Automated finite element modeling of the lumbar spine: Using a statistical shape model to generate a virtual population of models

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.

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.

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.

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.

Computational lumbar spine models: A literature review

BACKGROUND

Computational spine models of various types have been employed to understand spine function, assess the risk that different activities pose to the spine, and evaluate techniques to prevent injury. The areas in which these models are applied has expanded greatly, potentially beyond the appropriate scope of each, given their capabilities. A comprehensive understanding of the components of these models provides insight into their current capabilities and limitations.

METHODS

The objective of this review was to provide a critical assessment of the different characteristics of model elements employed across the spectrum of lumbar spine modeling and in newer combined methodologies to help better evaluate existing studies and delineate areas for future research and refinement.

FINDINGS

A total of 155 studies met selection criteria and were included in this review. Most current studies use either highly detailed Finite Element models or simpler Musculoskeletal models driven with in vivo data. Many models feature significant geometric or loading simplifications that limit their realism and validity. Frequently, studies only create a single model and thus can't account for the impact of subject variability. The lack of model representation for certain subject cohorts leaves significant gaps in spine knowledge. Combining features from both types of modeling could result in more accurate and predictive models.

INTERPRETATION

Development of integrated models combining elements from different model types in a framework that enables the evaluation of larger populations of subjects could address existing voids and enable more realistic representation of the biomechanics of the lumbar spine.

A Population-Based 3D Atlas of the Pathological Lumbar Spine Segment

The spine is the load-bearing structure of human beings and may present several disorders, with low back pain the most frequent problem during human life. Signs of a spine disorder or disease vary depending on the location and type of the spine condition. Therefore, we aim to develop a probabilistic atlas of the lumbar spine segment using statistical shape modeling (SSM) and then explore the variability of spine geometry using principal component analysis (PCA). Using computed tomography (CT), the human spine was reconstructed for 24 patients with spine disorders and then the mean shape was deformed upon specific boundaries (e.g., by ±3 or ±1.5 standard deviation). Results demonstrated that principal shape modes are associated with specific morphological features of the spine segment such as Cobb’s angle, lordosis degree, spine width and height. The lumbar spine atlas here developed has evinced the potential of SSM to investigate the association between shape and morphological parameters, with the goal of developing new treatments for the management of patients with spine disorders.

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.

Atlas-Based Evaluation of Hemodynamic in Ascending Thoracic Aortic Aneurysms

Atlas-based analyses of patients with cardiovascular diseases have recently been explored to understand the mechanistic link between shape and pathophysiology. The construction of probabilistic atlases is based on statistical shape modeling (SSM) to assess key anatomic features for a given patient population. Such an approach is relevant to study the complex nature of the ascending thoracic aortic aneurysm (ATAA) as characterized by different patterns of aortic shapes and valve phenotypes. This study was carried out to develop an SSM of the dilated aorta with both bicuspid aortic valve (BAV) and tricuspid aortic valve (TAV), and then assess the computational hemodynamic of virtual models obtained by the deformation of the mean template for specific shape boundaries (i.e., ±1.5 standard deviation, σ). Simulations demonstrated remarkable changes in the velocity streamlines, blood pressure, and fluid shear stress with the principal shape modes such as the aortic size (Mode 1), vessel tortuosity (Mode 2), and aortic valve morphologies (Mode 3). The atlas-based disease assessment can represent a powerful tool to reveal important insights on ATAA-derived hemodynamic, especially for aneurysms which are considered to have borderline anatomies, and thus challenging decision-making. The utilization of SSMs for creating probabilistic patient cohorts can facilitate the understanding of the heterogenous nature of the dilated ascending aorta.

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.

