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Background: 4D flow cardiovascular magnetic resonance (CMR) enables visualization of complex blood flow and quantification of biomarkers for vessel wall disease, such as wall shear stress (WSS). Because of the inherently long acquisition times, many efforts have been made to accelerate 4D flow acquisitions, however, no detailed analysis has been made on the effect of Cartesian compressed sensing accelerated 4D flow CMR at different undersampling rates on quantitative flow parameters and WSS. Methods: We implemented a retrospectively triggered 4D flow CMR acquisition with pseudo-spiral Cartesian k-space filling, which results in incoherent undersampling of k-t space. Additionally, this strategy leads to small jumps in k-space thereby minimizing eddy current related artifacts. The pseudo-spirals were rotated in a tiny golden-angle fashion, which provides optimal incoherence and a variable density sampling pattern with a fully sampled center. We evaluated this 4D flow protocol in a carotid flow phantom with accelerations of R = 2–20, as well as in carotids of 7 healthy subjects (27 ± 2 years, 4 male) for R = 10–30. Fully sampled 2D flow CMR served as a flow reference. Arteries were manually segmented and registered to enable voxel-wise comparisons of both velocity and WSS using a Bland-Altman analysis. Results: Magnitude images, velocity images, and pathline reconstructions from phantom and in vivo scans were similar for all accelerations. For the phantom data, mean differences at peak systole for the entire vessel volume in comparison to R = 2 ranged from − 2.3 to − 5.3% (WSS) and − 2.4 to − 2.2% (velocity) for acceleration factors R = 4–20. For the in vivo data, mean differences for the entire vessel volume at peak systole in comparison to R = 10 were − 9.9, − 13.4, and − 16.9% (WSS) and − 8.4, − 10.8, and − 14.0% (velocity), for R = 20, 25, and 30, respectively. Compared to single slice 2D flow CMR acquisitions, peak systolic flow rates of the phantom showed no differences, whereas peak systolic flow rates in the carotid artery in vivo became increasingly underestimated with increasing acceleration. Conclusion: Acquisition of 4D flow CMR of the carotid arteries can be highly accelerated by pseudo-spiral k-space sampling and compressed sensing reconstruction, with consistent data quality facilitating velocity pathline reconstructions, as well as quantitative flow rate and WSS estimations. At an acceleration factor of R = 20 the underestimation of peak velocity and peak WSS was acceptable (< 10%) in comparison to an R = 10 accelerated 4D flow CMR reference scan. Peak flow rates were underestimated in comparison with 2D flow CMR and decreased systematically with higher acceleration factors. [ABSTRACT FROM AUTHOR]

A general framework is given for applying the Newton–Raphson method to solve power flow problems, using power and current-mismatch functions in polar, Cartesian coordinates and complex form. These two mismatch functions and three coordinates, result in six possible ways to apply the Newton–Raphson method for the solution of power flow problems. We present a theoretical framework to analyze these variants for load (PQ) buses and generator (PV) buses. Furthermore, we compare newly developed versions in this paper with existing variants of the Newton power flow method. The convergence behavior of all methods is investigated by numerical experiments on transmission and distribution networks. We conclude that variants using the polar current-mismatch and Cartesian current-mismatch functions that are developed in this paper, performed the best result for both distribution and transmission networks. [ABSTRACT FROM AUTHOR]

Standard in-vitro spine testing methods have focused on application of isolated and/or constant load components while the in-vivo spine is subject to multiple components that can be resolved into resultant dynamic load vectors. To advance towards more in-vivo like simulations the objective of the current study was to develop a methodology to apply robotically-controlled, non-zero, real-time dynamic resultant forces during flexion-extension on human lumbar motion segment units (MSU) with initial application towards simulation of an ideal follower load (FL) force vector. A proportional-integral-derivative (PID) controller with custom algorithms coordinated the motion of a Cartesian serial manipulator comprised of six axes each capable of position- or load-control. Six lumbar MSUs (L4-L5) were tested with continuously increasing sagittal plane bending to 8Nm while force components were dynamically programmed to deliver a resultant 400N FL that remained normal to the moving midline of the intervertebral disc. Mean absolute load-control tracking errors between commanded and experimental loads were computed. Global spinal ranges of motion and sagittal plane inter-body translations were compared to previously published values for non-robotic applications. Mean TEs for zero-commanded force and moment axes were 0.7±0.4N and 0.03±0.02 Nm, respectively. For non-zero force axes mean TEs were 0.8±0.8 N, 1.3±1.6 Nm, and 1.3±1.6 N for Fx, Fz, and the resolved ideal follower load vector FLR, respectively. Mean extension and flexion ranges of motion were 2.6°±1.2° and 5.0°±1.7°, respectively. Relative vertebral body translations and rotations were very comparable to data collected with non-robotic systems in the literature. The robotically coordinated Cartesian load controlled testing system demonstrated robust real-time load-control that permitted application of a real-time dynamic non-zero load vector during flexion-extension. For single MSU investigations the methodology has potential to overcome conventional follower load limitations, most notably via application outside the sagittal plane. This methodology holds promise for future work aimed at reducing the gap between current in-vitro testing and in-vivo circumstances. [ABSTRACT FROM AUTHOR]

