Estimation of acoustic attentuation in liver using one megabyte of data and the zero-crossings technique

Statistical fluctuations due to scatter-induced frequency variations in reflected acoustic pulses are a major problem when estimating acoustic attenuation. Disagreement exists in the ultrasound community as to how much data is sufficient to overcome these statistical fluctuations. The range of attenuation values for normal livers and a tissue equivalent phantom, using 1 megabyte of data per liver and the zero-crossings technique, was investigated. The significance of statistical fluctuations and their effects on attenuation are discussed.     

Stochastic Homogenization of Nonconvex Unbounded Integral Functionals with Convex Growth

We consider the well-trodden ground of the problem of the homogenization of random integral functionals. When the integrand has standard growth conditions, the qualitative theory is well-understood. When it comes to unbounded functionals, that is, when the domain of the integrand is not the whole space and may depend on the space-variable, there is no satisfactory theory. In this contribution we develop a complete qualitative stochastic homogenization theory for nonconvex unbounded functionals with convex growth. We first prove that if the integrand is convex and has p-growth from below (with p > d, the dimension), then it admits homogenization regardless of growth conditions from above. This result, that crucially relies on the existence and sublinearity at infinity of correctors, is also new in the periodic case. In the case of nonconvex integrands, we prove that a similar homogenization result holds provided that the nonconvex integrand admits a two-sided estimate by a convex integrand (the domain of which may depend on the space variable) that itself admits homogenization. This result is of interest to the rigorous derivation of rubber elasticity from polymer physics, which involves the stochastic homogenization of such unbounded functionals.     

Well-posedness for mean-field evolutions arising in superconductivity

We establish the existence of a global solution for a new family of fluid-like equations, which are obtained in certain regimes in [24] as the mean-field evolution of the supercurrent density in a (2D section of a) type-II superconductor with pinning and with imposed electric current. We also consider general vortex-sheet initial data, and investigate the uniqueness and regularity properties of the solution. For some choice of parameters, the equation under investigation coincides with the so-called lake equation from 2D shallow water fluid dynamics, and our analysis then leads to a new existence result for rough initial data.     

Breathhold cine MRI of left ventricular function in patients with obstructive sleep apnea: work-in-progress

Obstructive sleep apnea (OSA) is a sleep-related breathing disorder that can cause left ventricular (LV) dysfunction. In patients with OSA, the LV dysfunction is usually evaluated by echocardiography. The purpose of this study was to evaluate whether the use of breathhold cine MRI for the study of LV dysfunction would be feasible and well tolerated by patients with OSA. Six volunteers and five patients underwent a breathhold cine MRI study of the LV using a 1.5 Tesla MR imager. Cine MRI was performed using a breathhold k-space segmented TurboFLASH technique during end-expiration. Systolic thickening of the LV septal wall was 49% +/- 16% in normals vs. 25% +/- 10.5% in patients (p < 0.05). Systolic thickening of the LV free wall was 42% +/- 12% in normals vs. 22% +/- 9% in patients (p < 0.05). There was a significant difference in end-diastolic wall thickness between the two groups. All patients tolerated the procedure well. The total duration of each study was relatively short (less than 11 min). Breathhold MRI techniques can be used to study LV dysfunction in patients with respiratory disability such as OSA.     

MR imaging of cervical spine motion with HASTE

The HASTE (half-Fourier acquisition single-shot turbo spin-echo) technique delivers images with T2-weighting in about half a second and could be ideal for fast dynamic studies when T2-weighting is needed. We evaluated cardiac-triggered HASTE to study cervical spine flexion/extension. The cervical spines of ten asymptomatic volunteers were studied during flexion/extension motion on a 1.5 Tesla imager using a cardiac triggered version of the HASTE technique. Midline sagittal images were acquired every 2 to 3 s during neck flexion and extension. Image quality was compared to traditional T2-weighted Turbo spin-echo. The study duration per flexion/ extension was typically less than 20 seconds and well tolerated. The cardiac-gated T2-weighted HASTE images compared favorably to the traditional T2-weighted TSE images in quality and overall anatomic detail. Range of motion averaged: flexion 30 degrees (range 8 degrees -48 degrees) and extension 23 degrees (range 0 degrees -57 degrees ). Greatest motion occurred in the lower cervical spine (C4-C7). At the intervertebral discs the canal diameter, anterior and posterior CSF spaces were widest in neutral position and decreased with flexion and extension. Therefore, Cardiac-gated T2 HASTE sequences provide diagnostic and time-efficient dynamic MR images of cervical spine motion.     

Analyticity of Homogenized Coefficients Under Bernoulli Perturbations and the Clausius–Mossotti Formulas

This paper is concerned with the behavior of the homogenized coefficients associated with some random stationary ergodic medium under a Bernoulli perturbation. Introducing a new family of energy estimates that combine probability and physical spaces, we prove the analyticity of the perturbed homogenized coefficients with respect to the Bernoulli parameter. Our approach holds under the minimal assumptions of stationarity and ergodicity, both in the scalar and vector cases, and gives analytical formulas for each derivative that essentially coincide with the so-called cluster expansion used by physicists. In particular, the first term yields the celebrated (electric and elastic) Clausius–Mossotti formulas for isotropic spherical random inclusions in an isotropic reference medium. This work constitutes the first general proof of these formulas in the case of random inclusions.