Ischiofemoral impingement: the evolutionary cost of pelvic obstetric adaptation

The risk for ischiofemoral impingement has been mainly related to a reduced ischiofemoral distance and morphological variance of the femur. From an evolutionary perspective, however, there are strong arguments that the condition may also be related to sexual dimorphism of the pelvis. We, therefore, investigated the impact of gender-specific differences in anatomy of the ischiofemoral space on the ischiofemoral clearance, during static and dynamic conditions. A random sampling Monte-Carlo experiment was performed to investigate ischiofemoral clearance during stance and gait in a large (n = 40 000) virtual study population, while using gender-specific kinematics. Subsequently, a validated gender-specific geometric morphometric analysis of the hip was performed and correlations between overall hip morphology (statistical shape analysis) and standard discrete measures (conventional metric approach) with the ischiofemoral distance were evaluated. The available ischiofemoral space is indeed highly sexually dimorphic and related primarily to differences in the pelvic anatomy. The mean ischiofemoral distance was 22.2 ± 4.3 mm in the females and 29.1 ± 4.1 mm in the males and this difference was statistically significant (P < 0.001). Additionally, the ischiofemoral distance was observed to be a dynamic measure, and smallest during femoral extension, and this in turn explains the clinical sign of pain in extension during long stride walking. In conclusion, the presence of a reduced ischiofemroal distance and related risk to develop a clinical syndrome of ischiofemoral impingement is strongly dominated by evolutionary effects in sexual dimorphism of the pelvis. This should be considered when female patients present with posterior thigh/buttock pain, particularly if worsened by extension. Controlled laboratory study.

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.

Patient-Specific Finite Element Models of Posterior Pedicle Screw Fixation: Effect of Screw's Size and Geometry

Pedicle screw fixation is extensively performed to treat spine injuries or diseases and it is common for thoracolumbar fractures. Post-operative complications may arise from this surgery leading to back pain or revisions. Finite element (FE) models could be used to predict the outcomes of surgeries but should be verified when both simplified and realistic designs of screws are used. The aim of this study was to generate patient-specific Computed Tomography (CT)-based FE models of human vertebrae with two pedicle screws, verify the models, and use them to evaluate the effect of the screws' size and geometry on the mechanical properties of the screws-vertebra structure. FE models of the lumbar vertebra implanted with two pedicle screws were created from anonymized CT-scans of three patients. Compressive loads were applied to the head of the screws. The mesh size was optimized for realistic and simplified geometry of the screws with a mesh refinement study. Finally, the optimal mesh size was used to evaluate the sensitivity of the model to changes in screw's size (diameter and length) and geometry (realistic or simplified). For both simplified and realistic models, element sizes of 0.6 mm in the screw and 1.0 mm in the bone allowed to obtain relative differences of approximately 5% or lower. Changes in screw's length resulted in 4-10% differences in maximum deflection, 1-6% differences in peak stress in the screws, 10-22% differences in mean strain in the bone around the screw; changes in screw's diameter resulted in 28-36% differences in maximum deflection, 6-27% differences in peak stress in the screws, and 30-47% differences in mean strain in the bone around the screw. The maximum deflection predicted with realistic or simplified screws correlated very well (R ² = 0.99). The peak stress in screws with realistic or simplified design correlated well (R ² = 0.82) but simplified models underestimated the peak stress. In conclusion, the results showed that the diameter of the screw has a major role on the mechanics of the screw-vertebral structure for each patient. Simplified screws can be used to estimate the mechanical properties of the implanted vertebrae, but the systematic underestimation of the peak stress should be considered when interpreting the results from the FE analyses.

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.

Automated Pipeline to Generate Anatomically Accurate Patient-Specific Biomechanical Models of Healthy and Pathological FSUs

