Investigating the change in three dimensional deformity for idiopathic scoliosis using axially loaded MRI

Background: Adolescent idiopathic scoliosis is a complex three-dimensional deformity, involving a lateral deformity in the coronal plane and axial rotation of the vertebrae in the transverse plane. Gravitational loading plays an important biomechanical role in governing the coronal deformity, however, less is known about how they influence the axial deformity. This study investigates the change in three-dimensional deformity of a series of scoliosis patients due to compressive axial loading. Methods: Magnetic resonance imaging scans were obtained and coronal deformity (measured using the coronal Cobb angle) and axial rotations measured for a group of 18 scoliosis patients (Mean major Cobb angle was 43.4 o). Each patient was scanned in an unloaded and loaded condition while compressive loads equivalent to 50% body mass were applied using a custom developed compressive device. Findings: The mean increase in major Cobb angle due to compressive loading was 7.4 o (SD 3.5 o). The most axially rotated vertebra was observed at the apex of the structural curve and the largest average intravertebral rotations were observed toward the limits of the coronal deformity. A level-wise comparison showed no significant difference between the average loaded and unloaded vertebral axial rotations (intra-observer error = 2.56 o) or intravertebral rotations at each spinal level. Interpretation: This study suggests that the biomechanical effects of axial loading primarily influence the coronal deformity, with no significant change in vertebral axial rotation or intravertebral rotation observed between the unloaded and loaded condition. However, the magnitude of changes in vertebral rotation with compressive loading may have been too small to detect given the resolution of the current technique.

Using axially loaded MRI to investigate the biomechanics of adolescent idiopathic scoliosis

Introduction. Spinal flexibility measurement is an important aspect of pre-operative clinical assessment in the treatment of Adolescent Idiopathic Scoliosis (AIS). Clinically, curve flexibility is a combined measure for all vertebral levels. We propose that in vivo flexibility for individual spinal joints could provide valuable additional information in planning treatment for scoliosis. Methods. Individual spinal joint flexibility in the coronal plane was measured for a series of AIS patients using axially loaded magnetic resonance imaging. Each patient underwent magnetic resonance imaging in the supine position, with no axial load, and then following application of an axial compressive load equal to half the patient’s bodyweight. Coronal plane disc wedge angles in the unloaded and loaded configurations were measured. Joint moments exerted by the axial compressive load were used to derive estimates of individual joint compliance. Results. Fifteen AIS patients were included in the study (mean clinical Cobb angle 46 degrees, mean age 15.3 years). Mean intra-observer measurement error for endplate inclination was 1.6˚. The mean increase in measured major Cobb angle between unloaded and loaded scans was 7.6˚. For certain spinal levels (+2,+1,-2 relative to the apex) there was a statistically significant relationship between change in wedge angle under load and initial wedge angle, such that initially highly wedged discs demonstrated a smaller change in wedge angle than less wedged discs. Highly wedged discs were observed near the apex of the curve, which corresponded to lower joint compliance in the apical region. Conclusion. Approaches such as this can provide valuable biomechanical data on in vivo spinal biomechanics in AIS. Knowledge of individual joint flexibility may assist surgeons to determine which spinal procedure is most appropriate for a patient, which levels should be included in a spinal fusion and the relative mobility of individual joints in the deformed region of the spine.

Design and evaluation of an MRI compatible axial compression device for 3D assessment of spinal deformity and flexibility

Magnetic Resonance Imaging (MRI) offers a valuable research tool for the assessment of 3D spinal deformity in AIS, however the horizontal patient position imposed by conventional scanners removes the axial compressive loading on the spine which is an important determinant of deformity shape and magnitude in standing scoliosis patients. The objective of this study was to design, construct and test an MRI compatible compression device for research into the effect of axial loading on spinal deformity using supine MRI scans. The compression device was designed and constructed, consisting of a vest worn by the patient, which was attached via straps to a pneumatically actuated footplate. An applied load of 0.5 x bodyweight was remotely controlled by a unit in the scanner operator’s console. The entire device was constructed using non-metallic components for MRI compatibility. The device was evaluated by performing unloaded and loaded supine MRI scans on a series of 10 AIS patients. The study concluded that an MRI compatible compression device had been successfully designed and constructed, providing a research tool for studies into the effect of axial loading on 3D spinal deformity in scoliosis. The 3D axially loaded MR imaging capability developed in this study will allow future research investigations of the effect of axial loading on spinal rotation, and for imaging the response of scoliotic spinal tissues to axial loading.

