The accuracy of active shape modelling and end-plate measurements for characterising the shape of the lumbar spine in the sagittal plane

Assessment of age-dependent sexual dimorphism in paediatric vertebral size and density using a statistical shape and statistical appearance modelling approach

This work focuses on the growth patterns of the human fourth lumbar vertebra (L4) in a paediatric population, with specific attention to sexual dimorphism. The study aims to understand morphological and density changes in the vertebrae through age-dependent statistical shape and statistical appearance models, which can describe full three-dimensional anatomy. Results show that the main growth patterns are associated with isotropic volumetric vertebral growth, a decrease in the relative size of the vertebral foramen, and an increase in the length of the transverse processes. Moreover, significant sexual dimorphism was demonstrated during puberty. We observe significant age and sex interaction in the anterior vertebral body height (P = 0.005), where females exhibited an earlier increase in rates of vertebral height evolution. Moreover, we also observe an increase in cross-sectional area (CSA) with age (P = 0.020), where the CSA is smaller in females than in males (significant sex effect P = 0.042). Finally, although no significant increase in trabecular bone density with age is observed (P = 0.363), a trend in the statistical appearance model suggests an increase in density with age.

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.

Comprehensive analysis of muscles wasting in disc herniation

Neuromuscular reeducation of the muscles that stabilize the spine is the basis of conservative treatment of disc herniation. Therefore, it is important to investigate how these muscles are affected by disc herniation. The aim of this study was to investigate the effect of disc herniation, herniation severity, patient age, and biomechanics on the lumbar stabilizer muscles. A total of 330 individuals, including 261 patients with disc herniations and 69 without disc herniation participated in this study. The cross-sectional areas (CSAs) of the lumbar stabilizer muscles and the lumbar lordosis angle were evaluated by magnetic resonance imaging (MRI), according to the severity of the disc herniation and the patient's age. In the patients with disc herniation, the CSAs of the quadratus lumborum (QL) and the multifidus (MF) muscles were decreased. The psoas major (PM) muscle CSA was higher in the patients with sequestered discs than in those with protruded and extruded discs. A negative relationship between the sagittal curve and the PM muscle CSA was found. In addition, MF muscle CSA was found to decrease at age 45 years and over. Although disc herniation negatively affects muscle CSAs, no linear relationship was found between the severity of the herniation and the muscle CSA. In addition, the PM muscle was found to be a strong compensatory muscle in disc herniation.

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 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.

Analysis of the Curvature and Morphologic Features of the Lumbar Vertebral Endplates Through the Transverse Section: A Radioanatomical Study

BACKGROUND

Knowledge concerning the curvature of the vertebrae through the transverse section is of clinical significance. However, relevant reports are scarce. This study investigated the features based on the cross-sections of lumbar vertebral endplates to provide information for clinical practice.

METHODS

Computed tomography images of 78 subjects were retrospectively reviewed. The geometric morphometrics was performed, and the curvature of the vertebral endplates was calculated by the self-written MATLAB algorithm. The principal component analysis, the canonical variate analysis, the discriminant function analysis, and the Mann-Whitney U test were performed. Statistical significance was set at P < 0.05.

RESULTS

No gender difference was found. In contrast, a morphologic difference was found between the superior and inferior lumbar vertebral endplates and between different segments. More specifically, the shape of the endplates gradually changes from the renal shape at superior L1 to the shell-like shape at inferior L5. The mean curvature values of the lateral anterior border were all around 0.60 cm^-1, whereas the mean curvature values of the lateral posterior borders range from 0.66 to 1.09 cm^-1 from L1 to L5. From L1 to L3, the mean and maximum curvature of the lateral posterior superior vertebral endplates decrease. The trend could also be found on the lateral posterior border of the inferior endplates from L1 to L3.

CONCLUSIONS

The current study described morphologic variations and curvature of the lumbar vertebral endplates, which have not been reported previously. The different curvature distribution could provide important information for surgeons and manufacturers.