State-of-the-art preoperative biomechanical analysis for the planning of spinal surgery not only requires the generation of three-dimensional patient-specific models but also the accurate biomechanical representation of vertebral joints. The benefits offered by computational models suitable for such purposes are still outweighed by the time and effort required for their generation, thus compromising their applicability in a clinical environment. In this work, we aim to ease the integration of computerized methods into patient-specific planning of spinal surgery. We present the first pipeline combining deep learning and finite element methods that allows a completely automated model generation of functional spine units (FSUs) of the lumbar spine for patient-specific FE simulations (FEBio). The pipeline consists of three steps: (a) multiclass segmentation of cropped 3D CT images containing lumbar vertebrae using the DenseVNet network, (b) automatic landmark-based mesh fitting of statistical shape models onto 3D semantic segmented meshes of the vertebral models, and (c) automatic generation of patient-specific FE models of lumbar segments for the simulation of flexion-extension, lateral bending, and axial rotation movements. The automatic segmentation of FSUs was evaluated against the gold standard (manual segmentation) using 10-fold cross-validation. The obtained Dice coefficient was 93.7% on average, with a mean surface distance of 0.88 mm and a mean Hausdorff distance of 11.16 mm (N = 150). Automatic generation of finite element models to simulate the range of motion (ROM) was successfully performed for five healthy and five pathological FSUs. The results of the simulations were evaluated against the literature and showed comparable ROMs in both healthy and pathological cases, including the alteration of ROM typically observed in severely degenerated FSUs. The major intent of this work is to automate the creation of anatomically accurate patient-specific models by a single pipeline allowing functional modeling of spinal motion in healthy and pathological FSUs. Our approach reduces manual efforts to a minimum and the execution of the entire pipeline including simulations takes approximately 2 h. The automation, time-efficiency and robustness level of the pipeline represents a first step toward its clinical integration.

Biomechanical Properties of Metastatically Involved Osteolytic Bone

PURPOSE OF REVIEW

Skeletal metastasis involves the uncoupling of physiologic bone remodeling resulting in abnormal bone turnover and radical changes in bony architecture, density, and quality. Bone strength assessment and fracture risk prediction are critical in clinical treatment decision-making. This review focuses on bone tissue and structural mechanisms altered by osteolytic metastasis and the resulting changes to its material and mechanical behavior.

RECENT FINDINGS

Both organic and mineral phases of bone tissue are altered by osteolytic metastatic disease, with diminished bone quality evident at multiple length-scales. The mechanical performance of bone with osteolytic lesions is influenced by a combination of tissue-level and structural changes. This review considers the effects of osteolytic metastasis on bone biomechanics demonstrating its negative impact at tissue and structural levels. Future studies need to assess the cumulative impact of cancer treatments on metastatically involved bone quality, and its utility in directing multimodal treatment planning.

Biomechanical modelling of the facet joints: a review of methods and validation processes in finite element analysis

There is an increased interest in studying the biomechanics of the facet joints. For in silico studies, it is therefore important to understand the level of reliability of models for outputs of interest related to the facet joints. In this work, a systematic review of finite element models of multi-level spinal section with facet joints output of interest was performed. The review focused on the methodology used to model the facet joints and its associated validation. From the 110 papers analysed, 18 presented some validation of the facet joints outputs. Validation was done by comparing outputs to literature data, either computational or experimental values; with the major drawback that, when comparing to computational values, the baseline data was rarely validated. Analysis of the modelling methodology showed that there seems to be a compromise made between accuracy of the geometry and nonlinearity of the cartilage behaviour in compression. Most models either used a soft contact representation of the cartilage layer at the joint or included a cartilage layer which was linear elastic. Most concerning, soft contact models usually did not contain much information on the pressure-overclosure law. This review shows that to increase the reliability of in silico model of the spine for facet joints outputs, more needs to be done regarding the description of the methods used to model the facet joints, and the validation for specific outputs of interest needs to be more thorough, with recommendation to systematically share input and output data of validation studies.

Combining statistical shape modeling, CFD, and meta-modeling to approximate the patient-specific pressure-drop across the aortic valve in real-time

BACKGROUND

Advances in medical imaging, segmentation techniques, and high performance computing have stimulated the use of complex, patient-specific, three-dimensional Computational Fluid Dynamics (CFD) simulations. Patient-specific, CFD-compatible geometries of the aortic valve are readily obtained. CFD can then be used to obtain the patient-specific pressure-flow relationship of the aortic valve. However, such CFD simulations are computationally expensive, and real-time alternatives are desired.

AIM

The aim of this work is to evaluate the performance of a meta-model with respect to high-fidelity, three-dimensional CFD simulations of the aortic valve.

