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

A Finite Element Model to Investigate the Stability of Osteochondral Grafts Within a Human Tibiofemoral Joint

Osteochondral grafting has demonstrated positive outcomes for treating articular cartilage defects by replacing the damaged region with a cylindrical graft consisting of bone with a layer of cartilage. However, factors that cause graft subsidence are not well understood. The aim of this study was to develop finite element (FE) models of osteochondral grafts within a tibiofemoral joint, suitable for an investigation of parameters affecting graft stability. Cadaveric femurs were used to experimentally calibrate the bone properties and graft-bone frictional forces for use in corresponding image-based FE models, generated from µCT scan data. Effects of cartilage defects and osteochondral graft repair were measured by examining contact pressure changes using further in vitro tests. Here, six defects were created in the femoral condyles, which were subsequently treated with osteochondral autografts or metal pins. Matching image-based FE models were created, and the contact patches were compared. The bone material properties and graft-bone frictional forces were successfully calibrated from the initial tests with good resulting levels of agreement (CCC = 0.87). The tibiofemoral joint experiment provided a range of cases that were accurately described in the resultant pressure maps and were well represented in the FE models. Cartilage defects and repair quality were experimentally measurable with good agreement in the FE model pressure maps. Model confidence was built through extensive validation and sensitivity testing. It was found that specimen-specific properties were required to accurately represent graft behaviour. The final models produced are suitable for a range of parametric testing to investigate immediate graft stability.

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.

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.

Contribution of Shape Features to Intradiscal Pressure and Facets Contact Pressure in L4/L5 FSUs: An In-Silico Study

Finite element models (FEMs) of the spine commonly use a limited number of simplified geometries. Nevertheless, the geometric features of the spine are important in determining its FEM outcomes. The link between a spinal segment's shape and its biomechanical response has been studied, but the co-variances of the shape features have been omitted. We used a principal component (PCA)-based statistical shape modelling (SSM) approach to investigate the contribution of shape features to the intradiscal pressure (IDP) and the facets contact pressure (FCP) in a cohort of synthetic L4/L5 functional spinal units under axial compression. We quantified the uncertainty in the FEM results, and the contribution of individual shape modes to these results. This parameterisation approach is able to capture the variability in the correlated anatomical features in a real population and sample plausible synthetic geometries. The first shape mode ([Formula: see text]) explained 22.6% of the shape variation in the subject-specific cohort used to train the SSM, and had the largest correlation with, and contribution to IDP (17%) and FCP (11%). The largest geometric variation in ([Formula: see text]) was in the annulus-nucleus ratio.

Tibial-fibular geometry and density variations associated with elevated bone strain and sex disparities in young active adults

Tibial stress fracture is a common injury in runners and military personnel. Elevated bone strain is believed to be associated with the development of stress fractures and is influenced by bone geometry and density. The purpose of this study was to characterize tibial-fibular geometry and density variations in young active adults, and to quantify the influence of these variations on finite element-predicted bone strain. A statistical appearance model characterising tibial-fibular geometry and density was developed from computed tomography scans of 48 young physically active adults. The model was perturbed ±1 and 2 standard deviations along each of the first five principal components to create finite element models. Average male and female finite element models, controlled for scale, were also generated. Muscle and joint forces in running, calculated using inverse dynamics-based static optimization, were applied to the finite element models. The resulting 95th percentile pressure-modified von Mises strain (peak strain) and strained volume (volume of elements above 4000 με) were quantified. Geometry and density variations described by principal components resulted in up to 12.0% differences in peak strain and 95.4% differences in strained volume when compared to the average tibia-fibula model. The average female illustrated 5.5% and 41.3% larger peak strain and strained volume, respectively, when compared to the average male, suggesting that sexual dimorphism in bone geometry may indeed contribute to greater stress fracture risk in females. Our findings identified important features in subject-specific geometry and density associated with elevated bone strain that may have implications for stress fracture risk.

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.