Alternating iteration and elliptic variational inequalities

Summary Free boundary value problems, too complicated for formulation as a variational inequality, are broken up into two problems on overlapping regions. On one region the problem is treated as an ordinary boundary value problem; on the second region, the free boundary part of the problem is reduced to a variational inequality. By solving the two problems successively it is shown that under certain conditions the successive solutions converge to a single function that gives a solution of the original problem. Application to a filtration problem is given.     

Formation of the surface charge on silica in mixed solvents

At sufficiently high concentrations of methanol and of alkali salts in aqueous silica dispersions, the negative -potentials of the particles are decreased. This effect is more pronounced with lithium than with other alkali cations, and it is independent on the anion. The NMR spectra indicate lithium adsorption on silica from mixed solvents, but not in the absence of alcohol.Supported by a contract with the XMX Corporation, Burlington, Massachusetts, USA     

MR diffusion - "diffraction" phenomenon in multi-pulse-field-gradient experiments

Using pulsed-field-gradient (PFG) experiments, the sizes of the pores in ordered porous media can be estimated from the "diffraction" pattern that the signal attenuation curves exhibit. A different diffraction pattern is observed when the experiment is extended to a larger number (N) of diffusion gradient pulse pairs. Simulations to calculate signal values from arbitrary gradient waveforms are performed for diffusion in restricted geometries using a matrix operator formalism. The simulations suggest that the differences in the characteristics of the attenuation curves are expected to make it possible to measure smaller pore sizes, to improve the accuracy of pore size measurements and potentially to distinguish different pore shapes using the N-PFG technique. Moreover, when an even number of PFG pairs is used, it is possible to observe the diffraction pattern at shorter diffusion times and measure an approximation to the average pore size even when the sample contains pores with a broad distribution of sizes.     

Pure uterine lipoma

Lipomatous tumors of the uterus are unusual, benign neoplasms seen in postmenopausal women. Although many of the mixed-type cases such as lipoleiomyoma and fibrolipoma have been reported, pure uterine lipomas are extremely rare. In the literature, a few cases with pure uterine lipoma have been reported. We first present the advanced magnetic resonance findings of pure uterine lipoma, followed by those of ultrasonography (US) and computed tomography (CT). We markedly detected lipid peaks on the magnetic resonance spectroscopy (MRS) and the apparent diffusion coefficient value to be 0.00 due to chemical-shift effects with diffusion-weighted imaging (DWI). Although pelvic lipomatous tumors can be diagnosed with US and CT, in some cases, further workup may be required to localize the lesion. MRI may yield more valuable data for differential diagnosis. MRS and DWI findings provide additional clues on the nature of the lesion.     

Simultaneous detection of resolved glutamate, glutamine, and gamma-aminobutyric acid at 4 T

A new approach is introduced to simultaneously detect resolved glutamate (Glu), glutamine (Gln), and gamma-aminobutyric acid (GABA) using a standard STEAM localization pulse sequence with the optimized sequence timing parameters. This approach exploits the dependence of the STEAM spectra of the strongly coupled spin systems of Glu, Gln, and GABA on the echo time TE and the mixing time TM at 4 T to find an optimized sequence parameter set, i.e., {TE, TM}, where the outer-wings of the Glu C4 multiplet resonances around 2.35 ppm, the Gln C4 multiplet resonances around 2.45 ppm, and the GABA C2 multiplet resonance around 2.28 ppm are significantly suppressed and the three resonances become virtual singlets simultaneously and thus resolved. Spectral simulation and optimization were conducted to find the optimized sequence parameters, and phantom and in vivo experiments (on normal human brains, one patient with traumatic brain injury, and one patient with brain tumor) were carried out for verification. The results have demonstrated that the Gln, Glu, and GABA signals at 2.2-2.5 ppm can be well resolved using a standard STEAM sequence with the optimized sequence timing parameters around {82 ms,48 ms} at 4 T, while the other main metabolites, such as N-acetyl aspartate (NAA), choline (tCho), and creatine (tCr), are still preserved in the same spectrum. The technique can be easily implemented and should prove to be a useful tool for the basic and clinical studies associated with metabolism of Glu, Gln, and/or GABA.     

Apparent diffusion coefficient of line scan diffusion image in normal prostate and prostate cancer—comparison with single-shot echo planner image

Purpose

This retrospective study was designed to evaluate the apparent diffusion coefficient (ADC) of line scan diffusion images (LSDI) in normal prostate and prostate cancer. Single-shot echo planner images (SS-EPI) were used for comparison.

Materials and Methods

Twenty prostate tumors were examined by conventional MRI in 14 patients prior to radical prostatectomy. All patients were examined with a 1.5-T MR imager (Signa CV/i ver. 9.1 GE Medical System Milwaukee, WI, USA). Diffusion-weighted MR imaging (DWI) using LSDI was performed with a pelvic phased-array coil, with b values of 5 and 800 s/mm². DWI using SS-EPI was performed with a body coil, with b values of 0 and 800 s/mm². The ADCs of each sequence for 14 normal prostate and 20 prostate cancers were histopathologically assessed. Signal-to-noise ratio (SNR) on DWI was estimated and compared for each sequence.

Results

The mean ADCs (±S.D.) of normal peripheral zones (PZ), transition zones (TZ) and cancer (in 10⁻³ mm²/s) that used LSDI were 1.42±0.12, 1.23±0.10 and 0.79±0.19, respectively. Those that used SS-EPI were 1.76±0.26, 1.38±0.20 and 1.05±0.27, respectively. Using unpaired t test (P<.05), we found a significant difference in each sequence between normal tissue (both PZ and TZ) and the cancer. Paired t test (P<.05) also registered a significant difference between LSDI and SS-EPI. Mean SNR for DWI using LSDI was 16.49±5.03, while the DWI using SS-EPI was 18.85±9.26. The difference between the SNR of each sequence was not statistically significant by paired t test.

