Energy-based nonlinear control of ship roll gyro-stabiliser with precession angle constraints

In this paper, we consider a passivity-based approach for the design of a control law of multiple ship-roll gyro-stabiliser units. We extend previous work on control of ship roll gyro-stabilisation by considering the problem within a nonlinear framework. In particular, we derive an energy-based model using the port-Hamiltonian theory and then design an active precession controller using passivity-based control interconnection and damping assignment. The design considers the possibility of having multiple gyro-stabiliser units, and the desired potential energy of the system (in closed loop) is chosen to behave like a barrier function, which allows us to enforce constraints on the precession angle of the gyros.

Supine to standing Cobb Angle change in idiopathic scoliosis: The effect of endplate preselection

Introduction Standing radiographs are the ‘gold standard’ for clinical assessment of adolescent idiopathic scoliosis (AIS), with the Cobb Angle used to measure the severity and progression of the scoliotic curve. Supine imaging modalities can provide valuable 3D information on scoliotic anatomy, however, due to changes in gravitational loading direction, the geometry of the spine alters between the supine and standing position which in turn affects the Cobb Angle measurement. Previous studies have consistently reported a 7-10° [1-3] Cobb Angle increase from supine to standing, however, none have reported the effect of endplate pre-selection and which (if any) curve parameters affect the supine to standing Cobb Angle difference. Methods Female AIS patients with right-sided thoracic major curves were included in the retrospective study. Clinically measured Cobb Angles from existing standing coronal radiographs and fulcrum bending radiographs [4] were compared to existing low-dose supine CT scans taken within 3 months of the reference radiograph. Reformatted coronal CT images were used to measure Cobb Angle variability with and without endplate pre-selection (end-plates selected on the radiographs used on the CT images). Inter and intra-observer measurement variability was assessed. Multi-linear regression was used to investigate whether there was a relationship between supine to standing Cobb Angle change and patient characteristics (SPSS, v.21, IBM, USA). Results Fifty-two patients were included, with mean age of 14.6 (SD 1.8) years; all curves were Lenke Type 1 with mean Cobb Angle on supine CT of 42° (SD 6.4°) and 52° (SD 6.7°) on standing radiographs. The mean fulcrum bending Cobb Angle for the group was 22.6° (SD 7.5°). The 10° increase from supine to standing is consistent with existing literature. Pre-selecting vertebral endplates was found to increase the Cobb Angle difference by a mean 2° (range 0-9°). Multi-linear regression revealed a statistically significant relationship between supine to standing Cobb Angle change with: fulcrum flexibility (p=0.001), age (p=0.027) and standing Cobb Angle (p<0.001). In patients with high fulcrum flexibility scores, the supine to standing Cobb Angle change was as great as 20°.The 95% confidence intervals for intra-observer and inter-observer measurement variability were 3.1° and 3.6°, respectively. Conclusion There is a statistically significant relationship between supine to standing Cobb Angle change and fulcrum flexibility. Therefore, this difference can be considered a measure of spinal flexibility. Pre-selecting vertebral endplates causes only minor changes.

What is the apparent angle of a Kelvin ship wave pattern?

While the half-angle which encloses a Kelvin ship wave pattern is commonly accepted to be 19.47 degrees, recent observations and calculations for sufficiently fast-moving ships suggest that the apparent wake angle decreases with ship speed. One explanation for this decrease in angle relies on the assumption that a ship cannot generate wavelengths much greater than its hull length. An alternative interpretation is that the wave pattern that is observed in practice is defined by the location of the highest peaks; for wakes created by sufficiently fast-moving objects, these highest peaks no longer lie on the outermost divergent waves, resulting in a smaller apparent angle. In this paper, we focus on the problems of free surface flow past a single submerged point source and past a submerged source doublet. In the linear version of these problems, we measure the apparent wake angle formed by the highest peaks, and observe the following three regimes: a small Froude number pattern, in which the divergent waves are not visible; standard wave patterns for which the maximum peaks occur on the outermost divergent waves; and a third regime in which the highest peaks form a V-shape with an angle much less than the Kelvin angle. For nonlinear flows, we demonstrate that nonlinearity has the effect of increasing the apparent wake angle so that some highly nonlinear solutions have apparent wake angles that are greater than Kelvin's angle. For large Froude numbers, the effect on apparent wake angle can be more dramatic, with the possibility of strong nonlinearity shifting the wave pattern from the third regime to the second. We expect our nonlinear results will translate to other more complicated flow configurations, such as flow due to a steadily moving closed body such as a submarine.

