Statistical shape modeling characterizes three-dimensional shape and alignment variability in the lumbar spine

Comprehensive assessment of global spinal sagittal alignment and related normal spinal loads in a healthy population

Abnormal postoperative global sagittal alignment (GSA) is associated with an increased risk of mechanical complications after spinal surgery. Typical assessment of sagittal alignment relies on a few selected measures, disregarding global complexity and variability of the sagittal curvature. The normative range of spinal loads associated with GSA has not yet been considered in clinical evaluation. The study objectives were to develop a new GSA assessment method that holistically describes the inherent relationships within GSA and to estimate the related spinal loads. Vertebral endplates were annotated on radiographs of 85 non-pathological subjects. A Principal Component Analysis (PCA) was performed to derive a Statistical Shape Model (SSM). Associations between identified GSA variability modes and conventional alignment measures were assessed. Simulations of respective Shape Modes (SMs) were performed using an established musculoskeletal AnyBody model to estimate normal variation in cervico-thoraco-lumbar loads. The first six principal components explained 97.96% of GSA variance. The SSM provides the normative range of GSA and a visual representation of the main variability modes. Normal variation relative to the population mean in identified alignment features was found to influence spinal loads, e.g. the lower bound of the second shape mode (SM2-2σ) corresponds to an increase in L4L5-compression by 378.64 N (67.86%). Six unique alignment features were sufficient to describe GSA almost entirely, demonstrating the value of the proposed method for an objective and comprehensive analysis of GSA. The influence of these features on spinal loads provides a normative biomechanical reference, eventually guiding surgical planning of deformity correction in the future.

Dataset of Finite Element Models of Normal and Deformed Thoracolumbar Spine

Adult spine deformity (ASD) is prevalent and leads to a sagittal misalignment in the vertebral column. Computational methods, including Finite Element (FE) Models, have emerged as valuable tools for investigating the causes and treatment of ASD through biomechanical simulations. However, the process of generating personalised FE models is often complex and time-consuming. To address this challenge, we present a dataset of FE models with diverse spine morphologies that statistically represent real geometries from a cohort of patients. These models are generated using EOS images, which are utilized to reconstruct 3D surface spine models. Subsequently, a Statistical Shape Model (SSM) is constructed, enabling the adaptation of a FE hexahedral mesh template for both the bone and soft tissues of the spine through mesh morphing. The SSM deformation fields facilitate the personalization of the mean hexahedral FE model based on sagittal balance measurements. Ultimately, this new hexahedral SSM tool offers a means to generate a virtual cohort of 16807 thoracolumbar FE spine models, which are openly shared in a public repository.

Three-dimensional lumbar spine generation using variational autoencoder

The disease analysis of the lumbar spine often requires a large number of three-dimensional (3D) models. Currently, there is a lack of 3D model of the lumbar spine for research, especially for the diseases such as scoliosis where it is difficult to collect sufficient data in a short period of time. To solve this problem, we develop an end-to-end network based on 3D variational autoencoder for randomly generating 3D lumbar spine model. In this network, the dual path encoder structure is used to fit two individual variables, i.e., mean and variance. Spatial coordinate attention modules are added to the encoder to improve the learning ability of the network to the 3D spatial structure of the lumbar spine. To enhance the power of the network to reconstruct the lumbar spine, a regularization loss is added to constrain the distribution loss. Additionally, Gaussian noise layers are added to the decoder to improve the authenticity and diversity of generated model. The experiments were conducted on the data of the entire lumbar spine and the individual lumbar vertebra, respectively. The results showed that the voxel intersection over union was 0.588 and 0.684, the voxel Dice coefficient was 0.739 and 0.811, the average surface distance was 0.807 and 1.189, and the Hausdorff distance was 2.615 and 3.710, for the entire lumbar spine and individual lumbar vertebra, respectively. The developed approach is comparable to the most commonly used model generation method of statistical shape model (SSM) in both visual and objective indicators, while the developed approach does not require the landmarks that is needed in the SSM method. Therefore, this fully automatic method can be easily used for population-based modeling of the lumbar spine which has the potential to be a powerful clinical tool.

