Development of a statistical shape model of the patellofemoral joint for investigating relationships between shape and function

Patellofemoral (PF)-related pathologies, including joint laxity, patellar maltracking, cartilage degradation and anterior knee pain, affect nearly 25% of the population. Researchers have investigated the influence of articular geometry on kinematics and contact mechanics in order to gain insight into the etiology of these conditions. The purpose of the current study was to create a three-dimensional statistical shape model of the PF joint and to characterize relationships between PF shape and function (kinematics and contact mechanics). A statistical shape model of the patellar and femoral articular surfaces and their relative alignment was developed from magnetic resonance images. Using 15 shape parameters, the model characterized 97% of the variation in the training set. The first three shape modes primarily described variation in size, patella alta-baja and depth of the sulcus groove. A previously verified finite element model was used to predict kinematics and contact mechanics for each subject. Combining the shape and joint mechanics data, a statistical shape-function model was developed that established quantitative relations of how changes in the shape of the PF joint influence mechanics. The predictive capability of the shape-function model was evaluated by comparing statistical model and finite element predictions, resulting in kinematic root mean square errors of less than 3° and 2.5 mm. The key results of the study are dually in the implementation of a novel approach linking statistical shape and finite element models and the relationships elucidated between PF articular geometry and mechanics.     

Linking statistical shape models and simulated function in the healthy adult human heart

Cardiac anatomy plays a crucial role in determining cardiac function. However, there is a poor understanding of how specific and localised anatomical changes affect different cardiac functional outputs. In this work, we test the hypothesis that in a statistical shape model (SSM), the modes that are most relevant for describing anatomy are also most important for determining the output of cardiac electromechanics simulations. We made patient-specific four-chamber heart meshes (n = 20) from cardiac CT images in asymptomatic subjects and created a SSM from 19 cases. Nine modes captured 90% of the anatomical variation in the SSM. Functional simulation outputs correlated best with modes 2, 3 and 9 on average (R = 0.49 ± 0.17, 0.37 ± 0.23 and 0.34 ± 0.17 respectively). We performed a global sensitivity analysis to identify the different modes responsible for different simulated electrical and mechanical measures of cardiac function. Modes 2 and 9 were the most important for determining simulated left ventricular mechanics and pressure-derived phenotypes. Mode 2 explained 28.56 ± 16.48% and 25.5 ± 20.85, and mode 9 explained 12.1 ± 8.74% and 13.54 ± 16.91% of the variances of mechanics and pressure-derived phenotypes, respectively. Electrophysiological biomarkers were explained by the interaction of 3 ± 1 modes. In the healthy adult human heart, shape modes that explain large portions of anatomical variance do not explain equivalent levels of electromechanical functional variation. As a result, in cardiac models, representing patient anatomy using a limited number of modes of anatomical variation can cause a loss in accuracy of simulated electromechanical function.     

A three-dimensional mathematical model of the thoracolumbar fascia and an estimate of its biomechanical effect

The thoracolumbar fascia (TLF) provides a means of attachment to the lumbar spine for several muscles including the transverse abdominis, and parts of the latissimus dorsi and internal oblique muscles. Previous biomechanical models of the lumbar spine either tend to omit the TLF on the assumption that its contribution would be negligible or incorporate only part of the TLF. Here, a three-dimensional model of the posterior and middle layers of the TLF is presented to enable its action to be included in future three-dimensional models of the spine. It is used illustratively to estimate the biomechanical influence of this structure on the lumbar spine. The formulation of the model allows the lines of action of the fibres comprising the fascia to be calculated for any posture whilst ensuring that anatomical constraints are satisfied. Application of the model suggests that the TLF produces moments primarily in flexion and extension. The simulated results demonstrate that the abdominal muscles, acting via the TLF, are capable of contributing extension moments comparable to those produced by other smaller muscles associated with the lumbar spine.     

