Objective: Low-cost, portable RGB-D cameras with integrated motion tracking functionality enable easy-to-use 3D motion analysis without requiring expensive facilities and specialized personnel. However, the accuracy of existing systems is insufficient for most clinical applications, particularly when applied to children. In previous work, we developed an RGB-D camera-based motion tracking method and showed that it accurately captures body joint positions of children and young adults in 3D. In this study, the validity and accuracy of clinically relevant motion parameters that were computed from kinematics of our motion tracking method are evaluated in children and young adults. Methods: Twenty-three typically developing children and healthy young adults (5-29 years, 110-189 cm) performed five movement tasks while being recorded simultaneously with a marker-based Vicon system and an Azure Kinect RGB-D camera. Motion parameters were computed from the extracted kinematics of both methods: time series measurements, i.e., measurements over time, peak measurements, i.e., measurements at a single time instant, and movement smoothness. The agreement of these parameter values was evaluated using Pearson's correlation coefficients r for time series data, and mean absolute error (MAE) and Bland-Altman plots with limits of agreement for peak measurements and smoothness. Results: Time series measurements showed strong to excellent correlations (r-values between 0.8 and 1.0), MAE for angles ranged from 1.5 to 5 degrees and for smoothness parameters (SPARC) from 0.02-0.09, while MAE for distance-related parameters ranged from 9 to 15 mm. Conclusion: Extracted motion parameters are valid and accurate for various movement tasks in children and young adults, demonstrating the suitability of our tracking method for clinical motion analysis. Clinical Impact: The low-cost portable hardware in combination with our tracking method enables motion analysis outside of specialized facilities while providing measurements that are close to those of the clinical gold-standard.

Low-cost, portable RGB-D cameras with integrated body tracking functionality enable easy-to-use 3D motion analysis without requiring expensive facilities and specialized personnel. However, the accuracy of existing systems is insufficient for most clinical applications. In this study, we investigated the concurrent validity of our custom tracking method based on RGB-D images with respect to a gold-standard marker-based system. Additionally, we analyzed the validity of the publicly available Microsoft Azure Kinect Body Tracking (K4ABT). We recorded 23 typically developing children and healthy young adults (aged 5 to 29 years) performing five different movement tasks using a Microsoft Azure Kinect RGB-D camera and a marker-based multi-camera Vicon system simultaneously. Our method achieved a mean per joint position error over all joints of 11.7 mm compared to the Vicon system, and 98.4% of the estimated joint positions had an error of less than 50 mm. Pearson’s correlation coefficients ${r}$ ranged from strong ( ${r}$ =0.64) to almost perfect ( ${r}>$ 0.99). K4ABT demonstrated satisfactory accuracy most of the time but showed short periods of tracking failures in nearly two-thirds of all sequences limiting its use for clinical motion analysis. In conclusion, our tracking method highly agrees with the gold standard system. It paves the way towards a low-cost, easy-to-use, portable 3D motion analysis system for children and young adults.

Background: Equinus deformity with or without concomitant drop foot is a common finding in children with unilateral spastic cerebral palsy and spastic hemiplegia of other causes. Hypothetically, these deformities may lead to pelvic retraction and hip internal rotation during gait. Orthoses are used to reduce pes equinus during gait and to restore hindfoot first contact. Objective: We aimed to investigate whether the use of orthotic equinus correction reduces rotational hip and pelvic asymmetries. Methods: In a retrospective study, 34 children with unilateral spastic cerebral palsy or spastic hemiplegia of other causes underwent standardized instrumented 3D gait analysis with and without orthotic equinus management. We analyzed the differences in the torsional profile during barefoot walking and while wearing orthoses, as well as investigated the influence of ankle dorsiflexion and femoral anteversion on pelvic and hip kinematics and hip kinetics. Results: Wearing orthoses corrected pes equinus and pelvic internal rotation at the end of the stance phase and in the swing phase compared to barefoot walking. Hip rotation and the rotational moment did not significantly change with orthoses. Orthotic management or femoral anteversion did not correlate to pelvic and hip asymmetry. Conclusion: The findings indicate that the correction of the equinus by using orthoses had a variable effect on the asymmetry of the hip and pelvis and internal rotation; both appear to have a multifactorial cause that is not primarily driven by the equinus component.

Recent analysis of the Planck measurements opened a possibility that we live in a non-flat universe. Given the renewed interest in non-zero spatial curvature, here we re-visit the light propagation in a non-flat universe and provide the gauge-invariant expressions for the cosmological probes: the luminosity distance, galaxy clustering, weak gravitational lensing, and cosmic microwave background anisotropies. With the positional dependence of the spatial metric, the light propagation in a non-flat universe is much more complicated than in a flat universe. Accounting for all the relativistic effects and including the vector and tensor contributions, we derive the expressions for the cosmological probes and explicitly verify their gauge invariance. We compare our results to previous work in a non-flat universe, if present, but this work represents the first comprehensive investigation of the cosmological probes in a non-flat universe. Our theoretical formalism in a non-flat universe will play a crucial role in constraining the spatial curvature in the upcoming large-scale surveys.

The standard theoretical description Theta((n) over cap) of the observed cosmic microwave background (CMB) temperature anisotropies is gauge dependent. It is, however, well known that the gauge mode is limited to the monopole and that the higher angular multipoles Theta(l) (l >= 1) are gauge invariant. Several attempts have been made in the past to properly define the monopole fluctuation, but the resulting values of the monopole power C-0 are infinite due to the infrared divergences. The infrared divergences arise from the contribution of the uniform gravitational potential to the monopole fluctuation, in violation of the equivalence principle. Here we present the gauge-invariant theoretical description of the observed CMB temperature anisotropies and compute the monopole power C-0 = 1.66 x 10(-9) in a Lambda CDM model. While the gauge dependence in the standard calculations originates from the ambiguity in defining the hypersurface for the background CMB temperature (T) over bar today, it is in fact well defined and one of the fundamental cosmological parameters. We argue that once the cosmological parameters are chosen, the monopole fluctuation can be unambiguously inferred from the angle average of the observed CMB temperature, making it a model-dependent "observable." Adopting simple approximations for the anisotropy formation, we derive a gauge-invariant analytical expression for the observed CMB temperature anisotropies to study the CMB monopole fluctuation and the cancellation of the uniform gravitational potential contributions on large scales.

Compact Galactic binary systems with orbital periods of a few hours are expected to be detected in gravitational waves (GW) by LISA or a similar mission. At present, these so-called verification binaries provide predictions for GW frequency and amplitude. A full polarisation prediction would provide a new method to calibrate LISA and other GW observatories, but requires resolving the orientation of the binary on the sky, which is not currently possible. We suggest a method to determine the elusive binary orientation and hence predict the GW polarisation, using km-scale optical intensity interferometry. The most promising candidate is CD-30$^{\circ}$ 11223, consisting of a hot helium subdwarf with $m_B = 12$ and a much fainter white dwarf companion, in a nearly edge-on orbit with period 70.5 min. We estimate that the brighter star is tidally stretched by 6%. Resolving the tidal stretching would provide the binary orientation. The resolution needed is far beyond any current instrument, but not beyond current technology. We consider scenarios where an array of telescopes with km-scale baselines and/or the Very Large Telescope (VLT) and Extremely Large Telescope (ELT) are equipped with recently-developed kilo-pixel sub-ns single-photon counters and used for intensity interferometry. We estimate that a team-up of the VLT and ELT could measure the orientation to $\pm 1^{\circ}$ at 2$\sigma$ confidence in 24 hours of observation.