Digital processing of diffusion-tensor images of avascular tissues

Diffusion is the process that leads to the mixing of substances as a result of spontaneous and random thermal motion of individual atoms and molecules. It was first detected by the English botanist Robert Brown in 1827, and the phenomenon became known as ‘Brownian motion’. More specifically, the motion observed by Brown was translational diffusion – thermal motion resulting in random variations of the position of a molecule. This type of motion was given a correct theoretical interpretation in 1905 by Albert Einstein, who derived the relationship between temperature, the viscosity of the medium, the size of the diffusing molecule, and its diffusion coefficient. It is translational diffusion that is indirectly observed in MR diffusion-tensor imaging (DTI). The relationship obtained by Einstein provides the physical basis for using translational diffusion to probe the microscopic environment surrounding the molecule.

A geometrical analysis of trajectory design for underwater vehicles

Designing trajectories for a submerged rigid body motivates this paper. Two approaches are addressed: the time optimal approach and the motion planning ap- proach using concatenation of kinematic motions. We focus on the structure of singular extremals and their relation to the existence of rank-one kinematic reduc- tions; thereby linking the optimization problem to the inherent geometric frame- work. Using these kinematic reductions, we provide a solution to the motion plan- ning problem in the under-actuated scenario, or equivalently, in the case of actuator failures. We finish the paper comparing a time optimal trajectory to one formed by concatenation of pure motions.

A geometrical approach to the motion planning problem for a submerged rigid body

The main focus of this paper is the motion planning problem for a deeply submerged rigid body. The equations of motion are formulated and presented by use of the framework of differential geometry and these equations incorporate external dissipative and restoring forces. We consider a kinematic reduction of the affine connection control system for the rigid body submerged in an ideal fluid, and present an extension of this reduction to the forced affine connection control system for the rigid body submerged in a viscous fluid. The motion planning strategy is based on kinematic motions; the integral curves of rank one kinematic reductions. This method is of particular interest to autonomous underwater vehicles which can not directly control all six degrees of freedom (such as torpedo shaped AUVs) or in case of actuator failure (i.e., under-actuated scenario). A practical example is included to illustrate our technique.

A first extension of geometric control theory to underwater vehicles

This paper serves as a first study on the implementation of control strategies developed using a kinematic reduction onto test bed autonomous underwater vehicles (AUVs). The equations of motion are presented in the framework of differential geometry, including external dissipative forces, as a forced affine connection control system. We show that the hydrodynamic drag forces can be included in the affine connection, resulting in an affine connection control system. The definitions of kinematic reduction and decoupling vector field are thus extended from the ideal fluid scenario. Control strategies are computed using this new extension and are reformulated for implementation onto a test-bed AUV. We compare these geometrically computed controls to time and energy optimal controls for the same trajectory which are computed using a previously developed algorithm. Through this comparison we are able to validate our theoretical results based on the experiments conducted using the time and energy efficient strategies.

Decoupled trajectory planning for a submerged rigid body subject to dissipative and potential forces

This paper studies the practical but challenging problem of motion planning for a deeply submerged rigid body. Here, we formulate the dynamic equations of motion of a submerged rigid body under the architecture of differential geometric mechanics and include external dissipative and potential forces. The mechanical system is represented as a forced affine-connection control system on the configuration space SE(3). Solutions to the motion planning problem are computed by concatenating and reparameterizing the integral curves of decoupling vector fields. We provide an extension to this inverse kinematic method to compensate for external potential forces caused by buoyancy and gravity. We present a mission scenario and implement the theoretically computed control strategy onto a test-bed autonomous underwater vehicle. This scenario emphasizes the use of this motion planning technique in the under-actuated situation; the vehicle loses direct control on one or more degrees of freedom. We include experimental results to illustrate our technique and validate our method.