Human L3L4 intervertebral disc mean 3D shape,modes of variation,and their relationship to degeneration

Intervertebral disc mechanics are affected by both disc shape and disc degeneration, which in turn each affect the other; disc mechanics additionally have a role in the etiology of disc degeneration. Finite element analysis (FEA) is a favored tool to investigate these relationships, but limited data for intervertebral disc 3D shape has forced the use of simplified or single-subject geometries, with the effect of inter-individual shape variation investigated only in specialized studies. Similarly, most data on disc shape variation with degeneration is based on 2D mid-sagittal images, which incompletely define 3D shape changes. Therefore, the objective of this study was to quantify inter-individual disc shape variation in 3D, classify this variation into independently-occurring modes using a statistical shape model, and identify correlations between disc shape and degeneration. Three-dimensional disc shapes were obtained from MRI of 13 human male cadaver L3L4 discs. An average disc shape and four major modes of shape variation (representing 90% of the variance) were identified. The first mode represented disc axial area and was significantly correlated to degeneration (R²=0.44), indicating larger axial area in degenerate discs. Disc height variation occurred in three distinct modes, each also involving non-height variation. The statistical shape model provides an average L3L4 disc shape for FEA that is fully defined in 3D, and makes it convenient to generate a set of shapes with which to represent aggregate inter-individual variation. Degeneration grade-specific shapes can also be generated. To facilitate application, the model is included in this paper?s supplemental content.     

Joint modeling of cell and nuclear shape variation

Modeling cell shape variation is critical to our understanding of cell biology. Previous work has demonstrated the utility of nonrigid image registration methods for the construction of nonparametric nuclear shape models in which pairwise deformation distances are measured between all shapes and are embedded into a low-dimensional shape space. Using these methods, we explore the relationship between cell shape and nuclear shape. We find that these are frequently dependent on each other and use this as the motivation for the development of combined cell and nuclear shape space models, extending nonparametric cell representations to multiple-component three-dimensional cellular shapes and identifying modes of joint shape variation. We learn a first-order dynamics model to predict cell and nuclear shapes, given shapes at a previous time point. We use this to determine the effects of endogenous protein tags or drugs on the shape dynamics of cell lines and show that tagged C1QBP reduces the correlation between cell and nuclear shape. To reduce the computational cost of learning these models, we demonstrate the ability to reconstruct shape spaces using a fraction of computed pairwise distances. The open-source tools provide a powerful basis for future studies of the molecular basis of cell organization.     

Abdominal muscles dominate contributions to vertebral joint stiffness during the push-up

The goal of this study was to quantify the relative contributions of each muscle group surrounding the spine to vertebral joint rotational stiffness (VJRS) during the push-up exercise. Upper-body kinematics, three-dimensional hand forces and lumbar spine postures, and 14 channels (bilaterally from rectus abdominis, external oblique, internal oblique, latissimus dorsi, thoracic erector spinae, lumbar erector spinae, and multifidus) of trunk electromyographic (EMG) activity were collected from 11 males and used as inputs to a biomechanical model that determined the individual contributions of 10 muscle groups surrounding the lumbar spine to VJRS at five lumbar vertebral joints (L1-L2 to L5-S1). On average, the abdominal muscles contributed 64.32 +/- 8.50%, 86.55 +/- 1.13%, and 83.84 +/- 1.95% to VJRS about the flexion/extension, lateral bend, and axial twist axes, respectively. Rectus abdominis contributed 43.16 +/- 3.44% to VJRS about the flexion/extension axis at each lumbar joint, and external oblique and internal oblique, respectively contributed 52.61 +/- 7.73% and 62.13 +/- 8.71% to VJRS about the lateral bend and axial twist axes, respectively, at all lumbar joints with the exception of L5-S1. Owing to changes in moment arm length, the external oblique and internal oblique, respectively contributed 55.89% and 50.01% to VJRS about the axial twist and lateral bend axes at L5-S1. Transversus abdominis, multifidus, and the spine extensors contributed minimally to VJRS during the push-up exercise. The push-up challenges the abdominal musculature to maintain VJRS. The orientation of the abdominal muscles suggests that each muscle primarily controls the rotational stiffness about a single axis.     