Supine to standing Cobb angle change in idiopathic scoliosis : the effect of endplate pre-selection

Background Supine imaging modalities provide valuable 3D information on scoliotic anatomy, but the altered spine geometry between the supine and standing positions affects the Cobb angle measurement. Previous studies report a mean 7°-10° Cobb angle increase from supine to standing, but none have reported the effect of endplate pre-selection or whether other parameters affect this Cobb angle difference. Methods Cobb angles from existing coronal radiographs were compared to those on existing low-dose CT scans taken within three months of the reference radiograph for a group of females with adolescent idiopathic scoliosis. Reformatted coronal CT images were used to measure supine Cobb angles with and without endplate pre-selection (end-plates selected from the radiographs) by two observers on three separate occasions. Inter and intra-observer measurement variability were assessed. Multi-linear regression was used to investigate whether there was a relationship between supine to standing Cobb angle change and eight variables: patient age, mass, standing Cobb angle, Risser sign, ligament laxity, Lenke type, fulcrum flexibility and time delay between radiograph and CT scan. Results Fifty-two patients with right thoracic Lenke Type 1 curves and mean age 14.6 years (SD 1.8) were included. The mean Cobb angle on standing radiographs was 51.9° (SD 6.7). The mean Cobb angle on supine CT images without pre-selection of endplates was 41.1° (SD 6.4). The mean Cobb angle on supine CT images with endplate pre-selection was 40.5° (SD 6.6). Pre-selecting vertebral endplates increased the mean Cobb change by 0.6° (SD 2.3, range −9° to 6°). When free to do so, observers chose different levels for the end vertebrae in 39% of cases. Multi-linear regression revealed a statistically significant relationship between supine to standing Cobb change and fulcrum flexibility (p = 0.001), age (p = 0.027) and standing Cobb angle (p < 0.001). The 95% confidence intervals for intra-observer and inter-observer measurement variability were 3.1° and 3.6°, respectively. Conclusions Pre-selecting vertebral endplates causes minor changes to the mean supine to standing Cobb change. There is a statistically significant relationship between supine to standing Cobb change and fulcrum flexibility such that this difference can be considered a potential alternative measure of spinal flexibility.

The effect of endplate preselection when measuring supine versus standing cobb angle change in idiopathic scoliosis

The primary aim of this study was to determine whether endplate pre-selection makes a difference to the Cobb Angle change between supine and standing which is known to occur in idiopathic scoliosis. A secondary aim of this study was to identify which (if any) patient characteristics were correlated with supine versus standing Cobb change. The study found that pre-selecting vertebral endplates causes only has a minor effect on supine to standing Cobb change in scoliosis. There is a statistically significant relationship between supine to standing Cobb Angle change and fulcrum flexibility. Therefore, supine to standing Cobb Angle change can be considered as a measure of spinal flexibility when both standing and supine images are clinically available.

Wake angle for surface gravity waves on a finite depth fluid

Linear water wave theory suggests that wave patterns caused by a steadily moving disturbance are contained within a wedge whose half-angle depends on the depth-based Froude number $F_H$. For the problem of flow past an axisymmetric pressure distribution in a finite-depth channel, we report on the apparent angle of the wake, which is the angle of maximum peaks. For moderately deep channels, the dependence of the apparent wake angle on the Froude number is very different to the wedge angle, and varies smoothly as $F_H$ passes through the critical value $F_H=1$. For shallow water, the two angles tend to follow each other more closely, which leads to very large apparent wake angles for certain regimes.

MRI reveals individual level deformities in the growing scoliotic spine that clinically are masked by the Cobb angle

Clinically, the Cobb angle method measures the overall scoliotic curve in the coronal plane but does not measure individual vertebra and disc wedging. The contributions of the vertebrae and discs in the growing scoliotic spine were measured using sequential MRI scans to investigate coronal plane deformity progression with growth. Sequential MRI data showed complex patterns of deformity progression. Changes to the wedging of individual vertebrae and discs may occur in patients who have no increase in overall Cobb angle measure; the Cobb method alone may be insufficient to capture the complex mechanisms of deformity progression.

Is there evidence to support the use of the angle of peak torque as a marker of hamstring injury and re-injury risk?

Hamstring strain injuries are the predominant injury in many sports, costing athletes and clubs a significant financial and performance burden. Therefore the ability to identify and intervene with individuals who are considered at a high risk of injury is important. One measure which has grown in popularity as an outcome variable following hamstring intervention/prevention studies and rehabilitation is the angle of peak knee flexor torque. This current opinion article will firstly introduce the measure and the processes behind it. Secondly, this article will summarise how the angle of peak knee flexor torque has been suggested to measure hamstring strain injury risk. Finally various limitations will be presented and outlined as to how they may influence the measure. These include the lack of muscle specificity, the common concentric contraction mode of assessment, reliability of the measure, various neural contributions (such as rate of force development and neuromuscular inhibition) as well as the lack of prospective data showing any predictive value in the measure.

