative planning of femoral stem in total hip arthroplasty from 3D CT data: atlas-based approach and comparative study

Atlas-based methods for automated preoperative planning of the femoral stem implant in total hip arthroplasty are described. Statistical atlases are constructed from a number of past preoperative plans prepared by experienced surgeons in order to represent the surgeon's expertise of the planning. Two types of atlases are considered. One is a statistical distance map atlas, which represents surgeon's preference of the contact pattern between the femoral canal (host bone) and stem (implant) surfaces. The other is an optimal reference plan, which is selected as the best representative plan expected to minimize the deviation from the surgeon's preferred contact pattern. These atlases are fitted to the patient data to automatically generate the preoperative plan of the femoral stem. In this paper, we formulate a general framework of atlas-based implant planning, and then describe the methods for construction and utilization of the two proposed atlases. In the experiments, we used 40 cases to evaluate the proposed methods and compare them with previous methods by defining the errors as differences between automated and surgeon's plans. By using the proposed methods, the positional and orientation errors were significantly reduced compared with the previous methods and the size error was superior to inter-surgeon variability in size selection using 2D templates on an X-ray image reported in previous work.

Construction of 3D human distal femoral surface models using a 3D statistical deformable model

Construction of 3D geometric surface models of human knee joint is always a challenge in biomedical engineering. This study introduced an improved statistical shape model (SSM) method that only uses 2D images of a joint to predict the 3D joint surface model. The SSM was constructed using 40 distal femur models of human knees. In this paper, a series validation and parametric analysis suggested that more than 25 distal femur models are needed to construct the SSM; each distal femur should be described using at least 3000 nodes in space; and two 2D fluoroscopic images taken in 45° directions should be used for the 3D surface shape prediction. Using this SSM method, ten independent distal femurs from 10 independent living subjects were predicted using their 2D plane fluoroscopic images. The predicted models were compared to their native 3D distal femur models constructed using their 3D MR images. The results demonstrated that using two fluoroscopic images of the knee, the overall difference between the predicted distal femur surface and the MR image-based surface was 0.16±1.16 mm. These data indicated that the SSM method could be a powerful method for construction of 3D surface geometries of the distal femur.

3D reconstruction of a patient-specific surface model of the proximal femur from calibrated x-ray radiographs: a validation study

Twenty-three femurs (one plastic bone and twenty-two cadaver bones) with both nonpathologic and pathologic cases were considered to validate a statistical shape model based technique for three-dimensional (3D) reconstruction of a patient-specific surface model from calibrated x-ray radiographs. The 3D reconstruction technique is based on an iterative nonrigid registration of the features extracted from a statistically instantiated 3D surface model to those interactively identified from the radiographs. The surface models reconstructed from the radiographs were compared to the associated ground truths derived either from a 3D CT-scan reconstruction method or from a 3D laser-scan reconstruction method and an average error distance of 0.95 mm were found. Compared to the existing works, our approach has the advantage of seamlessly handling both nonpathologic and pathologic cases even when the statistical shape model that we used was constructed from surface models of nonpathologic bones.

Robust gradient-based 3-D/2-D registration of CT and MR to X-ray images

One of the most important technical challenges in image-guided intervention is to obtain a precise transformation between the intrainterventional patient's anatomy and corresponding preinterventional 3-D image on which the intervention was planned. This goal can be achieved by acquiring intrainterventional 2-D images and matching them to the preinterventional 3-D image via 3-D/2-D image registration. A novel 3-D/2-D registration method is proposed in this paper. The method is based on robustly matching 3-D preinterventional image gradients and coarsely reconstructed 3-D gradients from the intrainterventional 2-D images. To improve the robustness of finding the correspondences between the two sets of gradients, hypothetical correspondences are searched for along normals to anatomical structures in 3-D images, while the final correspondences are established in an iterative process, combining the robust random sample consensus algorithm (RANSAC) and a special gradient matching criterion function. The proposed method was evaluated using the publicly available standardized evaluation methodology for 3-D/2-D registration, consisting of 3-D rotational X-ray, computed tomography, magnetic resonance (MR), and 2-D X-ray images of two spine segments, and standardized evaluation criteria. In this way, the proposed method could be objectively compared to the intensity, gradient, and reconstruction-based registration methods. The obtained results indicate that the proposed method performs favorably both in terms of registration accuracy and robustness. The method is especially superior when just a few X-ray images and when MR preinterventional images are used for registration, which are important advantages for many clinical applications.

3-D reconstruction of a surface model of the proximal femur from digital biplanar radiographs

Twenty-two femurs (one plastic bone and twenty-one cadaveric bones) with both nonpathologic and pathologic cases were considered to validate a point distribution model based three-dimensional (3-D) reconstruction technique using digital biplanar radiographs. The 3-D reconstruction technique is based on an iterative non-rigid registration of the features extracted from a statistically instantiated 3-D surface model to those identified from the radiographs. The surface models reconstructed from the radiographs were compared to the associated ground truths derived either from a 3-D CT-scan reconstruction method or from a 3-D laser-scan reconstruction method. Our experimental results demonstrated that our biplanar reconstruction technique could accurately reconstruct the surface models of both nonpathologic and pathologic femurs (average error distance=0.9 mm), even when the point distribution model that we used were constructed from surface models of nonpathologic femurs.