Intervertebral reaction force prediction using an enhanced assembly of OpenSim models

OpenSim offers a valuable approach to investigating otherwise difficult to assess yet important biomechanical parameters such as joint reaction forces. Although the range of available models in the public repository is continually increasing, there currently exists no OpenSim model for the computation of intervertebral joint reactions during flexion and lifting tasks. The current work combines and improves elements of existing models to develop an enhanced model of the upper body and lumbar spine. Models of the upper body with extremities, neck and head were combined with an improved version of a lumbar spine from the model repository. Translational motion was enabled for each lumbar vertebrae with six controllable degrees of freedom. Motion segment stiffness was implemented at lumbar levels and mass properties were assigned throughout the model. Moreover, body coordinate frames of the spine were modified to allow straightforward variation of sagittal alignment and to simplify interpretation of results. Evaluation of model predictions for level L1–L2, L3–L4 and L4–L5 in various postures of forward flexion and moderate lifting (8 kg) revealed an agreement within 10% to experimental studies and model-based computational analyses. However, in an extended posture or during lifting of heavier loads (20 kg), computed joint reactions differed substantially from reported in vivo measures using instrumented implants. We conclude that agreement between the model and available experimental data was good in view of limitations of both the model and the validation datasets. The presented model is useful in that it permits computation of realistic lumbar spine joint reaction forces during flexion and moderate lifting tasks. The model and corresponding documentation are now available in the online OpenSim repository.     

Biomechanical properties of human lumbar spine ligaments.

Biomechanical properties of the six major lumbar spine ligaments were determined from 38 fresh human cadaveric subjects for direct incorporation into mathematical and finite element models. Anterior and posterior longitudinal ligaments, joint capsules, ligamentum flavum, interspinous, and supraspinous ligaments were evaluated. Using the results from in situ isolation tests, individual force-deflection responses from 132 samples were transformed with a normalization procedure into mean force-deflection properties to describe the nonlinear characteristics. Ligament responses based on the mechanical characteristics as well as anatomical considerations, were grouped into T12-L2, L2-L4, and L4-S1 levels maintaining individuality and nonlinearity. A total of 18 data curves are presented. Geometrical measurements of original length and cross-sectional area for these six major ligaments were determined using cryomicrotomy techniques. Derived parameters including failure stress and strain were computed using the strength and geometry information. These properties for the lumbar spinal ligaments which are based on identical definitions used in mechanical testing and geometrical assay will permit more realistic and consistent inputs for analytical models.     

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

The 2D shape of the lumbar spine in the sagittal plane can be determined from lordosis angles measured between the corresponding end-plates of the vertebral bodies or by using an active shape model (ASM) of the vertebral body outline. The ASM was previously shown to be a more efficient and reliable method, but its accuracy has not been assessed. The aim of this study was to determine the accuracy of an ASM for characterising lumbar spine shape and compare this to conventional measurements. Images of 25 different lumbar spine shapes were generated and measured, using both methods, by three independent observers. The accuracy of the ASM, determined from lordosis angles predicted by the model, was found to be better than conventional measurements.     