Vulnerability of axially loaded columns subjected to transverse impact loads

Increased industrialisation has brought to the forefront the susceptibility of concrete columns in both buildings and bridges to vehicle impacts. Accurate vulnerability assessments are crucial in the design process due to possible catastrophic nature of the failures that can cause. This paper reports on research undertaken to investigate the impact capacity of the columns of low to medium raised building designed according to Australian Standards. Numerical simulation techniques were used in the process and validation was done by using experimental results published in the literature. The investigation thus far has confirmed that vulnerability of typical columns in five story buildings located in urban areas to medium velocity car impacts and hence these columns need to be re-designed (if possible) or retrofitted. In addition, accuracy of the simplified method presented in EN 1991 to quantify the impact damage was scrutinised. A simplified concept to assess the damage due to all collisions modes was introduced. The research information will be extended to generate a common data base to assess the vulnerability of columns in urban areas against new generation of vehicles.

Numerical simulation of axially loaded concrete columns under transverse impact and vulnerability assessment

With a view to assessing the vulnerability of columns to low elevation vehicular impacts, a non-linear explicit numerical model has been developed and validated using existing experimental results. The numerical model accounts for the effects of strain rate and confinement of the reinforced concrete, which are fundamental to the successful prediction of the impact response. The sensitivity of the material model parameters used for the validation is also scrutinised and numerical tests are performed to examine their suitability to simulate the shear failure conditions. Conflicting views on the strain gradient effects are discussed and the validation process is extended to investigate the ability of the equations developed under concentric loading conditions to simulate flexural failure events. Experimental data on impact force–time histories, mid span and residual deflections and support reactions have been verified against corresponding numerical results. A universal technique which can be applied to determine the vulnerability of the impacted columns against collisions with new generation vehicles under the most common impact modes is proposed. Additionally, the observed failure characteristics of the impacted columns are explained using extended outcomes. Based on the overall results, an analytical method is suggested to quantify the vulnerability of the columns.

Design and evaluation of an MRI compatible axial compression device for 3D assessment of spinal deformity and flexibility in adolescent idiopathic scoliosis

Magnetic Resonance Imaging (MRI) offers a valuable research tool for the assessment of 3D spinal deformity in AIS, however the horizontal patient position imposed by conventional scanners removes the axial compressive loading on the spine. The objective of this study was to design, construct and test an MRI compatible compression device for research into the effect of axial loading on spinal deformity using supine MRI scans. The device was evaluated by performing unloaded and loaded supine MRI scans on a series of 10 AIS patients. The patient group had a mean initial (unloaded) major Cobb angle of 43±7º, which increased to 50±9º on application of the compressive load. The 7° increase in mean Cobb angle is consistent with that reported by a previous study comparing standing versus supine posture in scoliosis patients (Torell et al, 1985. Spine 10:425-7).

Infrastructure sustainability : vulnerability of axially loaded columns subjected to transverse impact loads

Increased industrialisation has brought to the forefront the susceptibility of concrete columns in both buildings and bridges to vehicle impacts. Accurate vulnerability assessments are crucial in the design process due to possible catastrophic nature of the failures that can cause. This chapter reports on research undertaken to investigate the impact capacity of the columns of low to medium raised building designed according to the Australian standards. Numerical simulation techniques were used in the process and validation was done by using experimental results published in the literature. The investigation thus far has confirmed that vulnerability of typical columns in five story buildings located in urban areas to medium velocity car impacts and hence these columns need to be re-designed or retrofitted. In addition, accuracy of the simplified method presented in EN 1991-1-7 to quantify the impact damage was scrutinised. A simplified concept to assess the damage due to all collisions modes was introduced. The research information will be extended to generate a common data base to assess the vulnerability of columns in urban areas against new generation of vehicles.