Development, calibration and validation of a comprehensive customizable lumbar spine FE model for simulating fusion constructs

Instrumentation alters the biomechanics of the spine, and therefore prediction of all output quantities that have critical influence post-surgically is significant for engineering models to aid in clinical predictions. Geometrical morphological finite element models can bring down the development time and cost of custom intact and instrumented models and thus aids in the better inference of biomechanics of surgical instrumentation on patient-specific diseased spine segments. A comprehensive hexahedral morphological lumbosacral finite element model is developed in this work to predict the range of motions, disc pressures, and facet contact forces of the intact and instrumented spine. Facet contact forces are needed to predict the impact of fusion surgeries on adjacent facet contacts in bending, axial rotation, and extension motions. Extensive validation in major physiological loading regimes of the pure moment, pure compression, and combined loading is undertaken. In vitro, experimental corridor results from six different studies reported in the literature are compared and the generated model had statistically significant comparable values with these studies. Flexion, extension and bending moment rotation curves of all segments of the developed model were favourable and within two separately established experimental corridor windows as well as recent simulation results. Axial torque moment rotation curves were comparable to in vitro results for four out of five lumbar functional units. The facet contact force results also agreed with in vitro experimental results. The current model is also computationally efficient with respect to contemporary models since it uses significantly smaller number of elements without losing the accuracy in terms of response prediction. This model can further be used for predicting the impact of different instrumentation techniques on the lumbar vertebral column.

Prediction of the 3D shape of the L1 vertebral body from adjacent vertebrae

The aim of treatments of vertebral fractures is the anatomical reduction to restore the physiological biomechanics of the spine and the stabilization of the fracture to allow bone healing. However, the three-dimensional shape of the fractured vertebral body before the fracture is unknown in the clinical setting. Information about the pre-fracture vertebral body shape could help surgeons to select the optimal treatment. The goal of this study was to develop and validate a method based on Singular Value Decomposition (SVD) to predict the shape of the vertebral body of L1 from the shapes of T12 and L2. The geometry of the vertebral bodies of T12, L1 and L2 vertebrae of 40 patients were extracted from CT scans available from the VerSe2020 open-access dataset. Surface triangular meshes of each vertebra were morphed onto a template mesh. The set of vectors with the node coordinates of the morphed T12, L1 and L2 were compressed with SVD and used to build a system of linear equations. This system was used to solve a minimization problem and to reconstruct the shape of L1. A leave-one-out cross-validation was performed. Moreover, the approach was tested against an independent dataset with large osteophytes. The results of the study show a good prediction of the shape of the vertebral body of L1 from the shapes of the two adjacent vertebrae (mean error equal to 0.51 ± 0.11 mm on average, Hausdorff distance equal to 2.11 ± 0.56 mm on average), compared to current CT resolution typically used in the operating room. The error was slightly higher for patients presenting large osteophytes or severe bone degeneration (mean error equal to 0.65 ± 0.10 mm, Hausdorff distance equal to 3.54 ± 1.03 mm). The accuracy of the prediction was significantly better than approximating the shape of the vertebral body of L1 by the shape of T12 or L2. This approach could be used in the future to improve the pre-planning of spine surgeries to treat vertebral fractures.

Morphable models of the lumbar spine to vary geometry based on pathology, demographics, and anatomical measurements

The shape of the lumbar spine influences its function and dysfunction. Yet examining the influence of geometric differences associated with pathology or demographics on lumbar biomechanics is challenging in vivo where these effects cannot be isolated, and the use of simple anatomical measurements does not fully capture the complex three-dimensional geometry. The goal of this work was to develop and share morphable models of the lumbar spine that allow geometry to be varied according to pathology, demographics, or anatomical measurements. Partial least squares regression was used to generate statistical shape models that quantify geometric differences associated with pathology, demographics, and anatomical measurements from the lumbar spines of 87 patients. To determine if the morphable models detected meaningful geometric differences, the ability of the morphable models to classify spines was compared with models generated from random labels. The models for disc herniation (p < 0.04), spondylolisthesis (p < 0.001), and sex (p < 0.01) all performed significantly better than the random models. Age was predicted with a root mean square error of 14.1 years using the age-based model. The morphable models for anatomical measurements were able to produce instances with root mean square errors less than 0.8°, 0.3 cm², and 0.7 mm between desired and resulting measurements. This method can be used to produce morphable models that enable further analysis of the relationship among shape, pathology, demographics, and function through computational simulations. The morphable models and code are available at https://github.com/aclouthier/morphable-lumbar-model.

Statistical shape modelling of the thoracic spine for the development of pedicle screw insertion guides

Spinal fixation and fusion are surgical procedures undertaken to restore stability in the spine and restrict painful or degenerative motion. Malpositioning of pedicle screws during these procedures can result in major neurological and vascular damage. Patient-specific surgical guides offer clear benefits, reducing malposition rates by up to 25%. However, they suffer from long lead times and the manufacturing process is dependent on third-party specialists. The development of a standard set of surgical guides may eliminate the issues with the manufacturing process. To evaluate the feasibility of this option, a statistical shape model (SSM) was created and used to analyse the morphological variations of the T4-T6 vertebrae in a population of 90 specimens from the Visible Korean Human dataset (50 females and 40 males). The first three principal components, representing 39.7% of the variance within the population, were analysed. The model showed high variability in the transverse process (~ 4 mm) and spinous process (~ 4 mm) and relatively low variation (< 1 mm) in the vertebral lamina. For a Korean population, a standardised set of surgical guides would likely need to align with the lamina where the variance in the population is lower. It is recommended that this standard set of surgical guides should accommodate pedicle screw diameters of 3.5-6 mm and transverse pedicle screw angles of 3.5°-12.4°.