METHODS

Principal component analysis was used to build a statistical shape model (SSM) from a population of 74 iso-topological meshes of the aortic valve. Synthetic meshes were created with the SSM, and steady-state CFD simulations at flow-rates between 50 and 650 mL/s were performed to build a meta-model. The meta-model related the statistical shape variance, and flow-rate to the pressure-drop.

RESULTS

Even though the first three shape modes account for only 46% of shape variance, the features relevant for the pressure-drop seem to be captured. The three-mode shape-model approximates the pressure-drop with an average error of 8.8% to 10.6% for aortic valves with a geometric orifice area below 150 mm² . The proposed methodology was least accurate for aortic valve areas above 150 mm² . Further reduction to a meta-model introduces an additional 3% error.

CONCLUSIONS

Statistical shape modeling can be used to capture shape variation of the aortic valve. Meta-models trained by SSM-based CFD simulations can provide an estimate of the pressure-flow relationship in real-time.

Statistical shape modeling of the pelvic floor to evaluate women with obstructed defecation symptoms

Obstructed defecation (OD) is common and may be related to compromised pelvic floor integrity. Magnetic resonance (MR) defecography and statistical shape modeling were used to define pelvic floor shape variations, hypothesizing that State (rest vs peak evacuation) and Group (control vs case) would significantly influence shape. 16 women underwent MR defecography (9 cases vs 7 controls). Midsagittal, 2D pelvic floors were segmented and aligned by corresponding points. Principal component scores were compared using a Two-Way Mixed MANOVA. Three modes described differences between State (p < 0.001) and Group (p = 0.023). The pelvic floor shape differed significantly between women with and without OD and during evacuation.

Mechanics of Psoas Tendon Snapping. A Virtual Population Study

Internal snapping of the psoas tendon is a frequently reported condition, especially in young adolescents involved in sports. It is defined as an increased tendon excursion over bony or soft tissue prominence causing local irritation and inflammation of the tendon leading to groin pain and often is accompanied by an audible snap. Due to the lack of detailed dynamic visualization means, the exact mechanism of the condition remains poorly understood and different theories have been postulated related to the etiology and its location about the hip. In the present study we simulated psoas tendon behavior in a virtual population of 40,000 anatomies and compared tendon movement during combined abduction, flexion and external rotation and back to neutral extension and adduction. At risk phenotyopes for tendon snapping were defined as the morphologies presenting with excess tendon movement. There were little differences in tendon movement between the male and female models. In both populations, abnormal tendon excursion correlated with changes in mainly the femoral anatomy (male r = 0.72, p < 0.001, female r = 0.66, p < 0.001): increased anteversion and valgus as well as a decreasing femoral offset and ischiofemoral distance. The observed combination of shape components correlating with excess tendon movement in essence presented with a medial positioning of the minor trochanter. This finding suggest that psoas snapping and ischiofemoral impingement are possibly two presentations of a similar underlying rotational dysplasia of the femur.

Evaluation of Statistical Shape Modeling in Quantifying Femoral Morphologic Differences Between Symptomatic and Nonsymptomatic Hips in Patients with Unilateral Femoroacetabular Impingement Syndrome

Purpose

To determine whether statistical shape modeling can detect subtle morphologic differences in the shape of the proximal femur that correlate with clinical findings of unilateral femoroacetabular impingement syndrome.

Methods

Patients who had diagnoses of unilateral femoroacetabular impingement syndrome and who had existing computed tomography scans of their pelvises were included. Three-dimensional shape models in the form of triangle meshes were generated from the computed tomography images. Statistical shapes of cam-type and normal hips were compared to identify structural differences.

Results

The study included 33 hips in 17 subjects. Of the subjects, 7 (41.1%) were male, and 10 (58.9%) were female. The subjects ranged in age from 17-60 years of age (mean 36.3 ± 11.0 years old). The statistical shape modeling found mean shapes and modes after optimizing the groupwise correspondence. Symptomatic hips demonstrated 1 mm of thickening as compared to the femoral necks of asymptomatic hips, corresponding to cam lesions.