Motor development in infancy and spine shape in early old age: Findings from a British birth cohort study

Spine shape changes dramatically in early life, influenced by attainment of developmental milestones such as independent walking. Whether these associations persist across life is unknown. Therefore, we investigated associations between developmental milestones and spine shape, as determined using statistical shape models (SSMs) of lumbar spine from dual-energy X-ray absorptiometry scans in 1327 individuals (688 female) at 60 to 64 years in the MRC National Survey of Health and Development. Lumbar lordosis angle (L4 inferior endplate to T12 superior endplate) was measured using the two-line Cobb method. In analyses adjusted for sex, height, lean and fat mass, socioeconomic position, and birthweight, later walking age was associated with greater lordosis described by SSM1 (regression coefficient, 0.023; 95% CI, 0.000-0.047; P = .05) and direct angle measurement. Modest associations between walking age and less variation in anterior-posterior vertebral size caudally (SSM6) were also observed (0.021; 95% CI, -0.002 to 0.044; P = .07). Sex interactions showed that later walking was associated with larger relative vertebral anterior-posterior dimensions in men (SSM3; -0.043; 95% CI, -0.075 to 0.01; P = .01) but not women (0.018; 95% CI, -0.0007 to 0.043; P = .17). Similar associations were observed between age at independent standing and SSMs but there was little evidence of association between sitting age and spine shape. Unadjusted associations between walking age and SSMs 1 and 6 remained similar after adjustment for potential confounders and mediators. This suggests that these associations may be explained by altered mechanical loading of the spine during childhood growth, although other factors could contribute. Early life motor development, particularly walking, may have a lasting effect on the features of spine morphology with clinical significance.

Is intrinsic lumbar spine shape associated with lumbar disc degeneration? An exploratory study

Background

Lumbar disc degeneration (LDD) is a condition associated with recurrent low back pain (LBP). Knowledge regarding effective management is limited. As a step towards the identification of risk, prognostic or potentially modifiable factors in LDD patients, the aim of this study was to explore the hypothesis that intrinsic lumbar spine shape is associated with LDD and clinical outcomes in symptomatic adults.

Methods

3 T MRI was used to acquire T2-weighted sagittal images (L1-S1) from 70 healthy controls and LDD patients (mean age 49 years, SD 11, range 31–71 years). Statistical Shape Modelling (SSM) was used to describe lumbar spine shape. SSM identified variations in lumbar shape as ‘modes’ of variation and quantified deviation from the mean. Intrinsic shape differences were determined between LDD groups using analysis of variance with post-hoc comparisons. The relationship between intrinsic shape and self-reported function, mental health and quality of life were also examined.

Results

The first 7 modes of variation explained 91% of variance in lumbar shape. Higher LDD sum scores correlated with a larger lumbar lordosis (Mode 1 (55% variance), P = 0.02), even lumbar curve distribution (Mode 2 (12% variance), P = 0.05), larger anterior-posterior (A-P) vertebral diameter (Mode 3 (10% variance), P = 0.007) and smaller L4-S1 disc spaces (Mode 7 (2% variance), P ≤ 0.001). In the presence of recurrent LBP, LDD was associated with a larger A-P vertebral diameter (Mode 3) and a more even lumbar curvature with smaller L5/S1 disc spaces (Mode 4), which was significantly associated with patient quality of life (P = 0.002–0.04, r_p = 0.43–0.61)).

Conclusions

This exploratory study provides new evidence that intrinsic shape phenotypes are associated with LDD and quality of life in patients. Longitudinal studies are required to establish the potential role of these risk or prognostic shape phenotypes.

In Vivo Assessment of Thoracic Vertebral Shape From MRI Data Using a Shape Model

STUDY DESIGN

Feasibility study on characterizing thoracic vertebral shape from magnetic resonance images using a shape model.

OBJECTIVES

Assess the reliability of characterizing thoracic vertebral shape from magnetic resonance images and estimate the normal variation in vertebral shape using a shape model.

SUMMARY OF BACKGROUND DATA

The characterization of thoracic vertebra shape is important for understanding the initiation and progression of deformity and in developing surgical methods. Methods for characterizing shape need to be comprehensive, reliable, and suitable for use in vivo.

METHODS

Magnetic resonance images of the thoracic vertebrae were acquired from 20 adults. Repeat scans were acquired, after repositioning the participants, for T4, T8, and T12. Landmark points were placed around the vertebra on the images and used to create a shape model. The reliability was assessed using relative error (E%) and intraclass correlation (ICC). The effect of vertebral level, sex and age on vertebral shape was assessed using repeated measures analysis of variance.

RESULTS

Five modes of variation were retained from the shape model. Reliability was excellent for the first two modes (mode 1: E% = 7, ICC = 0.98; mode 2: E% = 11, ICC = 0.96). These modes described variation in the vertebral bodies, the pedicle width and orientation, and the facet joint position and orientation with respect to the pedicle axis. Variation in vertebral shape was found along the thoracic spine and between individuals, but there was little effect of age and sex.

CONCLUSIONS

Magnetic resonance images and shape modeling provides a reliable method for characterizing vertebral shape in vivo. The method is able to identify differences between vertebral levels and between individuals. The use of these methods may be advantageous for performing repeated measurements in longitudinal studies.

LEVEL OF EVIDENCE

N/A.