Ultimate strength of the lumbar spine in flexion--an in vitro study

The ultimate strength in flexion of 16 lumbar functional spinal units (FSU) was determined. The specimens were exposed to a combined static load of bending and shearing in the sagittal plane until overt rupture occurred (simulated flexion-distraction injuries). The biomechanical response of the FSU was measured with a force and moment platform. Mechanical displacement gauges were used to measure vertical displacements (flexion angulation) of the specimens. Photographs were taken after each loading step for determination of horizontal displacements and the centre of rotation. The lumbar FSU could resist a combination of bending moment and shear force of 156 Nm and 620 N respectively, before complete disruption occurred. The tension force acting on the posterior structures was 2.8 kN. The flexion angulation just before failure was 20 degrees and the anterior horizontal displacement between the upper and lower vertebrae was 9 mm. The centre of rotation was located in the posterior part of the lower vertebral body. The bone mineral content in the vertebrae appeared to be a good predictor of ultimate strength of the lumbar FSU. Knowledge of the biomechanical response of the lumbar spine under different static traumatic loads is a first step to better understand the injury mechanisms of the spine in traffic accidents.     

The dynamic flexion/extension properties of the lumbar spine in vitro using a novel pendulum system

The biomechanical properties of the ligamentous cadaver spine have been previously examined using a variety of experimental testing protocols. Ongoing technical challenges in the biomechanical testing of the spine include the application of physiologic compressive loads and the application of dynamic bending moments while allowing unconstrained three-dimensional motion. The purpose of this study was to report the development of a novel pendulum apparatus that addressed these challenges and to determine the effects of various axial compressive loads on the dynamic biomechanical properties of the lumbar functional spinal unit (FSU). Lumbar FSUs were tested in flexion and extension under five axial compressive loads chosen to represent physiologic loading conditions. After an initial rotation, the FSUs behaved as a dynamic, underdamped vibrating elastic system. Bending stiffness and coefficient of damping increased significantly as the compressive pendulum load increased. The apparatus described herein is a relatively simple approach to determining the dynamic bending properties of the FSU, and potentially disc arthroplasty devices. It is capable of applying physiologic compressive loads at dynamic rates without constraining the kinematics of the joints, crucial requirements for testing FSUs in vitro.     

Twente spine model: A complete and coherent dataset for musculo-skeletal modeling of the lumbar region of the human spine

Musculo-skeletal modeling can greatly help in understanding normal and pathological functioning of the spine. For such models to produce reliable muscle and joint force estimations, an adequate set of musculo-skeletal data is necessary. In this study, we present a complete and coherent dataset for the lumbar spine, based on medical images and dissection measurements from one embalmed human cadaver. We divided muscles into muscle-tendon elements, digitized their attachments at the bones and measured morphological parameters. In total, we measured 11 muscles from one body side, using 96 elements. For every muscle element, we measured three-dimensional coordinates of its attachments, fiber length, tendon length, sarcomere length, optimal fiber length, pennation angle, mass, and physiological cross-sectional area together with the geometry of the lumbar spine. Results were consistent with other anatomical studies and included new data for the serratus posterior inferior muscle. The dataset presented in this paper enables a complete and coherent musculo-skeletal model for the lumbar spine and will improve the current state-of-the art in predicting spinal loading.     

Characterization of the age-dependent shape of the pediatric thoracic spine and vertebrae using generalized procrustes analysis

Generalized Procrustes Analysis (GPA) is a superimposition method used to generate size-invariant distributions of homologous landmark points. Several studies have used GPA to assess the three-dimensional (3D) shapes of or to evaluate sex-related differences in the human brain, skull, rib cage, pelvis and lower limbs. Previous studies of the pediatric thoracic vertebrae suggest that they may undergo changes in shape as a result of normative growth. This study uses GPA and second order polynomial equations to model growth and age- and sex-related changes in shape of the pediatric thoracic spine. We present a thorough analysis of the normative 3D shape, size, and orientation of the pediatric thoracic spine and vertebrae as well as equations which can be used to generate models of the thoracic spine and vertebrae for any age between 1 and 19 years. Such models could be used to create more accurate 3D reconstructions of the thoracic spine, generate improved age-specific geometries for finite element models (FEMs) and used to assist clinicians with patient-specific planning and surgical interventions for spine deformity.     