Robotic methods applied to in-vitro biomechanical testing potentially offer more comprehensive evaluations however, standard position control algorithms make real-time load control problematic. This paper describes and evaluates a novel custom developed Cartesian force controlled biomechanical testing system with coordinated 6 degree of freedom (DOF) real-time load control. A custom developed 6-DOF serial manipulator with cascaded force over position control algorithms was designed, assembled, and programmed. Dial gauge tests assessed accuracy of custom linear axes. Standard test input and tuning procedures refined control performance. Two single motion segment units (L4-L5) and lumbar (L1-S) spine segments were tested under continuous pure moment application in flexion-extension, left-right lateral bending and axial rotation to 8 Nm under full 6-DOF load control. Mean load control tracking errors between commanded and experimental loads were computed. Global spinal ranges of motion were compared to previously published values for standard non-robotic protocols. Individual linear and rotational axis position control accuracies were equal to or less than 6.35 m and 0.0167° respectively. Pilot pure bending tests demonstrated stable load control performance, as well as load rates, rotational velocities, and ranges of motion comparable to those for standard non-robotic invitro tests. Tracking errors for zero commanded forces and all moment controlled axes were less than 0.81 7 0.68 N and 0.18 7 0.19 Nm over all tests, respectively. The Cartesian based system simplified control application and demonstrated robust position and load control that was not limited to single axis or zero commanded loads. In addition to emulating standard biomechanical tests, the novel Cartesian force controlled testing system developed is a promising tool for biomechanical assessments with coordinated dynamic load application and coupled motion response in 6DOF. [ABSTRACT FROM AUTHOR]

Abstract: T 2 decay during long echo trains of magnetic resonance (MR) imaging pulse sequences is known to cause a blurring effect, due to the peak broadening of the point spread function (PSF). In contrast, the simultaneous amplitude-loss effect, led by the peak reduction of the PSF, has gained much less attention. In this report, we analyzed the PSFs of both the truncation and T 2 decay for Cartesian (linear profile ordering and low-high ordering) and spiral trajectories, respectively. Then, we derived simple formulas to characterize both the blurring and amplitude-loss effects, which are functions of the ratios of the echo train duration (T k) over T 2 (T k/T 2). Signal-to-noise ratio (SNR) per unit time was thus analyzed considering both the amplitude-loss effect induced by the T 2 decay and the SNR gain from the long acquisition duration based on MR sampling theory. Optimum T k/T 2 ratios to achieve maximum SNR per unit time were 1.2 for the Cartesian trajectory and 0.8 for the spiral trajectory. [Copyright &y& Elsevier]

Abstract: An implementation of the fast multiple method (FMM) is performed for magnetic systems with long-ranged dipolar interactions. Expansion in spherical harmonics of the original FMM is replaced by expansion of polynomials in Cartesian coordinates, which is considerably simpler. Under open boundary conditions, an expression for multipole moments of point dipoles in a cell is derived. These make the program appropriate for nanomagnetic simulations, including magnetic nanoparticles and ferrofluids. The performance is optimized in terms of cell size and parameter set (expansion order and opening angle) and the trade off between computing time and accuracy is quantitatively studied. A rule of thumb is proposed to decide the appropriate average number of dipoles in the smallest cells, and an optimal choice of parameter set is suggested. Finally, the superiority of Cartesian coordinate FMM is demonstrated by comparison to spherical harmonics FMM and FFT. [Copyright &y& Elsevier]

I first identify two different distinctions: between Cartesian cognition and embodied cognition, and between calculative rationality and intuitive know-how. I then suggest that, in the nursing literature, these two distinctions are run together, to create an opposition between ‘Cartesian rationality’ and ‘embodied know-how’. However, it is vital to keep the two distinctions apart, because ‘embodied knowing’ is very frequently rational. In separating the idea of embodied cognition from non-rational intuition, I show how ‘embodiment’ leads to the concepts of distributed cognition and distributed expertise. This has extensive and important implications for how we understand clinical cognition in nursing. [Copyright &y& Elsevier]

• 3D tripod mechanism. • 3D Cartesian flexible hinge. • Analytical compliance model. The paper studies the tripod mechanisms that comprise novel spatial Cartesian flexible hinges and can be used in three-dimensional sensing/actuation applications. These hinges are formed of serially-connected straight- and circular-axis elastic segments that are located in planes parallel to the planes of a Cartesian reference frame. Two spatial flexible hinge designs are proposed and their compliance matrices are derived based on closed-form compliances of the basic segments. The hinge compliance matrices are utilized to formulate the stiffness matrix of tripod mechanisms that are parallel combinations of three identical hinges and a rigid link. The hinge analytical compliance model is confirmed through finite element code simulation while the tripod analytical stiffness is verified by both finite element analysis and experimental testing of fabricated specimens. Comprehensive simulation is subsequently performed to study the influence of the geometric parameter values on the hinge and tripod analytical compliance/stiffness. [ABSTRACT FROM AUTHOR]