Sequential MRI reveals individual level deformities in the growing scoliotic spine that are clinically masked by the Cobb angle

Introduction Clinically, the Cobb angle method measures the overall scoliotic curve in the coronal plane but does not measure individual vertebra and disc wedging. The contributions of the vertebrae and discs in the growing scoliotic spine were measured to investigate coronal plane deformity progression with growth. Methods A 0.49mm isotropic 3D MRI technique was developed to investigate the level-by-level changes that occur in the growing spine of a group of Adolescent Idiopathic Scoliosis (AIS) patients, who received two to four sequential scans (spaced 3-12 months apart). The coronal plane wedge angles of each vertebra and disc in the major curve were measured to capture any changes that occurred during their adolescent growth phase. Results Seventeen patients had at least two scans. Mean patient age was 12.9 years (SD 1.5 years). Sixteen were classified as right-sided major thoracic Lenke Type 1 (one left sided). Mean standing Cobb angle at initial presentation was 31° (SD 12°). Six received two scans, nine three scans and two four scans, with 65% showing a Cobb angle progression of 5° or more between scans. Overall, there was no clear pattern of deformity progression of individual vertebrae and discs, nor between patients who progressed and those who didn’t. There were measurable changes in the wedging of the vertebrae and discs in all patients. In sequential scans, change in direction of wedging was also seen. In several patients there was reverse wedging in the discs that counteracted increased wedging of the vertebrae such that no change in overall Cobb angle was seen. Conclusion Sequential MRI data showed complex patterns of deformity progression. Changes to the wedging of individual vertebrae and discs may occur in patients who have no increase in Cobb angle measure; the Cobb method alone may be insufficient to capture the complex mechanisms of deformity progression.

Sequential MRI of growing scoliotic spines reveals individual level deformities that are clinically masked by the cobb angle

INTRODUCTION. Clinically, the Cobb angle method measures the overall scoliotic curve in the coronal plane but does not measure individual vertebra and disc wedging. The contributions of the vertebrae and discs in the growing scoliotic spine were measured to investigate coronal plane deformity progression with growth. METHODS. A 0.49mm isotropic 3D MRI technique was developed to investigate the level-by-level changes that occur in the growing spine of a group of Adolescent Idiopathic Scoliosis (AIS) patients, who received two to four sequential scans (spaced 3-12 months apart). The coronal plane wedge angles of each vertebra and disc in the major curve were measured to capture any changes that occurred during their adolescent growth phase. RESULTS. Seventeen patients had at least two scans. Mean patient age was 12.9 years (SD 1.5 years). Sixteen were classified as right-sided major thoracic Lenke Type 1 (one left sided). Mean standing Cobb angle at initial presentation was 31° (SD 12°). Six received two scans, nine three scans and two four scans, with 65% showing a Cobb angle progression of 5° or more between scans. Overall, there was no clear pattern of deformity progression of individual vertebrae and discs, nor between patients who progressed and those who didn’t. There were measurable changes in the wedging of the vertebrae and discs in all patients. In sequential scans, change in direction of wedging was also seen. In several patients there was reverse wedging in the discs that counteracted increased wedging of the vertebrae such that no change in overall Cobb angle was seen. CONCLUSION. Sequential MRI data showed complex patterns of deformity progression. Changes to the wedging of individual vertebrae and discs may occur in patients who have no increase in Cobb angle measure; the Cobb method alone may be insufficient to capture the complex mechanisms of deformity progression.

Supine to standing cobb angle change in idiopathic scoliosis: The effect of endplate preselection

INTRODUCTION Standing radiographs are the ‘gold standard’ for clinical assessment of adolescent idiopathic scoliosis (AIS), with the Cobb Angle used to measure the severity and progression of the scoliotic curve. Supine imaging modalities can provide valuable 3D information on scoliotic anatomy, however, due to changes in gravitational loading direction, the geometry of the spine alters between the supine and standing position which in turn affects the Cobb Angle measurement. Previous studies have consistently reported a 7-10° [1-3] Cobb Angle increase from supine to standing, however, none have reported the effect of endplate pre-selection and which (if any) curve parameters affect the supine to standing Cobb Angle difference. CONCLUSION There is a statistically significant relationship between supine to standing Cobb Angle change and fulcrum flexibility. Therefore, this difference can be considered a measure of spinal flexibility. Pre-selecting vertebral endplates causes only minor changes.

Sequential MRI reveals individual level deformities in the growing scoliotic spine that are not seen clinically by the cobb angle

Clinically, the Cobb angle method measures the overall scoliotic curve in the coronal plane but does not measure individual vertebra and disc wedging. The contributions of the vertebrae and discs in the growing scoliotic spine were measured to investigate coronal plane deformity progression with growth. Sequential MRI data in this project showed complex patterns of deformity progression. Changes to the wedging of individual vertebrae and discs may occur in patients who have no increase in Cobb angle measure; the Cobb method alone may be insufficient to capture the complex mechanisms of deformity progression.

A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems

In order to simulate stiff biochemical reaction systems, an explicit exponential Euler scheme is derived for multidimensional, non-commutative stochastic differential equations with a semilinear drift term. The scheme is of strong order one half and A-stable in mean square. The combination with this and the projection method shows good performance in numerical experiments dealing with an alternative formulation of the chemical Langevin equation for a human ether a-go-go related gene ion channel mode