Geometric distortion in clinical MRI systems - Part I: evaluation using a 3D phantom

Recently, a 3D phantom that can provide a comprehensive and accurate measurement of the geometric distortion in MRI has been developed. Using this phantom, a full assessment of the geometric distortion in a number of clinical MRI systems (GE and Siemens) has been carried out and detailed results are presented in this paper. As expected, the main source of geometric distortion in modern superconducting MRI systems arises from the gradient field nonlinearity. Significantly large distortions with maximum absolute geometric errors ranged between 10 and 25 mm within a volume of 240 x 240 x 240 mm(3) were observed when imaging with the new generation of gradient systems that employs shorter coils. By comparison, the geometric distortion was much less in the older-generation gradient systems. With the vendor's correction method, the geometric distortion measured was significantly reduced but only within the plane in which these 2D correction methods were applied. Distortion along the axis normal to the plane was, as expected, virtually unchanged. Two-dimensional correction methods are a convenient approach and in principle they are the only methods that can be applied to correct geometric distortion in a single slice or in multiple noncontiguous slices. However, these methods only provide an incomplete solution to the problem and their value can be significantly reduced if the distortion along the normal of the correction plane is not small. (C) 2004 Elsevier Inc. All rights reserved.

Measuring geometric phases of scattering states in nanoscale electronic devices

We show how a quantum property, a geometric phase, associated with scattering states can be exhibited in nanoscale electronic devices. We propose an experiment to use interference to directly measure the effect of this geometric phase. The setup involves a double-path interferometer, adapted from that used to measure the phase evolution of electrons as they traverse a quantum dot (QD). Gate voltages on the QD could be varied cyclically and adiabatically, in a manner similar to that used to observe quantum adiabatic charge pumping. The interference due to the geometric phase results in oscillations in the current collected in the drain when a small bias across the device is applied. We illustrate the effect with examples of geometric phases resulting from both Abelian and non-Abelian gauge potentials.

Geometric phases of scattering states in a ring geometry: adiabatic pumping in mesoscopic devices

Geometric phases of scattering states in a ring geometry are studied on the basis of a variant of the adiabatic theorem. Three timescales, i.e., the adiabatic period, the system time and the dwell time, associated with adiabatic scattering in a ring geometry play a crucial role in determining geometric phases, in contrast to only two timescales, i.e., the adiabatic period and the dwell time, in an open system. We derive a formula connecting the gauge invariant geometric phases acquired by time-reversed scattering states and the circulating (pumping) current. A numerical calculation shows that the effect of the geometric phases is observable in a nanoscale electronic device.

A geometric approach to quantum circuit lower bounds

What is the minimal size quantum circuit required to exactly implement a specified n-qubit unitary operation, U, without the use of ancilla qubits? We show that a lower bound on the minimal size is provided by the length of the minimal geodesic between U and the identity, I, where length is defined by a suitable Finsler metric on the manifold SU(2(n)). The geodesic curves on these manifolds have the striking property that once an initial position and velocity are set, the remainder of the geodesic is completely determined by a second order differential equation known as the geodesic equation. This is in contrast with the usual case in circuit design, either classical or quantum, where being given part of an optimal circuit does not obviously assist in the design of the rest of the circuit. Geodesic analysis thus offers a potentially powerful approach to the problem of proving quantum circuit lower bounds. In this paper we construct several Finsler metrics whose minimal length geodesics provide lower bounds on quantum circuit size. For each Finsler metric we give a procedure to compute the corresponding geodesic equation. We also construct a large class of solutions to the geodesic equation, which we call Pauli geodesics, since they arise from isometries generated by the Pauli group. For any unitary U diagonal in the computational basis, we show that: (a) provided the minimal length geodesic is unique, it must be a Pauli geodesic; (b) finding the length of the minimal Pauli geodesic passing from I to U is equivalent to solving an exponential size instance of the closest vector in a lattice problem (CVP); and (c) all but a doubly exponentially small fraction of such unitaries have minimal Pauli geodesics of exponential length.

Local geometric changes in left ventricular remodeling post-infarction can lead to apparent reduction in scar thickness

Serial reduction in scar thickness has been shown in animal models. We sought whether this reduction in scar thickness may be a result of dilatation of the left ventricle (LV) with stretching and thinning of the wall. Contrast enhanced magnetic resonance imaging (CMRI) was performed to delineate radial scar thickness in 25 patients (age 63±10, 21 men) after myocardial infarction. The LV was divided into 16 segts and the absolute radial scar thickness (ST) and percentage scar to total wall thickness (%ST) were measured. Regional end diastolic (EDV) and end systolic volumes (ESV) of corresponding segments were measured on CMRI. All patients underwent revascularization and serial changes in ST, %ST, and regional volumes were assessed with a mean follow up of 15±5 months. CMRI identified a total of 93 scar segments. An increase in EDV or ESV was associated with a serial reduction inST(versusEDV, r =−0.3, p = 0.01; versusESV, r =−0.3, p = 0.005) and%ST(versusEDV, r =−0.2, p = 0.04; versus ESV, r =−0.3, p = 0.001). For segts associated with a positive increase in EDV (group I) or ESV (group II) there was a significant decrease in ST and %ST, but in those segts with stable EDV (group III) or ESV (group IV) there were no significant changes in ST and %ST (Table).

