Geometric sensitivity of patient-specific finite element models of the spine to variability in user-selected anatomical landmarks

Software to create individualised finite element (FE) models of the osseoligamentous spine using pre-operative computed tomography (CT) data-sets for spinal surgery patients has recently been developed. This study presents a geometric sensitivity analysis of this software to assess the effect of intra-observer variability in user-selected anatomical landmarks. User-selected landmarks on the osseous anatomy were defined from CT data-sets for three scoliosis patients and these landmarks were used to reconstruct patient-specific anatomy of the spine and ribcage using parametric descriptions. The intra-observer errors in landmark co-ordinates for these anatomical landmarks were calculated. FE models of the spine and ribcage were created using the reconstructed anatomy for each patient and these models were analysed for a loadcase simulating clinical flexibility assessment. The intra-observer error in the anatomical measurements was low in comparison to the initial dimensions, with the exception of the angular measurements for disc wedge and zygapophyseal joint (z-joint) orientation and disc height. This variability suggested that CT resolution may influence such angular measurements, particularly for small anatomical features, such as the z-joints, and may also affect disc height. The results of the FE analysis showed low variation in the model predictions for spinal curvature with the mean intra-observer variability substantially less than the accepted error in clinical measurement. These findings demonstrate that intra-observer variability in landmark point selection has minimal effect on the subsequent FE predictions for a clinical loadcase.

Total energy shaping of a class of underactuated Port-Hamiltonian Systems using a new set of closed-loop potential shape variables

This paper proposes a method for designing set-point regulation controllers for a class of underactuated mechanical systems in Port-Hamiltonian System (PHS) form. A new set of potential shape variables in closed loop is proposed, which can replace the set of open loop shape variables-the configuration variables that appear in the kinetic energy. With this choice, the closed-loop potential energy contains free functions of the new variables. By expressing the regulation objective in terms of these new potential shape variables, the desired equilibrium can be assigned and there is freedom to reshape the potential energy to achieve performance whilst maintaining the PHS form in closed loop. This complements contemporary results in the literature, which preserve the open-loop shape variables. As a case study, we consider a robotic manipulator mounted on a flexible base and compensate for the motion of the base while positioning the end effector with respect to the ground reference. We compare the proposed control strategy with special cases that correspond to other energy shaping strategies previously proposed in the literature.

Segmental torso masses and joint torques produced by gravity in the adolescent scoliotic spine

Introduction Calculating segmental torso masses in Adolescent Idiopathic Scoliosis (AIS) patients allows the gravitational loading on the scoliotic spine during relaxed standing to be estimated. Methods Low dose CT data was used to calculate vertebral level-by-level torso masses and spinal joint torques for 20 female AIS patients (mean age 15.0 ± 2.7 years, mean Cobb angle 53 ± 7.1°). ImageJ software (v1.45 NIH USA) was used to threshold the T1 to L5 CT images and calculate the segmental torso volume and mass for each vertebral level. Masses for the head, neck and arms were taken from published data. Intervertebral joint torques in the coronal and sagittal planes at each vertebral level were found from the position of the centroid of the segment masses relative to the joint centres (assumed to be at the centre of the intervertebral disc. The joint torque at each level was found by summing torque contributions for all segments above that joint. Results Segmental torso mass increased from 0.6kg at T1 to 1.5kg at L5. The coronal plane joint torques due to gravity were 5-7Nm at the apex of the curve; sagittal torques were 3-5.4Nm. Conclusion CT scans were in the supine position and curve magnitudes are known to be smaller than those in standing. Hence, this study has shown that gravity produces joint torques potentially of higher than 7Nm in the coronal plane and 5Nm in the sagittal plane during relaxed standing in scoliosis patients. The magnitude of these torques may help to explain the mechanics of AIS progression and the mechanics of bracing. This new data on torso segmental mass in AIS patients will assist biomechanical models of scoliosis.

