On the Jager-Kaul theorem concerning harmonic maps

In 1983, Jager and Kaul proved that the equator map u*(x) = (x/\x\,0) : B-n --> S-n is unstable for 3 less than or equal to n less than or equal to 6 and a minimizer for the energy functional E(u, B-n) = integral B-n \del u\(2) dx in the class H-1,H-2(B-n, S-n) with u = u* on partial derivative B-n when n greater than or equal to 7. In this paper, we give a new and elementary proof of this Jager-Kaul result. We also generalize the Jager-Kaul result to the case of p-harmonic maps.

A time-harmonic inverse methodology for the design of RF coils in MRI

An inverse methodology is described to assist in the design of radio-frequency (RF) coils for magnetic resonance imaging (MRI) applications. The time-harmonic electromagnetic Green's functions are used to calculate current on the coil and shield cylinders that will generate a specified internal magnetic field. Stream function techniques and the method of moments are then used to implement this theoretical current density into an RF coil. A novel asymmetric coil operating for a 4.5 T MRI machine was designed and constructed using this methodology and the results are presented.

On the minimality of the p-harmonic map - x/vertical bar x vertical bar : B-n -> Sn-1

We prove that for any real number p with 1 p less than or equal to n - 1, the map x/\x\ : B-n --> Sn-1 is the unique minimizer of the p-energy functional integral(Bn) \delu\(p) dx among all maps in W-1,W-p (B-n, Sn-1) with boundary value x on phiB(n).

NMR shim coil design utilising a rapid spherical harmonic calculation method

A rapid spherical harmonic calculation method is used for the design of Nuclear Magnetic Resonance shim coils. The aim is to design each shim such that it generates a field described purely by a single spherical harmonic. By applying simulated annealing techniques, coil arrangements are produced through the optimal positioning of current-carrying circular arc conductors of rectangular cross-section. This involves minimizing the undesirable harmonies in relation to a target harmonic. The design method is flexible enough to be applied for the production of coil arrangements that generate fields consisting significantly of either zonal or tesseral harmonics. Results are presented for several coil designs which generate tesseral harmonics of degree one.

Pure two-atom squeezed state in spontaneous emission from two non-identical atoms

We calculate the stationary state of the system of two non-identical two-level atoms driven by a finite-bandwidth two-mode squeezed vacuum. It is well known that two identical two-level atoms driven by a broadband squeezed vacuum may decay to a pure state, called the pure two-atom squeezed state, and that the presence of the antisymmetric state can change its purity. Here, we show that for small interatomic separations the stationary state of two non-identical atoms is not sensitive to the presence of the antisymmetric state and is the pure two-atom squeezed state. This effect is a consequence of the fact that in the system of two non-identical atoms the antisymmetric state is no longer the trapping state. We also calculate the squeezing properties of the emitted field and find that the squeezing spectrum of the output field may exhibit larger squeezing than that in the input squeezed vacuum. Moreover, we show that squeezing in the total field attains the optimum value which can ever be achieved in the field emitted by two atoms.

Correcting the effects of spontaneous emission on cold-trapped ions

We propose two quantum error-correction schemes which increase the maximum storage time for qubits in a system of cold-trapped ions, using a minimal number of ancillary qubits. Both schemes consider only the errors introduced by the decoherence due to spontaneous emission from the upper levels of the ions. Continuous monitoring of the ion fluorescence is used in conjunction with selective coherent feedback to eliminate these errors immediately following spontaneous emission events.