Subject-specific loads on the lumbar spine in detailed finite element models scaled geometrically and kinematic-driven by radiography images

Traditional load-control musculoskeletal and finite element (FE) models of the spine fail to accurately predict in vivo intervertebral joint loads due mainly to the simplifications and assumptions when estimating redundant trunk muscle forces. An alternative powerful protocol that bypasses the calculation of muscle forces is to drive the detailed FE models by image-based in vivo displacements. Development of subject-specific models, however, both involves the risk of extensive radiation exposures while imaging in supine and upright postures and is time consuming in terms of the reconstruction of the vertebrae, discs, ligaments, and facets geometries. This study therefore aimed to introduce a remedy for the development of subject-specific FE models by scaling the geometry of an existing detailed FE model of the T12-S1 lumbar spine. Five subject-specific scaled models were driven by their own radiography image-based displacements in order to predict joint loads, ligament forces, facet joint forces, and disc fiber strains during relaxed upright as well as moderate flexion and extension tasks. The predicted intradiscal pressures were found in adequate agreement with in vivo data for upright, flexion, and extension tasks. There were however large intersubject variations in the estimated joint loads and facet forces.

Variation in lifting kinematics related to individual intrinsic lumbar curvature: an investigation in healthy adults

Objective

Lifting postures are frequently implicated in back pain. We previously related responses to a static load with intrinsic spine shape, and here we investigate the role of lumbar spine shape in lifting kinematics.

Methods

Thirty healthy adults (18-65 years) performed freestyle, stoop and squat lifts with a weighted box (6-15 kg, self-selected) while being recorded by Vicon motion capture. Internal spine shape was characterised using statistical shape modelling (SSM) from standing mid-sagittal MRIs. Associations were investigated between spine shapes quantified by SSM and peak flexion angles.

Results

Two SSM modes described variations in overall lumbar curvature (mode 1 (M1), 55% variance) and the evenness of curvature distribution (mode 2 (M2), 12% variance). M1 was associated with greater peak pelvis (r=0.38, p=0.04) and smaller knee flexion (r=-0.40, p=0.03) angles; individuals with greater curviness preferred to lift with a stooped lifting posture. This was confirmed by analysis of those individuals with very curvy or very straight spines (|M1|>1 SD). There were no associations between peak flexion angles and mode scores in stoop or squat trials (p>0.05). Peak flexion angles were positively correlated between freestyle and squat trials but not between freestyle and stoop or squat and stoop, indicating that individuals adjusted knee flexion while maintaining their preferred range of lumbar flexion and that 'squatters' adapted better to different techniques than 'stoopers'.

Conclusion

Spinal curvature affects preferred lifting styles, and individuals with curvier spines adapt more easily to different lifting techniques. Lifting tasks may need to be tailored to an individual's lumbar spine shape.

Body mass index and waist circumference in early adulthood are associated with thoracolumbar spine shape at age 60-64: The Medical Research Council National Survey of Health and Development

This study investigated associations between measures of adiposity from age 36 and spine shape at 60-64 years. Thoracolumbar spine shape was characterised using statistical shape modelling on lateral dual-energy x-ray absorptiometry images of the spine from 1529 participants of the MRC National Survey of Health and Development, acquired at age 60-64. Associations of spine shape modes with: 1) contemporaneous measures of total and central adiposity (body mass index (BMI), waist circumference (WC)) and body composition (android:gynoid fat mass ratio and lean and fat mass indices, calculated as whole body (excluding the head) lean or fat mass (kg) divided by height2 (m)2); 2) changes in total and central adiposity between age 36 and 60-64 and 3) age at onset of overweight, were tested using linear regression models. Four modes described 79% of the total variance in spine shape. In men, greater lean mass index was associated with a larger lordosis whereas greater fat mass index was associated with straighter spines. Greater current BMI was associated with a more uneven curvature in men and with larger anterior-posterior (a-p) vertebral diameters in both sexes. Greater WC and fat mass index were also associated with a-p diameter in both sexes. There was no clear evidence that gains in BMI and WC during earlier stages of adulthood were associated with spine shape but younger onset of overweight was associated with a more uneven spine and greater a-p diameter. In conclusion, sagittal spine shapes had different associations with total and central adiposity; earlier onset of overweight and prior measures of WC were particularly important.

