Gravitational Test beyond the First Post-Newtonian Order with the Shadow of the M87 Black Hole.

The 2017 Event Horizon Telescope (EHT) observations of the central source in M87 have led to the first measurement of the size of a black-hole shadow. This observation offers a new and clean gravitational test of the black-hole metric in the strong-field regime. We show analytically that spacetimes that deviate from the Kerr metric but satisfy weak-field tests can lead to large deviations in the predicted black-hole shadows that are inconsistent with even the current EHT measurements. We use numerical calculations of regular, parametric, non-Kerr metrics to identify the common characteristic among these different parametrizations that control the predicted shadow size. We show that the shadow-size measurements place significant constraints on deviation parameters that control the second post-Newtonian and higher orders of each metric and are, therefore, inaccessible to weak-field tests. The new constraints are complementary to those imposed by observations of gravitational waves from stellar-mass sources.

A Randomized Controlled Trial to Evaluate the Clinical Effectiveness of 3D-Printed Orthosis in the Management of Adolescent Idiopathic Scoliosis.

STUDY DESIGN: Prospective randomized controlled trial. OBJECTIVE: To compare clinical effectiveness and quality of life (QoL) of the 3D-printed orthosis (3O) and conventional orthosis (CO) for adolescent idiopathic scoliosis (AIS). SUMMARY OF BACKGROUND DATA: Using 3D printing technology to design and fabricate orthoses to manage AIS aiming to improve in-orthosis correction and patients' compliance that are considered essential factors of effective treatment. Clinical evaluation was conducted to study the effectiveness of this innovative method. METHODS: Thirty females with AIS who met the criteria (age 10-14, Cobb 20-40°, Risser sign 0-2, ≤12 months after menarche) were recruited. Subjects were randomly allocated to the 3O group (n = 15, age 12.4, Cobb 31.8°) and CO group (n = 15, age 12.0, Cobb 29.3°). All patients were prescribed for full-time wearing (23 hours/d) and follow-up every 4 to 6 months until bone maturity. Compliance was monitored by thermosensors, while QoL was assessed using three validated questionnaires. RESULTS: Comparable immediate in-orthosis correction was observed between 3O (-11.6°, P < 0.001) and CO groups (-12.9°, P < 0.001). In the QoL study via SRS-22r, the 3O group got worse results after 3 months in aspects of function, self-image, and mental health (-0.5, -0.6, -0.7, P < 0.05) while the CO group had worse results in aspects of self-image and mental health (-0.3, -0.3, P < 0.05). No significant difference was found in QoL assessments between groups. After 2 years of follow-up, 22 patients were analyzed with 4 dropouts in each group. Comparable angle reduction was observed in both groups (3O: -2.2°, P = 0.364; CO: -3.5°, P = 0.193). There was one subject (9.1%) in the 3O group while two subjects (18.2%) in the CO group had curve progression >5°. Daily wearing hours were 1.9 hours longer in the 3O group than the CO group (17.1 vs. 15.2 hours, P = 0.934). CONCLUSION: The 3O group could provide comparable clinical effects as compared with the CO group while patients with 3O showed similar compliance and QoL compared to those with CO.Level of Evidence: 1.

Significance of recumbent curvature in prediction of in-orthosis correction for adolescent idiopathic scoliosis.