Conclusions

Symptomatic cam deformities were an average of 1 mm more prominent in the femoral neck region as compared to the asymptomatic hips when using statistical shape modeling. The present study provides a proof of the concept that statistical shape modeling can be used to examine and help define cam morphology and that subtle morphologic differences may account for developing femoroacetabular impingement syndrome.

Clinical Relevance

Using the methods presented in this study, it would be possible to define cam and pincer morphologies by creating statistical shape models, and this work could potentially lead to the development of a new classification system for femoroacetabular impingement syndrome lesions.

Lumbar model generator: a tool for the automated generation of a parametric scalable model of the lumbar spine

Low back pain is a major cause of disability and requires the development of new devices to treat pathologies and improve prognosis following surgery. Understanding the effects of new devices on the biomechanics of the spine is crucial in the development of new effective and functional devices. The aim of this study was to develop a preliminary parametric, scalable and anatomically accurate finite-element model of the lumbar spine allowing for the evaluation of the performance of spinal devices. The principal anatomical surfaces of the lumbar spine were first identified, and then accurately fitted from a previous model supplied by S14 Implants (Bordeaux, France). Finally, the reconstructed model was defined according to 17 parameters which are used to scale the model according to patient dimensions. The developed model, available as a toolbox named the lumbar model generator, enables generating a population of models using subject-specific dimensions obtained from data scans or averaged dimensions evaluated from the correlation analysis. This toolbox allows patient-specific assessment, taking into account individual morphological variation. The models have applications in the design process of new devices, evaluating the biomechanics of the spine and helping clinicians when deciding on treatment strategies.

Cervical spine morphology and ligament property variations: A finite element study of their influence on sagittal bending characteristics

Cervical spine finite element models reported in biomechanical literature usually represent a static morphology. Not considering morphology as a model parameter limits the predictive capabilities for applications in personalized medicine, a growing trend in modern clinical practice. The objective of the study was to investigate the influence of variations in spinal morphology on the flexion-extension responses, utilizing mesh-morphing-based parametrization and metamodel-based sensitivity analysis. A C5-C6 segment was used as the baseline model. Variations of intervertebral disc height, facet joint slope, facet joint articular processes height, vertebral body anterior-posterior depth, and segment size were parametrized. In addition, material property variations of ligaments were considered for sensitivity analysis. The influence of these variations on vertebral rotation and forces in the ligaments were analyzed. The disc height, segmental size, and body depth were found to be the most influential (in the cited order) morphology variations; while among the ligament material property variations, capsular ligament and ligamentum flavum influenced vertebral rotation the most. Changes in disc height influenced forces in the posterior ligaments, indicating that changes in the anterior load-bearing column of the spine could have consequences on the posterior column. A method to identify influential morphology variations is presented in this work, which will help automation efforts in modeling to focus on variations that matter. This study underscores the importance of incorporating influential morphology parameters, easily obtained through computed tomography/magnetic resonance images, to better predict subject-specific biomechanical responses for applications in personalized medicine.

Impact of material and morphological parameters on the mechanical response of the lumbar spine - A finite element sensitivity study

Finite element models are frequently used to study lumbar spinal biomechanics. Deterministic models are used to reflect a certain configuration, including the means of geometrical and material properties, while probabilistic models account for the inherent variability in the population. Because model parameters are generally uncertain, their predictive power is frequently questioned. In the present study, we determined the sensitivities of spinal forces and motions to material parameters of intervertebral discs, vertebrae, and ligaments and to lumbar morphology. We performed 1200 model simulations using a generic model of the human lumbar spine loaded under pure moments. Coefficients of determination and of variation were determined for all parameter and response combinations. Material properties of the vertebrae displayed the least impact on results, whereas those of the discs and morphology impacted most. The most affected results were the axial compression forces in the vertebral body and in several ligaments during flexion and the facet-joint forces during extension. Intervertebral rotations were considerably affected only when several parameters were varied simultaneously. Results can be used to decide which model parameters require careful consideration in deterministic models and which parameters might be omitted in probabilistic studies. Findings allow quantitative estimation of a model׳s precision.