Geometric Control Theory and its Application to Underwater Vehicles

This dissertation is based on theoretical study and experiments which extend geometric control theory to practical applications within the field of ocean engineering. We present a method for path planning and control design for underwater vehicles by use of the architecture of differential geometry. In addition to the theoretical design of the trajectory and control strategy, we demonstrate the effectiveness of the method via the implementation onto a test-bed autonomous underwater vehicle. Bridging the gap between theory and application is the ultimate goal of control theory. Major developments have occurred recently in the field of geometric control which narrow this gap and which promote research linking theory and application. In particular, Riemannian and affine differential geometry have proven to be a very effective approach to the modeling of mechanical systems such as underwater vehicles. In this framework, the application of a kinematic reduction allows us to calculate control strategies for fully and under-actuated vehicles via kinematic decoupled motion planning. However, this method has not yet been extended to account for external forces such as dissipative viscous drag and buoyancy induced potentials acting on a submerged vehicle. To fully bridge the gap between theory and application, this dissertation addresses the extension of this geometric control design method to include such forces. We incorporate the hydrodynamic drag experienced by the vehicle by modifying the Levi-Civita affine connection and demonstrate a method for the compensation of potential forces experienced during a prescribed motion. We present the design method for multiple different missions and include experimental results which validate both the extension of the theory and the ability to implement control strategies designed through the use of geometric techniques. By use of the extension presented in this dissertation, the underwater vehicle application successfully demonstrates the applicability of geometric methods to design implementable motion planning solutions for complex mechanical systems having equal or fewer input forces than available degrees of freedom. Thus, we provide another tool with which to further increase the autonomy of underwater vehicles.

Free surface flow into a horizontal slot with zero gravity

The two-dimensional free surface flow of a finite-depth fluid into a horizontal slot is considered. For this study, the effects of viscosity and gravity are ignored. A generalised Schwarz-Christoffel mapping is used to formulate the problem in terms of a linear integral equation, which is solved exactly with the use of a Fourier transform. The resulting free surface profile is given explicitly in closed-form.

Assessment of commercial network RTK user positioning performance over long inter-station distances

The paper provides an assessment of the performance of commercial Real Time Kinematic (RTK) systems over longer than recommended inter-station distances. The experiments were set up to test and analyse solutions from the i-MAX, MAX and VRS systems being operated with three triangle shaped network cells, each having an average inter-station distance of 69km, 118km and 166km. The performance characteristics appraised included initialization success rate, initialization time, RTK position accuracy and availability, ambiguity resolution risk and RTK integrity risk in order to provide a wider perspective of the performance of the testing systems. ----- ----- The results showed that the performances of all network RTK solutions assessed were affected by the increase in the inter-station distances to similar degrees. The MAX solution achieved the highest initialization success rate of 96.6% on average, albeit with a longer initialisation time. Two VRS approaches achieved lower initialization success rate of 80% over the large triangle. In terms of RTK positioning accuracy after successful initialisation, the results indicated a good agreement between the actual error growth in both horizontal and vertical components and the accuracy specified in the RMS and part per million (ppm) values by the manufacturers. ----- ----- Additionally, the VRS approaches performed better than the MAX and i-MAX when being tested under the standard triangle network with a mean inter-station distance of 69km. However as the inter-station distance increases, the network RTK software may fail to generate VRS correction and then may turn to operate in the nearest single-base RTK (or RAW) mode. The position uncertainty reached beyond 2 meters occasionally, showing that the RTK rover software was using an incorrect ambiguity fixed solution to estimate the rover position rather than automatically dropping back to using an ambiguity float solution. Results identified that the risk of incorrectly resolving ambiguities reached 18%, 20%, 13% and 25% for i-MAX, MAX, Leica VRS and Trimble VRS respectively when operating over the large triangle network. Additionally, the Coordinate Quality indicator values given by the Leica GX1230 GG rover receiver tended to be over-optimistic and not functioning well with the identification of incorrectly fixed integer ambiguity solutions. In summary, this independent assessment has identified some problems and failures that can occur in all of the systems tested, especially when being pushed beyond the recommended limits. While such failures are expected, they can offer useful insights into where users should be wary and how manufacturers might improve their products. The results also demonstrate that integrity monitoring of RTK solutions is indeed necessary for precision applications, thus deserving serious attention from researchers and system providers.