Conclusion

We found that ADCs using LSDI and SS-EPI showed similar tendencies in the same patients. However, in all regions, LSDI ADCs had smaller standard deviations than SS-EPI ADCs.     

MRI of hepatic lymphoma

Thirteen patients with biopsy proven hepatic lymphoma (2 Hodgkin, 11 Non-Hodgkin) and a control group of 15 patients with hepatic metastases were analyzed quantitatively and qualitatively by MRI. Focal hepatic lymphoma was most reliably detected (eight of eight patients) and appeared hypointense relative to liver on T₁ weighted (CNR − 7.4 ± 2.3) and hyperintense on T₂ weighted (CNR + 8.4 ± 2.9) images. The mean T₁ and T₂ relaxation times of focal hepatic lymphoma (T₁ = 832 ± 234 msec, T₂ = 84 ± 16 ms) differed significantly from adjacent non-tumorous liver (T₁ = 420 ± 121 ms, T₂ = 51 ± 9 ms; p < 0.05), however CNR values and relaxation times were similar to those of hepatic metastases. Diffuse hepatic lymphoma (microscopic periportal infiltration) was undetectable by MRI in three patients by either morphologic features or quantitative criteria. A mixed pattern of hepatic lymphoma (focal lesions and diffuse infiltration) showed focal areas of slightly decreased signal intensity on T₁ weighted images (CNR = −1.7 ± 0.4) while T₂ weighted images revealed multiple regions of focal hyperintensity (CNR = +13.3 ± 8.4) superimposed on a diffusely hyperintense liver. Our experience demonstrates that either T₁ or T₂ weighted techniques are useful in detecting focal and that T₂ weighted techniques are useful in detecting mixed hepatic lymphoma. Conventional image derived relaxation time measurements and quantitative parameters were of no additional diagnostic value.     

Superparamagnetic iron oxide particles and positive enhancement for myocardial perfusion studies assessed by subsecond T1-weighted MRI

Superparamagnetic iron oxide particles (SPIOs) are usually referred to as T₂ MR contrast agents, reducing signal intensity (SI) on T₂-weighted MR images (negative enhancement). This study reports the original use of SPIOs as T₁-enhancing contrast agents, primarily assessed in vitro, and then applied to an in vivo investigation of a myocardial perfusion defect. Using a strongly T₁-weighted subsecond MR sequence with SPIOs intravenous (IV) bolus injection, MR imaging of myocardial vascularization after reperfusion was performed, on a dog model of coronary occlusion followed by reperfusion. Immediately after the intravenous bolus injection of 20 μmol/kg of SPIOs, a positive signal intensity enhancement was observed respectively, in the right and left ventricular cavity and in the nonischemic left myocardium. Moreover, compared to normal myocardium, the remaining ischemic myocardial region (anterior wall of the left ventricle) appeared as a lower and delayed SI enhancing area (cold spot). Mean peak SIE in the nonischemic myocardium (posterior wall) was significantly higher than in the ischemic myocardium (anterior wall) (110 ± 23% vs. 74 ± 22%, Mann-Whitney test < 1%, n₁ = 6, n₂ − n₁ = 0, U > 2). In conclusion, the T₁ effect of SPIOs at low dose, during their first intravascular distribution, suggests their potential use as positive markers to investigate the regional myocardial blood flow and some perfusion defects such as the “no-reflow phenomenon”.     

Magnetic resonance imaging of the uterus in vivo and in vitro at an ultra low magnetic field (0.02 T): Assessment of its normal structure and of leiomyomas

The purpose of this investigation was to analyze the normal anatomy and leiomyomas of the uterus with an ultra low field (0.02 T) magnetic resonance imaging (MRI) device. MR imaging was performed on 18 uteri, 11 of which were imaged both preoperatively (in vivo) and as an operative specimen (in vitro), 6 only as an operative specimen, and 1 only preoperatively. All uteri were examined histologically after imaging. The junctional zone was much better delineated in vivo than in vitro, indicating that its appearance on MR is partly due to blood flow. No structures contributing to its visibility in vitro could be demonstrated histologically. Twenty leiomyomas (size range 7–79 mm) in 12 uteri were found with MRI. They were slightly better discerned in vivo than in vitro. The leiomyomas, having no degenerative changes, had a signal intensity which was the same or lower than that of the myometrium. On images obtained in vitro the signal intensity of these leiomyomas relative to that of myometrium correlated directly with their muscular content (R = 0.74, p = .002). The authors conclude that the junctional zone is a sum of physiological and structural factors, the latter being responsible for its in vitro delineation. MR imaging of the uterus in vitro did not give more information than MR imaging in vivo. All leiomyomas larger than 10 mm could be detected, indicating that MR imaging at 0.02 T is an accurate method for the imaging of the uterine leiomyomas.     

High resolution high field rodent cardiac imaging with flow enhancement suppression

A method that incorporates cardiorespiratory-gated 2DFT spin-echo imaging with blood flow enhancement suppression is described which enables high resolution microimaging of the rodent heart. This methodology was applied to obtain in vivo cardiac mouse and rat images with in-plane resolutions of 100–200 μm using high field vertical bore magnet systems. Suppression of intraventricular blood flow enhancement was achieved using a combined spin-echo/gradient-refocussed sequence to dephase magnetization from flowing spins prior to imaging.