Lateral impact response and parametric studies of axially loaded square concrete filled steel tube columns

This paper presents a numerical study on the response of axially loaded slender square concrete filled steel tube (CFST) columns under low velocity lateral impact loading. A finite element analysis (FEA) model was developed using the explicit dynamic nonlinear finite element code LS -DYNA in which the strain rate effects of both steel and concrete, contact between steel tube and concrete and confinement effect provided by the steel tube for the concrete were considered. The model also benefited from a relatively recent feature of LS-DYNA for applying a pre-loading in the explicit solver. The developed numerical model was verified for its accuracy and adequacy by comparing the results with experimental results available in the literature. The verified model was then employed to conduct a parametric study to investigate the influence of axial load level, impact location, support conditions, and slenderness ratio on the response of the CFST columns. A good agreement between the numerical and experimental results was achieved. The model could reasonably predict the impact load-deflection history and deformed shape of the column at the end of the impact event. The results of the parametric study showed that whilst impact location, axial load level and slenderness ratio can have a significant effect on the peak impact force, residual lateral deflection and maximum lateral deflection, the influence of support fixity is minimal. With an increase of axial load to up to a certain level, the peak force increases; however, a further increase in the axial load causes a decrease in the peak force. Both residual lateral deflection and maximum lateral deflection increase as axial load level increases. Shifting the impact location towards the supports increases the peak force and reduces both residual and maximum lateral deflections. A rise in slenderness ratio decreases the peak force and increases the residual and maximum lateral deflections.

Axially Loaded Timoshenko Rotors From A Prestressed Continuum Approach

We consider an axially loaded Timoshenko rotor rotating at a constant speed and derive its governing equations from a continuum viewpoint. The primary aim of this paper is to understand the source and role of gyroscopic terms, when the rotor is viewed not as a Timoshenko beam but as a genuine 3D continuum. We offer the primary insight that macroscopically observed gyroscopic terms may also, quite equivalently, be viewed as external manifestations of internally existing spin-induced prestresses at the continuum level. To demonstrate this idea with an analytical example (the Timoshenko rotor), we have studied the reliable equations of Choi et al. (Journal of Vibration and Acoustics, 114, 1992, 249-259). Using a straightforward application of our insight in the framework of nonlinear elasticity, we obtain equations that exactly match Choi et al. for the case with no axial load. For the case of axial preload, our straightforward formulation leads to a slightly different set of equations that have negligible numerical consequence for solid rotors. However, we offer a macroscopic, intuitive, justification for modifying our formulation so as to obtain the exact equations of Choi et al. with the axial load included.

Rotating beams isospectral to axially loaded nonrotating uniform beams

In this paper, the stiffness and mass per unit length distributions of a rotating beam, which is isospectral to a given uniform axially loaded nonrotating beam, are determined analytically. The Barcilon-Gottlieb transformation is extended so that it transforms the governing equation of a rotating beam into the governing equation of a uniform, axially loaded nonrotating beam. Analysis is limited to a certain class of Euler-Bernoulli cantilever beams, where the product between the stiffness and the cube of mass per unit length is a constant. The derived mass and stiffness distributions of the rotating beam are used in a finite element analysis to confirm the frequency equivalence of the given and derived beams. Examples of physically realizable beams that have a rectangular cross section are shown as a practical application of the analysis.