The role of vision in obese and normal-weight children's gait control

Previous research has suggested that perceptual-motor difficulties may account for obese children's lower motor competence; however, specific evidence is currently lacking. Therefore, this study examined the effect of altered visual conditions on spatiotemporal and kinematic gait parameters in obese versus normal-weight children. Thirty-two obese and normal-weight children (11.2 ± 1.5 years) walked barefoot on an instrumented walkway at constant self-selected speed during LIGHT and DARK conditions. Three-dimensional motion analysis was performed to calculate spatiotemporal parameters, as well as sagittal trunk segment and lower extremity joint angles at heel-strike and toe-off. Self-selected speed did not significantly differ between groups. In the DARK condition, all participants walked at a significantly slower speed, decreased stride length, and increased stride width. Without normal vision, obese children had a more pronounced increase in relative double support time compared to the normal-weight group, resulting in a significantly greater percentage of the gait cycle spent in stance. Walking in the DARK, both groups showed greater forward tilt of the trunk and restricted hip movement. All participants had increased knee flexion at heel-strike, as well as decreased knee extension and ankle plantarflexion at toe-off in the DARK condition. The removal of normal vision affected obese children's temporal gait pattern to a larger extent than that of normal-weight peers. Results suggest an increased dependency on vision in obese children to control locomotion. Next to the mechanical problem of moving excess mass, a different coupling between perception and action appears to be governing obese children's motor coordination and control.

HIFiRE re-entry observation using an image-based visual servoing system

This paper presents an image based visual servoing system that is intended to be used for tracking and obtaining scientific observations of the HIFiRE vehicles. The primary aim of this tracking platform is to acquire and track the thermal signature emitted from the surface of the vehicle during the re-entry phase of the mission using an infra-red camera. The implemented visual servoing scheme uses a classical image based approach to identify and track the target using visual kinematic control. The paper utilizes simulation and experimental results to show the tracking performance of the system using visual feedback. Discussions on current implementation and control techniques to further improve the performance of the system are also explored.

Study of the interaction between 10-hydroxycamptothecine and DNA with the use of ethidium bromide dye as a fluorescence probe

The interaction of 10-hydroxycamptothecine (HCPT) with DNA under pseudo-physiological conditions (Tris-HCl buffer of pH 7.4), using ethidium bromide (EB) dye as a probe, was investigated with the use of spectrofluorimetry, UV-vis spectrometry and viscosity measurement. The binding constant and binding number for HCPT with DNA were evaluated as (7.1 ± 0.5) × 104 M-1 and 1.1, respectively, by multivariate curve resolution-alternating least squares (MCR-ALS). Moreover, parallel factor analysis (PARAFAC) was applied to resolve the three-way fluorescence data obtained from the interaction system, and the concentration information for the three components of the system at equilibrium was simultaneously obtained. It was found that there was a cooperative interaction between the HCPT-DNA complex and EB, which produced a ternary complex of HCPT-DNA-EB. © 2011 Elsevier B.V.

Predicting wave glider speed from environmental measurements

In the ocean science community, researchers have begun employing novel sensor platforms as integral pieces in oceanographic data collection, which have significantly advanced the study and prediction of complex and dynamic ocean phenomena. These innovative tools are able to provide scientists with data at unprecedented spatiotemporal resolutions. This paper focuses on the newly developed Wave Glider platform from Liquid Robotics. This vehicle produces forward motion by harvesting abundant natural energy from ocean waves, and provides a persistent ocean presence for detailed ocean observation. This study is targeted at determining a kinematic model for offline planning that provides an accurate estimation of the vehicle speed for a desired heading and set of environmental parameters. Given the significant wave height, ocean surface and subsurface currents, wind speed and direction, we present the formulation of a system identification to provide the vehicle’s speed over a range of possible directions.

Large-Eddy Simulation of physiological pulsatile non-newtonian flow in a channel with double constriction

Physiological pulsatile flow in a 3D model of arterial double stenosis, using the modified Power-law blood viscosity model, is investigated by applying Large Eddy Simulation (LES) technique. The computational domain has been chosen is a simple channel with biological type stenoses. The physiological pulsation is generated at the inlet of the model using the first four harmonics of the Fourier series of the physiological pressure pulse. In LES, a top-hat spatial grid-filter is applied to the Navier-Stokes equations of motion to separate the large scale flows from the subgrid scale (SGS). The large scale flows are then resolved fully while the unresolved SGS motions are modelled using the localized dynamic model. The flow Reynolds numbers which are typical of those found in human large artery are chosen in the present work. Transitions to turbulent of the pulsatile non-Newtonian along with Newtonian flow in the post stenosis are examined through the mean velocity, wall shear stress, mean streamlines as well as turbulent kinetic energy and explained physically along with the relevant medical concerns.