FEBio finite element models of the human lumbar spine

Finite element analysis has proven to be a viable method for assessing many structure-function relationships in the human lumbar spine. Several validated models of the spine have been published, but they typically rely on commercial packages and are difficult to share between labs. The goal of this study is to present the development of the first open-access models of the human lumbar spine in FEBio. This modeling framework currently targets three deficient areas in the field of lumbar spine modeling: 1) open-access models, 2) accessibility for multiple meshing schemes, and 3) options to include advanced hyperelastic and biphasic constitutive models.     

Statistical shape modelling reveals large and distinct subchondral bony differences in osteoarthritic knees

Knee osteoarthritis (OA) results in changes such as joint-space narrowing and osteophyte formation. Radiographic classification systems group patients by the presence or absence of these gross anatomical features but are poorly correlated to function. Statistical-shape modelling (SSM) can detect subtle differences in 3D-bone geometry, providing an opportunity for accurate predictive models. The aim of this study was to describe and quantify the main modes of shape variation which distinguish end-stage OA from asymptomatic knees. Seventy-six patients with OA and 77 control participants received a CT of their knee. 3D models of the joint were created by manual segmentation. A template mesh was fitted to all meshes and rigidly aligned resulting in a set of correspondent meshes. Principal Component Analysis (PCA) was performed to create the SSM. Logistic regression was performed on the PCA weights to distinguish morphological features of the two groups. The first 7 modes of the SSM captured >90% shape variation with 6 modes best distinguishing between OA and asymptomatic knees. OA knees displayed sub-chondral bone expansion particularly in the condyles and posterior medial tibial plateau of up to 10 mm. The model classified the two groups with 95% accuracy, 96% sensitivity, 94% specificity, and 97% AUC. There were distinct features which differentiated OA from asymptomatic knees. Further research will elucidate how magnitude and location of shape changes in the knee influence clinical and functional outcomes.     

Morphological variation of the thoracolumbar vertebrae in Macropodidae and its functional relevance

The present study was designed to investigate how the form of the marsupial thoracolumbar vertebrae varies to cope with the particular demands of diverse loading and locomotor behaviors. The vertebral columns of 10 species of Macropodidae, with various body masses and modes of locomotion, together with two other arboreal marsupials, koala and cuscus, were selected. Seventy-four three-dimensional landmark coordinates were acquired on each of the 10 last presacral vertebrae of the 70 vertebral columns. The interspecific variations of the third lumbar vertebra (L3, which approximates the mean) and the transitional patterns of the thoracolumbar segments were examined using the combined approach of generalized Procrustes analysis (GPA) and principal components analysis (PCA). The results of analyses of an individual vertebra (L3) and of the transitional patterns indicate significant interspecific differences. In the L3 study the first PC shows allometric shape variation, while the second PC seems to relate to adaptation for terrestrial versus arboreal locomotion. When the L3 vertebrae of the common spotted cuscus and koala are included for comparison, the vertebra of the tree kangaroo occupies an intermediate position between the hopping kangaroo and these arboreal marsupials. The L3 vertebrae in the arboreal marsupials possess a distinct dorsoventrally expanded vertebral body, and perpendicularly orientated spinous and transverse processes. The results of the present study suggest that vertebral shape in the kangaroo and wallaroos provides a structural adaptation to hopping through a relatively enlarged loading area and powerful lever system. In contrast, the small-sized bettongs (or rat kangaroos) have a relatively flexible column and elongated levers for the action of back muscles that extend and laterally flex the spine. The complex pattern of vertebral shape transition in the last 10 presacral vertebrae was examined using PCAs that compare between species information about vertebral shape variation along the thoracolumbar column. The results reinforce and emphasize important aspects of the patterns of variation seen in the detailed analysis of the third lumbar vertebra. The results also imply that size, spinal loading pattern, and locomotor behavior exert an influence on shaping the vertebra. Further, the morphological adaptations are consistent within these marsupials and this opens up the possibility that this kind of analysis may be useful in making functional inferences from fossil material.     