BACKGROUND:: Prediction of in-orthosis curvature at pre-orthosis stage is valuable for the treatment planning for adolescent idiopathic scoliosis, while the position of spinal curvature assessment that is effective for this prediction is still unknown. OBJECTIVES:: To compare the spinal curvatures in different body positions for predicting the spinal curvature rendered by orthosis. STUDY DESIGN:: A prospective cohort study. METHODS:: Twenty-two patients with adolescent idiopathic scoliosis (mean Cobb angle: 28.1°± 7.3°) underwent ultrasound assessment of spinal curvature in five positions (standing, supine, prone, sitting bending, prone bending positions) and that within orthosis. Differences and correlations were analyzed between the spinal curvatures in the five positions and that within orthosis. RESULTS:: The mean in-orthosis curvature was 11.2° while the mean curvatures in five studied positions were 18.7° (standing), 10.7° (supine), 10.7° (prone), -3.5° (prone bending), and -6.5° (sitting bending). The correlation coefficients of the in-orthosis curvature and that in five studied positions were r = 0.65 (standing), r = 0.76 (supine), r = 0.87 (prone), r = 0.41 (prone bending), and r = 0.36 (sitting bending). CONCLUSION:: The curvature in recumbent positions (supine and prone) is highly correlated to the initial in-orthosis curvature without significant difference. Thus, the initial effect of spinal orthosis could be predicted by the curvature in the recumbent positions (especially prone position) at the pre-orthosis stage. CLINICAL RELEVANCE: Prediction of in-orthosis correction at pre-orthosis stage is valuable for spinal orthosis design. This study suggests assessing the spinal curvature in recumbent position (especially prone position) to predict the initial in-orthosis correction for optimizing the orthosis design.

An effective assessment method of spinal flexibility to predict the initial in-orthosis correction on the patients with adolescent idiopathic scoliosis (AIS).

BACKGROUND: Spinal flexibility is an essential parameter for clinical decision making on the patients with adolescent idiopathic scoliosis (AIS). Various methods are proposed to assess spinal flexibility, but which assessment method is more effective to predict the effect of orthotic treatment is unclear. OBJECTIVE: To investigate an effective assessment method of spinal flexibility to predict the initial in-orthosis correction, among the supine, prone, sitting with lateral bending and prone with lateral bending positions. METHODS: Thirty-five patients with AIS (mean Cobb angle: 28° ± 7°; mean age: 12 ± 2 years; Risser sign: 0-2) were recruited. Before orthosis fitting, spinal flexibility was assessed by an ultrasound system in 4 positions (apart from standing) including supine, prone, sitting with lateral bending and prone with lateral bending. After orthosis fitting, the initial in-orthosis correction was routinely assessed by whole spine standing radiograph. Comparisons and correlation analyses were performed between the spinal flexibility in the 4 positions and the initial in-orthosis correction. RESULTS: The mean in-orthosis correction was 41% while the mean curve correction (spinal flexibility) in the 4 studied positions were 40% (supine), 42% (prone), 127% (prone with lateral bending) and 143% (sitting with lateral bending). The correlation coefficients between initial in-orthosis correction and curve correction (spinal flexibility) in the 4 studied positions were r = 0.66 (supine), r = 0.75 (prone), r = 0.03 (prone with lateral bending) and r = 0.04 (sitting with lateral bending). CONCLUSIONS: The spinal flexibility in the prone position is the closest to and most correlated with the initial in-orthosis correction among the 4 studied positions. Thus, the prone position could be an effective method to predict the initial effect of orthotic treatment on the patients with AIS.

Dynamics of saturated energy condensation in two-dimensional turbulence.

In two-dimensional forced Navier-Stokes turbulence, energy cascades to the largest scales in the system to form a pair of coherent vortices known as the Bose condensate. We show, both numerically and analytically, that the energy condensation saturates and the system reaches a statistically stationary state. The time scale of saturation is inversely proportional to the viscosity and the saturation energy level is determined by both the viscosity and the force. We further show that, without sufficient resolution to resolve the small-scale enstrophy spectrum, numerical simulations can give a spurious result for the saturation energy level. We also find that the movement of the condensate is similar to the motion of an inertial particle with an effective drag force. Furthermore, we show that the profile of the saturated coherent vortices can be described by a Gaussian core with exponential wings.

Local model for angular-momentum transport in accretion disks driven by the magnetorotational instability.

We develop a local model for the exponential growth and saturation of the Reynolds and Maxwell stresses in turbulent flows driven by the magnetorotational instability. We first derive equations that describe the effects of the instability on the growth and pumping of the stresses. We highlight the relevance of a new type of correlations that couples the dynamical evolution of the Reynolds and Maxwell stresses and plays a key role in developing and sustaining the magnetorotational turbulence. We then supplement these equations with a phenomenological description of the triple correlations that lead to a saturated turbulent state. We show that the steady-state limit of the model describes successfully the correlations among stresses found in numerical simulations of shearing boxes.