Convergence analysis of a discrete-time single-unit gradient ICA algorithm

We revisit the one-unit gradient ICA algorithm derived from the kurtosis function. By carefully studying properties of the stationary points of the discrete-time one-unit gradient ICA algorithm, with suitable condition on the learning rate, convergence can be proved. The condition on the learning rate helps alleviate the guesswork that accompanies the problem of choosing suitable learning rate in practical computation. These results may be useful to extract independent source signals on-line.

Particle tracking in a salinity gradient: A method for measuring sinking rate of individual phytoplankton in the laboratory

This paper presents a new method to measure the sinking rates of individual phytoplankton “particles” (cells, chains, colonies, and aggregates) in the laboratory. Conventional particle tracking and high resolution video imaging were used to measure particle sinking rates and particle size. The stabilizing force of a very mild linear salinity gradient (1 ppt over 15 cm) prevented the formation of convection currents in the laboratory settling chamber. Whereas bulk settling methods such as SETCOL provide a single value of sinking rate for a population, this method allows the measurement of sinking rate and particle size for a large number of individual particles or phytoplankton within a population. The method has applications where sinking rates vary within a population, or where sinking rate-size relationships are important. Preliminary data from experiments with both laboratory and field samples of marine phytoplankton are presented here to illustrate the use of the technique, its applications, and limitations. Whereas this paper deals only with sinking phytoplankton, the method is equally valid for positively buoyant species, as well as nonbiological particles.

An equivalent distributed magnetic current based FDTD method for the calculation of e-fields induced by gradient coils in MRI

This paper evaluates a low-frequency FDTD method applied to the problem of induced E-fields/eddy currents in the human body resulting from the pulsed magnetic field gradients in MRI. In this algorithm, a distributed equivalent magnetic current (DEMC) is proposed as the electromagnetic source and is obtained by quasistatic calculation of the empty coil's vector potential or measurements therein. This technique circumvents the discretizing of complicated gradient coil geometries into a mesh of Yee cells, and thereby enables any type of gradient coil modeling or other complex low frequency sources. The proposed method has been verified against an example with an analytical solution. Results are presented showing the spatial distribution of gradient-induced electric fields in a multilayered spherical phantom model and a complete body model.

Comparative study of symmetric and asymmetric cylindrical MRI gradient Y-coils in terms of induced eddy currents

We have recently introduced the concept of whole-body asymmetric MRI systems [1]. In this theoretical study, we investigate the PNS characteristics of whole-body asymmetric gradient systems as compared to conventional symmetric systems. Recent experimental evidence [2] supports the hypothesis of transverse gradients being the largest contributor of PNS due to induced electric currents. Asymmetric head gradient coils have demonstrated benefits in the past [3]. The numerical results are based on an anatomically-accurate 2mm-human voxel-phantom NORMAN [4]. The results of this study can facilitate the optimization of whole-body asymmetric gradients in terms of patient comfort/safety (less PNS), while prospering the use of asymmetric MRI systems for in-vivo medical interventions.

Tailoring magnetic field gradient design to magnet cryostat geometry

Eddy currents induced within a magnetic resonance imaging (MRI) cryostat bore during pulsing of gradient coils can be applied constructively together with the gradient currents that generate them, to obtain good quality gradient uniformities within a specified imaging volume over time. This can be achieved by simultaneously optimizing the spatial distribution and temporal pre-emphasis of the gradient coil current, to account for the spatial and temporal variation of the secondary magnetic fields due to the induced eddy currents. This method allows the tailored design of gradient coil/magnet configurations and consequent engineering trade-offs. To compute the transient eddy currents within a realistic cryostat vessel, a low-frequency finite-difference time-domain (FDTD) method using total-field scattered-field (TFSF) scheme has been performed and validated