X23D-Intraoperative 3D Lumbar Spine Shape Reconstruction Based on Sparse Multi-View X-ray Data

Visual assessment based on intraoperative 2D X-rays remains the predominant aid for intraoperative decision-making, surgical guidance, and error prevention. However, correctly assessing the 3D shape of complex anatomies, such as the spine, based on planar fluoroscopic images remains a challenge even for experienced surgeons. This work proposes a novel deep learning-based method to intraoperatively estimate the 3D shape of patients' lumbar vertebrae directly from sparse, multi-view X-ray data. High-quality and accurate 3D reconstructions were achieved with a learned multi-view stereo machine approach capable of incorporating the X-ray calibration parameters in the neural network. This strategy allowed a priori knowledge of the spinal shape to be acquired while preserving patient specificity and achieving a higher accuracy compared to the state of the art. Our method was trained and evaluated on 17,420 fluoroscopy images that were digitally reconstructed from the public CTSpine1K dataset. As evaluated by unseen data, we achieved an 88% average F1 score and a 71% surface score. Furthermore, by utilizing the calibration parameters of the input X-rays, our method outperformed a counterpart method in the state of the art by 22% in terms of surface score. This increase in accuracy opens new possibilities for surgical navigation and intraoperative decision-making solely based on intraoperative data, especially in surgical applications where the acquisition of 3D image data is not part of the standard clinical workflow.

Anatomically Parameterized Statistical Shape Model: Explaining Morphometry through Statistical Learning

Objective: Statistical shape models (SSMs) are a popular tool to conduct morphological analysis of anatomical structures which is a crucial step in clinical practices. However, shape representations through SSMs are based on shape coefficients and lack an explicit one-to-one relationship with anatomical measures of clinical relevance. While a shape coefficient embeds a combination of anatomical measures, a formalized approach to find the relationship between them remains elusive in the literature. This limits the use of SSMs to subjective evaluations in clinical practices. We propose a novel SSM controlled by anatomical parameters derived from morphometric analysis. Methods: The proposed anatomically parameterized SSM (ANAT_SSM) is based on learning a linear mapping between shape coefficients (latent space) and selected anatomical parameters (anatomical space). This mapping is learned from a synthetic population generated by the standard SSM. Determining the pseudo-inverse of the mapping allows us to build the ANAT_SSM. We further impose orthogonality constraints to the anatomical parameterization (OC-ANAT_SSM) to obtain independent shape variation patterns. The proposed contribution was evaluated on two skeletal databases of femoral and scapular bone shapes using clinically relevant anatomical parameters within each (five for femoral and six for scapular bone). Results: Anatomical measures of the synthetically generated shapes exhibited realistic statistics. The learned matrices corroborated well with the obtained statistical relationship, while the two SSMs achieved moderate to excellent performance in predicting anatomical parameters on unseen shapes. Conclusion: This study demonstrates the use of anatomical representation for creating anatomically parameterized SSMs and as a result, removes the limited clinical interpretability of standard SSMs. Significance: The proposed models could help analyze differences in relevant bone morphometry between populations, and be integrated in patient-specific pre-surgery planning or in-surgery assessment.

Using Statistical Shape and Appearance Modelling to characterise the 3D shape and material properties of human lumbar vertebrae: A proof of concept study

Patient variation affects the outcomes of a range of spinal interventions, from disc replacement to vertebral fixation and vertebroplasty. Statistical Shape and Appearance Modelling (SSAM) can be used to describe anatomical variation and pathological differences within the population. To better understand how bone density and shape variation affect load transfer with respect to surgical treatments, Finite Element (FE) models can be generated from a SSAM. The aim for this study is to understand whether geometric and density variation as well as multiple vertebral levels can be incorporated into a single SSAM and whether this can be used to investigate the relationships between, and effects of, the various modes of variation. FE models of 14 human lumbar vertebrae that had been μCT imaged and validated through experimental testing were used as input specimens for a SSAM. The validity of the SSAM was evaluated by using principal component analysis to identify the primary modes of geometric and bone density variation and comparing to those in the input set. FE models were generated from the SSAM to examine the response to loading. The mean error between the input set and generated models for volume, mean density and FE compressive stiffness were 10%, 3% and 10% respectively. Principal Component (PC) 1 captured the majority of the bone density variation. The remaining PCs described specific geometric variation. The FE models generated from the SSAM showed the variations in vertebral stiffness as a result of complex relationships between bone density and shape. The SSAM created has limited data for its input set, however, it acts as a proof of concept for the novel combination of material and shape variation into a single shape model. This approach and the tools developed can be applied to wider patient groups and treatment scenarios to improve patient stratification and to optimise treatments.