Endoscopic treatment of Zenker`s diyerticulum by harmonic scalpel

Background: Zenker`s diverticulum (ZD) is a rare condition with a reported prevalence of 0.01% to 0.11% in the general population. Endoscopic treatment consists of the division of the septum between the diverticulum and the esophagus, within which the cricopharyngeal muscle is contained. Diathermic monopolar current, argon plasma coagulation, and laser have been used to incise the muscular septum with satisfactory results. The main limitation of endoscopic treatment is the occurrence of complications. Perforation and hemorrhage are reported in as many as 23% and 10% of patients, respectively. Objective: The aim of this study was to use the technique of endoscopic diverticulotomy by using a harmonic scalpel in patients with ZD and to demonstrate the feasibility of using flexible and rigid devices in ZD treatment. Design: Case series study. Standard protocol was used for patient management, endoscopic procedure, and data collection. Setting: Single endoscopist demonstrating preliminary results. Patients: Five patients (4 men; median standard deviation [SD] age 69.6 +/- 9.06 years, range 59-83 years) with ZD were treated with this technique. All patients reported dysphagia and halitosis. The diagnosis was based on clinical, endoscopic, and radiographic findings. Interventions: All patients received general anesthesia and were placed in the left lateral position. A standard videogastroscope (9.8 mm) and a stiff guidewire were used to insert and achieve an adequate exposure of the ZD septum. The septum was divided using a harmonic scalpel under thin endoscope (5.2 mm) visualization through a soft diverticuloscope. Main Outcome Measurement: Feasibility of an endoscopic technique by using rigid and flexible devices to treat ZD. Results: Four patients (80%) were successfully treated in 1 session. The median SD size of the diverticulum was 3.6 +/- 0.89 cm (range 3-5 cm). Median SD procedure time was 17.33 +/- 2.33 minutes (range 15-20 minutes) in 6 procedures. No hemorrhage or perforation occurred. One patient (20%) required a second session to complete dissection of the ZD septum. All patients demonstrated improvement of dysphagia score after treatment. Limitations: Small case series design. Conclusions: Endoscopic treatment of ZD by harmonic scalpel through a soft diverticuloscope was feasible and effective in this small case series. Larger studies are warranted to further evaluate this technique.

Quantum beats in spontaneous emission from two atoms in a detuned squeezed vacuum

The time evolution of the populations of the collective states of a two-atom system in a squeezed vacuum can exhibit quantum beats. We show that the effect appears only when the carrier frequency of the squeezed field is detuned from the atomic resonance. Moreover, we find that the quantum beats are not present for the case in which the two-photon correlation strength is the maximum possible for a field with a classical analog. We also show that the population inversion between the excited collective states, found for the resonant squeezed vacuum, is sensitive to the detuning and the two-photon correlations. For large detunings or a field with a classical analog there is no inversion between the collective states. Observation of the quantum beats or the population inversion would confirm the essentially quantum-mechanical nature of the squeezed vacuum. (C) 1997 Optical Society of America.

Age-Related Metabolic Profiles in Cognitively Healthy Elders: Results from a Voxel-Based [(18)F]Fluorodeoxyglucose-Positron-Emission Tomography Study with Partial Volume Effects Correction

BACKGROUND AND PURPOSE: Functional brain variability has been scarcely investigated in cognitively healthy elderly subjects, and it is currently debated whether previous findings of regional metabolic variability are artifacts associated with brain atrophy. The primary purpose of this study was to test whether there is regional cerebral age-related hypometabolism specifically in later stages of life. MATERIALS AND METHODS: MR imaging and FDG-PET data were acquired from 55 cognitively healthy elderly subjects, and voxel-based linear correlations between age and GM volume or regional cerebral metabolism were conducted by using SPM5 in images with and without correction for PVE. To investigate sex-specific differences in the pattern of brain aging, we repeated the above voxelwise calculations after dividing our sample by sex. RESULTS: Our analysis revealed 2 large clusters of age-related metabolic decrease in the overall sample, 1 in the left orbitofrontal cortex and the other in the right temporolimbic region, encompassing the hippocampus, the parahippocampal gyrus, and the amygdala. The division of our sample by sex revealed significant sex-specific age-related metabolic decrease in the left temporolimbic region of men and in the left dorsolateral frontal cortex of women. When we applied atrophy correction to our PET data, none of the above-mentioned correlations remained significant. CONCLUSIONS: Our findings suggest that age-related functional brain variability in cognitively healthy elderly individuals is largely secondary to the degree of regional brain atrophy, and the findings provide support to the notion that appropriate PVE correction is a key tool in neuroimaging investigations.

Cost Effectiveness of Positron Emission Tomography in Patients With Hodgkin`s Lymphoma in Unconfirmed Complete Remission or Partial Remission After First-Line Therapy

