Cube-Cut: Vertebral Body Segmentation in MRI-Data through Cubic-Shaped Divergences

In this article, we present a graph-based method using a cubic template for volumetric segmentation of vertebrae in magnetic resonance imaging (MRI) acquisitions. The user can define the degree of deviation from a regular cube via a smoothness value Delta. The Cube-Cut algorithm generates a directed graph with two terminal nodes (s-t-network), where the nodes of the graph correspond to a cubic-shaped subset of the image's voxels. The weightings of the graph's terminal edges, which connect every node with a virtual source s or a virtual sink t, represent the affinity of a voxel to the vertebra (source) and to the background (sink). Furthermore, a set of infinite weighted and non-terminal edges implements the smoothness term. After graph construction, a minimal s-t-cut is calculated within polynomial computation time, which splits the nodes into two disjoint units. Subsequently, the segmentation result is determined out of the source-set. A quantitative evaluation of a C++ implementation of the algorithm resulted in an average Dice Similarity Coefficient (DSC) of 81.33% and a running time of less than a minute.Comment: 23 figures, 2 tables, 43 references, PLoS ONE 9(4): e9338

Multi-Surface Simplex Spine Segmentation for Spine Surgery Simulation and Planning

This research proposes to develop a knowledge-based multi-surface simplex deformable model for segmentation of healthy as well as pathological lumbar spine data. It aims to provide a more accurate and robust segmentation scheme for identification of intervertebral disc pathologies to assist with spine surgery planning. A robust technique that combines multi-surface and shape statistics-aware variants of the deformable simplex model is presented. Statistical shape variation within the dataset has been captured by application of principal component analysis and incorporated during the segmentation process to refine results. In the case where shape statistics hinder detection of the pathological region, user-assistance is allowed to disable the prior shape influence during deformation. Results have been validated against user-assisted expert segmentation

Computationally Efficient Finite Element Models of the Lumbar Spine for the Evaluation of Spine Mechanics and Device Performance

Finite Element models of the lumbar spine are commonly used for the study of spine mechanics and device performance, but have limited usefulness in some applications such as clinical and design phase assessments due to long analysis times. In this study a computationally efficient L4-L5 FSU model and a L1-Sacrum multi-segment model were developed and validated. The FSU is a functional spine unit consisting of two adjacent vertebral bodies, in this case L4 and L5. The multi-segment model consists of all lumbar vertebrae and the sacrum. The models are able to accurately predict spine kinematics with significantly reduced analysis times, relative to fully deformable representations. Analysis times were reduced from 3 hrs and 20 min to 2 min and 1 min for the multi-segment and FSU models, respectively. The vertebrae geometries were reconstructed from CT scans of the cadaveric specimen. Prior to model development, experimental testing was performed on the specimen using a custom multi-axis spine simulator. Collection of kinematic data in response to external loading made tuning of the model stiffness possible. The improved computational efficiency of the models makes them more useful for applications requiring multiple iterations and short analysis times such as clinical and design phase assessments of implants. The model can also be used in efforts to develop lumbar musculoskeletal models, which may require multiple runs for the optimization of muscle forces

Multi-objective design optimization of a mobile-bearing total disc arthroplasty considering spinal kinematics, facet joint loads, and metal-on-polyethylene contact mechanics

Total disc arthroplasty (TDA) is a motion-preserving surgical technique used to treat spinal disorders, when more conservative medical therapies fail. Unfortunately, a high incidence of revision surgery exists due to postoperative complications including abnormal kinematics, facet joint arthritis, and implant failures. However, TDA is still an attractive option, since an optimally designed artificial disc is expected to reproduce native segmental biomechanics. Correspondingly, it would mitigate the development of adjacent segment diseases (a major concern of spinal fusion) caused by altered segmental biomechanics. Design optimization is a process of finding the best design parameters for a component/system to satisfy one/multiple design requirements using optimization algorithms. The shape of a candidate design is parametrized using computer-aided design, such that design parameters are manipulated to minimize one/multiple objective functions subject to performance constraints and design space bounds. Optimization algorithms typically require the gradients of the objective/constraint functions with respect to each design variable. In the traditional design optimization, due to the high computational cost to calculate the gradients by performing finite element analysis in each optimization iteration, it often results in a slow process to seek the optimal solution. To address the problem, an artificial neural network (ANN) was implemented to derive the analytical expressions of the objective/constraint function and their gradients. By incorporating analytical gradients, we successfully developed a multiobjective optimization (MOO) framework considering three performance metrics simultaneously. Furthermore, a new mobile-bearing TDA design concept featuring a biconcave polyethylene (PE) core was proposed, to strengthen the PE rim, where a high risk of fracture exists. It was hypothesized that there is a trade-off relationship among postoperative performance metrics in terms of spinal kinematics, facet joint loading, and metal-on-polyethylene contact mechanics. We tested this hypothesis by refining the new TDA to match normal segmental biomechanics and alleviate PE core stress. After performing MOO, the best-trade-off TDA design was determined by the solved three-dimensional Pareto frontier. The novel MOO framework can be also used to improve existing TDA designs, as well as to push the cutting edge of surgical techniques for the treatment of spinal disorders

Deformable Multisurface Segmentation of the Spine for Orthopedic Surgery Planning and Simulation