The stabilising role of the costovertebral joints and spinous processes on thoracic spine stability

Introduction The importance of in vitro biomechanical testing in today’s understanding of spinal pathology and treatment modalities cannot be stressed enough. Different studies have used differing levels of dissection of their spinal segments for their testing protocols[1, 2]. The aim of this study was to assess the impact of removing the costovertebral joints and partial resection of the spinous process sequentially, on the stiffness of the immature thoracic bovine spinal segment. Materials and Methods Thoracic spines from 6-8 week old calves were used. Each spine was dissected and divided into motion segments with 5cm of attached rib on each side and full spinous processes including levels T4-T11 (n=28). They were potted in polymethylemethacrylate. An Instron Biaxial materials testing machine with a custom made jig was used for testing. The segments were tested in flexion/extension, lateral bending and axial rotation at 37⁰C and 100% humidity, using moment control to a maximum 1.75 Nm with a loading rate of 0.3 Nm per second. They were first tested intact for ten load cycles with data collected from the tenth cycle. Progressive dissection was performed by removing first the attached ribs, followed by the spinous process at its base. Biomechanical testing was carried out after each level of dissection using the same protocol. Statistical analysis of the data was performed using repeated measures ANOVA. Results In combined flexion/extension there was a significant reduction in stiffness of 16% (p=0.002). This was mainly after resection of the ribs (14%, p=0.024) and mainly occurred in flexion where stiffness reduced by 22% (p=0.021). In extension, stiffness dropped by 13% (p=0.133). However there was no further significant change in stiffness on resection of the spinous process (<1%) (p=1.00). In lateral bending there was a significant decrease in stiffness of 13% (p<0.001). This comprised a drop of 11% on resection of the ribs (p=0.009) and a further 8% on resection of the spinous process (p=0.014). There was no difference between left and right bending. In axial rotation there was no significant change in stiffness after each stage of dissection (p=0.253). There was no difference between left and right rotation. Conclusion The costovertebral joints play a significant role in providing stability to the bovine thoracic spine in both flexion/extension and lateral bending, whereas the spinous processes play a minor role. Both elements have little effect on axial rotation stability.

Plasma-enabled, catalyst-free growth of carbon nanotubes on mechanically-written Si features with arbitrary shape

Simple, rapid, catalyst-free synthesis of complex patterns of long, vertically aligned multiwalled carbon nanotubes, strictly confined within mechanically-written features on a Si(1 0 0) surface is reported. It is shown that dense arrays of the nanotubes can nucleate and fully fill the features when the low-temperature microwave plasma is in a direct contact with the surface. This eliminates additional nanofabrication steps and inevitable contact losses in applications associated with carbon nanotube patterns. Using metal catalyst has long been considered essential for the nucleation and growth of surface-supported carbon nanotubes (CNTs) [1] and [2]. Only very recently, the possibility of CNT growth using non-metallic (e.g., oxide [3] and SiC [4]) catalysts or artificially created carbon-enriched surface layers [5] has been demonstrated. However, successful integration of carbon nanostructures into Si-based nanodevice platforms requires catalyst-free growth, as the catalyst nanoparticles introduce contact losses, and their catalytic activity is very difficult to control during the growth [6]. Furthermore, in many applications in microfluidics, biological and molecular filters, electronic, sensor, and energy conversion nanodevices, the CNTs need to be arranged in specific complex patterns [7] and [8]. These patterns need to contain the basic features (e.g., lines and dots) written using simple procedures and fully filled with dense arrays of high-quality, straight, yet separated nanotubes. In this paper, we report on a completely metal or oxide catalyst-free plasma-based approach for the direct and rapid growth of dense arrays of long vertically-aligned multi-walled carbon nanotubes arranged into complex patterns made of various combinations of basic features on a Si(1 0 0) surface written using simple mechanical techniques. The process was conducted in a plasma environment [9] and [10] produced by a microwave discharge which typically generates the low-temperature plasmas at the discharge power below 1 kW [11]. Our process starts from mechanical writing (scribing) a pattern of arbitrary features on pre-treated Si(1 0 0) wafers. Before and after the mechanical feature writing, the Si(1 0 0) substrates were cleaned in an aqueous solution of hydrofluoric acid for 2 min to remove any possible contaminations (such as oil traces which could decompose to free carbon at elevated temperatures) from the substrate surface. A piece of another silicon wafer cleaned in the same way as the substrate, or a diamond scriber were used to produce the growth patterns by a simple arbitrary mechanical writing, i.e., by making linear scratches or dot punctures on the Si wafer surface. The results were the same in both cases, i.e., when scratching the surface by Si or a diamond scriber. The procedure for preparation of the substrates did not involve any possibility of external metallic contaminations on the substrate surface. After the preparation, the substrates were loaded into an ASTeX model 5200 chemical vapour deposition (CVD) reactor, which was very carefully conditioned to remove any residue contamination. The samples were heated to at least 800 °C to remove any oxide that could have formed during the sample loading [12]. After loading the substrates into the reactor chamber, N2 gas was supplied into the chamber at the pressure of 7 Torr to ignite and sustain the discharge at the total power of 200 W. Then, a mixture of CH4 and 60% of N2 gases were supplied at 20 Torr, and the discharge power was increased to 700 W (power density of approximately 1.49 W/cm3). During the process, the microwave plasma was in a direct contact with the substrate. During the plasma exposure, no external heating source was used, and the substrate temperature (∼850 °C) was maintained merely due to the plasma heating. The features were exposed to a microwave plasma for 3–5 min. A photograph of the reactor and the plasma discharge is shown in Fig. 1a and b.