Non-uniform beams and stiff strings isospectral to axially loaded uniform beams and piano strings

In this paper, we derive analytical expressions for mass and stiffness functions of transversely vibrating clamped-clamped non-uniform beams under no axial loads, which are isospectral to a given uniform axially loaded beam. Examples of such axially loaded beams are beam columns (compressive axial load) and piano strings (tensile axial load). The Barcilon-Gottlieb transformation is invoked to transform the non-uniform beam equation into the axially loaded uniform beam equation. The coupled ODEs involved in this transformation are solved for two specific cases (pq (z) = k (0) and q = q (0)), and analytical solutions for mass and stiffness are obtained. Examples of beams having a rectangular cross section are shown as a practical application of the analysis. Some non-uniform beams are found whose frequencies are known exactly since uniform axially loaded beams with clamped ends have closed-form solutions. In addition, we show that the tension required in a stiff piano string with hinged ends can be adjusted by changing the mass and stiffness functions of a stiff string, retaining its natural frequencies.

Pull-out behaviour of axially loaded basalt fibre reinforced polymer (BFRP) rods bonded parallel to the grain of glulam elements

Synopsis: Bonded-in rod timber joints off er several advantages over conventional types of joint, including high local force transfer, very stiff connections, and improved ?re and aesthetic properties since the connection is completely hidden in the insulating timber members. More recently, the use of ?bre reinforced polymer (FRP) as a connecting rod, alternative to steel rods, in bonded-in rod connections for timber structures has been investigated. However, the investigation into the behaviour of such joints is limited, in particular, connections involving basalt ?bre reinforced polymers (BFRP) bars - which is the primary focus of this research. This paper presents an experimental programme conducted to investigate the behaviour of bonded-in BFRP bars loaded parallel to the grain of glulam members. Tensile pull-out tests were conducted to examine the effect of bonded length and bond stress-slip on the structural capacity of the connection. An analytical design expression for predicting pull-out capacity is proposed and the results have been compared with some established design equations. It was found that pull-out load increased approximately linearly with the bonded length, up to maximum which occurred at a bonded length of 15 times the hole diameter, and did not increase beyond this bonded length. The most signi?cant failure modes were failure at the timber/adhesive interface followed by pullout of the BFRP rod. Increased bonded lengths resulted in higher bond slip values compared to lower equivalent bonded lengths. The proposed design model gave the best predictions of pull-out capacity compared with other existing models.

Pull-out behaviour of axially loaded Basalt Fibre Reinforced Polymer (BFRP) rods bonded perpendicular to the grain of glulam elements

The behaviour of Basalt Fibre Reinforced Polymer (BFRP) loaded perpendicular to glulam timber elements was investigated. It was found that pull-out load increased approximately linearly with the bonded length up to maximum which occurred at a bonded length of 250 mm (~15 times the hole diameter) and did not increase beyond this bonded length. Failure mode of the samples was mostly shear fracture which was located at the cylindrical zone at the timber/adhesive interface. Increased bonded lengths resulted in corresponding decrease in interfacial bond stress. At 250 mm bonded length, the pull-out capacity of the proposed design model was about 2% lower than that of the tests. The results also showed that the bond stress of the theoretical model (at the ascending and descending branches) of the stress–slip curve was approximately 5–10% of that of the experiment.

Passive vibration isolation using axially loaded curved beams

A nonlinear spring element of a vibration isolator should ideally possess high static and low dynamic stiffness. A buckled beam may be a good candidate to fulfil this requirement provided its internal resonance frequencies are high enough to achieve a wide frequency range of isolation. If a straight beam is used, there is a singularity in the force-displacement characteristic. To smooth this characteristic and eliminate the singularity at the buckling point, beams with initial constant curvature along their length are investigated here as an alternative to the buckled straight beam. Their force displacement characteristics are compared with different initial curvature and with a straight buckled beam. The minimum achievable dynamic stiffness with its corresponding static stiffness is compared for different initial curvatures. A case study is considered where the beams are optimized to isolate a one kilogram mass and to achieve a natural frequency of 1 Hz, considering small amplitudes of vibration. Resonance frequencies of the optimized beams for different curvature are presented. It is shown that an order of magnitude reduction in stiffness compared with a linear spring is achievable, while the internal resonance frequencies of the curved beam are high enough to achieve an acceptable frequency range of isolation.