A statistical lumbar spine geometry model accounting for variations by Age, Sex, Stature, and body mass index

The objective of this study was to develop a statistical lumbar spine geometry model accounting for morphological variations among the adult population. Five lumber vertebrae and lumber spine curvature were collected from CT scans of 82 adult subjects through CT segmentation, landmark identification, and template mesh mapping. Generalized Procrustes Analysis (GPA), Principal Component Analysis (PCA), and multivariate regression analysis were conducted to develop the statistical lumbar spine model. Two statistical models were established to predict the vertebrae geometry and lumbar curvature respectively. Using the statistical models, a lumbar spine finite element (FE) model could be rapidly generated with a given set of age, sex, stature, and body mass index (BMI). The results showed that the lumbar spine vertebral size was significantly affected by stature, sex and age, and the lumbar spine curvature was significantly affected by stature and age. This statistical lumbar spine model could serve as the geometric basis for quantifying effects of human characteristics on lumbar spine injury risks in impact conditions.

A comparison of Cartesian-only vs. Cartesian-spherical hybrid coordinates for statistical shape modeling in the lumbar spine

OBJECTIVE

The purpose of this study was to compare two methods for quantifying differences in geometric shapes of human lumbar vertebra using statistical shape modeling (SSM).

METHODS

A novel 3D implementation of a previously published 2D, nonlinear SSM was implemented and compared to a commonly used, Cartesian method of SSM. The nonlinear method, or Hybrid SSM, and Cartesian SSM were applied to lumbar vertebra shapes from a cohort of 18 full lumbar triangle meshes derived from CT scans. The comparison included traditional metrics for cumulative variance, generality, and specificity and results from application-based biomechanics using finite element simulation.

RESULTS

The Hybrid SSM has less compactness - likely due to the increased number of mathematical constraints in the SSM formulation. Similar results were found between methods for specificity and generality. Compared to the previously validated, manually-segmented FE model, both SSM methods produced similar and agreeable results.

CONCLUSION

Visual, statistical, and biomechanical findings did not convincingly support the superiority of the Hybrid SSM over the simpler Cartesian SSM.

SIGNIFICANCE

This work suggests that, of the two methods compared, the Cartesian SSM is adequate to capture the variations in shape of the posterior spinal structures for biomechanical modeling applications.

Predicting Knee Joint Instability Using a Tibio-Femoral Statistical Shape Model

Statistical shape models (SSMs) are a well established computational technique to represent the morphological variability spread in a set of matching surfaces by means of compact descriptive quantities, traditionally called "modes of variation" (MoVs). SSMs of bony surfaces have been proposed in biomechanics and orthopedic clinics to investigate the relation between bone shape and joint biomechanics. In this work, an SSM of the tibio-femoral joint has been developed to elucidate the relation between MoVs and bone angular deformities causing knee instability. The SSM was built using 99 bony shapes (distal femur and proximal tibia surfaces obtained from segmented CT scans) of osteoarthritic patients. Hip-knee-ankle (HKA) angle, femoral varus-valgus (FVV) angle, internal-external femoral rotation (IER), tibial varus-valgus (TVV) angles, and tibial slope (TS) were available across the patient set. Discriminant analysis (DA) and logistic regression (LR) classifiers were adopted to underline specific MoVs accounting for knee instability. First, it was found that thirty-four MoVs were enough to describe 95% of the shape variability in the dataset. The most relevant MoVs were the one encoding the height of the femoral and tibial shafts (MoV #2) and the one representing variations of the axial section of the femoral shaft and its bending in the frontal plane (MoV #5). Second, using quadratic DA, the sensitivity results of the classification were very accurate, being all >0.85 (HKA: 0.96, FVV: 0.99, IER: 0.88, TVV: 1, TS: 0.87). The results of the LR classifier were mostly in agreement with DA, confirming statistical significance for MoV #2 (p = 0.02) in correspondence to IER and MoV #5 in correspondence to HKA (p = 0.0001), FVV (p = 0.001), and TS (p = 0.02). We can argue that the SSM successfully identified specific MoVs encoding ranges of alignment variability between distal femur and proximal tibia. This discloses the opportunity to use the SSM to predict potential misalignment in the knee for a new patient by processing the bone shapes, removing the need for measuring clinical landmarks as the rotation centers and mechanical axes.