Self-organized vertically aligned single-crystal silicon nanostructures with controlled shape and aspect ratio by reactive plasma etching

The formation of vertically aligned single-crystalline silicon nanostructures via "self-organized" maskless etching in Ar+ H 2 plasmas is studied. The shape and aspect ratio can be effectively controlled by the reactive plasma composition. In the optimum parameter space, single-crystalline pyramid-like nanostructures are produced; otherwise, nanocones and nanodots are formed. This generic nanostructure formation approach does not involve any external material deposition. It is based on a concurrent sputtering, etching, hydrogen termination, and atom/radical redeposition and can be applied to other nanomaterials.

Deterministic shape control in plasma-aided nanotip assembly

The possibility of deterministic plasma-assisted reshaping of capped cylindrical seed nanotips by manipulating the plasma parameter-dependent sheath width is shown. Multiscale hybrid gas phase/solid surface numerical experiments reveal that under the wide-sheath conditions the nanotips widen at the base and when the sheath is narrow, they sharpen up. By combining the wide- and narrow-sheath stages in a single process, it turns out possible to synthesize wide-base nanotips with long- and narrow-apex spikes, ideal for electron microemitter applications. This plasma-based approach is generic and can be applied to a larger number of multipurpose nanoassemblies. © 2005 American Institute of Physics.

Intervertebral staple grading system with micro-CT

Introduction Intervertebral stapling is a leading method of fusionless scoliosis treatment which attempts to control growth by applying pressure to the convex side of a scoliotic curve in accordance with the Hueter-Volkmann principle. In addition to that, staples have the potential to damage surrounding bone during insertion and subsequent loading. The aim of this study was to assess the extent of bony structural damage including epiphyseal injury as a result of intervertebral stapling using an in vitro bovine model. Materials and Methods Thoracic spines from 6-8 week old calves were dissected and divided into motion segments including levels T4-T11 (n=14). Each segment was potted in polymethylemethacrylate. An Instron Biaxial materials testing machine with a custom made jig was used for testing. The segments were tested in flexion/extension, lateral bending and axial rotation at 37⁰C and 100% humidity, using moment control to a maximum 1.75 Nm with a loading rate of 0.3 Nm per second for 10 cycles. The segments were initially tested uninstrumented with data collected from the tenth load cycle. Next an anterolateral 4-prong Shape Memory Alloy (SMA) staple (Medtronic Sofamor Danek, USA) was inserted into each segment. Biomechanical testing was repeated as before. The staples were cut in half with a diamond saw and carefully removed. Micro-CT scans were performed and sagittal, transverse and coronal reformatted images were produced using ImageJ (NIH, USA).The specimens were divided into 3 grades (0, 1 and 2) according to the number of epiphyses damaged by the staple prongs. Results: There were 9 (65%) segments with grade 1 staple insertions and 5 (35%) segments with grade 2 insertions. There were no grade 0 staples. Grade 2 spines had a higher stiffness level than grade 1 spines, in all axes of movement, by 28% (p=0.004). This was most noted in flexion/extension with an increase of 49% (p=0.042), followed by non-significant change in lateral bending 19% (p=0.129) and axial rotation 8% (p=0.456) stiffness. The cross sectional area of bone destruction from the prongs was only 0.4% larger in the grade 2 group compared to the grade 1 group (p=0.961). Conclusion Intervertebral staples cause epiphyseal damage. There is a difference in stiffness between grade 1 and grade 2 staple insertion segments in flexion/extension only. There is no difference in the cross section of bone destruction as a result of prong insertion and segment motion.