Exercise within lower body negative pressure partially counteracts lumbar spine deconditioning associated with 28-day bed rest.

Astronauts experience spine deconditioning during exposure to microgravity due to the lack of axial loads on the spine. Treadmill exercise in a lower body negative pressure (LBNP) chamber provides axial loads on the lumbar spine. We hypothesize that daily supine LBNP exercise helps counteract lumbar spine deconditioning during 28 days of microgravity simulated by bed rest. Twelve sets of healthy, identical twins underwent 6 degrees head-down-tilt bed rest for 28 days. One subject from each set of twins was randomly assigned to the exercise (Ex) group, whereas their sibling served as a nonexercise control (Con). The Ex group exercised in supine posture within a LBNP chamber for 45 min/day, 6 days/wk. All subjects underwent magnetic resonance imaging of their lumbar spine before and at the end of bed rest. Lumbar spinal length increased 3.7 +/- 0.5 mm in the Con group over 28-day bed rest, whereas, in the Ex group, lumbar spinal length increased significantly less (2.3 +/- 0.4 mm, P = 0.01). All lumbar intervertebral disk heights (L5-S1, L4-5, L3-4, L2-3, and L1-2) in the Con group increased significantly over the 28-day bed rest (P < 0.05). In the Ex group, there were no significant increases in L5-S1 and L4-5 disk heights. Lumbar lordosis decreased significantly by 3.3 +/- 1.2 degrees during bed rest in the Con group (P = 0.02), but it did not decrease significantly in the Ex group. Our results suggest that supine LBNP treadmill exercise partially counteracts lumbar spine lengthening and deconditioning associated with simulated microgravity.     

A statistical geometrical description of the human liver for probabilistic occupant models

Realistic numerical assessments of liver injury risk for the entire occupant population require incorporating inter-subject variations into numerical models. Statistical shape models of the abdominal organs have been shown to be useful tools for the investigation of the organ variations and could be applied to the development of statistical computational models. The main objective of this study was to establish a standard procedure to quantify the shape variations of a human liver in a seated posture, and construct three-dimensional (3D) statistical shape boundary models.     

Spinal shape changes resulting from scoliotic spine surgical instrumentation expressed as intervertebral rotations and centers of rotation

This paper reports the changes in spinal shape resulting from scoliotic spine surgical instrumentation expressed as intervertebral rotations and centers of rotation. The objective is to test the hypothesis that the type of spinal instrumentation system (Cotrel-Dubousset versus Colorado) does not influence these motion parameters. Intervertebral rotations and centers of rotation of the scoliotic spines were computed from the pre- and post-operative radiographs of 82 patients undergoing spinal correction. The three-dimensional (3D) reconstruction of six anatomical landmarks was achieved for each of the thoracic and lumbar vertebrae. A least-squares approach based on singular value decomposition was used to calculate the rigid body transformation parameters. Average centers of rotation for all intervertebral levels are located in the neural canal at the mid-sagittal plane and approximately at the superior endplate level of the inferior vertebra. Intervertebral rotations have components in all planes: 6.7 degrees (frontal), 5.5 degrees (sagittal) and 4.5 degrees (transverse) RMS for all intervertebral levels. Nearly all intervertebral rotations and centers of rotation are not significantly different for the two instrumentation systems. Various intervertebral rotations and 3D reconstruction errors were simulated on a theoretical model of a lumbar functional unit to assess the proposed method. Intervertebral rotation errors were 1.7 degrees when simulating 3D errors of 3mm on the position of the landmarks. Maximum errors for the position of centers of rotation were below 1cm in the case of intervertebral rotations larger than 2.5 degrees (most cases), but were larger (38 mm) for small intervertebral rotations (<1 degrees ). The type of instrumentation system did not influence intervertebral rotations and centers of rotation. These results provide valuable data for the development and validation of simulation models for surgical instrumentation of idiopathic scoliosis.