Purpose To assess the cost effectiveness of fluorine-18-fluorodeoxyglucose positron emission tomography (FDG-PET) in patients with Hodgkin`s lymphoma (HL) with unconfirmed complete remission (CRu) or partial remission (PR) after first-line treatment. Patients and Methods One hundred thirty patients with HL were prospectively studied. After treatment, all patients with CRu/PR were evaluated with FDG-PET. In addition, PET-negative patients were evaluated with standard follow-up, and PET-positive patients were evaluated with biopsies of the positive lesions. Local unit costs of procedures and tests were evaluated. Cost effectiveness was determined by evaluating projected annual economic impact of strategies without and with FDG-PET on HL management. Results After treatment, CRu/PR was observed in 50 (40.0%) of the 127 patients; the sensitivity, specificity, and positive and negative predictive values of FDG-PET were 100%, 92.0%, 92.3%, and 100%, respectively (accuracy of 95.9%). Local restaging costs without PET were $350,050 compared with $283,262 with PET, a 19% decrease. The incremental cost-effectiveness ratio is -$3,268 to detect one true case. PET costs represented 1% of total costs of HL treatment. Simulated costs in the 974 patients registered in the 2008 Brazilian public health care database showed that the strategy including restaging PET would have a total program cost of $56,498,314, which is $516,942 less than without restaging PET, resulting in a 1% cost saving. Conclusion FDG-PET demonstrated 95.9% accuracy in restaging for patients with HL with CRu/PR after first-line therapy. Given the observed probabilities, FDG-PET is highly cost effective and would reduce costs for the public health care program in Brazil.

Utility of Ictal Single Photon Emission Computed Tomography in Mesial Temporal Lobe Epilepsy With Hippocampal Atrophy: A Randomized Trial

BACKGROUND: The development of newer diagnostic technologies has reduced the need for invasive electroencephalographic (EEG) studies in identifying the epileptogenic zone, especially in adult patients with mesial temporal lobe epilepsy and hippocampal sclerosis (MTLE-HS). OBJECTIVE: To evaluate ictal single photon emission computed tomography (SPECT) in the evaluation and treatment of patients with MTLE-HS. METHODS: MTLE patients were randomly assigned to those with (SPECT, n = 124) and without ictal SPECT (non-SPECT, n = 116) in an intent-to-treat protocol. Primary end points were the proportion of patients with invasive EEG studies, and those offered surgery. Secondary end points were the length of hospital stay and the proportion of patients with secondarily generalized seizures (SGS) during video-EEG, postsurgical seizure outcome, and hospital cost. RESULTS: The proportion of patients offered surgery was similar in the SPECT (85%) and non-SPECT groups (81%), as well as the proportion that had invasive EEG studies (27% vs 23%). The mean duration of hospital stay was 1 day longer for the SPECT group (P < 0.001). SGS occurred in 51% of the SPECT and 26% of the non-SPECT group (P < 0.001). The cost of the presurgical evaluation was 35% higher for the SPECT compared with the non-SPECT group (P < 0.001). The proportion of patients seizure-free after surgery was similar in the SPECT (59%) compared with non-SPECT group (54%). CONCLUSION: Ictal-SPECT did not add localizing value beyond what was provided by EEG-video telemetry and structural MRI that altered the surgical decision and outcome for MTLE-HS patients. Ictal-SPECT increased hospital stay was associated with increased costs and a higher chance of SGS during video-EEG monitoring. These findings support the notion that a protocol including ictal SPECT is equivalent to one without SPECT in the presurgical evaluation of adult patients with MTLE-HS.

Ictal technetium-99 m ethyl cysteinate dimer single-photon emission tomographic findings in epileptic patients with polymicrogyria syndromes: A Subtraction of ictal-interictal SPECT coregistered to MRI study

Purpose To describe the ictal technetium-99 m-ECD SPECT findings in polymicrogyria syndromes (PMG) during epileptic seizures. Methods We investigated 17 patients with PMG syndromes during presurgical workup, which included long-term video-electroencephalographic (EEG) monitoring, neurological and psychiatry assessments, invasive EEG, and the subtraction of ictal-interictal SPECT coregistered to magnetic resonance imaging (MRI) (SISCOM). Results The analysis of the PMG cortex, using SISCOM, revealed intense hyperperfusion in the polymicrogyric lesion during epileptic seizures in all patients. Interestingly, other localizing investigations showed heterogeneous findings. Twelve patients underwent epilepsy surgery, three achieved seizure-freedom, five have worthwhile improvement, and four patients remained unchanged. Conclusions Our study strongly suggests the involvement of PMG in seizure generation or early propagation. Both conventional ictal single-photon emission computed tomography (SPECT) and SISCOM appeared as the single contributive exam to suggest the localization of the epileptogenic zone. Despite the limited number of resective epilepsy surgery in our study (n=9), we found a strong prognostic role of SISCOM in predicting surgical outcome. This result may be of great value on surgical decision-making of whether or not the whole or part of the PMG lesion should be surgically resected.