Purpose: We describe a shape-aware multisurface simplex deformable model for the segmentation of healthy as well as pathological lumbar spine in medical image data. Approach: This model provides an accurate and robust segmentation scheme for the identification of intervertebral disc pathologies to enable the minimally supervised planning and patient-specific simulation of spine surgery, in a manner that combines multisurface and shape statistics-based variants of the deformable simplex model. Statistical shape variation within the dataset has been captured by application of principal component analysis and incorporated during the segmentation process to refine results. In the case where shape statistics hinder detection of the pathological region, user assistance is allowed to disable the prior shape influence during deformation. Results: Results demonstrate validation against user-assisted expert segmentation, showing excellent boundary agreement and prevention of spatial overlap between neighboring surfaces. This section also plots the characteristics of the statistical shape model, such as compactness, generalizability and specificity, as a function of the number of modes used to represent the family of shapes. Final results demonstrate a proof-of-concept deformation application based on the open-source surgery simulation Simulation Open Framework Architecture toolkit. Conclusions: To summarize, we present a deformable multisurface model that embeds a shape statistics force, with applications to surgery planning and simulation

Multi-Scale Vertebral-Kinematics Based Simulation Pipeline of the Human Spine With Application to Spine Tissues Analysis

This study developed an analytical tool for understanding spine tissues’ behavior in response to vertebral kinematics and spine pathology over a range of body postures. It proposed a novel pipeline of computational models based on predicting individual vertebral kinematics from measurable body-level motions, using musculoskeletal dynamics simulations to drive the vertebrae in corresponding spine FEMs. A reformulated elastic surface node (ESN) lumbar model was developed for use in MSD simulations. The ESN model modifies the lumbar spine within an existing MSD model by removing non-physiological kinematic constraints and including elastic IVD behavior. The model was scaled using subject-specific anthropometrics and validated to predict in vivo vertebral kinematics and IVD pressures during trunk flexion/extension. The ESN model was integrated into a novel simulation pipeline that automatically maps it to a kinematics-driven FEM (KD-FEM). The KD-FEM consisted of lumbar vertebrae scaled to subject-specific geometries and actuated by subject-specific vertebral kinematics from the ESN model for different activities. The pipeline was validated for its ability to predict in vivo IVD pressures at L4-L5 level during flexion and load carrying postures. A detailed multi-layered multi-phase lumbar canal FE model was integrated into the KD-FEM to quantify risks to canal tissues due to vertebral kinematics and progressive canal narrowing (stenosis). This enabled distinct computation of proposed stenosis measures, including cerebrospinal fluid pressure, cauda equina deformation and related stresses/pressure/strains, among others. Model outputs included measures during flexion and comparison of three clinically relevant degrees of progressive stenosis of the bony vertebral foramen at L4 level

Intervertebral disc characterization by shear wave elastography: an in-vitro preliminary study

Patient-specific numerical simulation of the spine is a useful tool both in clinic and research. While geometrical personalization of the spine is no more an issue, thanks to recent technological advances, non-invasive personalization of soft tissue’s mechanical properties remains a challenge. Ultrasound elastography is a relatively recent measurement technique allowing the evaluation of soft tissue’s elastic modulus through the measurement of shear wave speed (SWS). The aim of this study was to determine the feasibility of elastographic measurements in intervertebral disc (IVD). An in-vitro approach was chosen to test the hypothesis that SWS can be used to evaluate IVD mechanical properties and to assess measurement repeatability. Eleven oxtail IVDs were tested in compression to determine their stiffness and apparent elastic modulus at rest and at 400 N. Elastographic measurements were performed in these two conditions and compared to these mechanical parameters. The protocol was repeated six times to determine elastographic measurement repeatability. Average SWS over all samples was 5.3 ± 1.0 m/s, with a repeatability of 7 % at rest and 4.6 % at 400 N; stiffness and apparent elastic modulus were 266.3 ± 70.5 N/mm and 5.4 ± 1.1 MPa at rest, respectively, while at 400 N they were 781.0 ± 153.8 N/mm and 13.2 ± 2.4 MPa. Correlations were found between elastographic measurements and IVD mechanical properties; these preliminary results are promising for further in-vivo application.The authors are grateful to the ParisTech BiomecAM chair program on subject-specific musculoskeletal modelling for funding (with the support of Proteor, ParisTech and Yves Cotrel Foundations)

Construction and Validation of a Hybrid Lumbar Spine Model For the Fast Evaluation of Intradiscal Pressure and Mobility

International audienceA novel hybrid model of the lumbar spine, allowing fast static and dynamic simulations of the disc pressure and the spine mobility, is introduced in this work. Our contribution is to combine rigid bodies, deformable finite elements, articular constraints, and springs into a unique model of the spine. Each vertebra is represented by a rigid body controlling a surface mesh to model contacts on the facet joints and the spinous process. The discs are modeled using a heterogeneous tetrahedral finite element model. The facet joints are represented as elastic joints with six degrees of freedom, while the ligaments are modeled using non-linear one-dimensional elastic elements. The challenge we tackle is to make these different models efficiently interact while respecting the principles of Anatomy and Mechanics. The mobility, the intradiscal pressure, the facet joint force and the instantaneous center of rotation of the lumbar spine are validated against the experimental and theoretical results of the literature on flexion, extension, lateral bending as well as axial rotation. Our hybrid model greatly simplifies the modeling task and dramatically accelerates the simulation of pressure within the discs, as well as the evaluation of the range of motion and the instantaneous centers of rotation, without penalizing precision. These results suggest that for some types of biomechanical simulations, simplified models allow far easier modeling and faster simulations compared to usual full-FEM approaches without any loss of accuracy