Statistical shape modelling of hip and lumbar spine morphology and their relationship in the MRC National Survey of Health and Development

The anatomical shape of bones and joints is important for their proper function but quantifying this, and detecting pathological variations, is difficult to do. Numerical descriptions would also enable correlations between joint shapes to be explored. Statistical shape modelling (SSM) is a method of image analysis employing pattern recognition statistics to describe and quantify such shapes from images; it uses principal components analysis to generate modes of variation describing each image in terms of a set of numerical scores after removing global size variation. We used SSM to quantify the shapes of the hip and the lumbar spine in dual-energy x-ray absorptiometry (DXA) images from 1511 individuals in the MRC National Survey of Health and Development at ages 60-64 years. We compared shapes of both joints in men and women and hypothesised that hip and spine shape would be strongly correlated. We also investigated associations with height, weight, body mass index (BMI) and local (hip or lumber spine) bone mineral density. In the hip, all except one of the first 10 modes differed between men and women. Men had a wider femoral neck, smaller neck-shaft angle, increased presence of osteophytes and a loss of the femoral head/neck curvature compared with women. Women presented with a flattening of the femoral head and greater acetabular coverage of the femoral head. Greater weight was associated with a shorter, wider femoral neck and larger greater and lesser trochanters. Taller height was accompanied by a flattening of the curve between superior head and neck and a larger lesser trochanter. Four of the first eight modes describing lumbar spine shape differed between men and women. Women tended to have a more lordotic spine than men with relatively smaller but caudally increasing anterior-posterior (a-p) vertebral diameters. Men were more likely to have a straighter spine with larger vertebral a-p diameters relative to vertebral height than women, increasing cranially. A weak correlation was found between body weight and a-p vertebral diameter. No correlations were found between shape modes and height in men, whereas in women there was a weak positive correlation between height and evenness of spinal curvature. Linear relationships between hip and spine shapes were weak and inconsistent in both sexes, thereby offering little support for our hypothesis. In conclusion, men and women entering their seventh decade have small but statistically significant differences in the shapes of their hips and their spines. Associations with height, weight, BMI and BMD are small and correspond to subtle variations whose anatomical significance is not yet clear. Correlations between hip and spine shapes are small.

The lumbar spine has an intrinsic shape specific to each individual that remains a characteristic throughout flexion and extension

PURPOSE

We have previously shown that the lumbar spine has an intrinsic shape specific to the individual and characteristic of sitting, standing and supine postures. The purpose of this study was to test the hypothesis that this intrinsic shape is detectable throughout a range of postures from extension to full flexion in healthy adults.

METHODS

Sagittal images of the lumbar spine were taken using a positional MRI with participants (n = 30) adopting six postures: seated extension, neutral standing, standing with 30, 45 and 60° and full flexion. Active shape modelling (ASM) was used to identify and quantify 'modes' of variation in the shape of the lumbar spine.

RESULTS

ASM showed that 89.5% of the variation in the shape of the spine could be explained by the first two modes; describing the overall curvature and the distribution of curvature of the spine. Mode scores were significantly correlated between all six postures (modes 1-9, r = 0.4-0.97, P < 0.05), showing that an element of intrinsic shape was maintained when changing postures. The spine was most even in seated extension (P < 0.001) and most uneven between 35 and 45° flexion (P < 0.05).

CONCLUSIONS

This study shows that an individual's intrinsic lumbar spine shape is quantifiable and detectable throughout lumbar flexion and extension. These findings will enable the role of lumbar curvature in injury and low back pain to be assessed in the clinic and in the working and recreational environments.

The relationship between sagittal curvature and extensor muscle volume in the lumbar spine

A previous modelling study predicted that the forces applied by the extensor muscles to stabilise the lumbar spine would be greater in spines that have a larger sagittal curvature (lordosis). Because the force-generating capacity of a muscle is related to its size, it was hypothesised that the size of the extensor muscles in a subject would be related to the size of their lumbar lordosis. Magnetic resonance imaging (MRI) data were obtained, together with age, height, body mass and back pain status, from 42 female subjects. The volume of the extensor muscles (multifidus and erector spinae) caudal to the mid-lumbar level was estimated from cross-sectional area measurements in axial T1-weighted MRIs spanning the lumbar spine. Lower lumbar curvature was determined from sagittal T1-weighted images. A stepwise linear regression model was used to determine the best predictors of muscle volume. The mean lower lumbar extensor muscle volume was 281 cm(3) (SD = 49 cm(3)). The mean lower lumbar curvature was 30 ° (SD = 7 °). Five subjects reported current back pain and were excluded from the regression analysis. Nearly half the variation in muscle volume was accounted for by the variables age (standardised coefficient, B = -3.2, P = 0.03) and lower lumbar curvature (B = 0.47, P = 0.002). The results support the hypothesis that extensor muscle volume in the lower lumbar spine is related to the magnitude of the sagittal curvature; this has implications for assessing muscle size as an indicator of muscle strength.