The Hierarchical Structure of the Firm: A Geometric Perspective

This paper incorporates hierarchical structure into the neoclassical theory of the firm. Firms are hierarchical in two respects: the organization of workers in production and the wage structure. The firm’s hierarchy is represented as the sector of a circle, where the radius represents the hierarchy’s height, the width of the sector represents the breadth of the hierarchy at a given height, and the angle of the sector represents span of control for any given supervisor. A perfectly competitive firm then chooses height and width, as well as capital inputs, in order to maximize profit. We analyze the short run and long run impact of changes in scale economies, input substitutability and input and output prices on the firm’s hierarchical structure. We find that the firm unambiguously becomes more hierarchical as the specialization of its workers increases or as its output price increases relative to input prices. The effect of changes in scale economies is contingent on the output price. The model also brings forth an analysis of wage inequality within the firm, which is found to be independent of technological considerations, and only depends on the firm’s wage schedule.

Geometric-optical modelling of a tropical forest canopy

Proceedings of the 11th Australasian Remote Sensing and Photogrammetry Conference

Achromatic optical phase shifter/modulator

We propose and demonstrate, theoretically and experimentally, a novel achromatic optical phase shifter modulator based on a frequency-domain optical delay line configured to maintain zero group delay as variable phase delay is generated by means of tilting a mirror. Compared with previously reported phase shifter modulators, e.g., based on the Pancharatnam (geometric) phase, our device is high speed and polarization insensitive and produces a large, bounded phase delay that, uniquely, is one-to-one mapped to a measurable parameter, the tilt angle.

Dynamic Similarity and Scale Effects Affecting Air Bubble Entrainment in Hydraulic Jumps

In an open channel, the transition from super- to sub-critical flow is a flow singularity (the hydraulic jump) characterised by a sharp rise in free-surface elevation, strong turbulence and air entrainment in the roller. A key feature of the hydraulic jump flow is the strong free-surface aeration and air-water flow turbulence. In the present study, similar experiments were conducted with identical inflow Froude numbers Fr1 using a geometric scaling ratio of 2:1. The results of the Froude-similar experiments showed some drastic scale effects in the smaller hydraulic jumps in terms of void fraction, bubble count rate and bubble chord time distributions. Void fraction distributions implied comparatively greater detrainment at low Reynolds numbers yielding some lesser aeration of the jump roller. The dimensionless bubble count rates were significantly lower in the smaller channel, especially in the mixing layer. The bubble chord time distributions were quantitatively close in both channels, and they were not scaled according to a Froude similitude. Simply the hydraulic jump remains a fascinating two-phase flow motion that is still poorly understood.

Two dimensional computational fluid dynamic models for waste stabilisation ponds

Traditional waste stabilisation pond (WSP) models encounter problems predicting pond performance because they cannot account for the influence of pond features, such as inlet structure or pond geometry, on fluid hydrodynamics. In this study, two dimensional (2-D) computational fluid dynamics (CFD) models were compared to experimental residence time distributions (RTD) from literature. In one of the-three geometries simulated, the 2-D CFD model successfully predicted the experimental RTD. However, flow patterns in the other two geometries were not well described due to the difficulty of representing the three dimensional (3-D) experimental inlet in the 2-D CFD model, and the sensitivity of the model results to the assumptions used to characterise the inlet. Neither a velocity similarity nor geometric similarity approach to inlet representation in 2-D gave results correlating with experimental data. However. it was shown that 2-D CFD models were not affected by changes in values of model parameters which are difficult to predict, particularly the turbulent inlet conditions. This work suggests that 2-D CFD models cannot be used a priori to give an adequate description of the hydrodynamic patterns in WSP. (C) 1998 Elsevier Science Ltd. All rights reserved.

Arterial heparan sulfate proteoglycans inhibit vascular smooth muscle cell proliferation and phenotype change in vitro and neointimal formation in vivo

Purpose: The aim of this study was to determine whether heparan sulfate proteoglycans (HSPGs) from the normal arterial wall inhibit neointimal formation after injury in vivo and smooth muscle cell (SMC) phenotype change and proliferation in vitro. Methods: Arterial HSPGs were extracted from rabbit aortae and separated by anion-exchange chromatography. The effect of HSPGs, applied in a periadventitial gel, on neointimal formation was assessed 14 days after balloon catheter injury of rabbit carotid arteries. Their effect on SMC phenotype and proliferation was measured by point-counting morphometry of the cytoplasmic volume fraction of myofilaments (Vvmyo) and H-3-thymidine incorporation in SMCs in culture. Results: Arterial HSPGs (680 mu g) reduced neointimal formation by 35% at 14 days after injury (P =.029), whereas 2000 mu g of the low-molecular-weight heparin Enoxaparin was ineffective. HSPGs at 34 mu g/mL maintained subconfluent primary cultured SMCs with the same high Vvmyo (52.1% +/- 13.8%) after 5 days in culture as did cells freshly isolated from the arterial wall (52.1% +/- 15.1%). In contrast, 100 mu g/mL Enoxaparin was ineffective in preventing phenotypic change over this time period (Vvmyo 38.9% +/- 14.6%, controls 35.9% +/- 12.8%). HSPGs also inhibited 3H-thymidine incorporation into primary cultured SMCs with an ID50 value of 0.4 mu g/mL compared with a value of 14 mu g/ml; for Enoxaparin (P