Gravity-induced coronal plane joint moments in the adolescent scoliotic spine

INTRODUCTION Calculating segmental (vertebral level-by-level) torso masses in Adolescent Idiopathic Scoliosis (AIS) patients allows the gravitational loading on the scoliotic spine during relaxed standing to be estimated. METHODS Existing low dose CT scans were used to calculate vertebral level-by-level torso masses and joint moments occurring in the spine for a group of female AIS patients with right-sided thoracic curves. Image processing software, ImageJ (v1.45 NIH USA) was used to reconstruct the torso segments and subsequently measure the torso volume and mass corresponding to each vertebral level. Body segment masses for the head, neck and arms were taken from published anthropometric data. Intervertebral joint moments at each vertebral level were found by summing each of the torso segment masses above the required joint and multiplying it by the perpendicular distance to the centre of the disc. RESULTS AND DISCUSSION Twenty patients were included in this study with a mean age of 15.0±2.7 years and a mean Cobb angle 52±5.9°. The mean total trunk mass, as a percentage of total body mass, was 27.8 (SD 0.5) %. Mean segmental torso mass increased inferiorly from 0.6kg at T1 to 1.5kg at L5. The coronal plane joint moments during relaxed standing were typically 5-7Nm at the apex of the curve (Figure 1), with the highest apex joint of 7Nm. CT scans were performed in the supine position and curve magnitudes are known to be 7-10° smaller than those measured in standing [1]. Therefore joint moments produced by gravity will be greater than those calculated here. CONCLUSIONS Coronal plane joint moments as high as 7Nm can occur during relaxed standing in scoliosis patients, which may help to explain the mechanics of AIS progression. The body mass distributions calculated in this study can be used to estimate joint moments derived using other imaging modalities such as MRI and subsequently determine if a relationship exists between joint moments and progressive vertebral deformity.

Comparison of eight published static finite element models of the intact lumbar spine : predictive power of models improves when combined together

Finite element (FE) model studies have made important contributions to our understanding of functional biomechanics of the lumbar spine. However, if a model is used to answer clinical and biomechanical questions over a certain population, their inherently large inter-subject variability has to be considered. Current FE model studies, however, generally account only for a single distinct spinal geometry with one set of material properties. This raises questions concerning their predictive power, their range of results and on their agreement with in vitro and in vivo values. Eight well-established FE models of the lumbar spine (L1-5) of different research centres around the globe were subjected to pure and combined loading modes and compared to in vitro and in vivo measurements for intervertebral rotations, disc pressures and facet joint forces. Under pure moment loading, the predicted L1-5 rotations of almost all models fell within the reported in vitro ranges, and their median values differed on average by only 2° for flexion-extension, 1° for lateral bending and 5° for axial rotation. Predicted median facet joint forces and disc pressures were also in good agreement with published median in vitro values. However, the ranges of predictions were larger and exceeded those reported in vitro, especially for the facet joint forces. For all combined loading modes, except for flexion, predicted median segmental intervertebral rotations and disc pressures were in good agreement with measured in vivo values. In light of high inter-subject variability, the generalization of results of a single model to a population remains a concern. This study demonstrated that the pooled median of individual model results, similar to a probabilistic approach, can be used as an improved predictive tool in order to estimate the response of the lumbar spine.

Clinically-based automatic implant fitting for shape optimization of fracture fixation plates

Complex bone contour and anatomical variations between individual bones complicate the process of deriving an implant shape that fits majority of the population. This thesis proposes an automatic fitting method for anatomically-precontoured plates based on clinical requirements, and investigated if 100% anatomical fit for a group of bone is achievable through manual bending of one plate shape. It was found that, for the plate used, 100% fit is impossible to achieve through manual bending alone. Rather, newly-developed shapes are also required to obtain anatomical fit in areas with more complex bone contour.